CA2054697A1 - Energy/matter conversion methods and structures - Google Patents

Abstract

2054697 9013126 PCTABS00002 Methods and structures of energy/matter conversion according to the present invention provides applications including the generation of power according to controlled relatively low temperature nuclear fusion by selective annihilation of the coulombic forces present in the fusion material atoms. The selective annihilation of electron orbital energies is provided according to a novel model of the atom described herein, which further provides the composition of superconductor materials by selective combination of matter to provide the conditions necessary to provide superconductivity. Furthermore, the present invention provides selective energy absorption, as illustrated by photon absorption and the creation of additional material according to the novel model of the atom described herein, which overcomes limitations of prior models and is consistent with basic principles, such as Maxwell's equations.

Description

WO90t13126 PCT/US90/01998 21~a4~

ENERGY/MATTER CONVERSION ME'rHODS AND STRUCTURES
.
. Field of the Invention This invention relates to methods and apparatus for energy/matter conversion according to a novei atomic model and the applications derived 05 therefrom including controlled nuclear fusion and the formation of materials such as superconductors.
~ACKGROUNI;
Toward the end uf the 19th century, many physicists believed that all of the principles of physics had been discovered. The laws then discussed 10 and accepted, now called "classical physics," included laws relating to Newton's mechanics, Gibb's thermodynamics, LaGrange and Harnilton's elasticity ancl hydrodynamics, Maxwell-Boltzmann molecular statistics, and Maxwell's equations. However, a discrepancy between nature and the understanding provided by prevaiiing laws was discovered in the case of - 15 bla~k body radiation, whsrein classical physics predict~d the intensity to go to infinity as a function of ternperature whila experimentally it goes to zero. In 1900, Planck made the revolutionary assumption that energy Ievels were quantized which resulted in a model which was consistent with experimentation. Models of the atom were developed by Bohr based on the eoncept of quantized energy ievels. Bohr's model was in agreement with the observed hydrogen spectrum; however, it failed with the helium spectrum and could not account for chemical bonds in molecules. It was reasoned that Bohrls model failed because it was based on the application of Newtonian rnechanics to a discrete particle, and its limited applicability was due to the unwarranted condition that the energy levels be quantized. Quantization occurs in wave m~tion; hence, in 1923 de Broglie suggested that electrons have a wave aspect analogous to light with ~ = h/p, where ~ is the wavelength, h is Planck's constant, and p is the momentum.
In 19~7, Davisson and Gerrner experimentally confirmed de Broglie's hypothesis by observing diffraction effacts by reflecting electrons from metals. Schrodinger reasoned further that if electrons have wave properties, then there must be a wave equation that governs their motion.
In 1926, Schrodinger proposed that the Schrodinger equation, HY' = EY', .

wo 9o/13126 Pcr/usgo/olggg

2~

was the law which governs the motion of electrons (where ~ is a wave function, H is a wave operator and E is the energy of the wave). This equation and its associated postulates provides the basis for the field of quantum mechanics. Quantum mechanics requires that physics on an 5 atomic scale are quite different from that on a macroscopic scale.
However, it entails postulates which are not proven1 but are ass~med to be absolute laws of nature. Central to quantum mechanics is that it is statistical in nature. Knowing the state, a position measurement cannot be predicted with certainty, and only the probabilities of various possible 10 results can be predicted as reflected in the Heisenberg Uncertainty Principle: ~p c~x 2 tl which is fundamental to the prevailing view of quantum mechanics and establishes the lower bound for the uncertainty of two observables. The Heinsberg Uncertainty Principle states that the product of the uncertainty in position and the uncertainty in mornentum of 15 an electron must be greater than ~ where ~ is Planck's constant divided by 2~. Prevailing understanding of quantum mechanics does not provide that an electron is distributed over a larger region of space as a wave is distributed. Rather, it is believed that the probability patterns (wave functions) used to describe the eiectron's motion behave like waves and 20 satisfy a wave equation ~Ir(x).
Max Born interpreted ~Ir~(x)~lr(x)dx to be the probability that the electron is located between x and x ~ dx, where ~ is the complex conjugate of yr(x), and this interpretation is generally accepted. However, Born's view results in intangible concepts which conflict with known 25 physical laws. For example, it results in overlap of negative probability density in molecules, the possibility of an electron instantaneously traveling from the nucleus to infinity and back which violates conservation of energy; radial kinetic energy which violates conservation of energy and angular momentum, and acceleration of a charged particle

3 0 without radiation which violates Maxwell's equations. Schrodinger had a different interpretation of ~r(x) as a charge density function, but his interpretation also produces radiation which is contrary to experimentation as described in Appendix lll.
With respect to the interpretations of Born and Schrodinger, problems 35 have arisen concerning the realiza~ion of kinetic energy, spin, and angular WO 90/131~6 PCI'/US90/01998 3 2~

momentum of the electron. For instance, there is no time dependence of the stationary state wave equation; furthermore, the hypothesized electron-electron repulsions in multiple ~31ectron atoms violates the law of conservation of energy. Moreover, the Schrodinger equation provides no 5 rational basis for the phenornenon of spin, the Paul Exclusion Principle, or Hund's Rule. Also, bonding requires exchange of electrons between atoms which would result in violation of conservation of energy and angular momentum.
As a result of the forgoing assumptions and incomplete or erroneous 10 models and theories, the numerous resulting conflicting models prevent the development of useful or functional systems and structures requiring an accurate understanding of atomic structure and energy transfer. The Schrodinger equation, for example, does not explain the high transition-temperature superconductors or "cold" nuclear fusion which comprise the 15 present invention. Thus, advances in materials and energy/matter conversion is largely limited to laboratory discoveries having limited or sub-optimal commercial application.
~lIMMARY OF THE 1~1~
The methods and structures according to the present invention provide 20 unique applications of energy/matter conversion according to a novel mathematical model of the atom consistent wiih Maxwell's equations and principles of conservation of energy and angular momentum. According to the present invention, methods and apparatus for the useful generation of energy are provided wherein fusionable material is selected from a wide 25 range of possible elements wherein the orbital energies of the fusionable material are determined. The energy of the electrons is selectively depleted by an energy hole provided by one or more selective materials - placed in close proximity to the fusionable material. Fusion is permitted to occur at a rate determined by the relative equality of the orbital 30 energies and the energy hole. According to one embodiment, the rate of fusion is adjusted by the external control of energies transferred into or out of the vicinity of the fusionable material and the energy hole to selectively adjust the equivalence of the energies. The energy produced by the resulting fusion of the nuclei of the fusionable material is received in 3-5 a surrounding material which serves to energize or propel apparatus for the generation of power, such as electric power or steam. ~, WO 90/13126 PCr/US9OtO1998 2054~
A fu~her product according to the pr~3sent invention is the selective production of matter, including byproducts of the above described fusion, and matter having special characteristics, such as superconductor material~ Furthermore, the atomic structure and energy of existing matter 5 is selectively adjustable according to the present invention, such as by selectively reducing or increasing the electron orbltals by depletion of energy as described above or selection absorption, such as resonant photon absorption described according to the present invention. Time and spherical harmonic angular charge density functions and their energies 10 and angular momenta which describe the electron before and after a transition are consistent with the laws of conservation of energy and angular momentum. The radial component of the charge density waves of the novel atomic model provides that the entire charge density function of three dimensional space and time does not radiate. The condition for zero 15 radiation is the absence of Fourier components of the space tirne transform that are synchronous with waves traveling at the speed of light as described in Appendix I and Appendix ll.
The boundary condition of the radial function which forces the charge density function to be nonradiative and the result that the moment of 20 inertia of each said function is a function of quantum numbers naturally give rise to the wavelike nature of the electron. The wavelength is identical to the de Broglie wavelength, ~ = h/p, for all these functions that describe the eiectron and its energy in space-time and are hereafter referred to as Mills orbitals possessing energy, hereafter referred to as 25 the Mills energy. To distinguish the basis of the present invention from the prior art, the mechanics of the present novel atomic model is her~inafter referred to as Mills mechanics.
The electron orbitals according to the novel atomic model, referred to as Mills orbitals, are spherically symmetric charge density functions 3 0 which are the product of a radial delta function, two angular spherical harmonic functions, and a time harmonic function. Each orbital is the sum of a constant Mills orbital which rotates with a quantized angular velocity and a Mills orbital charge density modulation function which also rotates with a quantized angular velocity to result in a traveling wave of charge 3 5 density on the surface of the sphere. The time harmonic motion of the former gives rise tQ the phenomenon of magnetic ~ spin of one Bohr 2 0 r~ r~
. .
magneton for the electron. The latter time harmonic traveling naturally gives rise to orbital angular momentum. The interaction of the independent time harmonic motions gives rise to spin-orbital coupling, and the predicted spin, orbital angular momentum, and the associated 5 energies are in exact agreement with experimentation.
The energy of an electron is stored in its electric and magnetic fields.
Orbital energies are approximately equal to ionization energies. The orbital energies of several one- and two-electron atoms juxtaposed with their experimentally determined ionization energies appear in Table I and 10 Table I I .
Photon absorption by an electron with a transition to a higher energy Mills orbital arises naturally where a standing traveling wave of the photon is formed inside of the Mills orbital. This photon wave is a solution of Laplace's equation in spherical coordinates; thus, it is a spherical 15 harmonic. The photon wave rotates in bo~h directior~s simultaneously, or it rotates in the opposite direction of the spin or angular momentum of the Mills orbital to change the spin or angular momentum by one quantum which is carried by the photon, thus, the selection rules ~M; ~S = O,+ 1 for transitions arise naturally from conservation of angular momentum.
20 The electric field of an electron of a Mills orbital in the ground state is zero inside the orbital and is the field of a point charge at the origin outside of the orbital; thus, electron-electron repulsions are naturally eliminated in multi-electron atoms.
The radii of orbitals in atoms are calculated in turn by setting the 25 centripetal force equal to the surn of the coulombic and magnetic forces.
Thus, the result that isolated Mills orbitals are stable where the couiombic attractive force does not cause the electron to coliapse into the nucleus arises naturally. For all atoms and ions, there exists a central coulombic force acting on each orbital that is proportional to the net 30 charge (that is the charge not cancelled by other electrons). A positive central magnetic spin pairing force exists between two unpaired electrons which results in pairing in the same shell with spins opposed. Thus, the Pauli Exclusion Principle arises naturally. A diamagnetic repulsive central force exists between paired electrons of an inner shell and an unpaired 35 electron of an outer shell. A four body problem does not arise because the change in the centripetal force of the inner shell electrons affected by the WO 90/13126 PCI'/US90/01998 2 0 ~
.

outer electron is exactly balanced by the Lorentzian force provided by the magnetic field of the outer shell electron; thus, it is possible to calculate the exact radius and exact energy of the Mills orbital of any electron of any atom. Illustrative examples appear in Table 1 and Table 2.
5 The electric field of a Mills orbital is zero inside the shell, and this feature naturally gives rise to the chemical bond. Bonding between atoms occurs because the overlap of Mills orbitals of two atoms reduces the total energy stored in the electric fields of the participating atoms. The bond distance of the H2 molecule is determined in accordance with the 10 present invention and shown Appendix V to be the experimentally confirrned value of .748A.
Mills orbitals are spherical, and the radius increases with the absorption of electromagnetic energy. When the electron is ionized the radius of the Mills orbital goes to infinity, and the electron is a plane 15 wave with the de Broglie wavelength. The plane wave nature of an electron is consistent with the results of prior double slit experiments.
Furthermore, coupling of two such plane waves which are 180 out of phase as a zero `phonon event provides Cooper pair formation and provides the basis of a model which provides ~or superconductors Qf high transition 20 temperature which is the present invention. These materials comprise one or two dimensional lattices that contain atoms whose electrons can be ionized by an applied electric or rnagnetic field. Moreover, the lattice is of low symrnetry so that the existence of symmetric phonons is improbable.
Interactions of said phonons and Cooper's pairs causes the pairs to break.
2 5 A representative two-dimensional unit cell is . .
~ ~11~3, where M is a metal and A, B, C, and D are different atoms or different oxidation states of the same atorn or atorns.
3û Mills orbitals can resonantly absorb an energy hole, and, as a consequence, the radius decreases. With sufficient decrease in radius the electron can annihilate a proton to form a neutron. Thus, K capture arises naturally from this phenomenon.
Furthermore, outside of the outermost Mills orbital of a neutral atom, 35 the electric field of the nucleus is zero; thus, as the radii of atoms resonan~ly decrease, atoms can approach more closely before nuclear WO 90/13126 PCl'/US90/01998 7 2 a ~ J

coulombic repulsive forces occur. And, with sufficient decrease, the nuclei of atoms, such as deuterium atoms in deuterium molecules, can approach sufficiently for fusion to occur at relatively low temperature.
This process of providing low temperature fusion according to the present 5 invention is hereafter referred to as Coulombic Annihilation Fusion (CAF).
For deuterium, CA~ requires a source of energy holes of slightly greater energy than 27 eV (n/2 27.21 eV; n - 2,3,4,...) to cause a resonant radius reduction of a Mills orbital of the deuterium atom. An iliustration of such an energy hole system is Pd2+ and Li+ which catalytically removes a 10 quantum of energy during each cycle of a reaction where the oxidation states increase and decrease by one, respectively, and are regenerated by the reverse redox reaction. Also, the present invention provides for many more such energy hole systems.
BRI~.F DESCRIPTIO~LOF~HE [:)RAWINGS
The present invention is further described with respect to the drawings haYing the following solely exemplary figures, wherein:
Figure 1 is a pictorial illustration of Milis orbitals of the novel atomic model;
Figure 2 is a pictorial illustration of the magnetic field lines of an 2 0 electron in a Mills orbital in an un-ionized state;
Figure 3 is a pictorial illustration of two approaching hydrogen atoms;
Figure 4 is a pictorial illustration of the two hydrogen molecules as their Mills orbitals spatially overlap;
Figure 5 is a pictorial illustration of the electric field vectors when the Mills orbitals of ~wo hydrogen atoms penetrate; and Figure 6 is a block diagram of a fusion reactor according to one embodiment of the present invention.
12ET~ILED DE$CRIPTI~QE IHE 1Ny~lllON
J~L!~i~L~S
3 0 Conservation of mass-energy, conservation of linear and angular momentum, Maxwell's equations, and Newtonian mechanics for sublight speeds are absolute laws of nature. Thus, a body in equilibrium which is not acting on or being acted on by another body possesses constant mass-energy, constant angular momentum, force balance, and is not radiating.
And, a body not at equilibrium exchanges mass-energy and angular momentum in a conservative manner until the body is again at equilibrium.

2 ~ 7 8 An isolated atom or molecule qualifies as such a body, and a novel model of the atom and molecules hereafter referred to as Mills mechanics is derived based solely on these principles, and the charge/mass density functions which describe the electron are Mills orbitals.
5 Mills Qrbital~
Consider the body of an isolated hydrogen atom at rest in three-dimensional space. All forces are central and the coordinate system is spherical. The mass-energy and angular momentum are constant which necessitates that the equation of motion of the electron of the atom be a 10 time harmonic. Conservation of angular momentum further necessitates that the electron space-time angular mass density function must be a solution of a wave equation given in general form as follows:
(v2 + 2 ~; 2) A(~, ~, t) = O
Spherical harmonics are general solutions of this equation. Conservation 15 of momentum and energy in the absence of external forces or energy exchange determine that ~he angular functions must be separable.
The electron has a charge of 1.6 X 10 -19C and possesses an angular space-time mass density function which is a spherical and time harmonic.
Charge is conserved and obeys superposition; thus, the mass density 20 function of an electron is equivalent to its charge density function which depending on the form of its separable radial function will radiate due to the time harmonic angular acceleration of charge. The condition for radiation by moving charge is derived from Maxwell's equations in Appendix 1. To radiate, the space-time Follrier transform of the charge 25 density function must possess components synchronous with waves traveling at the speed of light. Thus, the product of two spherical harmonic functions, a time harmonic function, and a radial function must not possess space-time Fourier components that are synchronous with waves traveling at the speed of light. The solution of this boundary value 0 problem is the radial function given as foilows:
f( r) = ~(r-rO) The boundary condition for the product of the said four functions which results in the absence of radiation is given in Appendix 11. For an angular frequency of ~ = coo, the space-time Fourier transform is zero when 2~r =
35 n~. This function, with the boundary condition 2~r = n~ is a Mills orbital.

wo 9O/13~26 PCltUS90/01998 2 ~

The boundary condition requires that the electron possess a wavelength ~. The wavelength of an electron jc, the de Broglie wavelength, h ;~, a The exact forms of the angular ,and time harmonic functions can now be 5 solved from the wave equation in spherical coordinates. The form of the wave equation for the angular and time harmonic functions is as follows:
(v2 ~ 1 ~2 ) A(~ ~ t) 0 ( 2 j ~ S~ (sin~ ) r,~ ~ 2 j 2 ~ (~,p~2) r,~ + 2 ~t2 ) A(~, ~, t) = O
The energy, E, of a rotating body is given as follows: E = 1/2 Ic~2, l O where I is the body's moment of inertia and ~ is its angular velocity. The angular velocity C3 is related to the frequency ~ as follows:
~ = 2~u And, the wavelength, ~, can be expressed in terms of the frequency u and velocity v as follows:
15u~ = v Substitution of these relationships into the wave equation gives the result, 2 1 [sin ~ ~ (sin~ 3 ) + Sjn2 ~ p2)] A(9, ~, t) = E A(fl, ~ t) The time harmonic function K(t) =ei~o is separable and is cancelled 20 yielding the following equation:
2 1 [sln ~ (sin~( ~6 ) + S jn2 ~ ~,p2 ] Y(~, ~) = E Y(~, ~) (6-46) If we multiply Eq. 6-46 by sin2~ and let 13 ~2 we find the partial differential equation 2~sin~ ~ ( sin~ ~) + ~;~2 + ~ sin2~Y = O (6-48) To solve this partial differential equation, we use the method of separation of variabies and let Y(~, ~) = 9(~) h(~) (6-49) If we substitute Eq. 6-49 into Eq. 6-48 and then divide by ~ ), we wo 90/13126 PCI/US90/01998 2 ~ 9 7 find 9(~) d~ ( sin~ d9 ) ~ ~ Sin2 ~ + 1 d2h (6-50) Because ~ and ~ are independent variables, we must have that ~(~) d~ ( sin~ d9 ) + ~ sin2 9 = m2 (6-51) 5 and 1 d2h -- 2= m2 (6-52) where rn2 is a constant. Note that Eqs. 6-51 and 6-52 add up to Eq. 6-50.
Equation 6-52 is relatively easy to solve, and its solutions are h(~) = Ameim~and h(~) = A me-im~ (6-53) 10 The requirement that h(~) be continuous is that h(~ + 2~) = h(~) (6-54) By substituting Eq. 6-53 into Eq. 6-54, we see that Ameim(~27~) = Ameim~ ~6-55 ) and that A me-im(~2~) - A me-im~ (6-56) Equations 6-55 and 6-56 together imply that e~i2~1m = 1 (6-57) In terms of sines and cosines, Eq. 6-57 is cos(27~m) + i sin (2~m) = 1 20 which implies that m = 0, +1, +2,..., because cos 2J~m = 1 and sin 2J~m = O
for m - 0, ~1, +2,... Thus Eq. 6-53 can be written as one equation hm(~) = Ameim~ m = 0, +1, +2,...... (6-58) We can find Am by requiring that the hrn(~) be normalized. The normalization condition is that 2r~
J d~ h (~)hm(~
m Using Eq. 6-58 for the hm(~), we have . 2~1 Aml2 ¦ d~ = 1 o or .

~ 1 2 ~ ~ ~L ~ ,-t g .. . ~ ., ::.

IAml2 2~ = 1 or Am = (211)-1/2 Thus, the normalized version of Eq . 6-58 is h,~ ) ~ (2 )1/2 eim~ m = 0, +1, +2,.. (6-59) The solution to Eq. 6-51 is obtained by the power series method. We shall not present atl the details for the solution to Eq. 6-51, but when one does solve Eq. 6-51, it turns out naturally that B in Eq. 6-47 must obey the condition B = 1(1+1) 1 = 0, 1, 2,.......... (6-60) Using the definition of B, Eq. 6-60 is equivalent to ~2 El = 2 1 i(l+ 1 ) I = 0,1,2,..... (6-61 ) A set of discrete energy levels are obtained.
The charge density func~ions of Mills orbitals are given by the solutions to 15 Eq. 6-46. To solve Eq. 6-46, we assumed separation of variables and wrote Y(~,~) = g(~) h(~) (Eq. 6-49) . The resulting differential equation for h~) (Eq. 6-52) is r~latively easy to solve, and we showed that its solutions are ~Eq. 6-59). The differential equation for 9(~)~ (Eq. 6-51), is not easy to solve. It is conveni~nt to let x = cos ~ and 9(~) = P(x) in Eq. 6-51. Because 0 20 < ~ < ~1, the range of x is -1 < x < +1. Under the change of variable, x - cos ~, Eq. 6-51 becomes (I - X2) dx2 - 2xdx + [1(1+1) - 1--x2]P(x) = o (6-69) In Eq. 6-69 we have used the fact that 13 = 1(1 + I)(Cf. Eq. 6-60). Equation 6-69 for P(x) is called Legendre~s equation and is a well-known equation in 25 classical physics. It occurs in a variety of problems that are formulated in spherical coordinates. When the power series method of solution is applied to Eq. 6-69, the series must bè truncated in order that the solutions be finite at x = +1. It is this truncation that yields Eq. 6-60. The soiutions to Eq. 6-69 when m - 0 are called Legendre polynornials and are 30 de.noted by Pl(x). Legendre polynomials arise in a number of physical problems. The first few Legendre polynomials are given in Table 6-1.
Table 6-1 The First Few Legendre Polynomials, Which Are the Solutions to Eq. 6-69 `' i ;, ' ' Wo 90tl3126 PCltUS90/0199 2~

with m = O. The Su~script Indexing the Legendre Polynomials Is the Value of I in Eq. 6-69.
.. . . .

Po (X) = 1 P1 (X) = x P2 (x) = 1/2 (3x2-1 ) P3 (X) = 1/2 (5X3-3X) P4 (X) = 1/8 (35x4-30x2+3) .
10 Notice from Table 6-1 that Pl(x) is an even function if I is even and an odd function if I is odd. The factors in front of the P1(X) are chosen such that Pl (1) = 1. In addition, although we shall not prove it, it can be shown generally that the P1(x) in Table 6-1 are orthogonal or that JdxPI (x)Pn(x) = O 1- n (~-70) 15 Keep in mind here that the limits on x correspond to the natural, physical limits on ~(O to J~) in spherical coordinates because x = cos~. The Legendre polynomials are normalized by the general relation, which we simply present:

Jdx [Pl (x)]2 = z 2l 1 (6-71 ) 2û Fquation 6-71 shows that the normalization constant of ~ (x) is (21 +1)~2]1 /2 Although the Legendre polynomials arise only in the case m = O, they are customarily studied first because the solutions for the rn - Ocase, called associated Legendre functions, are defined in terms of the ordinary 25 Legendre functions. If we denote the associated Legendre polynomials by Pl l(x), then their defining relation is Plml(x) = (1-X2)lml/2 ddm Pt(x) (6-72) wo 90~t3126 pcr/vs9o/o1998 1 3 ~ ?~ 7 Note that only the magnitude of m is relevant here because the defining differential equation, Eq. 6-69, depends on only m2. The first few associated Legendre functions are given in Table 6-2.
Before we go on to discuss a few of the properties of the associated 5 Legendre polynomials, let us be sure to realize that it is ~ and not x that is the variable of physical interest. Table 6-2 also lists the associated Legendre polynomials in terms of cos ~ and sin ~. Note that the factors (1 - x2)1/2 in Table 6-2 become sin ~ when the associated Legendre functions are expressed in the variable ~. Because x = cos ~, Eqs. 6-7û and 10 6-71 are Jt 2 ~ n JPI (X~Pn(x)dx = p~ sin~ Pl (Cos6)pn(cos~)=2l+1 (6-73) Because the differential volume element in spherical coordinates is d~ = r2 sin ~ dr d~ d~, we see that the factor sin ~ d~, in Eq. 6-73, is the "~
part" of d~ in spherical coordinates.

Wo 90/13126 . PCI/US90tO19 2 ~
Table 6-2 The First Few Associated Legendre Functions Pll l(x) . .
Po (x) =1 5 P1 (x) = x = cos~
P1 (x) = ~1 - x 2 = sin~
P2(x) = 1/2(3x2 - 1) = 1/2(3 cos P2(x) = 3X~11 - x2 = 3 cos~ sin~

P2(X) = 3(1 - x2) = 3 sin2 ~
1 0P3(x) = 1/2(5x3 - 3x) = 1/2(5 cos3 ~ - 3 cos ~) P3(x) = 3/2(5x2 1)(1 - x2)1/2 = 3/2(5 cos2 ~ - 1)sin P3(x) = 15x(1 - x2) = 15 cos ~ sin P3(x) = 15(1 - x2)3t2 = 15 sin3 9 .
15 The associated Legendre functions satisfy the relation Jdx pll l(x) plrt l(x)= Jd~ sin ~ pll l(cos ~) Pln l(cos ~) (21 + 1) (I - Iml)l ~In (6-74) Equation 6-74 can be used to show that the normalization constant of the associated Legendre functions is Nlm = E~ ( I; I m 1~ l] 1 / 2 (6-75) Returning to the original problem now, Eq. 6-46, the Mills orbitals WO 90/13126 PCTtUS~0/01998 1 5 2~ r~

functions are pll l(cos ~)hm(~). By referring to Eqs. 6-59 and 6-75, we see that the functions ylm(~, ~) = E~ (1 - I ml ) Il] pllm!(cos~) eim~ ~6-76) are solutions to Eq. 6-46. The Yl (~, ~) form an orthonormal set 27~ r~
k~ Jd9 sin~ ylm(~ ~)* yk( ~6-77) Note that the Yl (~, ~) are orthonormal with respect to sin~ d~ d~ and do not just d~ d~. The factor sina d~ d~ has a simple. physical interpretation.
The differential volume element in spherical coordinates is r2 sin~ dr d~
d~ If r is a constant, as it is in the case of a radial delta function, and set 10 equal to unity for convenience, then the spherical coordinate volume element becomes a surface element, dA = sin~ d~ d~. If this surface element is integrated over ~ and ~, we obtain 4~, the surface area of a sphere of unit radius. Thus, sin~ d~ d~ is an area element on the surface of a sphere of unit radius. According to Eq. 6-77, the Yl (~, ~) are orthonormal 15 over a spherical surface and so are called spherical harmonics. The first few spherical harmonics are given in Table 6-3.

;, WO 90/13126 PCI-/US9OtO1998 C~
Table 6-3 The First Few Spherical Harmonics yO= ' ' ' O - (4,~)1/2 Y10 = ( 3 ~1 / 2COS ~
y-l ( 3 ~1 / 2 j io y; 1 ( 3 ~ 1 / 2 -iip Y2 = (16~1) (3cos2 ~

Y2 = (81~) Sin ~ cos ~ ei~

10 Y21 = (85) sin ~ cos ~ e Y2 = (32--,~) sin2 ~ e Y2 = (3125 ) 1 / 2sin2 9 e-2i~

The angular functions of Mills orbitals are spherical harmonics, and 15 the angular kinetic energy is given as Ek=2~ I(l + 1) 1 = O, 1, 2, ...
The angular kinetio energy Ek is related to the angular momentum, L, by the following relationship:

Ek - 2 1 20 Thus,L=~1(1+1) 1 = O, 1, 2, ...
Mills orbitals are the product of the angular, radial, and time functions which are given as follows:

~0 90/13126 PCI/US~0/01998 1 7 2~ 3 M(r, ~, ~, t) = Y(~ (r- rO) ei'l~ot Y(~,~) is a function of eim~ for l ~ 0. The product ~?im~eic~ot = ei(m~ + ~ot) is a traveling wave with angular frequency ~,)0.
The angular frequency can be derived from the angular momentum 5 energy as follows:
E=2 1 o~2 = 21 1(1 + 1) C)2= ~2 1(1 + 1) Cl)= I \11(1 + 1 ) In addition to the spherical harmonics of Table 6-3, 10 Y1~2 and Y;l2, with I = 1/2 is also a solution to equation 6-46. A Mills orbital of one of these functions is a time harmonic spinning charge density function, and it can be shown that this Mills orbital always possesses a magnetic moment of one Bohr magneton, B, given as follows:
15~=e~
2~L
where e is the charge and 11 is the mass of the electron and ~ is Planck's constant divided by 27~. The angular momentum of these functions is distinguished from that of the former solutions by assigning it the variable S, the spin angular momentum of the electron which is given as 2 0 fol lows:

S=li~ls(s + 1) S = 1/2 ms = +1/2 And, the angular momentum, L, is defined as orbital angular momentum.
25 A sum of independent solutions to Eq. 6-46 is a solution, and the same condition applies to the boundary condition for nonradiation. Thus, the Mills orbital of the electron is given as the sum of the following functions:

., ' ' ' . . :, 2~a~

M(r, ~, ~, t) = Y ~ (r - rO) ei~lt ~ Y ~ (r - rO) ei~t s where C~1 = I '/I(i ~ 1) 1 = O, 1, 2, '~2= I ~s(s+ 1) s = 1/2 5 Thus, it is apparent that a Mills orbital is a spherical shell of charge/mass density of zero width where the charge/mass is a base function defined by Y s to which is added a component of modulation of s mass/charge density given by Y ' where the total charge is e, the charge of an electron, and the total mass is 1l, the mass of the electron.
10 (Diagrams of several representative Milis orbitals are given in Figure1.) The two components are independent time harmonics which rotate in the same or opposite directions. The interaction of the two independent components gives rise to spin-orbital coupling.
It can be demonstrated that the moment of inertia of the orbital 15 angular rnomentum and spin angular momentum are given respectively as follows:
I spin = ~r2~ s ( S + 1 ) langUlar = llr2~
where ~L is the mass of the electron and r is the radius of the Mills orbital.
20 Substitu~ion of this result into the angular frequency relationships gives:
cq = ~ 1) = r2 ~ r2 11 r ~ I S ( S + 1 ~ ~ -~S = I ys(s + 1) = ~r2~llS(S + 1 ) 11r2 The linear velocity is obtained from the angular velocity by the following equation:

WO 90/13~26 PCI/US90/01998 v = r cl) Thus, the linear velocity of the spin and orbital Mills orbitals is given as followS:
tl v =--llr 5 To prove this result is consistent with the boundary condition for nonradiation, the wavelength is derived from this result and the boundary condition, 2J~r= n~; n =1,2,3,... as follows:
2~
K = ;~ = v = ~.~r2V
h ~ ~ 2~r2~rllv 1 h ~ ~lV
h ~. = p Pnsition and Ener~ies Q~ s Or~al~
The radius of each Mills orbital can be calculated by equating the centripetal force with the other central forces. The forces are as follows:
1.) coulombic attractive force of the positively charged nucleus for the negatively charged Mills orbital;
2.) an attràctive magnetic spin pairing force between two unpaired electrons which causes them to be at the force balance at the same radius with vectorially opposed spins; thus, the magnetic moments cancel;
3.) a repulsive diamagnetic force between two paired electrons and an unpaired electron where the radius of the former is unaffected by this force.
Only the coulombic force is involved in the one electron atom. The coulombic and ~he spin-pairing forces are involved in two electron atoms, and the coulombic and diamagnetic forces are involved in calculating the radius of the third electron of a three electron atom, where the previously calculated radius of the inner shell comprising two spin-paired electrons is used in the calculation. The orbital energy of any electron can be 3 0 calculated from the calculated radius as the energy stored in its electricand magnetic fields. (The magnetic field of an electron and the energy , 2 ~

stored in the magnetic field of two electrons is given in Appendix IV. A
magnetic field diagram of an electron is given in Figure 2.) Examples of one-, two-, and three-electron atoms are given below which demonstrate the said forces. And, it is further demonstrated, in the case of lithium, 5 that the sum of the orbital energy and the change in orbital energies of the two remaining inner shell electrons foliowing ionization is equal to the experimentally determined first ionization energy of lithium.

WO 90/13126 PCr/US9~)/01998 21 2 ~ 7 The One-Electron Atom ~V2 centrlpetal force = r centripetal electrostatic force = (+Ze)( e)=

4~l0r2 47~EOr2 (obtained by taking the gradient of the electrostatic potential)

5 We can solve for the radius of the electron shell by balancing these forces.
~2 r = 4~l~0r2 The boundary condition is 2J~r = n~ which gives '~ = n r2; v = rc,); thus, v =
tl2 n r When an electron in the ground state absorbs a photon of sufficient energy to take it to a new non-radiative state, n = 2, 3, 4, ..., force balance 1 û must be maintained. This is possible only if we let Zeff = n and, therefore, Vn2 Zeff,,e2 rn 47~0rn2 The reduction of the charge from Ze to Ze/n is caused by trapping a photon in the orbitsphere cavity--a spherical cavity.
1 5 Therefore, 4~Er n?l2 naO ( 1 ) The energy stored in the electric field of the orbitsphere, Eele ,is naO naO
27~ 7~ Z 1 27~ 7~ Z
E I = (~ o ¦ ¦ ¦ E2dV = (2) ~ I I J167~2o2nr4 oo where the electric field,E, is E=O,r<aO;E=4 e r2 r ~ aO
naO

Eele=8 r n Jr2 dr=- 2=-n2 (2.17714(l0)-l8) J

6 PCr/US90/01998 205~6~ 22 z2 Eele = - n2 (13.583) eV (2) Equations (1) and (2) can be used for any one-electron atom. The energies for several one-electron atoms are shown in Table 1.
Table 1 Calculated energies (non-relativistic) and calculated ionization energies for sorne one-electron atoms (without realtivistic correction) .
Atom Energy (eV)alonization Energy (eV) H -13.589 13.595 He+ -54.35 54.587 1 0 Li2+ -122.28 122.45 Be3+ -217.40 217.71 B4+ -339.68 340.22 C5+ 489.14 489.98 N6+ 665.77 667.03 o7+ 869.58 871.39 afrOm equation (2) Wo 90/13126 PCI`/US90tO1998 2 ~

The Two-Electron Atom ~V2 centrlpetal force = r centripetal electrostatic force = - (Z~
4~l0r2 centripetal magnetic force = ~ Z r3 ~S(S + 1 ) 5 ~obtained by taking the gradient of the angular momentum energy) Consider two indistinguishable electrons where each is subject to an effective nuclear charge of Z-1 due to cancellation of one nuclear charge by the other electron. Each electron has a positive spin pairing force for the other. The balance of force equations is as follows:
10 For n = 1, v2 = r2 r llr3 41~0r2 7 r3 ~IS(S ~ 1 ) and, r=aO(z t ~ZS(S + 1)) The electrostatic energy is Eele = (8 ) (4) The magnetic energy is - 27~oe2~2 E(magnetic) = 2 3 (5) (The energy stored in the magnetic field of an electron is derived in Appendix IV.) .
` . ~ ' .
.. ..

WO 90/13126 PCI'/US90/0199~

.
2~4~7 24 Table ll The oalculated eiectrostatic and magnetic energies for some two-electron atoms (without relativistic corrections) .

5 Atom Atomic R(aO)a Electrostatic Magnetic Total Experimental Number Energyb EnergyC Energylonization (eV) (eV) (eV)Energy (eV) He 2 0.567-23.96 -0.63 -24.59 24.587 Li 3 0.356-76.41 -2.54 -78.95 75.638 1 0 Be - 4 0.261-156.08 -6.42 -162.50 153.893 B 5 0.207-262.94 -12.96 -275.90 259.368 G 6 0.171-396.98 -22.83 -419.81 392.077 N 7 0.146-558.20 -36.74 -594.93 552.057 O 8 0.127-746.59 -55.35 -801.95 739.315 1 5 F 9 0.113-962.17 -79.37 -1,041.54953.886 afrOm equation (3) bfrom equation ~4) cfrOm equation ~5) WO 90/1312~ PCI'/US90/01998 2 ~ ;i `'fi~

Three-Electron Atom (First ionization Energy of Lithium) From the Li2+ (see Table 2), it was determined that there are two oppositely spin-paired electrons in a sheil with the radius r = aO ~2 -- 6 The next electron is added to form a new shell. This is a consequence of a re~ulsive force that exists between the two spin-paired electrons and the spin unpaired electron. This repulsive magnetic force arises from the phenomenon of diamagnetism involving the magnetic field produced by the 10 outer electron and the two paired electrons of the inner shell.
(The following calculation is given by Edward Purcell in Electricity and Magnetism, p. 370-389. The diamagnetic force of the two paired inner shell electrons actiny on the outer shell electrons is given as -mvO~v ~v eB eB
r r = 211 = 4~ vO =--15 where r, is the radial distance of the first shell from the origin.
~ eB
F= ----4rl ~
The magnetic flux is that supplied by the constant field inside the shell of the outer electron and is given by:
~Oe~
B= ~3; therefore, 2 0 F = ~ O
41lr2 r1 llr ~=~s(s+l) ,ur F=-4 2 ~s(s + 1) The radius of the orbital for the outer electron of lithium is calculated by equating the centripetal force to the sum of the coulombic and 2 5 diamagnetic forces as follows:
v2 e2 ~2 r 41~or2 ~ ~ ~ r2 rl ~ls ( S + 1 ) .

' , :

. .. ...

WO 90/13126 PCT/US90/0199~

2 ~ 2 6 v = rand r1 = aO ~2 - ~6 , thus, ~2 e2 tl2 r3 47~or2 ~ s(s ~ 1 ) 4~lr2aO L2 - 6 a~
r = = 1 '13 /4 - = 2.~6 aO
4 (1 ~¦ 3/4 ) The energy stored in the electric field is calculated as follows:
e2 e2 5 318 V

The field due to the outer shell electron changes the angular velocities of the inner shell electron; however, the magnetic field of the outer electron provides a central Lorentzian force which exactly balances the change in centripetal force due to the change in angular velocity. Thus, the 10 radius of the inner shell is unchanged. Consequently, the electric energy of the inner shell is unchanged upon ionization. However, the outer field changes the magnetic moments of the inner shell electrons. The change per electron is given by Purcell as follows:
Bm =~ B B = 3 1~ where r1 is the radius of the inner shell and r2 is the radius~of the outer shell .
B e2r12 ~LOe~
411 ~r2 - ~Oe2 r = ~¦s ( s + 1 ) Bm = 4 r22 ~¦s(s + 1 ) ~B = 2 Bm 2~ r1 2 ~fs(S + 1) = 2 r22 ~IS(s ~ 1 ) WO 90/13126 . PCI/US90/01998 :~ 7 ~ 3 - [aO ~1 - ~6 ~ \/ 314 -4(1 ~3/4 ) Multiply the result by two because there are two electrons.
= ~9~~ 2 = 0.01 67 5 We add one and square to get the fractional change in the magnetic energy of the inner shell.(because the energy stored in the magnetic field is proportional to the magnetic field strength squared).
(1.0167)2 1.0338 Thus, the change in magnetic energy of the inner shell is 3.382% which is 1 0 given by: -2.543 eV (0.3382) = .0860 eV
(Where the magnetic energy of lithium~ appears in Table ll.) Eionization = .0860 eV + ~.318 eV = 5.4038 eV
The calculated ionization energy without relativistic correction is 15 5.40 eV.
The experimental ionization energy is 5.392 eV.
Energy due to Spin Nuclear Interactions If the magnetic quantum number of the nucleus is greater than 0, the nucleus has a magnetic moment and ~he magnetic field of the electron can 2 0 interact with the nuclear rnoment. This interaction is an important parameter for structural determinations by electron paramagnetic resonance spectroscopy and Mos~bauer spectroscopy. The energy of interaction is given as follows:
E = lln- B, where ',~n is the nuclear moment and B is the magnetic flux.
25 In the case of an electron, it can be seen from Figure 2 that the flux of an electron at the nucleus is uniform and is given in Appendix IV as follows:
B = ~r3 (Ir cos 9 ~ sin ~) WO 90/13126 PCI'/US90/01998 ,2.0~ 7 The magnetic moment of a proton is given as follows:
e~
~ lp = 2mp where, mp is the mass of the proton.
When the nuclear moment is aligned with the electron's field ~ = 0 and the 5 energy is given as follows:
E e~l ~Oe'fl 2mp ~r3 These energies are small. For example the energy of spin-nuclear interactions for hydrogen are 1.98 ~ 10-5 eV.
The Nature of the Chernical Bond The driving force of molecular bonding is the decrease in the energy stored in the electric fields of the participating atoms as a consequence of overlap of their Mills orbitals. (The magnetic stored energy is involved but is dominated by the electric stored energy.) Consider two isolated hydrogen atoms that approach each other along 15 the internuclear axis as shown in Figure 3. The electric field of each atom is zero for radial distance greater than aO, the radius of the Mills orbital of the electron. As the Mllls orbitals from one atom penetrates the space of the other, the electric field components add vectorially. The components parallel to the internuclear axis cancel, and the perpendicular 20 components add positively. The latter components have a positive tangential projection onto the angular vectors of the Mills orbitals in the region of overlap.
The energy stored in the electric fields of the atoms decreases as the internuclear distance decreases; however, it reaches a minimum then 25 increases rapidly as a function of the internuclear distance. The trajectory produces the classic potential well, and the internuclear distance is given the geome~ric calculation in Appendix V as ~12 aO = .748A
which is the exact experimental value. Thus, molecular bonding is demonstrated to result from interactions of the electric fields of atoms 30 which minimizes the energy. Starting with the case of the hydrogen-molecule of Appendix V, consider reducing the total char~e of one of the Mills orbitals. The internuclear distance increases as the charge decreasès. In the iimit of no charge, the internuclear distance is 2aO. Thls WO 90/1312S PCI-/US90/019g8 2 ~ 3 is apparent from the following argument, the addition of an infinitesimal amount of charge to the Mills orbital of zero charye produces an infinitesimal overlap due to an infinitesirnal lowering of the total energy.
Thus, the internuclear distance before the infinitesimal addition was 2aO
5 which is the exact experimentally measured distance for the H2+
molecule.
Furthermore, it can be shown that the diatomic molecule can be approximated by a harmonic oscillator with quantized energy levels given as follows:
EVib = (n + 1/2)hl)o n = 0, 1, 2, t)o =~ ~
where ,u is the reduced mass of ~he atoms, and k is the spring constant which is proportional to the bond strength; therefore, k is proportional to the gradient of the function of the bond energy as the internuclear 1 5 distance changes.
It can also be shown that the rotational energies of a diatomic molecule are given as follows Erot = hcB(J + 1) J = o, 1, 2,...
Selection Rules 2Q The electrons which are described by Mills orbitals can absorb energy and achieve an excited state, and they can lose or emit energy and achieve a lower energy state. In the case electromagnetic radiation, energy flow is governed by Poynting's theorem * * *
V S = ~ LH H ~ E E - J E
25 where the parameters are as follows:
S is the power; the first term is the rate of change in the stored magnetic energy, the second term is the rate of change in the stored electric energy, and the third term is the dissipated power. For electromagnetic radiation, the ground state is the lowest energy state. The ground state is 30 given b~ the balance of the centripetal and coulombic forces. For the hydrogan atom, the radius and energy appear in Table 2 as aO and t3.6 eV, respectively. The boundary condition for Mills orbitals was given in the Mills Orbital Section as 2~r= n~ where r = aO for n = 1.
Thus, the absorption or emission of a photon by a hydrogen atom causes WO 90~13126 PCr~US90/01998 2 0 ~ 7 the radius to change by an integer multiple of aO. The energy of the photon is the difference in energy of the initial and final orbitals where the equation for the energies of the orbitals is given in the One Electron Atom Section. Photon absorption by an electror1 creates a standing wave of the 5 photon's electric and magnetic fields inside of the Mills orbital. These fields are solutions to Laplace's equations in three dimensions which are spherical harmonic equations. The photon field exists as a standing wave where surface currents of the Mills orbital are generated by the said wave and are boundary conditions for its existence. The angular momentum and 10 spin angular momentum of all Mills orbitals are given by El = ~ l(l + 1 ) and -Es = tl~s(s ~
respectively.
The angular momentum is a vector; thus, it is apparent that the angular momentum can change by zero or +1 during a photon absorption or emission event, a transition. Angular momentum must be conserved;
therefore, the quantum of angular momentum is provided by the photon which carries the exact opposite quantum of angular momentum as that 20 imparted to the Mills orbital. The standing wave of the photon is a traveling standing wave where the Mills orbital surface currents, induced by the wave, provide one quantum of angular momentum to the Mills o!bital in the opposite direction to the angular direction of the traveling wave. Furthermore, angular momentum is also conserved if the wave does 25 not travel. In this case, the photon wave can be considered as the superposition of two traveling waves rotating in opposite directions with the same angular velocity and is analogous to plane polarized light. Thus, the selection rules for a photon induced transition of ~m, ~s = 0, ~1 arise naturally (~m is the change in angular momentum, and AS is the change in 30 spin angular momentum) where a change of zero is the nontraveling wave case and a change of 1 is the traveling wave case This is totally , c~nsistent with experimentation which. demonstrates these rules to be correct where the photon carries one or zero quantum of angular momentum. Consistently, a ~ransition has a rise time and, consequently, a 35 line width, as is the case in electrodynamics.

WO 90/13126 PCr/US90/01998 3 1 2~ 3 The standing photon wave has a nonzero electric field at the Mills orbital which has a radial component which combined with the induced surface currents provided by its tangential electric field cause the centripetal and central coulombic forces to be balanced at an integer 5 multiple of aO. Thus, the standing wave has an effective charge given by ~o~r which reduces the coulombic attraction of the nucleus. Because a photon can only reduce the coulombic attraction, the ground state, which contains no photon field, is the smallest radius possible for photon transitions. It will be shown in the Coulombic Annihilation Fusion Section 10 that the resonant absorption of energy holes can shrink the radius by quantized fractions of aO.
Effects of External Fields External magnetic fields align magnetic moments (Bohr magnetons) of atoms for those with unpaired electrons, or external magnetic fields 15 effect diamagnetic phenomenon in those materials that do not have unpaired electrons. Neither phenomenon affects the boundary conditions for nonradiation.
External electric fields cause a redistribution of the charge density of the Mills orbitals, the charge density functions, to create a dipole moment 20 in the atom or molecuie. This phenomenon is polarization. The orbital condition 2Jtr= n~ is not Yiolated, so no radiation occurs.
Electrons can absorb photons from magnetic or electric fields to become ionized. This occurs readily in a conductor or superconductor. Mills orbitals of electrons are spherically symmetric. As photons are absorbed 25 the radius expands from the ground state with radius r1 to nr1 where n =
2, 3,.... As n goes to infinity the radius r goes to infinity and the Mills orbital becomes a plane wave. The boundary condition for a Mills orbital 2ntr= n~ still applies; therefore, ~ _ p .The plane wave nature of the ionized electron is confirmed by double sli~ experiments that demonstrate 3 0 that the resulting interference pattern is consistent with the electron traveling through both slits simultaneously and possessing a wavelength h ~ = p.
Metals have electrons as Mills orbitals which indiv :ually absorb energy in the form of a photon from applied magnetic or electric fields to WO 90/13126 PCr/US~0/01998 2 ~

become ionized to produce individual plane waves which are scattered by phonons. There exists many electrons which can absorb the electric or magnetic energy to become ionized and propagate as plane waves through the material. In the case of superconductors, two electrons are ionized 5 simultaneously and pair 180 out of phase as a zero phonon event to form Cooper pairs which have a low probability of being scattered as they propagate. Superconductors are described in detail in the Superconductor Section .
Superconductors 10 The Mills orbital of an electron is a spherical shell. The shell annihilates photons during absorption to trap them as standing waves inside the Mills orbital. The radius of the Mills orbital increases as the energy stored in the field of the photonic wave increases. Because the Mills orbital is a sphere, the orbital approaches a plane wave of charge 15 density as the radius goes to infinity. Thus, an electron becomes a plane wave carrying a plane photon wave when it is ionized. Two electrons ca be ionized simultaneously to create two traveling waves. If they are initially oppositely paired in terms of spin and angular momentum, then the two electrons with their accompanying photonic waves may add 20 destructively. (180 out of phase, as plane waves when they are simultaneously ionized). This event occurs with no excitation of a phonon (lattice vibration). That is it must be a zero phonon event because phonons change the relative phases of the plane waves and exchange energy with the photonic fields.
25 These paired Mills orbital plane waves, which are 180 out of phase, carry the supercurrent in superconductors, and are known as Gooper pairs.
They possess a low phonon interaction cross section for dephasing and breaking in the superconductor. Breaking the pairs requires the simultaneous absorption by the pair of anti-symmetric phonons. This is 30 the boundary condition because Cooper pair creation was a zero phonon event; thus, anti-symmetric phonons must simultaneously be absorbed to break the Cooper pairs to conserve angular and linear momentum of the entire system-Cooper pair plus phonons (lattice distortions).
Thus, it is apparent that a superconductor with a high transition 3 5 temperature is a material with the following properties:
1.) a large population of atoms with electrons which can WO 90/13126 PCI'/US90/01998 3 3 ~ ~ ~c~

readily absorb energy from an electric or magnetic ~ield to become ionized in such a fashion that they can participate in Cooper pair formation 2.) a low population of phonons at high temperatures 3.) a low population of phonons of sufficient energy to break Cooper pairs at high ternperatures 4.) a low population or low probability ofopposite symmetry phonons of energy sufficient to break Cooper pairs.
Materials that contain atoms of transition elements satisfy condition 10 1. Materials which contain one of tWQ dimensional lattices with strong bond energies satis~y conditions 2 and 3. Ceramics are materials of condition 2. Materials which contain one or two dimensional lattices with mixed valency or all different atoms in the unit well satisfy condition 4.
The ideal unit cell is 1~
D_M B, where M is a transition metal and A, B, C, and D are different atoms or different oxidation states of the same or different atoms. Perovskite superconductors such as (Ba, Sr, Y) x La2 x CuO4 are 0 examples of materials which contain all of ~he said parameters.
Coulombic Annihilation Fusion - It was demonstrated in the Selection Rules Section that resonant photon absorption can only increase the radius of a Mills orbital. For resonant photon absorption, the ground state has the smallest radius possible. For the hydrogen, atom the radius of the ground state Mills orbital is given in Table 1 as aO. This orbital contains no photonic waves, and the outward centripetal force and the inward coulombic force of the electron exactiy balance. The relationship is as follows:
~V2 e2 where Y =
aO 4~0aO
3 0 It is apparent from this relationship that the radius would decrease ifthe velocity were somehow decreased To decrease the velocity, energy must be removed which is equivalent to the absorption of an energy hole by the electron. When energy is removed the Mills orbital will decrease to another allowed state where the boundary condition, 2J~r = n~, and the force balance is met.

; . . ' WO 90/13126 PCI'/US90/01998 2 ~ 9 7 Thus, it can be demonstrated, as appears in Appendix Vl, that the absorption of an energy hole with concomitant shrinkage of the radius of the Mills orbital is a resonant process with quantum numbers. The resonance "shrinkage" energy given in Appendix Vl for the hydrogen atom is n/~ 27.21 eV where n = 2, 3,..., and the radius shrinkage is aO( n1 - n2 ) where n~ is the quantum inte~er of the initial orbital and n2 is the quantum integer of the final orbital of a radius shrinkage transition.
The electrons in deuterium atoms are described by Mills orbitals which satisfy the boundary condition 2tlr= n~, and possess no space-time Fourier 10 components synchronous with waves traveling at the speed of light; thus, they do not radiate. The electric field of the Mills orbital of a deuterium atom is that of a point charge at the origin for radial distances greater than the orbital radius. For these distances, the field of the Mills orbital exactly cancels the field of the proton which is also that of a point charge 15 at the origin. The electric field of a Mills orbital is ~ero inside the orbital; thus, the electric field inside the orbital of the deuterium atom is the point charge field of the proton. It was demonstrated in the Nature of the Chemical Bond Section that ohemical bonding was due to this feature of electric fields of Mills orbitals where the total energy of the electric 2 0 fields of the participating atoms was minimized when the internuclear distance is ~2 times the radius of ~he Mills orbital. And, this feature together with resonant shrinkage of the Mills orbitals is the basis of "cold fusion" of deuterium, Coulombic Annihilation Fusion, the present invention. Coulombic repulsions of the nuclei prevent them from 25 approaching sufficiently for the strong nuclear force to dominate and for fusion to occur. However, outside of the Mills orbital of a deuterium atom there is no electric field; thus, for each of hNo deuterium atoms, when the Mills orbital is sufficiently decreased by the resonant absorption by energy holes, the internuclear distance of two deuterium atoms becomes 3 0 the distance at which the attractive strong nuclear force dominates the repulsive coulombic force, and fusion of deuterium to helium and tritium occurs with the release of 931 MeV/amu. The mass change for fusion of deuterium is 0.03 amu; therefore 28 MeV/atom of energy is.released.
It is demonstrated in Appendix Vl that the radius of the Mills orbital ~ . , :

WO 90/13126 PCr/US90/01~98 2 ~ 3 ~

of the deuterium atom will decrease by aO ( n1 ~ n ) when an energy hole of energy equal to n/2 27.21 eV; n = 2, 3, 4,..., is resonantly absorbed. With continued resonance shrinkage-absorption of energy holes-by the atom, the Mills orbital shrinks to small dimensions, and when approximately 100 5 KeV of energy holes have been absorbed the radius is sufficiently small that the deuterium atom will fuse with another atom of deuterium with a similar dimension of its Mills orbital.
A catalystic system to produce energy holes of 27.21 eV is a preferred embodiment of the present invention. For such a system the population of 10 energy holes is not exhausted because they are regenerated.
Palladium 2+ and lithium+ is such a systern. The catalytic cycle which affects the quantized decrease in the radius of the Mills orbital of the deuterium atom is as follows:
27.54 eV + Li+ + pd2+ + 2H[ p ] ~ Li + Pd3+ t 2H[(p + I) ] + [(p + 1)2 _ n2] x 13.6 eV
1 5 Li + Pd3~ = Li+ + Pd2+ + 27.54 eV
Overall reaction 2H[a ] _~ 2El[ ( aO l) ] + [(p + 1)2 _p2] x 13-6 eV
where p = 1, 2, 3,....
The Palladium lithium system involves three species. The rate of the 20 resonance shrinkage can be increased by reducing the number of species to two. Titanium, rubidium, or argon are effective catalysts. The catalytic reactions are as follows:
27.491 eV + Ti2+ + 2H[~ ~ Ti3+ + e~ + 2H[(p + I) ] + [(p + 1)2 _ p2] x 13.6 eV
Ti3+ + e- ~ Ti2+ + 27.491 eV
2 5 (8.8) And, the overall reaction is 2H~ p ] ~ 2H (p + l) ] + [(p + 1)2 _p2~ x 13.6 eV
where the ionization energy, Ejon, for Ti2+ is 27.491 eV; p is a integer 27.491 eV+ Rb+ ~ 2H[ p ] ~ Rb2+ + e~ + 2H[(p + ~~ ] + [(p + 1)2 _ p2] X 13.6 eV
Rb2+ +e~ ~ Rb+ + 27.28 eV
Overall reaction 2 ~

2H[a ~ ~ 2H[( l) ~ + [(p + 1)2 _p2] x 13.6 eV
where the ionization energy, Ejon, ~or Rb+ is 27.28 eV
27 63 eV+ Ar+ + 2H[a0 ] ~ Ar2~ + e~ + 2H[( + l) 1 + ~(P + 1)2 - p2] x 13.6 eV
Ar2+ +e~ ~ Ar~ + 27.63 eV
5 Overall reaction 2H[a0 ] ~ 2H¦ ( aO 1~ 1 + [(p ~1)2 _p2] x 13.6 eV
where the ionization energy, Ejon, for Ar+ is 27.629 eV.

WO 90/13126 PCI'/US90/01998 ~3 7 ~ h~ ~J

The present invention comprises a source of energy holes of approximately 27 eV to resonantly shrink the Mills orbitals of deuterium atoms, including a source of said holes produced by further electrochemical reactions or chemical, photochemical, thermal, free 5 radical, sonic, or nuclear reactions or inelastic particles, or photon scattering reactions. The closer the energy of the hole is to the quantum of 27.21 eV or the quanta of 2 27.21 eV: n = 2, 3, 4,..., the greater the rate of reaction because phonons ortranslational or rotational modes do not have to be simultaneously excited to match the resonant shrinkage energy.
l O Table 3 is a table of ionizatioh energies as given in Chemical Structure and Bonding, Rodger L. DeKock and Harry P. Gray, the Benjamim Cummings Publishing Company, Menlo Park, CA, (1980), pp. 76-77 which is incorporated by reference. Electrochemical couples with ionization energy differences of approximately 27 eV can catalyze the removal of energy 1~ from the electrons of deuterium and/or tritium atoms and molecules and catalyze cold fusion of deuterium and/or tritium.

Wo 9~ Pcr/usso/o1998 . 38 Representative electrochemical couples which generate energy holes of approximately 27 eV appear in Table 4, and some catalytic couples comprising single elements which are cations, neutral, or anions and single molecules which are cations, anions, or neutral or combinations of 5 the said species-reactants are also found in Table 4. For n - 2, the resonance energy is 27.21; for n = 16 the resonance energy is 217.68 eV;
for n = 54, the resonance energy is 734.67 eV.

WO 90/13126 PCI`/lJS90/01998 3 9 2 ~ 7 Table 4. Representative Electrochemical couples that catalytically produce energy holes of 27 eV to shrink deuterium atoms.
Electrochemical lonization Energy Hole Couple Ener~y_ ~ _ Lu3+ 45.19 27.768 F+ 17.422 Pb2+ 32.93 27.~38 Li+ 5.392 Ni2+ 35.17 27.3 Fe+ 7.~
Ag2+ 34.83 27.37 Rh+ -7.46 Zr3+ 34.34 27.241 1 5 Mo+ 7.099 Nb3+ 38.3 27.863 Hg+ 10.437 Cu2+ 36.83 27.605 Au~ 9.225 pb2+ 31.937 27.596 K+ 4.341 Ge2+ 34.22 27.34 Nb+ 6.88 Many others exist and are given in the above referenced Table 3 of 25 ionization energies.

WO 90/13126 PCl`tUS90/01998 r7 Table 4. Some representative single-ions capable of producing (con~t) energy holes for shrinking deuterium atoms. The number following the atomic symbol, (n), is the nth ionization energy of the atom. That is for example, TiZ* + 27.49 eV
= Ti3~ + e-.
Catalytic lon n nth lonization Energy Al 2+ 3 28.45 Ar 1+ 2 27.63 Ti 2+ 3 27.49 - As 2+ 3 28.35 Rb 1~ 2 27.28 Mo 2+ 3 27.16 Ru 2+ 3 28.47 In 2+ 3 28.03 Te 2+ 3 27.96 Table 4. Some represen~ative two-ion couples capable of (con't) producing energy holes for shrinking deuterium atoms.
The number following the ion, (n), is the nth iunization energy of the atom. That is for example, Pd2+ + 32.93 eV
= Pd3+ ~ e- and Li+ + e- = Li + 5.39 eV.
Atom n nth lon- A~om n nth lon-Energy Oxidiz- ization Redueed izationHole ed Energy Energy (eV) (eV~ (eV) Ne 1 + 2 40.96 H 1 + 1 13.60 27.36 Ar2+ 3 40.74 H 1 + 1 13.60 27.14 Sn3+ 4 40.73 H 1~ 1 13.60 27.14 Pm3 + 4 41.10 H 1 + 1 13.60 27.50 Sm 3 + 4 41.40 H 1 + 1 13.60 27.80 . Dy 3 + 4 41.50 H 1 + 1 13.60 27.90 Kr 3 + 4 52.50 He 1 + 1 24.59 27.91 Rb3+ 4 52.60 He1 + 1 24.59 28.01 K 4+ 5 ~2.66 He2+ 2 54.42 28.24 Zn 4 + 5 82.60 He 2 + 2 54.42 28.18 Se 5 + 6 81.70 He 2 + 2 54.42 27.28 He 1 + 2 54.42 Rb2~ 2 27.28 27.14 WO 90/131~6 PCI/US90/01998 ''. ;"
41 ~ ~ ~ J~

Zr 4 + 581.50 He 2 ~ 254.42 27.08 He 1 + 254.42 Mo3+ 327.16 27.26 Si 2 ~ 333.49 Li 1 + 15.39 2B.10 Mn 2+ 333.67 Li 1 + 15.39 28.27 Co 2 + 333.50 Li 1 + 15.39 28.11 Pd 2 + 332.93 Li 1 + 15.39 27.54 1 2 + 333.00 Li 1 + 15.39 27.61 Hf 3 + 433.33 Li 1 + 15.39 27.94 Li 1 + 275.64 C 3 ~ 347.89 27.75 l O Li 1 + 275.64 N 3 + 347.45 28.19 Li 1 + 275.64 Na2+ 247.29 28.35 Li 1 + 275.64 S 4 + 447.30 28.34 Cu 5+ 6103.00 Li 2 + 275.64 27.36 Li 1 + 275.64 Br 4 + 447.30 28.34 Br 6 + 7103.00 Li 2 + 275.64 27.36 V 6 + 7150.17 Li 3 + 3122.45 27.72 Li ~ + 3122.45 Mn6+ 695.00 27.45 Cu 2+ 336.83 Be 1 + 19.32 27.51 Kr 2 + 336.95 Be 1 ~ 19.32 27.63 Cd2+ 337.48 Be 1 + 19.32 - 28.16 Te 3 + 437.41 Be 1 * 19.32 28.09 Ce 3 + 436.76 Be 1 + 19.32 27.44 K 2 + 345.72 Be 2 + 218.21 27.51 V 3 + 446.71 Be ~ ~ 218.21 28.50 Ge 3 + 445.71 Be ~ + 218.21 27.50 Mo3+ 446.40 Be2+ 218.2i 28.19 Bi 3 + 44~.30 Be2+ 218.21 27.09 Be 2 + 3153.89 Ne 5 ~ 5126.21 27.68 Be 2 + 3153.89 Kr 8 + 8126.00 27.89 Be 2 + 3l 53.89 Mo 7 ~ 7126.80 27.09 Be 3 + 4217.71 Al 6 + 6190.47 27.24 Br 2 + 336.00 B 1 + 18.30 27.70 Ce3+ 436.76 B 1 + 18.30 28.46 Cl 3 + 453.46 B 2+ 225.15 28.31 Kr 3 + 452.50 B 2 + 225.15 27.35 Rb 3 + 452.60 B 2 ~ 225.15 27.45 WO 90t13126 PCr/US90/01998 2 ~

B 2 + 3 37.93 P 1 + 1 10.49 27.44 P 4 + 5 65.02 B 3 + 3 37.93 27.09 B 2 + 3 37.93 S 1 + 1 10.36 27.57 V 4 + 5 65.23 B 3 + 3 37.93 27.30 5B 2+ 3 37.93 As 1 + 1 9.81 28.12 B 2+ 3 37.93 Se 1 + 1 9.75 28.18 B 2+ 3 37.93 1 1 + 1 10.45 27.48 B 2 + 3 37.93 Ba 2 + 2 10.00 27.93 B 2 + 3 37.93 Ce 2 + 2 10.85 27.08 10B 2 + 3 37.93 Pr 2 + 2 10.55 27.38 B 2 + 3 37.93 Nd 2 + 2 10.73 27.20 B 2 ~ 3 37.93 Pm 2 + 2 10.90 27.03 B 2 + 3 37.93 Hg 1 + 1 10.44 27.49 B 2+ 3 37.93 Rn 1 + 1 10.75 27.18 15B 2 + 3 37.93 Ra 2 + 2 10.15 27.78 Cl 2 + 3 39.61 C 1 ~ 1 11.26 28.35 Zn2+ 3 39.72 C 1 + 1 11.26 23.46 Nb3+ 4 38.30 C 1 ~ 1 11.26 27.04 Pr 3 ~ 4 38.98 C 1 + 1 11.26 27.72 20Kr 3 + 4 52.50 C 2 + 2 24.38 28.12 Rb 3 + 4 52.60 C 2 + 2 24.38 28.22 C 2+ 3 47.89 P 2+ 2 19.73 28.16 Ar 4 + 5 75.02 C 3 ~ 3 47.89 27.13 Fe 4 ~ 5 75.00 C 3 + 3 47.89 27.11 25Ni 4 + 5 75.50 C 3 + 3 47.89 27.61 C 2+ 3 47.89 Cu2+ 2 20.29 27.60 C 2 + 3 47.89 Ga 2 + 220.51 27.38 ~ 2~ 3 47.~9 Y 3+ 320.52 27.37 C 2 + 3 47.89 Pd 2 + 219.43 28.46 30C 2+ 3 47.89 Ce3+ 320.20 27.69 C 2 + 3 47.89 Gd 3 + 320.63 27.26 C 2+ 3 47.89 Au 2 + 220.50 27.39 C 2+ 3 47.89 Tl 2 + 220.43 27.46 Sc 4 + 5 91.~6 C 4 + 464.49 27.17 3`5~ - 3 ~ 4 64.49 Cu 3 + 336.83 27.66 C 3 + 4 64.49 Br 3 + 336Ø0 28.4.9 WO 90/13126 PCI'/US90/01998 43 ~3~ )t~!

C 3 + 4 64.49 Kr 3 + 3 36.95 27.54 C 3 + 4 64.49 Cd 3 + 3 37.48 27.01 C 3 + 4 64.49 Te 4 + 4 37.41 27.08 C 3 + 4 64.49 Ce 4 + 4 36.76 27.73 Se3+ 4 42.94 N 1 + 1 14.53 28.41 Eu 3 + 4 42.60 N 1 + 1 14.53 28.07 Ho 3 + 4 42.50 N 1 + 1 14.53 27.97 Er 3 + 4 42.60 N 1 + 1 14.53 28.07 Tm 3 + 4 42.70 N 1 + 1 14.53 28.17 Pb 3 + 4 42.32 N 1 + 1 14.53 27.79 Sr 3 + 4 57.00 N 2 + 2 29.60 27.40 N 2 + 3 47.45 P 2 ~ 2 19.73 27.72 Ar 4 + 5 75.02 N 3 + 3 47.45 27.57 Fe 4 + 5 75.00 N 3 + 3 47.45 27.55 1~ Ni 4 + 5 75.50 N 3 + 3 47.45 28.05 N 2 + 3 47.45 Cu 2 + 2 20.29 27.16 N 2 + 3 47.45 Pd 2 + 2 19.43 28.02 N 2 + 3 47.45 1 2 + 2 19.13 28.32 N 2 + 3 47.45 La 3 + 3 19.18 28.27 N 2 + 3 ~7.45 Ce 3 + 3 20.20 27.25 N 2+ 3 47.45 Tl 2 + 2 20.43 27.02 N 3 + 4 77.47 Cr 4 + 4 49.10 28.37 N 3 + 4 77.47 As 4 + 4 50.13 27.34 N 3 + 4 77.47 La 4 + 4 49.95 27.52 Ne4+ 5 126.21 N ~ 5 97.89 28.32 Fe 6 + 7 1 ~5.00 N 5 + 5 97.89 27.11 Kr 7 + 8 126.00 N 5 + 5 97.89 28.11 Nb6+ 7 125.00 N 5+ 5 97.89 27.11 N 4 + 5 97.89 Te 6 + 6 70.70 27.19 Ne 1 + 2 40.96 O 1 + 1 13.62 27.34 Ar ~ ~ 3 40.74 O 1 + 1 13.62 27.12 Sn 3 + 4 40.73 O 1 + 1 13.62 27.12 Pm 3 + 4 41.10 O 1 + 1 13.62 27.48 Sm 3 + 4 41.~0 O 1 + 1 13.62 27.78 Dy3 ~ 4 41.50 O 1 + 1 13.62 27.88 F ;2+ 3 62.71 O 2+ 2 35.12 27.59 WO 90/13126 P~/US90/01998 .
2 ~ nJ 7 Ne2+ 3 63.45 O 2+ 235.12 28.33 O 1 ~ 2 35.12 Mg 1 + 17.65 27.47 O 1 + 2 35.12 Ti 1 + 16.82 28.30 O 1 + 2 35.12 V 1 + 16.74 28.38 O 1 + 2 35.12 Cr 1 + 16.77 28.35 O 1 + 2 35.12 Mn 1 + 17.43 27.68 O 1 + 2 35.12 Fe 1 + 17.87 27.25 O '. + 2 35.12 Co 1 + 17.86 27.26 O 1 + 2 35.12 Ni 1 + 17.64 27.48 O 1 + 2 35.12 Cu 1 + 17.73 27.39 O 1 + 2 35.12 Ge 1 ~ 17.90 27.22 O 1 + 2 35.12 Zr 1 + 16.84 28.28 O 1 + 2 35.12 Nb 1 + 16.88 28.24 O 1 + 2 35.12 Mo 1 + 17.10 28.02 O 1+ 2 35.12 Tc1+ 17.28 27.84 O 1 + 2 35.12 Ru 1 + 17.37 27.75 O 1 + 2 35.12 Rh 1 + 17.46 27.66 O 1 + 2 35.12 Ag 1 + 17.58 27.54 O 1 + 2 35.12 Sn 1 + 17.34 27.77 O 1 + 2 35.12 Ta 1 + 17.89 27.23 O 1 + 2 35.12 W 1 + 17.98 27.14 O 1 + 2 35.12 Re 1 + 17.88 27.24 O 1 + 2 35.12 Pb 1 + 17.42 27.7~
O 1 ~ 2 35.12 Bi 1 + 17.29 27.83 O 2+ 3 ~4.93 Ar 2 + 227.63 27.30 K 4 + 5 82.66 O 3 + 354.93 27.73 O 2+ 3 54.93 Ti 3 + 327.49 27.44 Zn4+ 5 82.60 O 3+ 354.93 27.67 O 2+ 3 54.93 Rb2+ 227.28 27.6~
O 2+ 3 54.93 Mo3 ~ 327.16 27.77 O 3+ 4 77.41 Cr4+ 449.10 28.31 O 3 + 4 77.4 As 4 + 450.13 27.28 O 3+ 4 77.41 La4+ 449.95 27.46 Mg 4 + 5 141.26 O 5 + 5113.90 27.36 O 5+ 6138.12 Sc6+ 6111.10 27.02 Cu 7 ~ 8166.00 O 6 + 6138.12 27.88 WO ~0/131~6 PCT/US90/01998 O 5+ 6138.12 Kr 7 + 7111.00 27.12 S; 3 + 4 45.14 F 1 + 117.42 27.72 K 2+ 3 45.72 F 1 + 117.42 28.30 Ge3+ 4 45.71 F 1 + 117.42 28.29 LU 3 + 4 45.19 F 1 + 117.42 27.77 B; 3 + 4 45.30 F 1 + 117.42 27.88 F 2+ 3 62.71 F 2+ 234.97 27.74 Ne 2 + 3 63.45 F 2 + 234.97 28.48 F 1 + 2 34.97 Mg 1 + 1 7.65 27.32 F 1 ~ 2 34.97 SC 1 + 1 6.54 28.43 F 1 + 2 34.97 T; 1 ~ 1 6.82 28.15 F 1 + 2 34.97 V 1 + 1 6.74 28.23 F 1 + 2 34.97 Cr 1 + 1 6.77 28.20 F 1 + 2 34.97 Mn 1 + 1 7.43 27.54 F 1 + 2 34.97 Fe 1 + 1 7.87 27.10 F 1 + 2 34.97 CO 1 + 1 7.86 27.11 F 1 + 2 34.97 N; 1 + 1 7.64 27.34 F 1 + 2 34.97 CU 1 + 1 7.73 27.24 F 1 + 2 34.97 Ge 1 + 1 7.90 27.07 F 1 ~ 2 34.97 Zr 1 ~ - 1 6.84 28.13 F 1 + 2 34.97 Nb 1 + ~ 16.88 28.09 F 1 + 2 34.97 MQ 1 + 1 7.10 27.87 F 1 + 2 34.97 TC 1 + 1 7.28 27.69 F 1 + 2 34.97 RU 1 I 1 7.37 27.60 F 1 + 2 34.97 Rh 1 + 1 7.46 27.51 F 1 + 2 34.97 A91 + -1 7.58 27.39 F 1 + 2 34.97 Sn 1 1 7.34 27.63 F 1 + 2 34.97 Hf 1 + 1 6.60 28.37 F 1 + 2 34.97 Ta 1 + 1 7.89 27.08 F 1+ 2 34.97 Re1+ 1 7.88 27.09 F 1 ~ 2 34.97 Pb 1 + 1 7.42 27.55 F 1 + 234.97 B; 1 + 1 7.29 27.68 F 2 + 362.71 F 2 + 234.97 27.74 F 2 + 362.71 S 3 + 334.83 27.88 Ar 5 + 691.01 F 3 ~ 362.71 28.30 Cr 5 + 690.56 F 3 + 362.71 -~7.85 ' , ' .

WO 90/13126 PCl/US90/01998 .

2 ~
F 2+ 3 62.71 Ni 3 + 3 35.17 27.54 F 2+ 3 62.71 Ge3+ 3 34.22 28.49 Sr ~ + 6 90.80 F 3 + 3 62.71 28.09 F 2 + 3 62.71 Zr 4 + 4 34.34 28.37 F 2 ~ 3 62.71 Ag 3 + 8 34.83 27.88 F 4+ 5114.24 F 4+ 4 87.14 27.10 Cl 6 + 7114.19 F 4 + 4 87.14 27.06 F 3 + 4 87.14 Ar 4 + 4 59.81 27.33 F 3 + 4 87.14 Zn 4 + 4 59.40 Z7.74 F 3 + 4 87.14 Br 5 + 5 ~9.70 27.44 F 3 + 4 87.14 Te 5 + 5 58.75 23.3g F 4+ 5114.24 F 4+ 4 87.14 27.10 Mg 4 + 5141.26 F 5 + 5114.24 27.02 F 6+ 7185.18 F 6+ 6157.16 28.02 Cr 7 ~ 8184.70 F 6 + 6157.16 27.54 F 5~ 6157.16 Co7~ 7129.00 28.16 F 5+ 6157.16 Y 8+ 8129.00 28.16 F 6+ 7185.18 F 6 + 6157.16 28.02 F 6+ 7185.18 Ne6+ 6157.93 27.25 F 6+ 7185.18 Co8+ 8157.00 28.18 Cr3 + 4 49.10 Ne 1 + 1 21.56 27.54 La3 + 4 49.95 Ne 1 + 1 21.56 28.39 Ne 1 + 2 40.96 Cl 1 + 1 12.97 28.00 Ne 1 + 2 40.96 Sc 2 + 2 12.80 28.16 Ne 1 + 2 40.96 Ti 2 + 2 13.58 27.38 Cr 4 + 5 69.30 Ne 2 + 2 40.96 28.34 Se 4 + 5 68.30 Ne 2 ~ 2 40.96 27.34 Ne 1 + 2 40.96 Zr 2 + 213.13 27.83 Mo 5 + 6 68.00 Ne 2 + 240.96 27.04 Ne 1 + 2 40.96 Lu 2 + 213.90 27.06 Pb 4 + 5 68.80 Ne 2 + 240.96 27.84 Ar 5 + 6 91.01 Ne3+ 363.45 27.~6 Sc 4 + 5 91.66 Ne 3 ~ 363.45 28.21 Cr 5 + 6 90.56 Ne 3 + 363.45 27.11 3~ Ne2~ 3 63.45 Ni 3 + 335.17 28.28 Ne2+ 3 63.45 Br 3 + 336.00 27.45 , ~

WO 90/13126 PCrtUS90/01998 . .

Sr 5 + 690.80 Ne 3+ 363.45 27.35 Ar 6 + 7124.32 Ne 4 + 497.11 27.21 Ne 3 + 497.11 Cr 5 + 569.30 27.81 Fe 6 + 7125.00 Ne 4 ~ 497.11 27.8g Nb6+ 7125.00 Ne4+ 497.11 27.89 Ne 3 + 497.11 Pb 5 + 568.~0 28.31 Ne 4 + 5126.21 Na 4 + 498.91 27.30 Al 4 + 5153.71 Ne5+ 5126.21 27.50 Ne 4 + 5126.21 Fe 6 + 699.00 27.21 Ne 4 + 5126.21 Rb 7 ~ 799.20 27.01 Si 2 + 333.49 Na 1 + 15.14 28.35 Co 7+ 333.50 Na1 + 15.14 28.36 Pd2+ 332.93 Na 1 ~ 15.14 27.79 1 2 + 333.00 Na 1 + 15.14 27.86 Hf3+ 433.33 Na1+ 15.14 28.19 Na 1 + 247.29 Al 2 + 2~8.83 28.46 Na 1 + 247.29 P 2 + 219.73 27.56 Ar 4 + 575.02 Na 2 ~ 247.29 27.73 Fe 4 + 575.00 Na 2 + 247.29 27.71 Ni 4 + ~75.50 Na 2 + 247.29 28.21 Na 1 + 247.29 Pd 2 + 219.43 27.86 Na 1 + 247.29 In 2 + 218.87 28.42 Na 1 + 247.29 1 2 ~ 21g.13 28.15 Na1 + 247.29 La3+ 319.18 28.11 Na 1 + 247.29 Ce 3 + 320.20 27.09 Na 3 + 498.91 Na 3 + 371.64 27.27 K 5 + 6100.00 Na 3 + 3 71.64 28.36 Na2+ 371.64 Ti 4 + 4 43.27 28.37 Ti 4 + 599.22 Na3+ 371.64 27.58 Fe 5 + 699.00 Na 3 + 3 71.64 27.36 Rb 6 ~ 799.20 Na 3 + 3 71.64 27.56 Na 2 + 371.64 Sr 3 + 3 43.60 28.04 Na 2 + 371.64 Sb 4 + 4 44.20 27.44 Na 2 + 371.64 Gd 4 ~ 4 44.00 27.64 Na 2 + 371.64 ~b 4 + 4 43.70 27.94 Na 3 + 498.91 Na 3 + 3 71.64 27.27 .

wo 9o/13126 PCr/US90/01998 20~69 1 Kr 7 + 8 126.00 Na 4 + 4 98.91 27.09 Na 3 + 4 98.91 Rb 5 + 5 71.00 27.91 Na 3 + 4 98.91 Sr 5 + 5 71.60 27.31 Mo 6 + 7 126.80 Na 4 + 4 98.91 27.89 Na 3 + 4 98.91 Te 6 + 6 70.70 28.21 Si 4 + 5 166.77 Na5+ 5 138.39 28.38 Na4+ 5138.39 Sc6+ 6111.10 27.29 Cu 7 + 8 166.00 Na 5 + 5 138.39 27.61 Na 4 + 5 138.39 Kr 7 + 7 111.00 27.39 S 2~ 3- 34.83 Mg1+ 17.65 27.18 Ni 2 + 3 35.17 Mg 1 + 1 7.65 27.52 Br 2 + 3 36.00 Mg 1 + 1 7.65 `28.35 Ag 2 + 3 34.83 Mg 1 + 1 7.65 27.18 Ti 3 + 4 43.27 Mg 2+ 2 15.03 28.23 Se 3 + 4 42.94 Mg 2 + 1 ~.03 27.91 Eu 3 + 4 42.60 Mg 2 + 2 15.03 27.56 Ho 3 + 4 42.50 Mg 2 + 2 15.03 27.47 Er 3 + 4 42.60 Mg 2 + 2 1 ~.03 27.56 Tm 3 + 4 42.70 Mg 2 + 2 15.03 27.67 Pb 3 + 4 42.32 Mg 2 + 2 15.03 27.28 Ni 5 + 6 108.00 Mg 3 ~ 3 80.14 27.86 ~n 5 + 6 108.00 Mg 3 + 3 80.14 27.86 Mg 2+ 3 80.14 Kr 4 + 4 52.50 27.64 Mg 2 + 3 80.14 Rb 4 + 4 52.60 27.54 Sb 5 + 6 108.00 Mg 3 + 3 80.14 27.86 Mg 3 + 4 109.24 Se 6 + 6 81.70 27.54 Mg 3 + 4 109.24 Zr 5 + 5 81.50 27.74 Te 6 + 7 137.00 Mg 4 + 4 109.24 27.76 Mg 4 + 5 141.26 Cl 7 + 7 114.19 27.07 Ti 7 + 8 168.50 Mg5+ 5 141.26 27.24 Mg 5 + 6 186.50 Sc 8 + 8 158.70 27.80 Mg 6 + 7 224.94 Mn 8 + 8 196.46 28.48 Si 2 + 3 33.49 Al 1 + 1 5.99 27.51 Mn2+ 3 33.67 Al 1 ~ 15.99 27.68 Co 2 + 3 33.50 Al 1 + 1 5.99 27.51 Ge2+ 334~22 Al 1 + 1 5.~9 .28.23 Zr 3 + 4 34.34 Al 1 + 15.99 28.35 1 2 + 3 33.00 Al 1 + 15.99 27.01 Hf 3 + 4 33.33 Al l + 15.99 27.34 Hg 2+ 3 34.20 Al 1 + 15.99 28.21 S 3+ 4 47.30 Al 2 + 218.83 28.47 V 3 + 4 46.71 Al 2 + 218.83 27.88 Br 3 + 4 47.30 Al 2 + 218.83 28.47 Mo 3+ 4 46.40 Al 2 + 218.83 27.57 Sb4 + 5 56.00 Al 3 + 328.45 27.55 Bi 4 + 5 56.00 Al 3 + 328.45 27.55 Ca7+ 8 147.24 Al 4 + 4119.99 27.25 Al 3 + 4 119.99 Sc 5 + 591.66 28.33 Al 4 + 5 153.71 Kr 8 + 8126.00 27.71 Al 5 + 6 190.47 Ni 8 + 8162.00 28.47 Ni 2~ 3 35.17 Si 1 + 18.15 27.02 ~r 2 + 3 36.00 Si 1 + 18.15 27.85 Sr 2 + 3 43.60 Si 2 ~ 216.34 27.25 Sb 3 ~ 4 44.20 Si 2 + 216.34 27.86 Gd3~ 4 44.00 Si 2 ~ 216.34 27.66 ~0 Yb3+ 4 43.70 Si 2 ~ 216.34 27.36 K 3 + 4 60.91 Si 3 + 333.49 27.42 Si 2 + 3 33.49 Ca 1 ~ 16.11 27.38 Si 2 + 3 33.49 Ga1 + 16.00 27.49 Si 2 + 3 33.49 Sr 1 + 15.70 27.80 Si 2 + 3 33.49 Y 1 ~ 16.38 27.11 Y 3 + 3 61.80 Si 3 + 333.49 28.31 Mo4+ 5 61.20 Si 3 ~ 333.49 27.71 Si 2 + 3 33.49 In 1 + 15.79 27.71 Si 2 + 3 33.49 Ba 1 ~ 15.21 28.28 Si 2 + 3 33.49 La 1 + 15.58 27.92 Si 2 + 3 33.49 Ce 1 + 15.47 28.02 Si 2 + 3 33.49 Pr 1 + 15.42 28.07 Si 2 + 3 33.49 Nd 1 -~ 15.49 28.00 Si 2 + 3 33.49 Pm 1 f 15.~5 27.94 Si 2 + 3 33.49 Sm 1 + 15.63 27.86 Si 2 + 3 33.. 49 Eu 1 + 1 5.67 27.83 WO 90/13126 PCI'/US90/01998 2 ~ 9 ~

Si 2 + 3 33.49 Gd 1 + 16.14 27.3~
Si 2 + 3 33.49 Tb 1 + 15.85 27.64 Si 2 + 3 33.49 Dy 1 + 15.93 27.57 Si 2 + 3 33.49 Ho l + 16.02 27.47 Si 2 + 3 33.49 Er 1 + 16.10 27.39 Si 2 + 3 33.49 Tm 1 + 16.18 27.31 Si 2 + 3 33.49 Yb 1 + 16.25 27.24 Si 2 + 3 33.49 Lu 1 ~ 15.43 28.07 Si 2 + 3 33.49 Tl 1 + 16.11 27.38 Si 2 + 3 33.49 Ra 1 + 15.28 28.21 Si 2 + 3 33.49 Ac 1 + 15.20 28.29 Si 2 + 3 33.49 Th 1 + 16.10 27.39 Si 2 + 3 33.49 Pa 1 + 15.90 27.59 Si 2 + 3 33.49 U 1 + 16.05 27.44 Si 2 t 3 33.49 Np 1 + 16.20 27.29 Si 2 + 3 33.49 Pu 1 + 16.06 27.43 Si 2 + 3 33.49 Am 1 + 15.99 27.50 Si 2 + 3 33.49 Cm 1 ~ 16.02 27.47 Si 2 + 3 33.49 Bk 1 + 16.23 27.~6 Si 2 + 3 33.49 Cf 1 + 16.30 27.19 Si 2 + 3 33.49 Es 1 + 16.42 27.07 S 4+ 5 72.68 Si 4 + 445.14 27.54 Sc 3 + 4 73.47 Si 4 + 445.14 28.33 Mn4+ 5 72.40 Si 4 + 445.14 27.26 Si 3 + 4 45.14 Co2~ 217.06 28.08 Si3+ 4 45.14 Zn2+ 217.96 27.18 Si 3 + 4 45.14 Ru2+ 216.76 28.38 Si 3 + 4 45.14 Rh2+ 218.08 27.06 Si 3 + 4 45.14 Cd 2 + 216.91 28.23 Sn 4 + 5 72.28 Si 4 + 445.14 27.14 Si 3 + 4 45.14 Bi 2 + 216.69 2B.45 Si 4 + 5166.77 Cu 7 ~ 7139.00 27.~7 Nb3+ 4 38.30 P 1 + 110.49 27.8t Pr 3 + 438.98 P 1 + 110.49 28.49 S 3+ 447.30 P 2~ 219.73 27.57 Br 3 + 447.30 P 2 + 219.73 27.57 WO 90/13126 PCl`/US91)/01998 P 3 + 451.37 S 2 + 223.33 28.04 P 3 + 451.37 Cl 2 + 223.81 27.56 Co 4 + ~79.50 P 4 + 451.37 28.13 P 3+ 45t.37 Kr 2 + 224.36 27.01 5Kr 5 + 678.50 P 4 + 451.37 27.13 P 3 + 451.37 Zr 3 + 322.99 28.38 P 3+ 451.37 Sm 3 + 323.40 27.97 P 3+ 451.37 Tm 3 + 323.68 27.69 P 3 + 4~1.37 Hf 3 + 323.30 28.07 10P 4+ 565.02 Cu3+ 336.83 28.19 Ge 4 + 593.50 P 5 + 565.02 28.48 P 4+ 565.02 Kr 3 + 336.95 28.07 Y 5+ 693.00 P 5+ 565.02 27.98 P 4 + 565.02 Cd 3 + 337.48 27.54 15P 4 ~ 565.02 Te 4 + 437.41 27.61 P 4+ 56~.02 C~4+ 436.76 28.27 P 5 ~ 6220.43 Br B + 8192.80 27.63 P 7+ 8309.41 S 7+ 7280.93 28.48 Nb3+ 438.30 S 1 ~ 110.36 27.94 20Cd2+ 337.48 S 1 + 110.36 27.12 Te 3 + 437.41 S 1 + 110.36 27.05 Ca 2 + 350.91 S 2 + 223.33 27.58 Mn 3 + 4~ .20 S 2 + 223.33 27.87 Co 3 + 4~1.30 S 2 + 223.33 27.97 25Nb4+ 550 55 S 2+ 223.33 27.22 S 2+ 334.83 Sc 1 ~ 16.54 28.29 S 2+ 334.83 Ti 1 + 16.82 28.01 S 2+ 334.83 V 1 + 16.74 28.09 S 2+ 334.83 Cr 1 + 16.77 28.06 30S 2~ 334.83 Mn 1 ~ 17.43 27.40 S 2 + 334.83 Ni 1 + 17.64 27.20 S 2 + 334.83 Cu 1 + 17.73 27.10 S 2 + 334.83 Y 1 + 16.38 28.45 S 2+ 334.83 Zr 1 + 16.84 27.9g 35S 2 ~ 334.83 Nb 1 + 16.88 27.g5 S 2 + 334.83 Mo 1 + 17.10 27.73 WO 90/13126 PCl/US90/01998 2 ~

S 2+ 3 34.83 Tc 1 + 17.28 27.55 S 2 + 3 34.83 Ru 1 + 17.37 27.46 S 2 + 3 34.83 Rh 1 + 17.46 27.37 S 2 + 3 34.83 Ag 1 ~ 17.58 27.25 5S 2 + 3 34.83 Sn 1 + 17.34 27.49 S 2 + 3 34.B3 Hf 1 + 16.60 28.23 S 2 + 3 34.83 Pb 1 + 17.42 27.41 S 2 + 3 34.83 Bi 1 + 17.29 27.54 S 2+ 3 34.83 Es 1 ~ 16.42 28.41 10Ar 4 + 5 75.02 S 4 + 447.30 27.72 Fe 4 + 5 75.00 S 4 + 447.30 27.70 Ni 4 + 5 75.50 S 4 + 447.30 28.20 S 3 + 4 47.30 Cu 2 + 220.29 27.01 S 3 + 4 47.30 Pd 2 + 219.43 27.87 15S 3 + 4 47.30 In 2 + 218.87 28.43 S 3 + 4 47.30 i 2 + 219.13 28.17 S 3 + 4 47.30 La 3 + 319.18 28.12 S 3 + 4 47.30 Ce 3 ~ 320.20 27.10 K 5 + 6100.00 S 5 + 572.68 27.32 20S 4 + 5 72.68 Sb 4 + 444.20 28.48 -S 4 + 5 72.68 Lu 4 + 445.19 27.49 S 4+ 5 7~.68 Bi 4 + 445.30 27.38 S 5+ 6 88.05 Ar 4 + 459.81 28.24 S 5 + 6 88.05 K 4 + 460.91 27.14 25S 5 + 6 88.05 Br 5 + 559.70 28.35 Y 6 + 7116.00 S 6 + 688.05 27.95 Ar 2 + 3 40.74 Cl 1 + 112.97 27.77 Rb2~ 3 40.00 C11 + 112.97 27.03 Sn 3 ~ 4 40.73 Cl l + 112.97 27.77 30Nd3+ 4 40.41 Cl l + 112.97 27.44 Pm3 + 4 41.10 Cl 1 ~ 112.97 28.13 Sm 3 + 4 41.40 Cl l + 112.97 28.43 Ca2+ 3 50.91 Cl 2 + 223.81 27.10 Mn 3 + 4 51.20 Cl 2 ~ 223.81 27.39 35Co 3 + 4 51.30 Cl 2 ~ 223.81 27.49 ~1.4+ 5 ~7.80 ~13 + 33~.61 28.19 . :

. ;

WO 90/13126 PCI/US90/019g8 r;~

Cl 2 + 3 39.61 Ca2+ 211.87 27.74 Ca3 ~ 4 67.10 Cl 3 + 339.61 27.49 Cl 2 + 3 39.81 Br 1 + 111.81 27.80 Cl 2 + 3 39.61 Y 2 + 212.24 27.37 Mo 5+ 6 68.00 Cl 3 + 339.61 28.39 Cl 2 + 3 39.61 Xe 1 + 112.13 27.48 Cl 2 + 3 39.61 Eu 2 + 211.24 28.37 Cl 2 + 3 39.61 Gd2+ 212.09 27.52 Cl 2 + 3 39.61 Tb 2 + 211.52 28.09 Cl 2 + 3 39.61 Dy 2 + 211.67 27.94 Cl 2 + 3 39.61 Ho 2 + 211.80 27.81 Cl 2 + 3 39.61 Er 2 + 211.93 27.68 Cl 2 + 3 39.61 Tm 2 + 212.05 27.56 Cl 2 + 3 39.61 Yb 2 + 212.18 27.43 Se 5 + 6 81.70 C14 + 453.46 28.24 Zr 4 + 5 81.50 Cl 4 + 453.46 28.04 Ct 3 + 4 53.46 Nb3 + 325.04 28.42 Cl 3 + 4 53.46 Sb 3 + 325.30 28.16 Cl 3 + 4 53.46 Cs 2 + 225.10 28.36 Cl 3 + 4 53.46 Yb 3 + 325.03 28.43 Cl 3 + 4 53.46 Bi 3 + 325.56 27.90 Cl ~ + 5 67.~0 C13 + 339.61 28.19 Cl 4 + 5 67.80 Ar 3 + 340.74 27.06 Mn 5 + 6 95.00 Cl 5 + 567.80 27.20 C14 + 5 67.80 7n 3 + 339.72 28.08 Cl 4 + 5 67.80 Rb3 + 340.00 27.80 Cl 4 + ~ 67.80 Sn 4 ~ 440.73 27.07 Cl 4 + 5 67.80 Nd 4 + 4- 40.41 27.39 Cl 4 + 567.80 Tb 4 + 439.80 28.00 Ar 6 + 7124.32 Cl 6 + 697.03 27.29 Cl 5 + 697.03 Cr 5 + 569.30 27.73 Fe 6 + 7125.00 C16 + 697.03 27.97 Nb6+ 7125.00 Cl 6 + 697.03 27.97 Cl 5 ~ 697.03 Pb 5 + 568.80 28.23 Ti 3 + 443.27 Ar 1 + 115.76 27.51 ~e3+ 442.94 Ar 1 + 115.76 27.19 wo go/13126 Pcr/us~O/01998 2~ 54 Sr 2 + 343.60 Ar 1 + 115.76 27.84 Sb3 ~ 444.20 Ar 1 + 115.76 28.44 Gd3+ 444.00 Ar 1 ~ 115.76 28.24 Yb3~ 443.70 Ar 1 + 115.76 27.94 5 Fe 3 + 454.80 Ar 2 + 227.63 27.17 Ni 3 + 454.90 Ar 2 + 227.63 27.27 Cu 3+ 455.20 Ar 2 + 227.63 27.57 Sb4+ 556.00 Ar 2 + 227.63 28.37 Bi 4 + 556.00 Ar 2 ~ 227.63 28.37 1 0Ar 2 + 340.74 Sc 2 + 212.80 27.94 Ar 2 + 340.74 Ti 2 + 213.58 27.16 Se4 + 568.30 Ar 3 + 340.74 27.56 Ar 2 + 340.74 Zr 2 + 213.13 27.61 Mo5+ 668.00 Ar 3 + 340.74 27.26 15 Pb4+ 568.80 Ar 3 + 340.74 28.06 Ar 3 + 459.81 K 2 + 231.63 28.19 Ar 3 + 459.81 Xe3+ 332.10 27.71 Ar 3 ~ 459.81 Pb 3 + 331.94 27.87 Bi 5 + 688.30 Ar 4 + 459.81 28.49 20Ar 4 + 575.02 V 4 + 446.71 28.31 Cu ~ + 6103.~0 Ar 5 + 575.02 27.98 Ar 4 + 575.02 Br 4 ~ 447.30 27.72 Br 6 + 7103.00 Ar 5 + 575.02 77.98 Nb5+ 6102.60 Ar 5 + 575.02 27.58 25Ti 5 + 6119.36 Ar 6 + 691.01 28.35 Mn 6 ~ 7119.27 Ar 6 + 691.01 28.26 Ar 5 + 691.01 Ga4+ 464.00 27.01 Ar 5 + 691.01 As 5 + 563.63 27.38 Ar 7 + 8143.46 Y 7 + 7116.00 27.46 30 K 1 + 231.63 K 1 ~ 14.34 27.28 Xe2+ 332.10 K 1 + 14.34 27.76 Pb 2 + 331.94 K 1 * 14.34 27.60 K 1 + 231.63 K 1 ~ 14.34 27.28 Zn 3 + 459.40 K 2 ~ 231.63 27.78 35Br 4 + 559.70 K 2 + 231.63 28.08 K 1 + 231.63 Rb 1 + 14.18 27.45 Z~;@~

Te 4 + 5 ~8.75 K 2 + 231.63 27.13 K 1 + 2 31.63 Cs 1 + 13.89 27.73 Sc 3 + 4 73.47 K 3 + 345.72 27.75 K 2+ 3 45.72 Ni 2 + 218.17 27.55 K 2 + 3 45.72 Zn ~ + 217!96 27.76 K 2+ 3 45.72 As 2 + 218.63 27.09 K 2 + 3 4S.72 Rh 2 + 2i 8.08 27.64 K 2 + 3 45.72 Te 2 + 218.60 27.12 K 2+ 3 45.72 Pt 2 + 218.56 27.16 K 3 + 4 60.91 Mn 3 + 333.67 27.24 K 3 + 4 60.91 Co 3 + 333.50 27.41 Br 5 + 6 88.60 K 4 + 4 60.91 27.69 K 3+ 4 60.91 Pd 3 + 332.93 27.98 K 3+ 4 60.91 1 3 + 333.00 27.91 K 3 + 4 60.91 Hf 4 + 433.33 27.58 Bi 5 + 6 88.30 K 4 ~ 4 60.91 27.39 Sc 5 + 6 111.10 K 5 + 5 82.66 28.44 K 4+ 5 82.66 Fe4+ 454.80 27.86 K 4+ 5 8~.66 Ni 4 + 454.90 27.76 K 4 + 5 82.66 Cu 4 + 455.20 27.46 Kr 6 + 7 111.00 K 5 + 5 82.66 28.34 Ca 6 + 7 127.70 K 6 + 6 100.00 27.70 V 5+ 6128.12 K 6+ 6100.00 28.12 K 5 + 6100.00 Mn 5 + 572.40 27.60 As 5 + 6 t27.60 K 6 + 6 100.00 27.60 K 5 + 6tO0.00 Sr 5 + 571.60 28.40 K 5 + 6100.00 Sn 5 + 572.28 27.72 K 7 + 8l 54.86 Ca 7 + 7127.70 27.16 K 7 + 8l 54.86 As 6 + 6127.60 27.26 K 7 + 8l 54.86 Mo 7 + 7126.80 28.06 Mn 2+ 333.67 Ca 1 + 16.11 27.55 Co2 333.50 Ca 1 + 16.11 27.39 Ge2+ 334.22 Cal + 16.11 28.11 Zr 3 + 4 34.34 Ca 1 + 1 6.11 28.23 Hf 3 + 4 33.33 Ca 1 + 1 6.11 27.22 Hg2+ 334.20 Ga 1 + 16.11 28.Q9 .. . . ... .

- ;

.~

wo go/13126 PCI-/US90/01998 2 ~

Zn 2 + 3 39.72 Ca 2 + 211.87 27.85 Rb2+ 3 40.00 Ca2+ 211.87 28.13 Pr 3 + 4 38.98 Ca2+ 211.87 27.11 ~s Tb 3 + 4 39.80 Ca 2 + 211.87 27.93 Kr 5 + 6 78.50 Ca 3 + 350.91 27.~9 Ca2+ 3 50.91 Zr 3 + 322.99 27.92 Ca 2 + 3 50.91 Sm 3 + 323.40 27.51 Ca2+ 3 50.91 Dy3+ 322.80 28.11 Ca 2 + 3 50.91 Ho 3 + 322.84 28.07 Ca2+ 3 -50.91 Er 3 + 322.74 28.17 Ca2+ 3 50.91 Tm 3 + 323.68 27.23 Ca2+ 3 50.91 Hf 3 + 323.30 27.61 Mn5+ 6 95.00 Ca4+ 467.10 27.90 Ca3+ 4 67.10 ?n3+ 339.72 27.38 ~a3+ 4 67.10 Rb3+ 340.00 27.10 Ca 3 + 4 67.10 Pr 4 + 43B.98 28.12 Ca3+ 4 67.10 Tb4+ 439.~0 27.30 Ca 4 + 5 84.41 Sr 4 + 457.00 27.41 Ca 4 + 5 84.41 Sb 5 + ~56.00 28.41 Ca4+ ~ 84.41 Bi 5 + 556.00 28.41 Ca 5 + 6 108.78 Se 6 + 681.70 27.08 Rb 7 + 8 136.00 Ca 6 + 6108.78 27.22 Ca5+ 6 108.78 Zr 5 + 581.50 27.28 Te 6 + 7 137.00 Ca 6 + 6108.78 28.22 Ca6+ 7 127.70 Ti 5 ~ 599.22 28.48 Se 6 + 7 155.40 Ca 7 + 7127.70 27.70 Ca7+ 8 147.24 Ti 6 + 6119.36 27.88 Ca7+ 8 147.24 Mn7+ 7119.27 27.97 Mn2+ 3 33.67 Sc1~ 16.54 i27.13 Ge2+ 3 34.22 Sc 1 + 16.54 27.68 Zr 3 + 4 34.34 Sc 1 + 16.54 27.80 Ag 2 + 3 34.83 Sc l ~ 16.54 28.29 119 2+ 3 34.20 Sc 1 + 16.54 27.66 Rb 2 + 3 40.00 Sc 2 + 212.80 27.20 Sn3+ 4 40.73 Sc2~ 212.80 27.93 Nd 3 ~ 4 40.41 .Sc 2 + 212,80 .27.~61 . . . .

WO 90/13126 PCr/lUS90/01~98 57 2 ~ 9 1 Pm 3 + 4 41.10 Sc 2 + 2 12.80 28.30 Kr 3 + 4 52.50 Sc3 + 324.76 27.74 Rb 3 + 4 52.60 Sc 3 + 3 24.76 27.84 Sc 3 + 4 73.47 Ge 4 + 4 45.71 27.76 Sc 3 + 4 73.47 Mo 4 + 4 46.40 27.07 Sc 3 + 4 73.47 Lu 4 + 4 45.19 28.28 Sc 3 + 4 73.47 Bi 4 + 4 45.30 28.17 Ti 5 + 6 119.36Sc 5 + 5 91.66 27.70 Mn 6 + 7 119.27Sc 5 + 5 91.66 27.61 Sc 4 + 5 91.66 Ga 4 + 4 64.00 2~.66 Sc 4 + 5 91.66 As 5 + 5 63.63 28.03 Cu6+ 7139.00 Sc6~ 6111.10 27.90 Cu 7 + 8 166.00Sc 7 + 7 138.00 28.00 Ni 2 + 3 35.17 Ti 1 + 1 6.82 28.35 Ge2+ 3 34.22 Ti 1 + 1 6.82 27.40 Zr 3 + 4 34.34 Ti 1 + 1 6.82 27.52 Ag 2 + 3 34.83 Ti 1 + 1 6.82 28.01 Hg 2+ 3 34.20 Ti 1 + 1 6.82 27.38 Sn 3 + 4 40.73 Ti 2 ~ 2 13.53 27.15 Pm 3 + 4 41.10 Ti 2 + 2 13.58 27.52 Sm 3 + 4 41.40 Ti 2 + 2 13.58 27.82 Dy3+ 4 41.50 Ti 2 + 2 13058 27.92 Fe3 + 4 54.80 Ti 3 + 3 27.49 27.31 Ni 3 + 4 54.90 Ti 3 + 3 27.49 27.41 Cu 3 + 4 55.20 Ti 3 ~ 3 27.49 27.71 Ti 3 + 4 43.27 Mn2+ 2 15.64 27.63 Ti 3 + 4 43.27 F~ 2 + 2 16.18 27.09 Ti 3 + 4 43.27 Ge2+ 2 15.93 27.33 Rb 4+ 5 71.00 Ti 4 + 4 43.27 27.73 Sr 4 + 5 71.60 Ti 4 + 4 43.27 28.33 Ti 3 + 4 43.27 Mo 2+ 2 16.15 27.12 Ti 3 + 4 43.27 Tc 2 + 2 15.26 28.01 Te 5 + 6 70.70 Ti 4 + ~ 43.27 27.43 Ti 3 + 4 43.27 Hf 2 + 2 14.90 28.37 Ti 3 ~ 4 43.27 Pb 2 + 2 15.03 28.23 As 5 ~ 6 127.60 Ti 5 + 5 99.22 28.38 WO 90/13126 PCI/US90tO199B

2~ 58 Ti 4 ~ 599.22 Rb 5+ ~71.00 28.22 Ti 4 + 599.22 Sr 5 + 571.60 27.62 Mo 6+ 7126.80 Ti 5 + 599.22 27.58 Ti 7 + 8168.50 Ti 7 + 7140.80 27.70 5Ti 7 + 8163.50 Ti 7 + 7140.80 27.70 Mn7+ 8196.46 Ti 8 + 8 168.50 27.96 Ni 2 + 335.17 V 1 + 16.74 28.43 Ge2+ 334.22 V 1 + 16.74 27.48 Zr 3 + 434.34 V 1 + 16.74 27.60 10Ag 2 + 334.83 V 1 + 16.74 28.09 Hg 2 + 334.20 V 1 + 16.74 27.46 Se 3 + 442.94 V 2 + 214.65 28.29 Eu 3 + 442.60 V 2 + 214.65 27.95 Ho 3 + 442.50 V 2 + 214.65 27.85 15Er 3 + 442.60 V 2 + 214.65 27.95 Tm 3 + 442.70 V 2 + 214.65 28.05 Pb 3 + 442.32 V 2 + 214.65 27.67 Sr 3 ~ 457.00 V 3 + 329.31 27.69 Fe 4 + 575.00 V 4 + 446.71 28.29 20V 3 + 446.71 As 2 + 218.63 28.07 V 3 + 446.71 Pd 2 + 2 19.43 27.28 V 3 + 446.71 In 2 + 2 18.87 27.84 V 3 + 446.71 Te 2 + 2 18.60 28.11 V 3 + 446.71 1 2 ~ 219.13 27.58 25V 3 + 446.71 La 3 + 3 lg.18 27.53 V 3 + 446.71 Pt 2 + 2 18.56 28.14 V 3 + 446.71 Hg 2 + 2 18.76 27.95 V 4+ ~65.23 Cu3+ 336.83 28.40 Ge 4 + 593.50 V 5 + 565.23 28.27 30V 4+ 565.23 Kr 3 + 3 36.95 28.28 Y 5+ 693.00 V 5+ 56~.23 27.77 V 4 + 565.23 Cd 3 + 3 37.48 27.75 V 4+ 565.23 Te 4 + 4 37.41 27.82 V 4 ~ 565.23 Ce 4 + 4 36.76 28.47 35Se 6+ 7155.40 V 6 + 612812 27.28 V 6+ 7150.17 Sr 8 + 8 122.30 27.87 , .

WO 90/13126 PCI'/US90/01998 59 2 ~ ~r~ J ~ 7qJ

Ni 2 + 3 35.17 Cr 1 + 16.7728.40 Ge2+ 3 34.22 Cr 1 + 16.7727.45 Zr 3 + 4 34.34 Cr 1 + 16.7727.57 Ag 2 + 3 34.83 Cr 1 + 16.7728.06 Hg 2+ 3 34.20 Cr 1 + 16.7727.43 Sr2+ 3 43.60 Cr2~ 216.5û27.10 Sb 3 + 4 44.20 Cr 2 + 2 16.50 27.70 Gd 3 + 4 44.00 Cr 2 + 2 16.50 27.50 Yb 3 + 4 43.70 Cr 2 + 2 16.50 27.20 Zn3+ 4 59.40 Cr3 ~ 330.9628.44 Te 4 + 5 58.75 Cr3 + 3 30.96 27.79 Cr 2 + 3 30.96 Cs 1 ~ 1 3.89 27.07 Cr 3 + 4 49.10 Se 2 + 2 21.19 27.91 Cr 3 + 4 49.10 Br 2 + 2 21.80 27.30 1 5 Y 4 + 5 77.00 Cr 4 + 449.1027.90 Cr 3 + 4 49.10 Ag 2 + 2 21.49 27.61 Cr3 + 4 49.10 Xe2+ 221.2127.89 Cr 3 + 4 49.10 Pr 3 + 3 21.62 27.48 Cr3+ 4 49.10 (3d3~ 320.6328.47 Cr 3 + 4 49.10 Tb 3 + 3 21.91 27.19 Cr 3 + 4 49.10 Lu 3 + 3 20.96 28.14 Cr 4 + 5 69.30 Pm 4 + 4 41.10 28.20 Cr4 + 5 69.30 Sm4 + 441.4027.90 Cr 4 + 5 69.30 Dy 4 + 4 41.~0 27.80 Cr 6 + 7 161.10 Ni 7 + 7 133.00 28.10 Cr6+ 7161.10 Zn7+ 7134.0027.10 Cr 7 + 8 184.70 Co 8 + 8 157.00 27.70 Ni 2 + 3 35.17 Mn 1 + 1 7.43 27.73 Ag 2 + 3 34.83 Mn 1 + 1 7.43 27.40 Se3+ 4 42.94 Mn2+ 215.6427.30 Sr 2 + 3 43.60 Mn 2+ 2 15.64 27.96 Gd 3 + 4 44.00 Mn 2 + 2 15.64 28.36 Tm 3 + 4 42.70 Mn 2 + 2 15.64 27.06 Yb 3 + 4 43.70 Mn 2 + 2 15.64 28.06 Mn2~ 3 33.67 Ga1 + 16.0027.67 Mn 2 + 3 33.67 Sr 1 + 1 5.70 27.97 w~ 90/13126 P~T/US90/01998 2 Q ~ 60 Mn2~ 3 33.67 Y 1 + 16.38 27.29 Y 3 + 4 61.80 Mn 3 + 333.67 28.13 Mo 4 + 5 61 .2n Mn 3 + 333.67 27.53 Mn 2+ 3 33.67 In 1 + 15.79 27.88 5Mn 2 + 3 33.67 Ba 1 + 15.21 28.45 Mn 2 + 3 33.67 La 1 + 15.58 28.09 Mn2+ 3 33.67 Ce1 + 15.47 28.20 Mn 2+ 3 33.67 Pr 1 + 15.42 28.24 Mn2+ 3 33.67 Nd1 + 15.49 28.18 10Mn 2+ 3 - 33.67 Pm 1 + l5.55 28.11 Mn 2+ 3 33.67 Sm 1 + 15.63 28.04 Mn2+ 3 33.67 Eu 1 + 15.67 28.00 Mn 2 + 3 33.67 Gd 1 + 16.14 27.53 Mn 2 + 3 33.67 Tb 1 + 15.85 27.82 15Mn 2+ 3 33.67 Dy 1 + 15.93 27.74 Mn2+ 3 33.67 Ho ~ + 16.02 27.65 Mn 2+ 3 33.67 Er 1 + 1 6.10 27.57 Mn2+ 3 33.67 Tm 1 + 16.18 27.48 Mn 2+ 3 33.67 Ybl + 16.25 27.41 20Mn 2+ 3 33.67 Lu 1 + 1 5.43 28.24 Mn 2+ 3 33.67 Hf 1 + 1 6.60 27.07 Mn2+ 3 33.67 TI 1 + 1 6.11 27.56 Mn2+ 3 33.67 Ra 1 + 1 5.28 28.39 Mn 2 + 3 33.67 Ac 1 + 1 5.20 28.47 25Mn2+ 3 33.67 Th 1 + 1 6.10 27.57 Mn 2+ 3 33.67 Pa 1 + 1 5.90 27.77 Mn 2+ 3 33.67 U 1 + 16.05 27.62 Mn2+ 3 33.67 Np 1 + 1 6.20 27.47 Mn2+ 3 33.67 Pu 1 + 1 6.06 27.61 30Mn 2+ 3 33.67 Am 1 + 1 5.99 27.68 Mrl 2+ 3 33.67 Cm 1 + 1 6.02 27.65 Mn 2 + 3 33.67 Bk 1 + 1 6.23 27.44 Mn 2+ 3 33.67 Cf 1 + 1 6.30 27.37 Mn 2+ 3 33.67 Es 1 + 1 6.42 27.25 3 5 Co 4 + 5 79.50 Mn 4 + 451.20 28.30 Kr 5 + 6 78.50 Mn 4 + 451.20 27.30 WO 90/13126 PCI/US90/~1998 .

61 2 ~ 3 ~

Mn3+ 4 51.20 Zr 3 ~ 322.99 28.21 Mn 3+ 4 51.20 Sm 3 + 323.40 27.80 Mn3+ 4 51.20 Dy 3~ 322.80 28.40 Mn 3 + 4 51.20 Ho 3 + 322.84 28.36 Mn 3 + 4 51.20 Er 3 + 322.74 28.46 Mn 3+ 4 51.20 Tm 3 ~ 323.68 27.52 Mn3+ 4 51.20 Hf 3 + 323.30 27.90 Mn 4 ~ 5 72.40 Sb 4 + 444.20 28.20 Mn 4 + 5 72.40 Gd 4 + 444.00 28.40 Mn 4 + 5 72.40 1 u 4 + 445.19 27.21 Mn4+ 5 72.40 Bi 4 + 445.30 27.10 Sr 7 + 8122.30 Mn 6 + 695.00 27.30 Mn 6 + 7119.27 Sr 6 + 690.80 28.47 Ni 2 + 3 35.17 Fe 1 + 17.87 27.30 Br 2 + 3 36.00 Fe 1 ~ 17.87 28.13 Sr 2 + 3 43.60 Fe 2 ~ 216.18 27.42 Sb 3 + 4 44.20 Fe 2 + 216.18 28.02 Gd 3 + 4 44.00 Fe 2 ~ 216.18 27.82 Yb 3 + 4 43.70 Fe 2 + 216.18 27.52 -Te 4 + 5 58.75 Fe 3 + 330.65 28.10 Zn 4 + 5 82.60 Fe 4 + 454.80 27.80 Fe 3 + 4 S4.80 Rb 2 ~ 227.28 27.52 Fe 3 + 4 54.80 Mo 3 + 327.16 27.64 Cu 5 + 6103.00 Fe 5 + 575.00 28.00 Fe~+ 5 75.00 Br 4 + 447.30 27.70 Br 6 ~ 7103.00 Fe 5 + 575.0028.00 Nb 5 + 6102.60 Fe 5 + 575.0027.60 Fe 5 + 699.00 Rb 5 + 571.0028.00 . Fe5+ 699.00 Sr 5 + 571.6027.40 Mo 6 + 7l 26.80 Fe 6 + 699.0027.80 Fe5~ 699.00 Te 6 ~ 670.7028.30 Mo 7 + 8153.00 Fe 7 + 7125.0028.00 Ni 2 + 335.17 Co 1 + 17.86 27.31 Br 2 + 336.00 Co 1 + 17.86 28.14 Sb3+ 444.20 Co2+ 217.0627.14 Lu 3 + 445.19 Co.2 + 217.0628.13 Wo 90/~3126 PCT/US90/û1998 2 0~ 62 Bi 3 + 4 45.30 Co 2+ 217.06 28.24 Co2+ 3 33.50 Ga1 ~ 16.00 27.50 Co 2 + 3 33.50 Sr 1 + 15.70 27.81 Co2+ 3 33.50 Y 1 + 16.38 27.12 5 Y 3 + 4 61.80 Co 3 + 333.50 28.30 Mo 4 + 5 61.20 Co 3 + 333.50 27.70 Co2+ 3 33.50 In 1 + 15.79 27.71 Co2+ 3 33.50 Ba 1 + 15.21 28.29 Co 2+ 3 33.50 La 1 + ~5.58 27.92 10Co 2 + 3 33.50 Ce 1 + 15.47 28.03 Co 2+ 3 33.50 Pr 1 + 15.42 28.08 Co 2 + 3 33.50 Nd 1 + 15.49 28.01 Co2+ 3 33.50 Pm 1 + 15.55 27.95 Co 2 + 3 33.50 Sm 1 + 15.63 27.87 15Co 2+ 3 33.50 Eu 1 + 15.67 27.83 Co 2+ 3 33.50 Gd 1 + 16.14 27.36 Co 2 + 3 33.50 Tb 1 + 15.85 27.65 Co 2 + 3 33.50 Dy 1 ~ 15.93 27.57 Co 2 + 3 33.50 Ho l + 16.02 27.48 20Co 2+ 3 33.50 Er 1 + 1 6.10 27.40 Co2+ 3 33.50 Tm 1 ~ 16.18 27.32 Co 2 + 3 33.50 Yb 1 + 16.25 27.25 Co 2 + 3 33.50 Lu 1 + 1 5.43 28.07 Co2+ 3 33.50 Tl 1 + 1 6.11 27.39 2~Co2+ 3 33.50 Ra1 + 15.28 ~8.22 Co 2+ 3 33.50 Ac 1 + 1 5.20 28.30 Co 2+ 3 33.50 Th 1 + 1 6.10 27.40 Co2+ 3 33.50 Pa 1 + 1 5.90 27.60 Co 2+ 3 33.50 U 1 ~ 16.05 27.45 30Co2 + 3 33.50 Np 1 + 1 6.20 27.30 Co 2 + 3 33.50 Pu 1 + 1 6.06 27.44 Co2+ 3 33.50 Am 1 + t 5.99 27.51 Co 2+ 3 33.50 Cm 1 + 1 6.02 27.48 Co2+ 3 33.50 Bk 1 + 1 6.23 27.27 35Co2+ 3 33.50 Cf 1 + 1 6.30 27.20 Co 2+ 3 33.50 Es 1 + 1 6.42 27.08 :, .

WO 90/13126 PCI'/US90/01998 6 3 ~ r~

CO 4 + 579.50 CO 4 ~ 451.30 28.20 Kr 5 + 678.50 Co 4 + 451.30 27.20 ~o 3 + 451.30 Zr 3 + 322.99 28.31 Co 3 + 4~1.30 Sm 3 ~ 323.40 27.90 Co 3 + 4 51.30 Ho 3 + 3 22.84 28.46 Co3+ 451.30 Tm 3 -~ 323.68 27.62 Co 3 + 4 51.30 Hf 3 + 3 23.30 28.00 Co 4 + 5 79.50 Co 4 + 4 51.30 2~.~0 Co 7 + 8 157.00 Co 7 + 7 129.00 28.00 Co 7 + 8 157.00 Co 7 + 7 129.00 28.00 Co 7 + 8 157.00 Y 8 + 8 129.00 28.00 Ni 2 + 3 35.17 Ni 1 + 1 7.64 27.53 Br 2 + 3 36.00 Ni 1 + 1 7.64 28.36 Ag 2 + 3 34.83 Ni 1 + 1 7.64 27.20 Ge 3 + 4 45.71 Ni 2 ~ 2 18.17 27.54 Mo3+ 446.40 Ni 2 + 218.17 28.23 Lu3+ 445.19 Ni2+ 218.17 27.02 Bi 3 + 4 45.30 Ni 2 + 2 18.17 27.13 Ni 2 ~ 3 35.17 Ni 1 + 1 7.64 27.53 Ni2+ 335.17 Cu1+ 17.73 27.44 Ni2+ 335.17 Ge1~ 17.90 27.27 As 4 + 5 63.63 Ni 3 + 3 35.17 28.46 Ni 2 + 3 35.17 Zr 1 + 1 6.84 28.33 Ni 2 + 3 35.17 Nb 1 + 1 6.88 28.29 Ni 2 + 3 35.17 Mo 1 + 1 7.10 28.07 Ni2~ 335.17 Tc1 + 17.28 27.89 Ni 2 + 3 35.17 ~u 1 + 1 7.37 27.80 Ni 2 + 3 35.17 Rh 1 ~ 1 7.46 27.71 Ni 2 + 3 35.17 Ag 1 ~ 1 7.58 27.59 Ni 2+ 335.17 Sn 1 + 1 7.34 27.83 Ni 2 ~ 3 35.17 Ta 1 + 1 7.8g 27.28 Ni 2 + 3 35.17 W 1 + 1 7.98 27.19 Ni 2 + 3 35.17 Re 1 + 1 7.88 27.29 Ni 2 + 3 35.17 Pb 1 + 1 7.42 27.75 Ni 2+ 335.17 Bi 1 + 1 7.29 27.88 Zn 4 + 5 82.60 Ni 4 + 4 54.90 27.70 .

WO 90/ 1 31 26 Pcr/ US90/0 1 998 ~4~

Ni 3 + 4 54.90 Rb 2 + 227.28 27.62 Ni 3 4 54.90 Mo3+ 327.16 27.74 Cu 5 + 6103.00 Ni 5 + 575.50 27.50 Ni 4 + ~ 75.50 Br 4 + 447.30 28.20 5Br 6 + 7103.00 Ni 5 + 575.50 27.50 Nb 5 + 6102.60 Ni 5 + 575.50 27.10 Ni 5 + 6108.00 Cu 5 + 579.90 28.10 Rb 7 + 8136.00 Ni 6 + 6108.00 28.00 Ni 7 + 8162.00 Zn 7 + 7134.00 28.00 10Br 2 + 3 36.00 Cu 1 + 17.73 28.27 Ag 2 + 3 34.83 Cu 1 + 17.73 27.10 Br 3 + 4 47.30 Cu 2 + 220.29 27.01 Cu 2+ 3 36.83 Zn 1 + 19.39 27.44 ~a 3 + 4 64.00 Cu 3 + 336.83 27.17 15Cu 2+ 3 36.83 As 1 + 19.81 27.02 Cu2+ 3 36.83 Se 1 + 19.75 27.08 Kr 4 ~ 5 64.70 Cu 3 + 336.83 27.87 Cu 2 + 3 36.83 Pd 1 + 18.34 28.49 Cu 2 + 3 36.83 Cd 1 + 18.99 27.84 20Cu2+ 3 36.83 Sbl + 18.64 28.19 Cu 2 + 3 36.83 Te 1 + 19.01 27.82 Cu 2+ 3 36.83 Os 1 + 18.70 28.13 Cu2+ 3 36.83 Ir 1 + 19.10 27.73 Cu 2 + 3 36.83 Pt 1 + 19.00 27.83 25Cu 2+ 3 36.83 Au 1 + 19.23 27.61 Cu 2 + 336.83 Po 1 + 18.42 28.41 Zn 4 + 582.60 Cu 4 + 455.20 27.40 Cu 3 + 455.20 Rb 2 + 227.28 27.92 Cu 3 + 455.20 Mo 3 + 327.16 28.04 30Cu 3 + 455.20 In 3 + 328.03 27.17 Cu 3 + 455.20 Te 3 + 327.96 27.24 -Zn 5 + 6108.00 Cu 5 + 579.90 28.10 Cu 4 + 579.90 Kr 4 ~ 452.50 27.40 Cu 4 + 579.90 Rb 4 + 452.60 27.30 35Sb5+ 6108.00 Cu5+ 579.90 2R.10 Cu 6 + 7139.00 Kr 7 + 7111.00 ~8.00 6 5 2 ~

Kr 2 + 3 36.95 Zn 1 + 1 9.39 27.56 Cd2+ 3 37.48 Zn 1 + 19.39 28.09 Te 3 + 4 37.41 Zn 1 + 1 9.39 28.02 Ce 3 ~ 4 36.76 Zn 1 + 1 9.39 27.36 Ge 3 + 4 45.71 Zn 2 + 2 17.96 27.75 Mo 3 + 4 46.40 Zn 2 + 2 17.96 28.44 Lu 3 + 4 45.19 Zn 2 ~ 2 17.96 27.23 Bi 3 + 4 45.30 Zn 2+ 2 17.96 27.34 Zn 2+ 3 39.72 Br 1 + 111.81 27.91 1 0 Zn 2 + 3 39.72 Y 2 + 2 12.24 27.48 Mo 5 + 6 68.00 Zn 3 + 3 39.72 28.28 Zn2+ 3 39.72 Xe 1 + 112.13 27.59 Zn 2+ 3 39.72 Eu2+ 211.24 28.48 Zn 2 + 3 39.72 Gd 2 + 2 12.09 27.63 1 5 Zn 2 + 3 39.72 Tb 2 + 2 11.52 28.20 Zn 2 + 3 39.72 Dy 2 + 2 11.67 28.05 Zn 2 + 3 39.72 Ho 2 + 2 11.80 27.92 Zn 2 + 3 39.72 Er 2 + 2 11.93 27.79 Zn 2 + 3 39.72 Tm 2 + 2 12.05 27.67 Zn ? ~ 3 39.72 Yb 2 + 2 12.18 27.54 Zn 3 + 4 59.40 Rh 3 + 3 31.06 28.34 Zn 3 + 4 59.40 X~ 3 ~ 3 32.1û 27.30 Zn 3 + 4 59.40 Pb 3 + 3 31.94 27.46 Kr 6 + 7 111.00 Zn 5+ 5 82.60 28.40 Rb7+ 8136.00 Zn 6+ 6108.00 28.00 Zn 6 + 7 134.00 Sr 7 ~ 7 106.00 28.00 Ge2+ 3 34.22 Gal + 16.00 28.22 Zr 3 + 4 34.34 t3al + 1 6.00 28.34 1 2 + 333.00 Ga1 + 16.00 27.00 Hf 3 + 4 33.33 Ga 1 + 1 6.00 27.33 Hg 2+ 334.20 Ga1 + 16.00 28.20 Te 4 + 5 58.75 ~;a 3 + 3 30.71 28.04 Ga3+ 464.00 Br 3 ~ 336.00 28.00 ~;a 3 + 4 64.00 Kr 3 ~ 3 36.95 27.05 Ga 3 + 464.00 Ge 4 + ~36.76 27.24 Br 2 + 336.00 Ge 1 + 17.90 28.10 WO 90tl3126 PCI-/US90/019 2~ 6~ ~;6 Se 3 + 4 42.94 Ge 2 + 215.93 27.01 Sr 2 + 3 43.60 Ge 2 + 2t5.93 27.67 Sb 3 + 4 44.20 Ge 2 ~ 215.93 28.27 Gd 3 + 4 44.00 Ge 2 + 215.93 28.07 Yb 3 + 4 43.70 Ge 2 + 215.93 27.77 Ge2+ 3 34.22 Y 1 + 16.38 27.84 Y 3+ 4 61.80 Ge3+ 334.22 27.58 - Ge2+ 3 34.22 Zr1 + 16.84 27.38 Ge 2 + 3 34.22 Nb 1 + 1 6.88 27.34 1 0 Ge2+ 3 34.22 Mo 1 + 17.10 27.12 Ge2+ 3 34.22 In 1 + 15.79 28.43 Ge 2 ~ 3 34.22 Gd 1 + 1 6.14 28.08 Ge2+ 3 34.22 Tb 1 + 15.85 28.37 Ge2+ 3 34.22 Dy 1 ~ 15.93 2~.29 t 5 Ge 2 + 3 34.22 Ho l + 1 6.02 28.20 Ge2+ 3 34.22 Erl + 16.10 28.12 Ge2+ 3 34.22 Tm 1 + 16.18 28.04 Ge2+ 3 34.22 Yb 1 + 16.25 27.97 Ge2+ 3 34.22 Hf 1 + 1 6.60 27.62 Ge2+ 3 34.22 Tl 1 + 16.11 28.11 Ge2+ 3 34.~2 Th 1 + 1 6.10 28.12 Ge2+ 3 34.22 Pa 1 + 1 5.90 28.32 Ge2+ 3 34.22 U 1 + 16.0~ 28.17 Ge2+ 3 34.22 Np 1 + 1 6.20 28.02 Ge2+ 3 34.22 Pu 1 + 1 6.06 28.16 Ge2+ 3 34.22 Am 1 + 1 5.99 28.23 Ge2+ 3 34.22 Cm 1 + 1 6.02 28.20 Ge2+ 3 34.22 Bk 1 + 1 6.23 27.99 Ge2+ 3 34.22 Cf1 + 16.30 27.92 Ge2+ 3 34.22 Es 1 ~ 1 6.42 27.80 Ge3+ 4 45.71 As 2 + 2 18.63 27.08 Ge 3 + 4 45.71 Rh 2 + 2 18.08 27.63 Ge 3 + 4 45.71 Te 2 + 2 18.60 27.11 Ge3~ 4 45.71 Pt 2 + 2 t8.~6 27.15 Kr 2 + 3 36.95 As 1 + 1 9.81 27.14 Nb3 + 4 38.30 As 1 ~ 1 9.81 28.~9 67 Q ~ r~

Cd 2 ~ 3 37.48 AS 1 + 1 9.81 27.67 Te 3 + 4 37.41 As 1 + 19.81 27.60 Mo3+ 4 46.40 As 2 + 218.63 27.77 Sb4 + 5 56.00 As 3 + 328.35 27.65 Bi 4 ~ 5 56.00 As 3 + 3 28.35 27.65 As 3 + 4 50.13 Br 2 + 2 21.80 28.33 Kr 5 + 6 78.50 As 4 + 4 50.13 28.37 As 3 + 4 50.13 Zr 3 + 3 22.99 27.14 As 3 + 4 50.13 Nd3~ 3 22.10 28.03 As 3 ~ 4 50.13 Pm 3 + 3 22.30 27.83 As 3 + 4 50.13 Tb 3 + 3 21.91 28.22 As 3 + 4 50.13 Dy 3 + 3 22.80 27.33 As 3 ~ 4 50.13 Ho 3 + 3 22.84 27 29 As 3 + 4 50.13 Er 3 + 3 22.74 27.39 As 4 + 5 63.63 Br3 + 3 36.00 27.63 Sr 5 + 6 90.80 As 5 + 5 63.63 27.17 Se 6 + 7 155.40 As 6 + 6 127.60 27.80 As 5 + 6 127.60 Rb 7 + 7 99.20 28.40 Kr 2 + 3 36.95 Se 1 + 1 9.75 27.20 Cd2+ 3 37.48 Se 1 + 19.75 27.73 Te 3 + 4 37.41 Se 1 + 1 9.75 27.66 C~3 + 4 36.76 Se 1 + 1 9.75 27.01 Te4 + 5 58.75 Se3+ 330.82 27.93 Rb 4 + 5 71.00 Se 4 + 4 42.94 28.06 Se 3 + 4 42.94 Tc 2 + 2 15.26 27.68 Se 3 + 4 42.94 Sn 2 + 2 14.63 28.31 Te 5 + 6 70.70 Se 4 + 4 42.94 27.76 Se 3 + 4 42.94 Hf 2 + 2 14.90 28.04 Se3+ 4 42.~4 Pb2+ 21~.03 27.91 Se 4 + 5 68.30 Rb 3 + 3 40.00 28.30 Se 4 + 5 68.30 Sn 4 + 4 40.73 27.57 Se 4 + 5 68.30 Nd 4 + 4 40.41 27.89 Se 4 + 5 68.30 Pm 4 + 4 41.10 27.20 Se5+ 681.70 In 4 + 4 54.00 27.70 Rb2+ 340.00 Br 1 + 1 11.81 28.19 Pr 3 ~ 4 38.98 Br 1 + 1 11.81 27.17 WO 90/13126 PCI'/US90/01998 ~5`~ 68 Tb 3 ~ 4 39.80 Br 1 + 1 11.81 27.99 La 3 + 4 49.95 Br 2 + 2 21.80 28.15 Br 2 + 3 36.00 Pd 1 + 1 8.34 27.66 Br 2 ~ 3 36.00 Ag 1 + 1 7.58 28.42 Br 2 + 3 36.00 Cd 1 + 1 8.99 27.01 Br 2 + 3 36.00 Sb 1 + 1 8.64 27.36 Br 2 + 3 36.00 Ta t + 1 7.89 28.11 Br 2 + 3 36.00 W 1 + 1 7.98 28.02 Br 2 + 3 36.00 Re 1 + 1 7.88 28.12 1 0 Br 2 + 3 36.00 Os 1 + 1 8.70 27.30 Br 2 + 3 36.00 Po 1 + 1 8.42 27.58 Br 3 + 4 47.30 Pd 2 + 2 19.43 27.87 Br 3 + 4 47.30 In 2 + 2 18.87 28.43 Br3 ~ 4 47.30 1 2+ 2 19.13 28.17 1 5 Br 3 + 4 47.30 La 3 + 3 19.18 28.12 Br 3 + 4 47.30 Ce 3 + 3 20.20 27.10 Br 4 ~ 5 59.70 Xe 3 + 3 32.1 G 27.60 Br 4 ~ 5 59.70 Pb 3 + 3 31.94 27.76 Y 6+ 7116.00 Br 6 ~ 688.60 27.40 Br 5 + 6 83.60 Mo 5 + 5 61.20 27.40 Pm3+ 4 41.10 Kr 1 + 1 14.00 27.10 Sm 3 + 4 41.40 Kr 1 + 1 14.00 27.40 Dy3 + 4 41.50 Kr 1 + 1 14.00 27.50 Pb3 + 4 42.32 Kr 1 + 1 14.00 28.32 Kr 3 + 4 52.50 Kr 2 + 2 24.36 28.14 Rb3+ 4 52.60 Kr 2 + 2 24.36 28.24 Kr4 + 5 64.70 Kr 3 + 3 38.95 27.75 Kr 2 + 3 36.95 Cd 1 + 1 8.99 27.96 Kr 2 + 3 36.95 Sb 1 + 1 8.64 28.31 Kr 2 + 3 36.95 Te 1 + 1 9.01 27.94 Kr 2 + 3 36.95 Os 1 + 1 8.70 28.25 Kr 2 + 3 36.95 Ir 1 + 1 9.10 27.85 Kr 2 + 3 36.95 Pt 1 + 1 9.00 27.95 Kr 2 + 3 36.95 Au 1 + 1 9.2~ 27.73 Kr 3 + 4 52.50 Kr 2 + 2 24.36 28.14 Kr 3 + 4 52.50 ~Ib 3 + 3 25.04 27.46 .

. . .

WO 90/13126 PCT/US90/019g8 69 ~A~7 Kr 3 + 452.50 Sb3+ 325.30 27.20 Kr 3 + 452.50 Cs 2 + 225.10 27.40 Kr 3 + 4~2.50 Eu 3 + 324.90 27.60 Kr 3 + 452.50 Yb3 + 325.03 27.47 5Kr 4 + 564.70 Kr 3 + 336.95 27.75 Y 5+ 693.00 Kr~ ~64.70 28.30 Kr 4 + 564.70 Cd3+ 337.48 27.22 Kr 4 + 564.70 Te 4 + 437.41 27.29 Kr 4 + 564.70 Ce4+ 436.76 27.94 10Sr 6 ~ 7106.00 Kr 6 + 678.50 27.50 Kr 5 + 678.50 Nb5+ 550.55 27.95 Xe2~ 332.10 Rb1 + 14.18 27.92 Pb 2 + 331.94 Rb 1 + 14.18 27.76 `Rb 2 + 340.00 Y 2 + 212.24 27.76 Mo 5 + 668.00 Rb 3 + 340.00 28.00 Rb2~ 340.00 Xe1 ~ 112.13 27.87 Rb 2 + 340.00 Gd 2 ~ 212.~9 27.91 Rb 2 + 340.00 Tb 2 ~ 211.52 28.48 Rb 2 + 34Q.00 Dy 2 + 211.67 28.33 Rb 2 + 340.00 Ho 2 + 211.80 28.20 Rb 2 + 340.00 Er 2 ~ 211.93 28.07 Rb 2 + 340.00 Tm 2 + 212.05 27.95 Rb2+ 340.00 Yb21 212.18 27.82 Rb 3 + 452.~0 Nb 3 + 325.04 27.56 Rb 3 + 452.60 Sb 3 + 325.30 27.30 -Rb 3 + 452.60 Cs 2 + 225.10 27.50 Rb 3 + 452.60 Eu 3 + 324.90 27.70 Rb 3 + 452.60 Yb 3 + 325.03 27.57 Rb3+ 452.60 Bi 3 + 325.56 27.04 Rb 6 + 799.20 Rb 5 + 571.00 28.20 Rb4 + 571.00 Sr 3 + 343.60 27.40 Rb 4 + 571.00 Eu 4 + 442.60 28.40 Rb 4 + 571.00 Er 4 + 442.60 28.40 Rb4+ 571.00 Tm 4 ~ 442.70 .28.30 Rb 4 + 5-71.00 Yb 4 + 443.70 27.30 Rb5+ 684.40 Sr 4 + 457.00 27.40 '~ ' " ' ' .

WO 90/13~26 PCll/US90/01998 ~5~6~

Rb 5 + 6 84.40 Sb 5 ~ 556.00 28.40 Rb5+ 6 84.40 Bi 5 + 556.00. 28.40 Rb 6 + 7 99.20 Rb 5 ~ 571.00 28.~0 Rb 6 + 7 99.20 Sr 5 + 571.60 27.60 Mo 6 + 7126.80 Rb 7 + 799.20 27.60 Rb 7 + 8136.00 Sb 6 ~ 6108.00 28.00 Pd 2 + 3 32.93 Sr 1 + 15.70 27.24 i 2 + 3 33.00 Sr 1 + 15.70 27.31 Hf 3 + 4 33.33 Sr 1 + 15.70 27.64 Nb3 + 4 38.30 Sr 2 + 211.03 27.27 Pr 3 + 4 38.98 Sr 2 + 211.03 27.95 Sr 4 + 5 71.60 Sr 3 + 343.60 28.00 Sr2+ 3 43.60 Mo2+ 216.15 27.45 Sr 2 + 3 43.60 Tc 2 + 215.26 28.34 Sr 2 + 3 43.60 Sb 2 ~ 216.53 27.07 Te 5 + 6 70.70 Sr 3 + 343.60 27.10 Sr 3 + 4 57.00 Tc 3 + 329.54 27.46 Sr 3 + 4 57.00 Tl 3 + 329.83 27.17 Sr 4 + 5 71.60 Sr 3 + 343.60 28.00 Sr 4 + 5 71.60 Sb4+ 444.20 27.40 Sr 4 + 5 71.60 Gd 4 + 444.00 27.60 Sr 4 + 5 71.60 Yb 4 + 443.70 27.90 Zr 3 + 4 34.34 Y 1 + 16.38 27.96 Ag 2 + 3 34.83 Y 1 + 16.38 28.45 Hg 2 + 3 34.20 Y 1 + 16.38 27.82 Sn3+ 4 40.73 Y 2+ 212.24 28.49 Nd 3 ~ 4 40.41 Y 2 + 212.24 28.17 Tb 3 + 4 39.80 Y 2 + 212.24 27.56 Y 3+ 4 61.80 Zr 4 + 434.34 27.4.6 Y 3+ 4 61.80 Hf4+ 433.33 28.47 Y 3 + 4 61.80 Hg 3 + 334.20 27.60 Y 4+ 577.00 La4+ 449.95 27.05 Y 6~ 7t16.00 Bi 6 + 688.30 27.70 Zr 3 + 434.34 Zr 1 + 16.84 - 27.50 Ag2+ 334.83 Zr1 + 16.84 27.99 Hg 2+ 334.20 Zr 1 + 16.84 27.36 71 2~3~ ~7 Srl 3 + 4 40.73 Zr 2 ~ 2 13.13 27.60 Nd 3 + 4 40.41 Zr 2 + 2 13.13 27.28 Pm 3 + 4 41.10 Zr 2 + 2 13.13 27.97 Sm 3 + 4 41.40 Zr 2 + 2 13.13 28.27 Dy 3 + 4 41.50 Zr 2 + 2 13.13 28.37 Nb4+ 5 50.55 Zr 3 + 3 22.99 27.56 7r 3 + 4 34.34 Zr 1 + 1 6.84 27.50 Zr 3 + 4 34.34 Nb 1 + 1 6.88 27.46 Zr 3 + 4 34.34 Mo 1 + 1 7.10 27.24 10 Zr 3 + 4 34.34 Tc 1 + 1 7.28 27.06 Zr 3 + 4 34.34 Gd 1 + 1 6.14 28.20 Zr 3 + 4 34.34 Tb 1 + 1 5.85 28.49 Zr 3 + 4 34.34 Dy 1 + 1 5.93 28.41 Zr 3 + 4 34.34 Ho t + 1 6.02 28.32 15 Zr 3 + 4 34.34 Er 1 + 1 6.10 28.24 Zr 3 + 4 34.34 Tm 1 + 1 6.18 28.16 Zr 3 + 4 34.34 Yb 1 + 1 6.25 28.09 Zr 3 + 4 34.34 Hf 1 ~ 1 6.60 27.74 7r 3 + 4 34.34 Tl 1 + 1 6.11 28.23 20 Zr 3 ~ 4 34.34 Bi 1 + 1 7.29 27.05 7r 3 + 4 34.34 Th 1 + 1 6.10 28.24 Zr 3 + 4 34.34 Pa 1 + 1 5.90 28.44 Zr 3 + 4 34.34 U 1 + 16.0528.29 Zr 3 + 4 34.34 Np 1 + 1 6.20 28.14 25 Zr 3 + 4 34.34 Pu 1 + 1 6.06 28.28 ~r 3 + 4 34.34 Am 1 + 1 5.99 28.35 Zr 3 + 4 34.34 Cm 1 + 1 8.02 28.32 Zr 3 + 4 34.34 Bk 1 + 1 6.23 28.11 Zr 3 + 4 34.34 Cf 1 + 1 6.30 28.04 30 Zr 3 ~ 4 34.34 Es 1 + 1 6.42 27.92 Zr 4 + 5 81.50 In 4 + 4 54.00 27.50 Ag 2 + 3 34.83 Nb 1 + 1 6.88 27.95 Hg 2 + 3 34.20 Nb 1 + 1 6.88 27.32 Sm 3 ~ 4 41.40 Nb 2 + 2 14.32 27.08 35 Eu 3 + 4 42.60 Nb 2 + 2 14.32 28.28 Dy3+ 4 41.50 Nb2+ 214.3227.18 2 ~ 3~ 7 7 2 Ho 3 + 4 42.50 Nb 2 + 2 14.32 28.18 Er 3 + 4 42.60 Nb 2 ~ 2 14.32 28.28 Tm 3 + 4 42.70 Nb 2 + 2 14.32 28.38 Pb 3 + 4 42.32 Nb 2 + 2 14.32 28.00 Nb3+ 4 38.30 1 1 ~ 110.45 27.85 Nb 3 + 4 38.30 Ba 2 + 2 10.00 28.30 Nb 3 + 4 38.30 La 2 + 2 11.06 27.24 Nb 3 + 4 38.30 Ce 2 + 2 10.85 27.45 Nb 3 + 4 38.30 Pr 2 + 2 10.55 27.75 1û Nb 3 + 4 - 38.30 Nd 2 + 2 10.73 27.57 Nb 3 + 4 38.30 Pm 2 + 2 lO.90 27.40 Nb3+ 4 38.30 Sm 2 + 211.07 27.23 Nb3+ 4 38.30 Eu2+ 211.24 27.06 Nb 3 + 4 38.30 Hg 1 + 1 10.44 27.86 1 5 Nb3+ 4 38.30 Rn 1 + 110.75 27.55 Nb3+ 4 38.30 Ra2+ 210.15 28.15 Nb 4 ~ 5 50.55 Nd 3 + 3 22.10 28.45 Nb 4 + 5 50.55 Pm 3 + 3 22.30 28.25 Nb4+ 5 50.55 Sm 3 + 3 23.40 27.15 Nb 4 + 5 50.55 Dy 3 + 3 22.80 27.75 Nb4+ 5 50.55 Ho 3+ 322.84 27.71 Nb 4 + 5 50.55 Er 3 + 3 22.74 27.81 Nb4+ 5 50.55 Hf 3 + 3 23.30 27.25 Mo 7 + 8 153.00 Nb 7 + 7 125.00 28.00 Ag 2 + 3 34.83 Mo 1 + 1 7.10 27.73 Hg 2+ 3 34.20 Mo 1 + 1 7.10 27.10 Sb 3 + 4 44.20 Mo 2 + 2 16.15 28.05 Gd3+ 4 44.00 Mo2~ 216.15 27.85 Yb3+ 4 43.70 Mo2+ 216.15 27.55 Mo 3 ~ 4 46.40 Rh 2 + 2 18.08 28.32 Mo 3 + 4 46.40 In 2 + 2 18.87 27.53 Mo 3 + 4 46.40 Te 2 + 2 18.60 27.80 Mo 3 + 4 46.40 1 2 + 2 19.13 27.27 Mo 3 + 4 46.40 La 3 + 3 19.18 27.22 Mo 3 ~ 4 46.40 Pt 2 + 2 18.56 27.84 Mo 3 + 4 46.40 Hg 2 + 2 18.76 27.64 ..

WO 90/13126 PCI-/US"0/0199 2 ~ 3 Mo 4 + 5 61.20 Pd 3 ~ 332.93 28.27 Mo 4~ 5 61.20 1 3 + 333.00 28.20 Mo4+ 5 61.20 Hf 4 + 433.33 27.87 Bi 5 + 6 88.30 Mo5+ 561.20 27.10 Mo 5 + 6 68.00 Sn 4 + 440.73 27.27 Mo 5 + 6 68.00 Nd 4 + 440.41 27.59 Mo 5 + 6 68.00 Tb 4 + 439.80 28.20 Ag 2 + 3 34.83 Tc 1 + 17.28 27.55 Eu 3+ 4 42.60 Tc 2 + 215.26 27.34 1 0 Ho 3 + 4 42.50 Tc 2 + 215.26 27.24 Er 3 + 4 42.60 Tc 2 + 215.26 27.34 Tm 3 + 4 42.70 Tc 2 + 215.26 27.44 Yb3~ 4 43.70 Tc 2 + 215.26 28.44 Pb 3 + 4 42.32 Tc 2 + 215.26 27.06 Ag 2 + 3 34.83 Ru 1 + 17.37 27.46 Sb 3 + 4 44.20 Ru 2 + 216.76 27.44 Gd 3 + 4 44.00 Ru 2 + 216.76 27.24 Lu 3 + 4 45.19 Ru 2 + 216;76 28.43 Sb 4 + 5 56.00 Ru 3 + 328.47 27.53 Bi 4 + 5 56.00 Ru 3+ 328.47 27.53 As 2 + 3 34.83 Rh 1 + 17.46 27.37 Lu3+ 4 45.19 Rh2+ 218.38 27.11 Bi 3 + 4 45.30 Rh 2+ 218.08 27.22 Te 4 + 5 58.75 Rh 3 + 331.06 27.69 Rh 2+ 3 31.06 Cs 1 ~ 13.B9 27.17 Ce3+ 4 36.76 Pd 1 + 18.34 28.42 Pd2+ 3 32.93 In 1 + 15.79 27.14 Pd2 + 3 32.93 Ba 1 ~ 15.21 27.72 Pd 2 + 3 32.93 La 1 + 15.58 27.35 Pd2 + 3 32.93 Ce 1 + 15.47 27.46 Pd 2 + 3 32.93 Pr 1 ~ 15.42 27.51 Pd 2 + 3 32.93 Nd 1 + 15.49 27.44 Pd 2 ~ 3 32.93 Pm 1 + l5.55 27.38 Pd 2 + 3 32.93 Sm 1 + 15.63 27.30 Pd 2 + 3 32.93 Eu 1 + 15.67 27.26 Pd 2 + 3 32.93 Tb 1 ~ 15.85 27.08 .

': `

2 ~ 7 Pd 2 + 3 32.93 Dy 1 + 15.93 27.00 Pd 2 + 3 32.93 Lu 1 + 15.43 27.50 Pd 2 + 3 32.93 Ra 1 + 15.28 27.65 Pd 2 + 3 32.93 Ac 1 + 15.20 27.73 Pd 2 + 3 32.93 Pa 1 + 15.90 27.03 Ag 2 + 3 34.83 Ag 1 + 17.58 27.25 La3 + 4 49.95 Ag 2 + 221.49 28.46 Ag 2 + 3 34.83 Ag 1 + 17.58 27.25 Ag 2 + 3 34.83 Sn 1 + 17.34 27.49 Ag 2 + 3 34.83 Hf 1 + 16.60 28.23 Ag 2 + 3 34.83 Pb 1 ~ 17.42 27.41 Ag 2 + 3 34.83 Bi 1 + 17.29 27.54 Ag 2 + 3 34.83 Es 1 + 16.42 28.41 Cd 2 + 3 37.48 Cd 1 ~ 18.99 28.49 Te 3 + 4 37.~1 Cd 1 + 18.99 28.42 Ce3+ 4 36.76 Cd 1 + 18.99 27.76 Sb 3 + 4 44.20 Cd 2 + 216.91 27.29 Gd 3 + 4 44.00 Cd 2 + 216.91 27.09 Lu 3 + 4 45.19 Cd 2 + 216.91 28.28 Bi 3 + 4 45.30 Cd 2 + 216.91 28.39 Cd 2 + 3 37.48 Cd 1 + 18.99 28.49 Cd2+ 3 37.48 Te l + 19.01 28.47 Cd 2 + 3 37.48 1 1 + 110.45 27.03 Cd 2 + 3 37.48 Ba 2 + 210.00 27.48 Cd2+ 3 37.48 Ir 1 + 19.10 28.38 Cd2+ 3 37.48 Pt 1 + 19.00 28.48 Cd2+ 3 37.48 Au 1 ~ 19.23 28.25 Cd2+ 3 37.48 Hg 1 + 110.44 27.04 Cd 2 + 3 37.48 Ra 2 + 210.15 27.33 It'2;+ 3 33.00 In 1 + 15.79 27.21 Hf 3 + 4 33.33 In 1 + 1~.79 27.54 Hg2~ 3 34.20 In 1 + 15.79 28.41 Sb 4 + 5 s6.do in 3 + 328.03 27.97 Bi 4 + ~ 56.00 In 3 + 328.03 27.97 In 3 + 4 54.00 Bi 3 + 325.56 28.44 Eu3+ 4 42.60 Sn 2+ 214.63 27.97 YVO 90/131t6 PCI'IUS90/01998 ~ ~ 3 L~ 7 . :~

Ho 3 + 4 42.50 Sn 2 ~ 214.63 27.87 Er 3 + 4 42.60 Sn 2 + 214.63 27.97 Tm 3 + 4 42.70 Sn 2 + 214.63 28.07 Pb 3 + 4 42.32 Sn 2 + 214.63 27.69 Te 4 + 5 58.75 Sn 3 + 330.50 28.25 Pb 4 + 5 68.80 Sn 4 + 440.73 28.07 Sn4 + 5 72.28 Sb4+ 444.20 28.08 Sn 4 + 5 72.28 Gd 4 + 444.00 28.28 Sn 4+ 5 72.28 Lu 4 + 445 19 27.09 1 0 Ce 3 + 4 36.76 Sb 1 + 18.64 28.12 Sb 3 + 4 44.20 Sb 2 + 216.53 27.67 Gd 3 + 4 44.00 Sb 2 + 216.53 27.47 Yb 3 + 4 43.70 Sb 2 + 216.53 27.17 Sb 3 + 4 44.20 Sb 2 + 216.53 27.67 1 5 Sb 3 + 4 44.20 Bi 2 ~ 216.69 27.51 Sb 4 + 5 56.~0 Te 3 + 327.96 28.04 Te 3 + 4 37.41 Te 1 + 19.01 28.40 Ce3+ 4 36.76 Te 1 + 19.01 27.75 Bi 4 + 5 56.00 Te 3 + 327.96 28.04 Te 3 + 4 37.41 Te 1 + 19.01 28.40 Te 3 + 4 37.41 Ba 2 + 210.00 27.41 Te 3 + 4 37.41 Ir 1 + 19.10 28.31 Te 3 + 4 37.41 Pt 1 + 19.00 28.41 Te 3 + 4 37.41 Au 1 + 19.23 28.18 Te 3 + 4 37.41 Ra 2 + 210.15 27.26 Te 5 + 6 70.70 Eu 4 + 442.60 28.10 Te 5 + 6 70;70 Ho 4+ 442.50 28.20 Te 5 + 6 70.70 Er 4 + 442.60 28.10 Te 5 + 6 70.70 Tm 4 + 442.70 28.00 Te 5 + 6 70.70 Pb 4 + 442.32 28.38 1 2 + 3 33.00 Ba 1 + 15.21 27.79 1 2 + 3 33.00 La l + l5.58 27.42 1 2 + 3 33.00 Ce 1 ~ 1~.47 27.53 1 2 ~ 3 33.00 Pr 1 ~ 15.42 27.58 1 2 + 3 33.00 Nd 1 + 15.49 27.51 1 2 + 3 33.00 Pm 1 + 15.55 27.45 .

.
:.

WO 90/l3l2~6~ ~ rt PCI/US90/019!~8 I 2 + 3 33.00 Sm 1 t- 15.63 27.37 I 2 + 3 33.00 Eu 1 + 15.67 27.33 I 2 + 3 33.00 Tb 1 + 15.85 27.15 I 2 + 3 33.00 Dy 1 + 15.93 27.07 I 2 ~ 3 33.00 Lu 1 + 15.43 27.57 I 2 + 3 33.00 Ra 1 + 15.28 27.72 I 2 + 3 33.00 Ac l + 15.20 27.80 I 2 + 3 33.00 Pa 1 ~ 15.90 27.10 I 2 + 3 33.00 Am 1 + 15.99 27.01 Nd3+ 4 40.41 Xel + 112.13 28.28 Tb 3 + 4 39.80 Xe 1 + 112.13 27.67 Xe2+ 3 32.10 Cs 1 + 13!89 28.21 Pb 2 + 3 31.94 Cs 1 + 13.89 28.04 Hf 3 + 4 33.33 Ba 1 + ~5.21 28.12 Hf 3 + 4 33.33 La ~ + 15.58 27.75 Pr 3 + 4 38.98 La 2+ 211.06 27.92 La 3 + 4 49.95 Pr 3 + 321.62 28.33 La 3 + 4 49.95 Nd 3 + 322.10 27.~5 La3 + 4 49.95 Pm 3 + 322.30 27.65 La3 + 4 49.9~ Tb 3 + 321.91 28.04 La 3 + 4 49.95 Dy 3 + 322.80 27.15 La 3 + 4 49.95 Ho 3 + 322.84 27.11 La3 + 4 49.9~ Er 3 + 322.74 27.21 Hf 3 + 4 33.33 Ce 1 + 15.47 27.86 Pr 3 + 4 38.. ~8 Ce2+2 10.85 28.13 Ce 3 + 4 36.76 Os 1 ~ 18.70 28.06 Ce3+ 4 36.76 Ir 1 + 19.10 27.66 Ce3+ 4 36.76 Pt 1 + 19.00 27.76 Ce 3 + 4 36.76 Au 1 + 19.23 27.53 Ce3+ 4 36.76 Po l ~ 18.42 28.34 Hf 3 + 4 33.33 Pr 1 + 15.42 27.91 Pr 3 + 4 38.98 Pr 2 + 210.55 28.43 Pr 3 + 4 38.98 Pr ~ + 210.55 28.43 Pr 3 + 4 38.98 Nd 2 + 210.73 28.25 Pr 3 + 4 38.98 Pm 2 + 210.90 28.08 Pr 3 + 4 38.98 Sm 2 + 211.07 27.91 WO gO/13126 PCr/USgO/01998 77 2~

Pr 3 + 4 38.98 Eu 2 + 211.24 27.74 Pr 3 + 4 38.98 Tb 2 + 211.52 27.46 Pr 3 + 4 38.98 Dy 2 + 211.67 27.31 Pr 3 + 4 38.98 Ho 2 + 211.80 27.18 Pr 3 + 4 38.98 Er 2 + 211.93 27.05 Pr 3 + 4 38.98 Rn 1 + 110.75 28.23 Hf 3 + 4 33.33 Nd 1 ~ 15.49 27.84 Nd 3 + 4 40.41 Gd 2 + 212.09 28.32 Nd3+ 4 40.41 Er2 + 21t.93 28.48 Nd 3 + 4 40.41 Tm 2 + 212.05 28.36 Nd 3 + 4 40.41 Yb 2 + 212.18 28.23 Pb 4 + ~ 68.80 Nd 4 + 440.41 28.39 Hf 3 + 4 33.33 Pm 1 + 15.55 27.78 Pm 3 + 4 41.10 Lu 2 + 213.90 27.20 Pb4+ 5 68.80 Pm4~ 441.10 27.70 Hf 3 + 4 33.33 Sm 1 + 15.63 27.70 Sm 3 + 4 41.40 Lu 2 ~ 213.90 27.50 Pb4 + 5 68.80 Sm 4 + 441.40 27.40 Hf 3 + 4 33.33 Eu 1 ~ 15.67 27.66 Eu3 + 4 42.60 Hf 2 + 214.90 27.70 Eu 3 + 4 42.60 Pb 2 + 215.03 27.57 Hf 3 + 4 33.33 Gd 1 + 16.14 27.19 Hg 2+ 3 34.20 Gd 1 ~ 16.14 28.06 Tb 3 + 4 39.80 Gd 2 + 212.09 27.71 Gd3+ 4 44.00 Bi 2 ~ 216.69 27.31 Hf 3 + 4 33.33 Tb 1 + 15.85 27.48 Hg 2 + 3 34.20 Tb 1 + 15.85 28.35 Tb 3 + 4 39.80 Tb 2 + 211.52 28.28 Tb 3 + 4 39.80 Tb 2 ~ 211.52 28.28 Tb3+ 4 39.80 Dy2-~ 211.67 28.13 Tb 3 + 4 39.80 Ho 2 + 211.80 28.00 Tb 3 + 4 39.80 Er 2 + 211.93 27.87 Tb 3 + 4 39.80 Tm 2 + 212.05 27.75 Tb 3 + 4 39.80 Yb 2 + 212.13 27.62 Hf 3 + 4 33.33 Dy 1 + 15.93 27.40 Hg 2 + 3 34.20 Dy 1 + 15.93 28.27 WO 90/13126 PCI'/lJS90/01998 2~ 9~

Dy3 ~ 4 41.50 Lu 2 + 213.90 27.60 Pb 4 + 5 68.80 Dy 4 + 441.50 27.30 Hf 3 + 4 33.33 Ho 1 + 16.02 27.31 Hg2+ 3 34.20 Ho1+ 16.02 28.18 Ho3+ 4 42.50 Hf 2 + 214.90 27.60 Ho 3 + 4 42.50 Pb 2 ~ 215.03 27.47 Hf 3 + 4 33.33 Er 1 + 16.10 27.23 Hg2+ 3 34.20 Erl + 16.10 28.10 Er3 + 4 42.60 Hf 2 + 214.90 27.70 Er 3 + 4 42.60 Pb 2 + 215.03 27.57 Hf 3 ~ 4 33.33 Tm 1 + 16.18 27.15 Hg2+ 3 34.20 Tm 1 + 16.18 28.02 Tm 3 + 4 42.70 Hf 2 + 214.90 27.80 Tm 3 + 4 42.70 Pb2+ 215.03 27.67 Hf 3 + 4 33.33 Yb 1 ~ 16.25 27.08 H92+ 3 34.20 Ybl + 16.25 27.95 Yb3+ 4 43.70 Bi 2 + 216.69 27.01 Hf 3 + 4 33.33 Lu 1 + 15.43 27.90 Pb 3 + 4 42.32 Lu 2 + 213.90 28.42 Lu 3 + 4 45.19 Bi 2 + 216.69 28.50 Hg2+ 3 34.20 Hf 1 + 16.6û 27.60 Pb3 + 4 42.32 Hf 2 + 214.90 27.42 Hf 3 + 4 33.33 Tl 1 + 16.11 27.22 Hf 3 + 4 33.33 Ra 1 + 15.28 28.û5 Hf 3 + 4 33.33 Ac 1 + 15.20 28.13 Hf 3 + 4 33.33 Th 1 + 16.10 27.23 Hf 3 + 4 33.33 Pa 1 + 15.90 27.43 Hf 3 + 4 33.33 U 1 + 16.05 27.28 Hf 3 + 4 33.33 Np 1 + 16.20 27.13 Hf 3 + 4 33.33 Pu 1 + 16.06 27.~7 Hf 3 + 4 33.33 Am 1 + 1~.99 27.34 Hf 3 + 4 33.33 Cm 1 + 16.02 27.31 Hf-3 + 4 3~.33 Bk 1 + 16.~3 27.10 Hf 3 + 4 33.33 Cf 1 ~ 16.30 27.03 3~ !Ig2+ 3 34.20 Tl 1 + 16.11 28.09 Hg2+ 3 34.20 Th 1 + 16.10 28.10 WO 90/13126 PCI'/US90/0199~
79 2 0 ~

Hg 2 + 3 34.20 Pa 1 + 1 5.90 23.30 Hg2+ 3 34.20 U 1 + 16.05 28.15 Hg 2 + 3 34.20 Np 1 + 1 6.20 28.00 H~2+ 3 34.20 Pu 1 + 16.06 28.14 Hg2~ 3 34.20 Am 1 + 15.99 28.21 Hg 2 + 3 34.20 Cm 1 + 1 6.02 28.18 Hg 2 + 3 34.20 Bk 1 + 1 6.23 27.97 Hg 2 + 3 34.20 Cf 1 + 1 6.30 27.90 Hg 2 + 3 34.20 Es 1 + 1 6.42 27.78 1 0 Pb 3 + 4 42.32 Pb 2 ~ 2 15.03 27.29 Pb 3 + 4 42.32 Pb 2+ 2 15.03 27.29 n = 16 (resonance shrinkage energy is given by 2 27.21 eV; with n = 16, the resonance shrinkage energy is 217.68) Atom nnth lon- Atom nnth lon- Energy 1 5 Oxidiz- ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) Ne 7 + 8239.09 He 1 + 124.59 214.50 Al 6 + 7241.43 He 1 + 124.59 216.84 Mg6+ 7224.94 Li 1 + 15.39 219.55 P 5+ 6220.43 Li 1 + 15.39 215.04 B 4 + 5340.22 Li 3 + 3122.45 217.77 Mg 6+ 7224.94 Be 1 + 19.32 215.62 Ne 7 + 8239.09 Be 2 + 218.21 220.88 Mg6+ 7224.94 B 1 ~ 18.30 216.64 Al 6 + 7241.43 B 2 + 225.15 216.28 B 3 1 4259.37 Ne2+ 240.96 218.41 B 3 + 4259.37 Si 4 ~ 445.14 214.23 B 3 + 4259.37 C! 3 + 339.61 219.76 B 3 + 4259.37 Ar 3 + 340.74 218.63 B 3 + 4259.37 Ti 4 + 443.27 216.10 B 3 + 4259.37 Zn 3 + 339.72 219.65 B 3 + 4259.37 Se 4 ~ 442.94 216.42 B 3 + 4259.37 Rb 3 + 340.00 219.37 B 3 + 4259.37 Sr 3 ~ 343.60 215.77 .~ ~

WO 90/13126 PCl/US9~/01~98 - 2~ 6~7 80 B 3 + 4 259.37 Sn 4 + 4 40.73 218.63 B 3 + 4 259.37 Sb 4 ~ 4 44.20 215.17 B 3+ 4 259.37 Pr 4 ~ 4 38.98 220.39 B 3 + 4 259.37 Nd 4 + 4 40.41 218.96 B 3 + 4 259.37 Pm 4 ~ 4 41.10 218.27 B 3 + 4 259.37 Sm 4 + 4 41.40 217.97 B 3 + 4 2~9.37 Eu 4 + 4 42.60 216.77 B 3 + 4 259.37 Gd 4 + 4 44.00 215.37 B 3 + 4 259.37 Tb 4 ~ 4 39.80 219.57 B 3 + 4 259.37 Dy 4 + 4 41.50 217.87 B 3 + 4 259.37 Ho 4 -~ 4 42.50 216.87 B 3 + 4 259.37 Er 4 + 4 42.60 216.77 B 3 + 4 259.37 Tm 4 + 4 42.70 216.67 B 3 + 4 259.37 Yb 4 + 4 43.70 215.67 B 3 + 4 259.37 Lu 4 + 4 45.19 214.18 ~ 3 + 4 259.37 Pb 4 + 4 42.32 217.05 B 3 + 4 259.37 Bi 4 + 4 45.30 214.07 B 4 + 5 340.22 Ne 5 + 5 126.21 214.01 B 4+ 5 340.22 Al 4 + 4 119.99 220.23 B 4+ 5 340.22 Ar 7 + 7 1~4.32 215.90 B 4 + 5 340.22 Ti 6 + 6 119.36 220.86 B 4 + 5 340.22 Mn 7 + 7 119.27 220.95 B 4 + 5 340.22 Fe 7 + 7 125.00 215.22 B 4 + 5 340.22 Kr 8 + 8 126.00 214.22 B 4 + 5 340.22 Sr 8 + 8 122.30 217.92 B 4 + 5 340.22 Nb 7 + 7 125.00 215.22 Ne 7 + 8 239.09 C 2 + 2 24.38 214.71 Al 6 + 7 241.43 C 2+ 2 24.38 217.05 Na 7 ~ 8 264.18 G 3 + 3 47.89 216.29 Mg 7 + 8 265.90 C 3 + 3 47.89 218.01 P 6 + 7 263.22 C 3 + 3 47.89 215.33 Al 7 + 8 284.59 C 4+ 4 64.49 220.10 S 6+ ~7 2~0.93 C~ 4+ 4 64.49 216.44 C 4+ 5 392.08 Na6+ 6 172.15 219.93 C 4+ 5 392.08 V 8 + 8 173.70 218.38 C 4 + 5 392.08 Zn 8 + 8 174.00 218.08 .
, .

, ~

WO 90/13126 PCI'/~JS90/01998 81 2 ~ 3 ~

Si 6 + 7 246.52 N 2+ 2 29.60 216.92 Na 7 + 8 264.18 N 3 + 3 47.45 2~6.73 M9 7 + 8 ?65.90 N 3 + 3 47.45 218.45 P 6 + 7 263.22 N 3 + 3 47.45 215.77 S 7 + 8 328.23 O 5 + 5113.90 214.33 F 7 + 8 953.89 O 7 ~ 7739.32 214.57 S 6 + 7 280.93 F 3 + 3 62.71 218.22 Si 7 + 8 303.17 F 4~ 4 87.14 216.03 Ne 7 + 8 239.09 Ne 1 + 1 21.56 217 53 1 0 Al 6 + 7 2~1.43 Ne 1 ~ 1 21.56 219.87 S 6 + 7 280.93 Ne 3 + 3 63.45 217.48 Ne7+ 8 239.09 Ne1 + 1 21.56 217.53 Ne7+ 8 239.09 Al 2 + 2 18.83 ?20 26 Ne 7 ~ 8 23g.09 P 2 + 2 19.73 219.36 1~ Ne 7 + 8 239.09 S 2 + 2 23.33 215.76 Ne 7 + 8 239.09 Cl 2 ~ 2 23.81 215.28 Ne 7 + 8 239.09 Sc 3 ~ 3 24.76 214.33 Ne7+ 8 239.09 Ni2 + 2 18.17 220.92 Ne 7 + 8 239.09 Cu 2 + 2 20.29 218.80 Ne 7 + 8 239.09 Ga 2 + 2 20.51 218.58 Ne 7 + 8 239.0g As ~ + 2 18.63 220.46 Ne 7 + 8 239.09 Se 2 + 2 21.19 217.90 Ne 7 + 8 23g.09 Br 2 + 2 21.80 217.29 Ne 7 + 8 239.09 Kr 2 + 2 24.36- 214.73 Ne7+ 8 239.09 Y 3+ 3 20.52 218.57 Ne 7 + 8 239.09 7r 3 + 3 22.99 216.10 Ne 7 + 8 239.09 Nb 3 + 3 25.04 214.05 Ne 7 + 8 239.09 Pd 2 + 219.43 219.66 Ne 7 + 8 239.09 Ag 2 + 221.49 217.60 Ne7+ 8 239.09 In 2 + 218.87 220.22 Ne 7 + 8 239.09 Te 2 + 218.60 220.49 Ne7+ 8 239.09 1 2 + 219.13 219.9~
Ne 7 + 8 239.09 Xe 2 ~ 221.21 217.88 Ne 7 + 8 239.09 La 3 + 319.18 219.91 Ne 7 + 8 239.09 Ce 3 + 32û.20 218.89 Ne 7 1 8 239.09 Pr 3 + 321.62 217.47 WO 90/13126 PCT/US90/l)l998 r 82 2 ~ $ ~ I
Ne 7 + 8 239.09 Nd 3-~ 322.10 216.99 Ne 7 + 8 239.09 Pm 3 + 322.30 216.79 Ne 7 + 8 239.û9 Sm 3 + 323.40 215.69 Ne 7 + 8 239.09 Eu 3~- 324.90 214.19 Ne 7 + 8 239.09 Gd 3 + 320.63 218.46 Ne7+ 8 239.09 Tb3+ 321.91 217.18 Ne 7 + 8 239.09 Dy 3 + 322.80 216.29 Ne 7 + 8 239.09 Ho 3 + 322.84 216.25 Ne 7 + 8 239.09 Er 3 + 322.74 216.35 1 0Ne 7 + 8 239.09 Tm 3 + 323.68 215.41 Ne 7 + 8 239.09 Yb 3 + 325.03 214.06 Ne 7 + 8 239.09 Lu 3 + 320.96 218.13 Ne7+ 8 239.09 Hf 3 + 323.30 215.79 Ne 7 + 8 239.09 Pt 2 + 218.56 220.53 1 5Ne 7 + 8 239.09 Au 2 + 220.50 218.59 Ne 7 + 8 239.09 Hg 2 + 218.76 220.33 Ne7+ 8 239.09 Tl 2 + 220.43 218.66 Mg 6~ 7 224.94 Na 1 + 15.14 219.80 P 5 ~ 6 220.43 Na 1 ~ 15.14 215.29 Na7+ 8 264.18 Na2~ 247.29 216.89 Mg 7 ~ 8 265.90 Na 2 + 247.29 218.61 P 6 ~ 7 263.22 Na 2 + 247.29 215.93 Na 7 + 8 264.1 8 Na 2 + 247.29 216.89 Na7+ 8 264.18 Si4 ~ 445.14 219.04 25 Na 7 + 8 264.18 S 4 + 447.30 216.88 Na 7 + 8 264.1 8 K 3 ~ 345.72 218.46 Na7+ 8 264.18 Ti 4 + 443.27 220.91 Na7+ 8 264.18 V 4 ~ 446.71 217.47 Na 7 + 8 264.1 8 Cr4 ~ 449.10 215.08 Na7+ 8 264.18 Ge4+ 445.71 218.~7 Na7+ 8 264.18 As 4 ~ 450.13 214.05 Na 7 + 8 264.1 8 Br4 ~ 447.30 216.88 Na 7 + 8 264.18 Sr3 + 343.60 220.58 Na 7 + 8 264.1 8 Mo 4 + 446.40 217.78 Na7+ 8 264.18 Sb4+ 444.20 219.98 Na 7 + 8 264.18 La 4 ~ 449.95 214.23 : , WO 90/13126 PCr/US90/01998 8 3 2 Q ~

Na7+ 8 264.18 Gd4+ 4 44.00 220.18 Na7+ 8 264.18 Yb4+ 4 43.70 220.48 Na7+ 8 264.18 Lu4+ 4 45.19 218.99 Na7+ 8 264.18 Bi4+ 4 45.30 218.88 Mg6+ 7 224.94 Mg1~ 17.65 217.29 S 7 + 8 328.23 Mg4 t- 4109.24 218.99 Mg6+ 7 224.94 Mg1~ 17.65 217.29 Mg6+ 7 224.94 Al1+ 15.99 218.95 Mg6+ 7 224.94 Si1+ 18.15 216.79 Mg6+ 7 224.94 P1+ 110.49 214.45 Mg6+ 7 224.94 S1+ 110.36 214.58 Mg6+ 7 224.94 K1+ 14.34 220.60 Mg6+ 7 224.94 Ca1+ 16.11 218.83 Mg6+ 7 224.94 Scl+ 16.54 218.40 Mg6+ 7 224.94 Til+ 16.82 218.12 Mg6+ 7 224.94 V 1~ 16.74 218.20 Mg6+ 7 224.94 Cr1+ 16.77 218.17 Mg6+ 7 224.94 Mnl+ 17.43 217.51 Mg6+ 7 224.94 Fel+ 17.87 217.07 Mg6+ 7 224.94 Co1+ 17.86 217.08 Mg6+ 7 224.94 Ni1+ 17.64 217.31 Mg6+ 7 224.94 Cu1+ 17.73 217.21 Mg6+ 7 224.94 Zn1+ 19.39 215.55 Mg6+ 7 224.94 Ga1+ 16.00 218.94 Mg6+ 7 224.94 Ge1+ 17.90 217.04 Mg6+ 7 224.94 Asl+ 19.81 215.13 Mg6+ 7 224.94 Se1+ 19.75 215.19 Mg6+ 7 224.94 Rb1+ 14.18 220.76 Mg6+ 7 224.94 Sr1+ 15.70 219.24 Mg6+ 7 224.94 ~ 16,38 218.56 Mg6+ 7 224.94 Zr1+ 16.84 218.10 Mg6+ 7 224.94 Nb1+ 16.88 218.06 Mg6+ 7 224.94 Mo1+ 17.1~ 217.84 Mg6+ 7 224.94 Tc1+ 17.28 217.66 Mg6+ 7 224.94 Ru1+ 17.37 217.57 Mg6+ 7 224.94 Rh1+ 17.46 217.48 WO go/13126 P~/VS90/01998 ~8S~ 84 Mg 6 + 7 224.94Pd 1 ~ 18.34 216.60 Mg6+ 7 ~24.94Ag 1 + 17.58 217.36 Mg 6+ 7 224.94Cd 1 + 18.9g 215.95 Mg6+ 7 224.94In 1 -~ 15.79 219.15 5Mg6+ 7 224.94Sn 1 + 17.34 217.60 Mg 6 ~ 7 224.94Sb 1 + 18.64 216.30 Mg 6+ 7 224.94Te ~ + 19.01 215.93 Mg 6 + 7 224.941 1 + 110.45 214.49 Mg 6+ 7 224.94Ba 1 + 15.21 219.73 10Mg 6 + 7 224.94Ba 2 + ~10.00 214.94 Mg 6+ 7 224.94La 1 + 15.58 ~19.36 - Mg 6+ 7 224.94Ce 1 + 15.47 219.47 Mg 6 + 7 224.94Ce 2 + 210.85 214.09 Mg6+ 7 224.94Pr1 + 15.42 219.52 15Mg 6 + 7 224.94Pr 2 + 210.55 214.39 Mg6+ 7 224.94Nd 1 + 15.49 219.45 Mg 6 + 7 224.94Nd 2 + 210.73 214.21 Mg ~+ ~ 224.94Pm 1 + 15.55 219.39 Mg 6 + 7 224.94Pm 2 + 210.90 214.04 20Mg6+ 7 224.94Sm 1 + 15.63 219.31 Mg 6+ 7 224.94Eu 1 + 15.67 219.27 Mg 6 + 7 224.94Gd 1 + 16.14 218.80 Mg6+ 7 224.94Tb 1 ~ 15.85 219.09 Mg 6+ 7 224.94Dy 1 + 15.93 219.01 25Mg 6+ 7 224.94Ho l ~ 16.02 218.92 Mg6+ 7 224.94Er1 + 16.10 218.84 Mg 6+ 7 224.94Tm 1 + 16.18 218.76 Mg6+ 7 224.94Yb 1 + 16.25 218.69 -- Mg 6 + 7 224.94Lu 1 + 15.43 219.51 30Mg6+ 7 224.94Hf 1 + 16.60 218.34 Mg 6 + 7 224.94Ta 1 + 17.89 217.05 Mg 6+ 7 224.94W 1 + 17.98 216.96 Mg6 + 7 224.94R~ 1 + 17~88 217.06 Mg 6~ 7 224.94Os 1 ~ 18.70 216.24 35M~ 6+ 7 224.94Ir 1 + 19.10 215.84 Mg 6 + 7 224.94- Pt 1 ~ 19.00 215.94 WO 90/13126 P~/US90/01998 2a~l~$~

Mg 6+ 7 224.94 Au 1 + 19.23 215.71 Mg6+ 7 224.94 Hg1 + 110.44 214.50 Mg6+ 7 224.94 Tl 1 + 16.11 218.83 Mg 6+ 7 224.94 Pb 1 + 17.42 217.52 5Mg6+ 7 224.94 Bi 1 + 17.29 217.65 Mg 6 + 7 224.94 Po 1 + 18.42 216.52 Mg6+ 7 224.94 Rn1+ 110.75 214.19 Mg 6 + 7 224.94 Ra 1 + 15.28 219.66 Mg 6 + 7 224.94 Ra 2 + 210.15 214.79 10Mg 6 + 7 224.94 Ac 1 + 15.20 219.74 Mg 6+ 7 224.94 Th 1 + 16.10 218.84 Mg 6+ 7 224.94 Pa 1 + 15.90 219.04 Mg 6 + 7 224.94 U 1 + 16.05 218.89 Mg 6+ 7 224.94 Np 1 + 16.20 218.74 15Mg 6 + 7 224.94 Pu 1 + 16.06 218.88 Mg 6 + 7 224.94 Am 1 + 15.99 218.95 Mg6+ 7 224.94 Cm 1 + 16.02 218.92 Mg 6~ 7 224.94 Bk 1 + 16.23 218.71 M9 6+ 7 2?4.94 Cf 1 + 16.30 218.64 20Mg6+ 7 224.94 Es1 + 16.42 218.52 Mg7+ 8 265.90 Si 4 + 445.14 220.76 Mg 7 + 8 265.90 P 4 ~ 451.37 214.53 Mg 7 + 8 265.90 S 4 + 447.30 218.60 Mg 7 + 8 265.90 K 3 + 345.72 220.18 25Mg 7 + 8 265.90 Ca 3 + 350.91 214.99 Mg 7 + 8 265.90 V 4 + 446.71 219.19 Mg 7 + 8 265.90 Cr 4 + 449.10 216.80 Mg 7 ~ 8 265.90 Mn 4 ~ 451.20 214.70 Mg 7 + 8 265.90 Co 4 + 451.30 214.60 30Mg 7 + 8 265.90 Ge 4 + 445.71 220.19 Mg 7 + 8 265.90 As 4 + 450.13 215.77 Mg 7 + 8 265.90 Br 4 + 447.30 218.60 Mg 7 + 8 265.90 Nb 5 + 550.55 215.35 Mg 7 + 8 265.90 Mo 4 + 446.40 219.50 35Mg 7 + 8 265.90 La 4 ~ 449.95 215.95 Mg 7 + 8 265.90 Lu 4 ~ 445.19 220.71 WO 90/13126 P~/USgO/01998 20~69~

Mg 7+ 8 265.90 Bi 4 ~ 445.30 220.60 P 5+ 6 220.43 Al l + 15.99 214.44 Si 6 + 7 246.52 Al 3 ~- 328.45 218.07 Al 6 + 7 241.43 S 2+ 223.33 218.10 Al 6 + 7 241.43 Cl 2 t 223.81 217.62 Al 6 + 7 241.43 Sc 3 + 324.76 216.67 Al 6 + 7 241.43 Ga2~ 220.51 220.92 Al 6 + 7 241.43 Se 2+ 221.19 220.24 Al 6 + 7 241.43 Br 2 + 221.80 219.63 Al 6 + 7 241.43 Kr 2 + 224.36 217.07 Al 6 + 7 241.43 Rb 2 + 227.28 214.15 Al 6 + 7 241.43 Y 3 + 320.52 220.91 Al 6 + 7 241.43 Zr 3 + 322.99 218.44 Al 6 + 7 241.43 Nb3 + 325.04 216.39 Al 6 + 7 241.43 Mo 3+ 327.16 214.27 Al 6 + 7 241.43 A3 2 + 221.49 219.94 Ai 6 + 7 241.43 Sb 3 + 325.30 216.13 Al 6 + 7 241.43 Xe2+ 221.21 220.22 Al 6 + 7 241.43 Cs 2+ 225.10 216.33 20 . Al 6 + 7 241.43 Pr 3 + 321.62 219.81 Al 6 + 7 241.43 Nd3+ 322.10 219.33 Al 6 + 7 241.43 Pm 3 + 322.30 219.13 Al 6 + 7 241.43 Sm 3 + 323.40 218.03 Al 6 + 7 241.43 Eu 3 ~ 324.90 216.53 Al 6 + 7 241.43 Gd3+ 320.63 220.80 Al 6 + 7 241.43 Tb 3 + 321.91 219.52 Al 6 + 7 24i .43 Dy 3 + 322.80 218.63 Al 6 + 7 241.43 Ho 3 + 322.84 218.59 Al 6 + 7 241.43 Er 3 + 322.74 218.69 Al 6 + 7 241.43 Tm 3 ~ 323.68 217.75 Al 6 + 7 241.43 Yb3+ 325.03 216.40 Al 6 + 7 241.43 Lu 3 + 320.96 220.47 ~16 ~ 7 241.43' Hf 3 + 323.3b 218.13 Al 6 + 7 241.43 Au 2 + 220.50 220.93 Al 6 + 7 241.43 Bi 3 ~ 325.56 215.87 Al 7 + 8 284.59 P 5 + 565.02 219.57 WO 90/1312~ PCT/US90/01998 87 ~ r~ ~J

Al 7 + 8 284.59 Cl 5 t 5 67.80 216.79 Al 7 + 8 284.59 Ca4-~ 4 67.10 217.49 Al 7 + 8 284.59 V 5 t- 5 65.23 219.36 Al 7 ~ 8 284.59 Cr 5 ~- ~ 69.30 215.29 Al 7 + 8 2~4.59 ~a4-~ 4 64.00 220.59 Al 7 + 8 284.59 As 5-~ 5 63.63 220.96 Al 7 + 8 284.59 Se 5-~ 5 68.30 216.29 Al 7 + 8 284.59 Kr 5 + 5 64.70 219.89 Al 7 + 8 284.59 Mo 6+ 6 68.00 216.59 Al 7 + 8 284.59 Pb 5 + 5 68.80 215.79 P 6+ 7 263.22 Si 4 + 4 45.14 218.08 Si 6 + 7 246.52 P 3 + 3 30.18 216.34 Si 6 + 7 246.52 Ar 2 + 2 27.63 218.89 Si 6 + 7 246.52 K 2 + 2 31.63 214.90 Si 6 + 7 246.5~ Ti 3 + 3 27.49 219.03 Si 6 + 7 246.52 V 3 + 3 29.31 217.21 Si 6 + 7 246.52 Cr 3 + 3 30.96 215.56 Si 6 + 7 246.52 Fe 3 + 3 30.65 215.87 Si 6 + 7 2~6.52 Ga 3 + ` 3 30.71 215.81 Si 6 + 7 246.52 As 3 + 3 28.35 218.17 Si 6 + 7 246.52 Se 3 + 3 30.82 215.70 Si 6 + 7 246.52 Rb 2 + 2 27.28 219.24 Si 6 + 7 246.52 Mo 3 + 3 27.16 219.36 Si 6 + 7 246.52 Tc 3 + 3 29.54 216.98 Si 6 + 7 246.52 Ru 3 + 3 28.47 218.05 Si 6 + 7 246.52 Rh 3 ~ 3 31.06 215.46 Si 6 + 7 246.52 In 3 + 3 28.03 218.4g Si 6 + 7 246.52 Sn 3+ 3 30.50 216.02 Si 6 + 7 246.52 Te 3 + 3 27.96 218.56 Si 6 + 7 246.~2 Xe3+ 3 32.10 214.~2 Si 6 + 7 246.52 Tl 3 + 3 29.83 216.69 Si 6 + 7 246.52 Pb 3 + 3 31.94 214.58 Si 6 + 7 ?46.52 Bi 3 + 3 25.56 220.96 Si 7 + 8 303.17 S 6 + 6 88.05 215.12 Si 7 + 8 303.17 K 5 + 5 82.66 220.51 Si 7 + 8 303.17 Ca5+ 5 84.41 218.76 WO 90/13126 PCr/US90/01998 2 ~
Si 7 ~ 8 303.17 Zn 5 + 5 82.60 220.57 Si 7 + 8 303.17 Br 6 + 6 88.60 214.57 Si 7 + 8 303.17 Rb 6 + 6 84.40 218.77 Si 7 + 8 303.17 Bi 6 ~ 6 88.30 214.87 S 6+ 7 280.93 P 5 ~ 565.02 215.91 P 5 + 6 220.43 K 1 -~ 14.34 216.09 P 5 + 6 220.43 Ca 1 + 16.11 214.32 P 5 + 6 220.43 Ga 1 + 16.00 214.43 P 5 ~ 6 220.43 Rb 1 + 14.18 216.25 P 5 + 6 220.43 Sr 1 + 15.70 214.73 P 5+ 6 220.43 Y 1 ~ 16.38 214.05 P 5+ 6 220.43 In 1 + 15.79 214.64 P 5 + 6 220.43 Cs 1 + 13.89 216.54 P 5~ 6 220.43 Ba 1 + 15.21 215.22 P 5 + 6 220.43 La 1 + 15.58 214.85 P 5~ 6 220.43 Ce 1 ~ 15.47 214.96 P 5+ 6 220.43 Pr 1 + 15.42 215.01 P 5 + 6 220.43 Nd 1 + 1 5.49 214.94 P 5+ 6 220.43 Pm t + 15.55 214.88 P 5+ 6 220.43 Sm 1 + 15.63 214.80 P 5 + 6 220.43 Eu 1 + 1 5.67 214.76 P 5 + 6 220.43 Gd 1 + 1 6.14 214.29 P 5 + 6 220.43 Tb 1 + i 5.85 214.58 P 5 + 6 220.43 Dy 1 + 1 5.93 214.50 P 5 + 6 220.43 Ho 1 + 1 6.02 214.41 P 5+ 6 220.43 Er 1 ~ 1 6.10 214.33 P 5+ 6 220.43 Tm 1 ~ 16.18 214.25 P 5+ 6 220.43 Yb 1 + 1 6.25 214.18 P 5+ 6 220.43 Lu 1 ~ 1 5.43 215.00 P 5+ 6 220.43 Tl 1 + 1 6.11 214.32 P 5+ 5 220.43 Ra 1 + 1 5.28 215.15 P 5 + 6 220.43 Ac l + 1 5.20 215.23 P 5+ 6 220.43 Th 1 + 1 6.10 214.33 P ~ + 6 220.43 Pa 1 ~ 1 5.90 214.53 P 5+ 6 220.43 U 1 + 16.05 214.38 P 5 + 6 220.43 Np l + 1 6.20 214.23 WO ~0/13~6 PCI'/US90/01998 8 9 2 ~
. . , ` .

P 5 + 6 220.43 Pu 1 + 16.06 214.37 P 5+ 6 220.43 Am 1 ~ 15.99 214.44 P 5+ 6 220.43 Cm 1 ~ 16.02 214.41 P 5 + 6 220.43 Bk 1 + 16.23 214.Z0 P 5+ 6 220.43 Cf 1 + 16.30 214.13 P 5+ 6 220.43 Es1 + 16.42 214.01 P 6 + 7 263.22 S 4 ~ 447.30 215.92 P 6 + 7 263.22 K 3 + 345.72 217.50 P 6+ 7 263.22 Ti 4 + 443.27 219.95 P 6 + 7 263.22 V 4 + 446.71 216.51 P 6 + 7 263.22 Cr 4 + 449.10 214.12 P 6 + 7 263.22 Ge 4 + 445.71 217.51 P 6 + 7 263.22 Se 4 + 442.94 220.28 P 6 + 7 263.22 Br 4 + 447.30 215.92 P 6 + 7 263.22 Sr 3 + 343.60 219.62 P 6 + 7 263.22 Mo 4 + 446.40 216.82 P 6 + 7 263.22 Sb 4 + 444.20 219.02 P 6 + 7 263.22 Eu4+ 442.60 220.62 P 6 + 7 263.22 Gd 4 ~ 444.00 219.22 P 6 + 7 Z63.22 Ho 4 + 442.50 220.72 P 6 + 7 263.22 Er 4 + 442.60 220.62 P 6~ 7 263.22 Tm 4 + 442.70 220.52 P 6 + 7 263.22 Yb 4 + 443.70 219.52 P 6 + 7 263.22 Lu 4 + 445.19 218.03 P 6 + 7 263.22 Pb 4 + 442.32 220.90 P 6 + 7 263.22 Bi 4 + 445.30 217.92 P 7 + 8 309.41 Ar 6 + 691.01 218.40 P 7 ~ 8 309.41 Sc 5 + 591.66 217.75 P 7 + 8 309.41 Cr 6 + 690.56 218.85 P 7 + 8 309.41 Mn 6 + 695.00 214.41 P 7 + 8 309.41 Ge 5 ~ 593.50 215.91 P 7+ 8 309.41 Br 6 ~ 688.60 220.81 P 7 + 8 309.41 Sr 6 ~ 690.80 218.61 P 7 + 8 309.41 Y 6 + 693.00 216.41 S 6 + 7 280.93 K 4 + 460.91 220.02 S 6 + 7 280.93 V 5 + 565.23 215.70 WO 90/13126 PCI'/US90/01998 2 ~ 9 ~ g o S 6 + 7 280.93 Ga 4 + 464,00 216.93 S 6 + 7 280.93 As 5 + 563.63 217.30 S 6 + 7 280.93 Kr 5 + 564.70 216.23 S 6+ 7 280.93 Y 4+ 461.80 219.13 S 6 + 7 280.93 Mo 5 + 561.20 219.73 S 7 + 8 328.23 Cl 7 + 7114.19 214.04 S 7 + 8 328.23 Ca 6 + 6108.78 219.45 S 7 + 8 328.23 Sc 6 + 6111.10 217.13 S 7 + 8 328.23 Ni 6 + 6108.00 220.23 S 7 + 8 328.23 Zn 6 + 6108.00 220.23 S 7 + 8 328.23 Kr 7 + 7111.00 217.23 S 7 + 8 328.23 Sb 6 + 6108.00 220.23 Cl 7 ~ 8 348.28 Ca 7 + 7127.70 220.58 Cl 7 + 8 348.28 V 6 + 6128.12 220.16 C17 + 8 348.28 Co7+ 7129.00 219.28 Cl 7 ~ 8 343.28 Ni 7 + 7133.00 215.28 Cl 7 + 8 348.28 Zn 7 + 7134.00 214.28 Cl 7 + 8 348.28 As 6 + 6127.60 220.68 Cl 7 + 8 348.28 Y 8 + 8129.00 219.28 20 n = 54 (resonance shrinkage energy is given by 2 27.21 eV; with n = 54, the resonance shrinkage energy is 734.67) Atom n nth lon- Atom nnth lon- Energy Oxidiz- ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) O 6+ 7 739.32 Li 1 + 15.39 733.92 F 7 + 8 953.89 Be 4 + 4217.71 736.17 O 6+ 7 739.32 B 1 + 18.30 731.02 0 7+ 8871.39 0.6+ 6138.12 733.27 O 6+ 7 739.32 Na l + 15.14 734.18 0 6+ 7739.32 Mg 1 + 17.65 731.67 O 6+ 7739.32 Al 1 + 15.99 733.33 O 6+ 7739.32 Si 1 + 18.15 731.16 O 6+ 7739.32 K 1 ~ 14.34 734.97 0 6+ i739.32 Ca 1 + 16.11 733.20 WO 90/13126 PCl-/US90/01998 2 ~

O 6+ 7 739.32 Sc l + 1 6.54 732.78 O 6+ 7 739.32 Ti 1 ~ 1 6.82 732.49 O 6+ 7 739.32 V 1 + 1 6.74 732.58 O 6+ 7 739.32 Cr 1 ~ 1 6.77 732.55 5O 6+ 7 739.32 Mn 1 + 1 7.43 731.88 O 6+ 7 739.32 Fe 1 + 1 7.87 731.45 O 6 + 7 739.32 Co 1 + 1 7.86 731.46 O 6+ 7 739.32 Ni 1 + 1 7.64 731.68 O 6~ 7 739.32 Cu 1 + 1 7.73 731.59 10O 6+ 7 739.32 Ga1 + 1 6.00 733.32 O 6+ 7 739.32 Ge 1 + 1 7.90 731.42 O 6+ 7 739.32 Rb 1 + 1 4.18 735.14 O 6+ 7 739.32 Sr 1 + 1 5.70 733.62 O 6+ 7 739.32 Y 1 ~ 1 6.38 732.93 15O 6+ 7 739.32 Zr 1 + 1 6.84 732.47 O 6+ 7 739.32 Nb 1 + 1 6.88 732.43 O 6+ 7 739.32 Mo 1 + 1 7.10 732.22 O 6+ 7 739.32 Tc 1 + 1 7.28 732.03 O 6~ 7 739.32 Ru 1 ~ 1 7.37 731.95 20O 6+ 7 739.32 Rh 1 + 1 7.46 731.85 O 6+ 7 739.32 Pd 1 + 1 8.34 730.97 O 6+ 7 739.32 Ag 1 + 1 7.58 731.74 O 8 + 7 739.32 Cd 1 + 1 8.99 730.32 O 6+ 7 739.32 In 1 + 1 5.79 733.53 25O 6+ 7 739.32 Sn 1 + 1 7.34 731.97 O 6 + 7 739.32 Sb 1 + 1 8.64 730.67 O 6~ 7 739.32 Te 1 + 1 9.01 730.31 O 6 + 7 739.32 Cs 1 + 1 3.89 735.42 O 6+ 7 739;32 Ba 1 + 1 5.21 734.10 30O 6+ 7 739.32 La 1 + 1 5.58 733.74 O 6 + 7 739.32 Ce 1 + 1 5.47 733.85 O 6+ 7 739.32 Pr 1 ~ 1 5.42 733.89 O 6+ 7 739.32 Nd 1 ~ 1 5.49 733.83 O 6+ 7 739.32 Pm 1 ~ 1 5.55 733.76 35O 6~ 7 739.32 Sm 1 ~ 1 5.63 733.68 O 6 + 7 739.32 Eu l ~ 1 5.67 733.65 w~ so/13126 PCT/uS9o/01998 2 Q ~ 92 O 6+ 7 739.32 Gd 1 -~ 1 6.14 733.17 O 6+ 7 739.32 Tb 1 -~ 1 5.85 733.47 O 6+ 7 739.32 Dy 1 -~ 1 5.93 733.39 O 6 + 7 739.32 Ho 1 -~ 1 6.02 733.29 O 6+ 7 739.32 Er 1 ~ 1 6.10 733.22 O 6+ 7 739.32 Tm 1 + 1 6.18 733.13 V 6~ 7 739.32 Yb 1 + 1 6.25 733.06 O 6+ 7 739.32 Lu 1 + 1 5.43 733.89 O 6+ 7 739.32 Hf 1 + 1 6.60 732.72 l OO 6+ 7 739.32 Ta 1 + 1 7.89 731.42 O 6+ 7 739.32 W 1 + 1 7.98 731.34 O 6+ 7 739.32 Re 1 + 1 7.88 731.43 O 6+ 7 739.32 Os l + 1 8.7~ 730.61 O 6+ 7 739.32 Ir 1 + 1 9.iO 730.22 15 O 6+ 7 739.32 . Pt 1 + 1 9.00 730.32 O 6+ 7 739.32 Au 1 + 1 9.23 730.09 O 6+ 7 739.32 Tl 1 + 1 6.11 733.21 O 6+ 7 739.32 Pb 1 + 1 7.42 731.90 O 6~ 7 739.32 Bi 1 + 1 7.29 732.03 20 O 6+ 7 739.32 Po 1 + 1 8.42 730.90 O 6+ 7 739.32 Ra1 + 1 5.28 734.04 O 6+ 7 739.32 Ac 1 + 1 5.20 734.11 O 6+ 7 739.32 Th 1 + 1 6.10 733.22 O 6 + 7 739.32 Pa 1 + 1 5.90 733.41 25 - O 6+ 7 739.32 U 1 + 16.05 733.27 O 6+ 7 739.32 Np 1 + 16.20 733.11 O 6+ 7 739.32 Pu 1 + 16.06 733.26 O 6+ 7 73g.32 Am 1 + 15.99 733.33 O 6 + 7 739.32 Cm 1 + 16.02 733.29 30- O 6+ 7 739.32 Bk 1 + 16.23 733.0g O 6+ 7 739.32 Cf 1 + 16.30 733.02 O 6 + 7 739.32 Es 1 ~ 16.42 732.gO
O 7+ 8 871.39 O 6+ 6138.12 733.27 O 7+ 8 871.39 Na5+ 5138.39 733.00 O 7+ 8 871.39 Mg 5+ 5141.26 730.13 O 7+ 8 871.39 Sc 7 + 7138.00 733.39 2 ~

O 7+ 8871.39 Ti 7 ~ 7140.80 730.59 O 7 + 8871.39 Cu 7 + 7139.00 732.39 O 7+ 8871.39 Zn7~ 7134.00 737.39 O 7 + 887t .39 Rb 8 + 8136.00 735.39 O 7+ 8871.39 Te7+ 7137.00 734.39 F 7 + 8953.89 P 6 + 6220.43 733.46 Two-ion couples capable of producing energy holes for shrinking deuterium atoms involving cations and anions. The number in the column following the ion, (n), is the nth ionization energy of ~he atom. For 10 example, Ga2+ + 30.71 eV = Ga3+ ~ e- and H ~ e- - H- + 3.08 eV.
Ato m nnth lon- Ato m n nth lon- Energy Oxidiz- ization Reduced ization Hole ed Energy Energy (eV) (eV~ (eV) 1 5 As 2 + 3 28.35 H - 10.80 27.55 Ru 2+ 3 28.47 H - 10.80 27.67 In 2 + 3 28.03 H - 10.80 27.23 Te2+ 3 27.96 H -10.80 27.16 Al 2 + 3 28.45 H - 10.80 27.65 Ar 1 + 2 27.63 H - 10.80 26.83 As 2 + 3 28.35 Li - 10.61 27.74 Ru 2 + 3 28.47 Li - 10.61 27.86 In 2 + 3 28.03 Li - 10.61 27.42 Te 2 ~ 3 27.96 Li - 10.61 27.35 Al 2 ~ 3 28.45 Li - 10.61 27.84 Ar 1 + 2 27.63 Li - 10.61 27.02 Ti 2 + 3 27.49 Li - 10.61 26.88 As 2 + 3 28.35 B - 10.30 28.05 Rb 1 + 2 27.28 B - 10.30 26.98 Mo2+ 3 27.16 B -1 0.30 26.86 Ru 2 + 3 28.47 B - 1 0.30 28.17 In 2 + 3 28.03 B - 1 0.30 27.73 Te2 + 327.96 B - 1 0.30 27.66 Al 2 ~ 328.45 B - 1 û.30 28.15 Ar 1 ~ 227.63 B - 1 0.30 27.33 Ti 2 ~ 327.49 B - 1 0.30 27.19 ` .2~S ~
9~

As 2 ~ 3 28.35 C - 1 1.12 27.23 Tc 2 + 3 29.54 C - 1 1.12 28.42 Ru 2 + 3 28.47 C - 1 1.12 27.35 In 2 + 3 28.03 C - 1 1.12 26.91 Te 2 + 3 27.96 C - 1 1.12 26.84 N 1 + 2 29.60 C - 1 1.12 28.48 AI 2 + 3 28.45 C - 1 1.12 27.33 V 2 + 3 29.31 C - 1 1.12 28.19 As 2 + 3 28.35 O - 1 1.47 26.89 Tc 2 + 3 29.54 O - 1 1.47 28.07-Ru 2+ 3 28.47 O - 1 1.47 27.00 TI 2 + 3 29.83 O - 1 1.47 28.36 N 1 + 2 29.60 O - 1 1.47 28.14 AI 2 + 3 28.45 O - 1 1.47 26.98 V 2 + 3 29.31 O - 1 1.47 27.84 Ga 2 + 3 30.71 F - 1 3.~5 27.26 Se2 + 3 30.82 F - 1 3.45 27.37 Rh 2 + 3 31.06 F - 1 3.45 27.61 Sn 2+ 3 30.50 F - 1 3.45 27.05 Pb 2 + 3 31.94 F - 1 3.45 28.49 K 1+ 2 31.63 F -1 3.45 28.18 Cr 2 + -3 30.96 F - 1 3.45 27.51 Fe2 3 30.65 F - 1 3.45 27.20 As 2 + 3 28.35 Na - 1 0.52 27.83 Ru 2 + 3 28.47 Na - 1 0.52 27.95 In 2 ~ 3 28.03 Na - 1 0.52 27.51 Te 2 + 3 27.96 Na - 1 0.52 27.44 AI 2 + 3 28.45 Na - 1 0.52 27.93 Ar 1 + 2 27.63 Na - 1 0.52 27.11 Ti 2 + 3 27.49 Na - 1 0.52 26.97 As 2 + 3 28.35 AI ~ 1 0.52 27.83 Ru 2+ 3 28.47 AI - 1 0.52 27.95 ln 2 + 3 28;03 AI -1 0.52 27.51 Te 2 + 3 27.96 A I - 1 0.52 27.44 AI 2 + 3 28.45 AI - 1 0.52 27.93 Ar 1 ~ 2 27.63 AI - 1 0.52 27.11 WO 90tl3126 PCr/lJS90/01998 2~3~7 Ti 2 ~ 3 27.49 Al - 1 0.52 26.97 As 2 + 3 28.35 Si - 1 1.39 26.96 Tc 2 + 3 29.54 Si - 1 1.39 28.15 Ru 2 + 3 28.47 Si - 1 1.39 27.08 Tl 2 + 3 29.83 Si - 1 1.39 28.44 N 1 + 2 29.60 Si - 1 1.39 28.21 Al 2 + 3 28.45 Si - 1 1.39 27.06 V 2 + 3 29.31 Si - l 1.39 27.92 As 2 + 3 28.35 P - 1 0.78 27.57 Ru 2 + 3 28.47 p - 1 0.78 27.69 In 2 + 3 28.03 P - 1 0.78 27.25 Te 2 + 3 27.96 P - 1 0.78 27.18 Al 2 + 3 28.45 P - 1 0.78 27.67 Ar 1 + 2 27.63 P - 1 0.78 26.85 Tc 2 + 3 29.54 S - 1 2.07 27.47 Sn 2 + 3 30.50 S - 1 2.07 28.43 T12 + 3 29.83 S - 1 2.07 27.76 N 1 + 2 29.60 S - 1 2.07 27.53 P 2 + 3 30.18 S - 1 2.07 28.11 V 2 + 3 29.31 S - 1 2.07 27.24 Ga2+ 3 30.71 Cl - 1 3.61 27.10 Se 2 + 3 30.82 Cl - 1 3.61 27.21 Rh 2+ 3 31.06 Cl - 1 3.61 27.45 Sn 2 ~ 3 30.50 Cl - 1 3.61 26.89 Xe2+ 3 32.10 Cl - 1 3.61 28.49 Pb 2 + 3 31.94 Cl - 1 3.61 28.32 K 1 ~ 2 31.63 Cl - 1 3.61 28.01 Cr 2 + 3 30.96 Cl - 1 3.61 27.35 Fe 2 + 3 30.65 Cl - 1 3.61 27.04 A~ 2 + 3 2B.35 ~ - 1 0.69 27.66 Ru 2+ 3 28.47 K - 1 0.69 27.78 In 2 + 3 28.03 K - 1 0.69 27.3~
Te2+ 3 27.96 K - 1 0.69 27.27 Al 2 + 3 28.45 K - 1 0.69 27.75 Ar 1 + 2 27.63 K - 1 Q69 26.93 As 2 + 3 28.35 Fe - 1 0.56 27.79 WO 90/13126 PCl-tUS90/01998 ' 6 2 ~ 3 ~J ~

Ru 2 + 3 28.47 Fe - 1 0.56 27.91 In 2 + 3 28.03 Fe - 1 0.~6 27.47 Te 2 + 3 27.96 Fe - 1 0.56 27.40 Al 2 + 3 28.45 Fe - 1 0.56 27.89 Ar 1 + 2 27.63 Fe - 1 0.56 27.07 Ti 2 + 3 27.49 Fe - 1 0.56 26.93 As 2 + 3 28.35 Co - 1 0.95 27.40 Ru 2 + 3 28.47 Co - 1 0.95 27.52 In 2 + 3 28.03 Co - 1 0.95 27.08 Te 2 + 3 27.96 Co - 1 0.95 27.01 Al 2 + 3 28.45 Co - 1 0.95 27.49 V 2 + 3 29.31 Co - 1 0.95 28.36 Tc 2 + 3 29.54 Cu - 1 1.82 27.72 Tl 2 + 3 29.83 Cu - 1 1.82 28.01 N 1 + 2 29.60 Cu - 1 1.82 27.78 P 2 + 3 30.18 Cu - 1 1.82 28.36 V 2 ~ 3 29.31 Cu - 1 1.82 27.49 Ga 2 + 3 30.71 Br - 1 3.36 27.35 Se 2 + 3 30.82 Br - 1 3.36 27.46 Rh 2 + 3 31.06 Br - 1 3.36 27.70 Sn 2 + 3 30.50 Br - 1 3.36 27.14 P 2 + 3 30.18 Br - 1 3.36 26.82 K 1 + 2 31.63 Br - 1 3.36 28.26 Cr 2 + 3 30.96 Br - 1 3.36 27.60 Fe 2 + 3 30.6~ Br - 1 3.36 27.29 As 2 + 3 28.35 Rb - 1 0.30 28.05 Rb 1 ~ 2 27.28 Rb - 1 0.30 26.98 Mo 2 + 3 27.16 Rb - 1 0.30 26.86 Ru 2 + 3 28.47 Rb - 1 0.30 28.17 In 2 + 3 28.03 Rb - 1 0.30 27.73 Te 2 + 3 27.96 Rb - 1 0.30 27.66 Al 2 + 3 28.45 Rb - 1 0.30 28.15 Ar 1 ~ 2 27.63 Rb - 1 0.30 27.33 Ti 2 + 3 27.49 Rb - 1 0.30 27.19 Ga 2 + 3 30.71 1 - 1 3.06 27.65 Se2+ 3 30.82 I - 1 3.06 27.76 WO 90/13126 PCr/US90/01~98 9 7 2 ~ ~ f.~ 3 Rh 2 + 3 31.06 1 - 1 3.06 28.00 Sn 2 + 3 30.50 I - 1 3.06 27.44 P 2 + 3 30.18 1 - 1 3.0627.12 Cr2 + 3 30.96 1 - 1 3.0627.90 Fe 2+ 3 30.65 1 - 1 3.0627.59 As 2 + 3 28.35 Cs - 1 0.30 28.05 Rb 1 + 2 27.28 Cs - 1 0.30 26.98 Mo 2 + 3 27.16 Cs - 1 0.30 26.86 Ru 2 + 3 28.47 Cs - 1 0.30 28.17 In 2 + 3 28.03 Cs 1 0.30 27.73 Te 2 + 3 27.96 Cs - 1 0.30 27.66 Al 2 + 3 28.45 Cs - 1 0.30 28.15 Ar 1 + 2 27.63 Cs - 1 0.30 27.33 Ti 2 + 3 27.49 Cs - 1 0.30 27.19 Tc 2 + 3 29.54 Se - 1 1.70 27.84 Tl 2 + 3 29.83 Se - 1 1.70 28.13 N 1 + 2 29.60 Se- 1 1.7027.90 P 2 + 3 30.18 Se- 1 1.7028.48 V 2 + 3 29.31 Se- 1 1.7027.61 Tc 2 + 3 29.54 Te - 1 2.20 27.34 Sn2+ 3 30.50 Te- 1 2.2028.30 Tl 2 + 3 29.83 Te - 1 2.20 27.63 N 1 + 2 29.60 Te- 1 2.2027.40 P 2 + 3 30.18 Te- 1 2.2027.98 V 2 + 3 29.31 Te- 1 2.2027.11 Fe 2+ 3 30.65 Te- 1 2.2028.45 As 2 + 3 28.35 As- 1 0.60 27.75 Ru 2+ 3 28.47 As- 1 0.60 27.87 In 2 + 3 28.03 As- 1 0.60 27.43 Te 2 ~ 3 27.96 As- 1 0.60 27.36 Al 2 + 3 28.45 A~- 1 0.60 27.85 Ar 1 + 2 27.63 As- 1 0.60 27.03 Ti 2 + 3 27.49 As - 1 0.60 26.89 Tc 2 ~ 3 29.54 Sb - 1 2.00 27.54 Tl 2 + 3 29.83 Sb - 1 2.00 27.83 N 1 + 2 29.60 Sb -1 2.00 27.60 , . . .
, 2 ~ 7 9 8 P 2 + 3 30.18 Sb - 1 2.00 28.18 V 2 + 3 29.31 Sb - 1 2.00 27.31 As 2 ~ 3 23.35 Bi - 1 0.70 27.65 Ru 2 + 3 28.47 Bi - 1 0.70 27.77 In 2 + 3 28.03 Bi - 1 0.70 27.33 Te 2 + 3 27.96 Bi - 1 0.70 27.26 Al 2 + 3 28.45 Bi - 1 0.70 27.75 Ar 1 + 2 27.63 Bi - 1 0.70 26.93 Tc 2 + 3 29.54 Tl - 1 2.10 27.44 l O Sn 2 + 3 30.50 Tl - 1 2.10 28.40 Tl 2 + 3 29.83 Tl - l 2.10 27.73 N 1 + 2 29.60 Tl - 1 2.10 27.50 P 2 + 3 30.18 Tl - 1 2.10 28.08 V 2+ 3 29.31 Tl - I 2.10 27.21 Tc 2 + 3 29.54 Au - 1 2.10 27.44 Sn 2 + 3 30.50 Au - 1 2.10 28.40 Tl 2 + 3 29.83 Au - 1 2.10 27.73 N 1 + 2 29.60 Au - 1 2.10 27.50 P 2 + 3 30.18 Au - 1 2.10 28.08 V 2 + 3 29.31 Au - 1 2.10 27.21 As 2 + 3 28.35 Hb - 1 1.54 26.81 Tc 2 + 3 29.54 Hb - 1 1.54 28.00 Ru 2 + 3 28.47 Hg - 1 1.54 26.93 Tl 2 + 3 29.83 Hb - 1 1.54 28.29 N 1 + 2 29.60 Hg - 1 1.54 28.06 Al 2 + 3 ~8.45 Hb - 1 1.54 26.91 V 2 + 3 29.31 Hb - 1 1.54 27.77 As 2 + 3 28.35 As - 1 0.60 27.75 Ru 2+ 3 23.47 As - 1 0.60 27.87 In 2 ~ 3 28.03 As - 1 0.60 27.43 Te 2 + 3 27.96 As - 1 0.60 27.36 Al 2 ~ 3 28.45 As - 1 0.60 27.85 Ar 1 + 2 27.63 As - 1 0.60 27.03 Ti 2 + 3 27.49 As - 1 0.60 26.89 A~- 2 + 3 28.35 Ce - 1 1.20 27.15 Tc 2 + 3 29.54 Ce - 1 1.20 28.34 . .

WO 90/13126 PC~/US90/01998 9 9 2 0 ~ J

Ru 2+ 3 28.47 Ce - 1 1.20 27.27 In 2 + 3 28.03 Ce -1 1.20 26.83 N 1 + 2 29.60 Ce - 1 1.20 28.40 Al 2 + 3 28.45 Ce - 1 1.20 27.25 V 2 ~ 3 29.31 Ce - 1 1.20 28.11 As 2 + 3 28.35 Fr - 1 0.46 27.89 Rb 1 ~ 2 27.28 Fr -1 0.46 26.82 Ru 2 + 3 28.47 Fr - 1 0.46 28.01 In 2 + 3 28.03 Fr - 1 0.46 27.57 Te 2 + 3 27.96 Fr - 1 0.46 27.50 Al 2 + 3 28.45 Fr - 1 0.46 27.99 Ar 1 + 2 27.63 Fr - 1 0.46 27.17 Ti 2 + 3 27.49 Fr - 1 0.46 27.03 As 2 + 3 28.35 Ge - 1 1.20 27.15 Tc 2 + 3 29.54 G~ - 1 1.20 28.34 Ru 2+ 3 28.47 G~ - 1 1.20 27.27 In 2 + 3 28.03 G~ - 1 1.20 26.83 N 1 + 2 29.60 Ge - 1 1.20 28.40 Al 2 + 3 28.45 Ge - 1 1.20 27.25 V 2 + 3 29.31 G~ - 1 1.20 28.11 As 2 + 3 28.35 Sn - 1 1.25 27.10 Tc 2 + 3 29.54 Sn - 1 1.25 28.29 Ru 2+ 3 28.47 Sn - 1 1.25 27.22 N 1 + 2 29.60 Sn - 1 1.25 28.35 Al 2 + 3 28.45 Sn - 1 1.25 27.20 V 2 + 3 29.31 Sn - 1 1.25 28.06 As 2 + 3 28.35 Pb - 1 1.05 27.30 Tc 2 + 3 29.54 Pb - 1 1.05 28.49 Ru 2+ 3 28.47 Pb - l 1.05 27.42 In 2 + 3 28.03 Pb - 1 1.05 26.98 Te 2 + 3 27.96 Pb - 1 1.05 26.91 Al 2 + 3 28.45 Pb - 1 1.0S 27.40 V 2 + 3 29.31 Pb - 1 1.05 28.26 Tc 2 + 3 29.54 Po - 1 1.80 27.74 Tl 2 + 3 29.83 Po ~1 1.80 28.03 N 1 + 2 29.60 Po - 1 1.80 27.80 WO 90/13126 PCI/US90/01~8 : :: 100 2 ~
P 2+ 3 30.18 Po - 1 1.80 28.38 V 2 + 3 29.31 Po - 1 1.80 27.51 Ga2+ 3 30.71 At - 1 ~.80 27.91 Se 2 ~ 3 30.82 At - l 2.80 28.02 Rh 2~ 3 31.06 At - 1 2.80 28.26 Sn 2 + 3 30.50 A t - 1 2.80 27.70 Tl 2 + 3 29.83 At - 1 2.80 27.03 N 1 + 2 29.60 At - 1 2.80 26.80 P 2+ 3 30.18 At -1 2.80 27 38 Cr 2 + 3 30.96 At - 1 2.80 28.16 Fe 2 + 3 30.65 At - 1 2.80 27.85 As 2 ~ 3 28.35 G~ - 1 1.20 27.15 Tc 2 + 3 29.54 G~ - 1 1.20 28.34 Ru 2 + 3 28.47 Ge ~ 1 1.20 27.27 In 2 + 3 28.03 G~ - 1 1.20 26.83 N 1 + 2 29.60 G~ - 1 1.20 28.40 Al 2 + 3 28.45 G~ - 1 1.20 27.25 V 2 + 3 29.31 G~ - 1 1.20 28.11 As 2 + 3 28.3~ Q~ - 1 0.37 27.98 Rb 1 + 2 27.28 Ga - 1 0.37 26.91 Ru 2 + 3 28.47 Ga - 1 0.37 28.10 In 2 ~ 3 28.03 Ga 1 0.37 27.66 Te 2 + 3 27.96 G~ - 1 0.37 27.59 - Al 2 ~ 3 28.45 Ga - 1 0.37 28.08 Ar 1 + 2 27.63 ~a - 1 0.37 27.26 Ti 2 + 3 27.49 G~ - 1 0.37 27.12 As 2 + 3 28.35 In - 1 0.35 28.00 Rb 1 + 2 27.28 In - 1 0.35 26.93 Mo 2 ~ 3 27.16 In - 1 0.35 26.81 Ru 2 + 3 28.~7 I n - 1 0.35 28.12 In 2 + 3 28.03 In - 1 0.35 27.68 Te 2 + 3 27.96 In - 1 0.35 27.61 Al 2 + 3 28.45 In - 1 0.35 28.10 Ar ~ + 2 27.63 In - 1 0.35 27.28 Ti 2 + 3 27.49 In - 1 0.35 27.14 As 2 + 3 28.35 Ag - 1 1.30 27.05 WO 90/13126 P~T/US90/019~8 101 2Q~ J~

Tc 2 + 3 29.54 Ag - 1 1.30 28.24 Ru 2 + 3 28.47 Ag - 1 1.30 27.1 7 N 1 + 2 29.60 Ag - 1 1.30 28.30 Al 2 + 3 28.45 Ag - 1 1.30 27.15 V 2 + 3 29.31 Ag - 1 1.30 28.01 Cations and anions with n - 16 (resonance shrinkage energy is given by 2 27.21; with n = 16, the resonance shrinkage energy is 217.68) Atom nnth lon- Atom n nth lon-Energy Oxidiz- ization Reduced izationHole ed Energy Energy (eV) (eV) (eV) Be 3 + 4217.71 H - 1 0.8021 6.91 Be3+ 4217.71 Li -1 0.61217.10 Be 3 + 4217.71 R - 1 0.30?17 41 1 5 Be 3 + 4217.71 C - 1 1.12216.59 Be 3 + 4217.71 O - 1 1.4721 6.25 P 5 ~ 6220.43 O - 1 1.4721 8.96 P ~ + 6220.43 F r 1 3.45216.98 Be3+ 4217.71 Nb -1 0.52217.19 Be 3 + 4217.71 Al - 1 0.52217.19 Be 3 + 4217.71 Si - 1 1.39216.32 Be 3 + 4217.71 P - 1 0.78216.94 Be 3 + 4217.71 S - 1 2.0721 5.64 P 5 + 6220.43 S - 1 2.07218.36 P~5 + 6220.4~ Cl - 1 3.61216.82 Be 3 + 4217.71 K . - 1 0.6921 7.02 Be 3 + 4217.71 Fe - 1 0.5621 7.1 5 Be 3 + 421 7.71 Co - 1 0.9521 6.76 Be 3 + 4217.71 Cu - 1 1.8221 5.89 P 5 + 6220.43 CU -1 1.8221 8.61 P 5 + 6220.43 E3r -1 3.36217.07 Be 3 + 4217.71 Rb - 1 0.30217.41 P 5 + 6220.43 1 - 1 3.0621 7.37 Be 3 + 4217.71 Cs - 1 0.30217.41 Be 3 ~ 4217.71 Se - 1 1.70216.01 WO 90/13126 PC'r/US90/0199~
2 ~ 9 '~

P 5 + 6 220.43 Se - 11.70 218.73 P 5 ~ 6 220.43 Te - 12.20 218.23 Be 3 + 4 217.71 As - 10.60 217.11 P 5 + 6 220.43 As - 10.60 219.83 5 P 5 + 6 220.43 Sb - 12.00 218.43 Be 3 + 4 217.71 Bi - 10.70 217.01 P 5 ~ 6 220.43 Bi - 10.70 219.73 P 5 + 6 220.43 Tl - 12.10 218.33 - P 5 + 6 220.43 Au - 12.10 218.33 1 0 Be 3 + 4 217.71 Hg - 11.54 216.17 P 5 + 6 220.43 Hg - 11.54 218.39 Be3+ 4 217.71 As -1 0.60 217.11 P 5 + 6 220.43 As - 10.60 219.83 Be 3 + 4 217.71 Ce - 11.20 216.51 1 5 P 5 + 6 220.43 Ce - 11.20 219.23 Be 3 + 4 217.71 Fr - 10.46 217.25 P 5+ 6 220.43 Fr - 10.46 219.97 Be 3 + ~ 217.71 G9 - 11.20 216.51 P 5 + 6 220.43 G~ - 11.20 219.23 Be 3 ~ 4 217.71 Sn - 11.25 216.46 P 5 + 6 220.43 Sn - 11.25 219.18 Be 3 + 4 217.71 Pb - 11.05 216.66 P 5 + 6 220.43 Pb - 11.05 219.38 P 5 + 6 220.43 Po - 11.80 218.63 P 5+ 6 220.43 At - 12.80 217.63 Be 3 + 4 217.71 Ge - 11.20 216.51 P 5 + 6 220.43 Ge - 11.~0 219.23 Be 3 + 4 217.71 (~ - 10.37 217.34 Be 3 ~ 4 217.71 In - 10.35 217.36 Be 3 ~ 4 217.71 Ag - 11.30 216.41 P 5 + 6 220.43 Ag - 11.30 219.13 Cations and anions with n = 54 (resonance shrinkage energy is giYen by 27.21; with n = 54, the resonance shrinkage energy is 734.67) Atom n nth lon- A~om n nth lon- Energy Oxidiz- ization Reduced ization Hole WO 90/13126 PCI/USgO/01998 103 20~9~

ed Energy Energy (eV) (eV) (eV) O 6 + 7739.32 H - 10.80 738.52 O 6 + 7739.32 L i - 10.61 738.70 O 6 + 7739.32 C - 11.12 738.20 O 6+ 7739.32 O - 11.47 737.85 O 6+ 7739.32 F - 13.45 735.87 0 6~ 7739.32 Na - 10.52 738.80 O 6~ 7739.32 Al - 10.52 738.80 O 6+ 7739.32 Si - 11.39 737.93 O 6+ 7739.32 P - 10.78 738.54 O 6+ 7739.32 S - 12.07 737.24 O 6+ 7739.32 Cl - 13.61 735.70 O 6 + 7739.32 K - 10.69 738.62 O 6 + 7739.32 Fe - 10.56 738.76 0 6+ 7739.32 Co - 10.95 738.36 O 6+ 7739.32 Cu - 11.82 737.49 O 6+ 7739.32 Br -13.36 735.95 O 6+ 7739.32 i - 13.06 736.25 O 6 + 7739.32 Se - 11.70 737.61 O 6+ 7739.32 Te - 12.20 737.11 O 6+ 7739.32 As - 10.60 738.72 O 6+ 7739.32 Sb - 12.00 737.32 O 6 ~ 7739.32 Bi - 10.70 738.61 O 6+ 7739.32 Tl - 12.10 737.22 O 6+ 7739.32 Au - 12.10 737.22 0 6~ 7739.32 Hb - 11.54 737.78 O 6+ 7739.32 As - 10.60 738.72 0 6~ 7739.32 Ce - 11.20 738.11 O 6+ 7739.32 Fr -10.46 738.85 0 6+ 7739.32 Gb - 11.20 738.11 O 6+ 7739.32 Sn - 11.25 738.07 O 6+ 7739.32 Pb - 1 1.05 738.27 O 6+ 7739.32 Po - 1 1.80 737.52 O 6 + 7739.32 At - 1 2.80 736.52 0 6 + 7739.32 G~ - 1 1.20 738.11 ..,,:
.
.

WO 90t13126 PCI'/US90/01998 . :~ . 104 0 6+ 7739.32 Ga - 10.37 738.95 O 6+ 7739.32 In -1 0.35 738.97 O 6+ 7739.32 Ag - 11.30 738.02 Some representative couples comprising a c~tion and a molecule capable 5 of producing energy holes for shrinking deuterium atoms where the molecule is reduced. The number in the column following the ion or molecule, (n), is the nth ionization energy of the atom or molecule. For exampie, Ga2~ + 30.71 eV = Ga3+ + e- and BF3 + e- = BF3 + 2.65 eV.
Atom nnth lon- Atom n nth lon- Energy 1 0 Oxidiz- ization Reduced ization Hole ed Energy Energy (eV) (eV3 ~eV) Ga2+ 330.71 BF3 - 12.65 28.06 Se 2 + ~30.82 BF3 - 12.65 28.17 1 5 Tc 2 + 329.54 BF3 - 12.65 26.89 Rh 2 + 331.06 BF3 - 12.65 28.41 Sn 2 + 330.50 BF3 - 12.65 27.85 Tl 2 + 329.83 BF3 - 12.65 27.18 N 1 + 229.60 BF3 - 12.65 26.95 P 2 + 330.18 BF3 - 12.65 27.53 Cr2 + 330.96 BF3 - 12.65 28.31 Fe2+ 330.6~ BF3 - 12.65 28.00 Se2 + 330.82 NO2 - 13.91 26.91 Rh 2 + 331.06 NO~ - 13.91 27.15 - Xe2+ 33~.10 NO2 - 13.91 28.19 Pb 2 + 331.94 NO2 - 13.91 28.03 K 1 + 231.63 NO2 - 13.~1 27.72 Cr2 + 330.96 NO~ - 13.91 27.05 As 2 + 328.35 2 - 10.45 27.90 Rb 1 ~ 227.28 2 - 10.45 26.83 Ru2 + 328.47 ~2 - 10.45 28.02 In 2 + 328.03 2 - 10.45 27.58 Te 2 + 327.96 O2 - 10.45 27.51 Al 2 + 328.45 2 - 10.45 28.00 Ar 1 + 227.63 2 - 10.45 27.18 Ti 2 + 327.49 2 - 10.45 27.04 WO 9û/13126 PCl'tUS90tOt998 105 2 ~ 9 As 2 + 3 28.35 SF6 -1 1.43 26.92 Tc 2 + 3 29.54 SF6 - 1 1.43 28.11 Ru 2+ 3 28.47 SF6 - 1 1.43 27.04 Tl 2 + 3 29.83 SF6 - 1 1.43 28.40 N 1 + 2 29.60 SF6 - 1 1.43 28.17 Al 2 + 3 28.45 SF6 - 1 1.43 27.02 V 2 + 3 29.31 SF6 - 1 1.43 27.88 Ga 2 + 3 30.71 WF6 - 1 2.74 27.97 Se 2+ 3 30.82 WF6 - 1 2.74 28.08 Tc 2 ~ 3 29.54 WF6 - 1 2.74 26.80 Rh 2+ 3 31.06 WF6 -1 2.74 28.32 Sn 2 + 3 30.50 WF6 - 1 2.74 27.76 Tl 2 + 3 29.83 WF6 - 1 2.74 27.09 N 1 + 2 29.60 WF6 - 1 2.74 26.86 P 2 + 3 30.18 WF6 - 1 2.74 27.44 Cr 2 + 3 30.96 WF6 - 1 2.74 28.22 Fe 2 + 3 30.65 WF6 - 1 2.74 27.91 Ga 2 + 3 30.71 UF6 - 1 2.91 27.80 Se2 l 3 30.82 UF6 - 1 2.91 27.91 Rh 2 + 3 31.06 UF6 - 1 2.91 28.15 Sn 2 + 3 30.50 UF6 - 1 2.91 27.59 Tl 2 + 3 29.83 UF6 - 1 2.91 26.92 P 2 + 3 30.18 UF6 - 1 2.91 27.27 Cr 2 + 3 30.96 UF6 - 1 2.91 28.05 Fe 2 + 3 30.65 UF6 - 1 2.91 27.74 tc 2 + 3 29.54 CF3 - 1 1.8~ 27.69 Tl 2 + 3 29.83 CF3 - 1 1.85 27.98 N 1 + 2 29.60 CF3 - 1 1.85 27.75 P 2 + 3 30.18 CF3 - 1 1.85 28.33 V 2 + 3 29.31 CF3 - 1 1.85 27.46 As 2 + 3 28.35 CCI3 - 1 1.22 27.13 - Tc 2 + 3 29.54 CCI3 -1 1.22 28.32 Ru 2~ 3 28.47 CCI3 - 1 1.22 27.25 In 2 + 3 28.03 CCI3 - 1 1.22 26.81 N 1 + 2 29.60 CCI3 -1 1.22 28.38 Al 2 + 3 28.45 CCI3 -1 1.22 27.23 .

2 a ~3 L ~3 ~ ~ 1 0 6 V 2 + 3 29.31 CCI3 - 1 1.22 28.09 Ga2+ 3 30 71 SiF3 - 1 3.35 27.36 Se2+ 3 30.82 SiF3 - 1 3.35 27.47 Rh 2 + 3 31.06 SiF3 - 1 3.35 27.71 Sn 2 + 3 30.5C SiF3 - 1 3.35 27.15 P 2 + 3 30.18 SiF3 - 1 3.35 26.83 K 1 + 2 31.63 SiF3 - 1 3.35 28.27 Cr 2 + 3 30.96 SiF3 - 1 3.35 27.61 Fe 2+ 3 30.65 SiF3 - 1 3.35 27.30 1 0 As 2 + 3 28.35 NH2 - 1 1.12 27.23 Tc 2 + 3 29.54 NH2 - 1 1.12 28.42 Ru 2 + 3 28.47 NH2 - 1 1.12 27.35 In 2 + 3 28.03 NH2 - 1 1.12 26.91 Te 2 + 3 27.96 NH2 - 1 1.12 26.84 1 5 N 1 + 2 29.60 NH2 - 1 1.12 28.48 Al 2 + 3 28.45 NH2 - 1 1.12 27.33 V 2 + 3 29.31 NH2 - 1 1.12 28.19 Tc 2 + 3 29.54 PH2 - 1 1.60 27.94 Ru 2+ 3 28.47 PH2 - 1 1.60 - 26.87 Tl 2 + 3 29.83 PH 2 ~ 1 1.60 28.23 N 1 + 2 29.60 Pl 12 - 1 1.60 28.00 Al 2 + 3 28.45 PH 2 - 1 1.60 26.85 V 2 + 3 29.31 PH 2 - 1 1.60 27.71 Tc 2 + 3 29.54 al - 1 1.83 27.71 Tl 2 + 3 29.83 CH - 1 1.83 28.00 N 1 + 2 29.60 a~ - 1 1.83 27.77 P 2 + 3 30.18 ~1 - 1 1.83 - ~ 28.35 V 2 + 3 29.31 a I -1 1.83 27.48 Tc 2 + 3 29.54 S~l - 1 2.19 27.35 Sn 2 + 3 30.50 StJ - 1 2.19 28.31 Tl 2 + 3 29.83 S~l - 1 2.19 27.64 N 1 + 2 29.60 S~l - 1 2.19 27.41 P 2 + 3 30.18 S~J - 1 2.19 27.99 V 2 ~ 3 29.31 S~J - 1 2.19 27.12 Fe 2 ~ 3 30.65 S~l - 1 2.19 28.46 Ga2+ 3 30.71 CN - 1 3.17 27.54 WO 90/13126 PCltUS90/01998 107 . ~2.~ 9 ~

Se 2 + 3 30.82 Cl\t ^ 1 3.17 27.65 Rh 2 + 3 31.06 C~ - 1 3.17 27.89 Sn 2 + 3 30.50 Ci~t - 1 3.17 27.33 P 2 + 3 30.18 CN - 1 3.17 27.01 K 1 + 2 31.63 CN - 1 3.17 28.45 Cr 2 + 3 30.96 CN -1 3.17 27.79 Fe 2 + 3 30.65 CN - 1 3.17 27.48 Tc 2 + 3 29.54 SGN - 1 2.17 27.37 Sn 2 + 3 30.50 SCN - 1 2.17 28.33 1 0 Tl 2 + 3 29.83 SCN - 1 2.17 27.66 N 1 + 2 29.60 SCN - 1 2.17 27.43 P 2 + 3 30.18 SCt~t - 1 2.17 28.01 V 2 + 3 29.31 SCN - 1 2.17 27.14 Fe 2+ 3 30.65 SCN - 1 2.17 28.48 1 5 Ga 2 ~ 3 30.71 SeC~t - 1 2.64 28.07Se 2 ~ 3 30.82 SeCN - 1 2.64 23.18 Tc 2 + 3 29.54 SeCN - 1 2.64 26.90 Rh 2 + 3 31.06 SeCN - 1 2.64 28.42 Sn 2 + 3 30.50 SeCN - 1 2.64 27.86 Tl 2 + 3 29.83 Se~N - 1 2.64 27.19 N 1 + 2 29.60 SeCN ~ 12.64 26.96 P 2 + 3 30.18 SeCN - 1 2.64 27.54 Cr 2 + 3 30.96 SeCN - 1 2.64 28.32 Fe 2 + 3 30.65 SeCN - 1 2.64 28.01 25 Cations and molecular anions with n = 16 (resonance shrinkage energy is given by 2 27.21 with n = 16, the resonance shrinkage energy is 217.68) Atom nnth ion- Atom nnth lon- Energy Oxidiz- i~ation Reduced ization Hote ed Energy Energy (eV) (eV) (eV) P 5 + 6220.43 BF3 - 12.65 217.78 P 5 + 6220.43 NQ2 - 13.91 216.52 Be 3 + 4217.71 2 - 10.45 217.26 P 5 + 6220.43 0~ - 10.45 219.98 Be 3 ~ 4217.71 SF6 - 11.43 216.28 ~, .

. .
, WO 90/13126 PCT/US90/~1998 2 ~ 7~
P 5 + 6 220.43 SF6 - l 1.43 219.00 P ~ + 6 220.43 WF6 - 1 2.74 217.69 P 5 + 6 220.43 UF6 - 1 2.91 217.52 P 5+ 6 220.43 CF3 - 1 1.85 218.58 Be 3 + 4 217.71CCI3 - 1 1.22 216.49 P 5 + 6 220.43 CCI3 - 1 1.22 219.21 P 5 ~ 6 220.43 SiF3 - 1 3.35 217.08 Be 3 + 4 217.71 NH2 - 1 1.12 216.59 P 5 + 6 220.43 NH2 - 1 1.12 219.31 Be3+ 4 217.71 PH2 -1 1.60 216.11 P 5 + 6 220.43 PH2 - 1 1.60 218.83 P 5 + 6 220.43 CH - 1 1.83 218.60 P 5 + 6 220.43 SH - 1 2.19 218.24 P 5 + 6 220.43 CN - 1 3.17 217.26 1 5 P 5 + 6 220.43 SCN - 1 2.17 218.26 P 5 + 6 220.43 SeCN - 1 2.64 217.79 Cations and molecular anions with n = 54 (resonance shrinkage energy is given by 2 27.21 with n = 54, the resonance shrinkage energy is 734.67) Atom n nth lon- Atomn nth lon- Energy Oxidiz- ization Reduced ization Hole ed Energy Energy (eV) (eV) (eV) O 6+ 7 739.32 BF3 - 1 2.65 736.66 0 6+ 7 739.32 NC~ - 1 3.91 735.41 O~ 6+ 7 739.32 O2 - 1 0.45 738.86 O 6+ 7 739.32 SF6 - 1 1.43 737.89 O 6~ 7 739.32 WF6 - 1 2.74 738.58 0 6 ~ 7 739.32 UF6 - 1 2.91 736.41 O 6+ 7 739.32 CF3 - 1 1.85 737.47 O 6~ 7 739.32 CCI3 - 1 1.22 738.10 0 6+ 7739.32 SiF3 1 3.35 735 97 0 6+ 7739.32 NH2 - 1 1.12 738.20 0 6+ 7739.32 PH2 - 1 1.60 737.72 0 6+ 7739.32 CH - 1 1.83 737.48 0 6+ 7739.32 SH - 1 2.19 737.13 109 2 ~ 7 0 6 + 7 739.32 CN - 1 3.17 736.15 0 6+ 7 739.32 SCN - 1 2.17 737.15 0 6 + 7 739.32 SeCN -1 2.64 736.67 The fusion of deuterium to 3He releases neutron which can effect the 5 fusion of 6Li to helium. In one embodiment of Coulombic Annihilation Fusion, 6Li is present in the fusion reaction mixture of deuterium where fusion of deuterium further drives the fusion of 6Li.
Other atoms in addition to deuterium can be caused to fuse by Coulombic Annihilation as described for deuterium.
The quantum of energy hole is calculated for the atoms involved and a reaction or process which removes this much energy and regenerates the atoms or molecules to be fused is effected until sufficient energy is removed from the Mills orbitals so that the internuclear distance is sufficient for the nuclear strong force to dominate the coulombic 15 repulsive force. Fusion then occurs.
Fusion Reactor The fusion reactor 50, shown in Figure 6 comprises a vessel 52 which contains the fusion reaction mixture 54, a heat exchanger 60, and a steam generator 62 where the heat exchanger 60 absorbs heat released by CAF
20 and exchanges it with the steam generator 62 which absorbs heat from the exchanger 60 and produces steam. The fusion reactor 50 further comprises a turbine 70 which receives steam from the steam generator 62 and supplies mechanical power to a power generator 80 which converts the steam energy into electrical energy, which is received by a load 90 to 25 produce work or for dissipation.
Thè fusion reaction mixture 54 comprises a source of deuterium atoms 56 or a source of molecular deuterium, and a source of energy holes 58 which resonantly remove 2 27.21 eV; n = 2, 3, 4,..., of energy from deuterium to effect shrinkage to the point of fusion. The source of 3 0 deuterium can be deuterium gas, electrolysis of deuterium oxide, deuterium from hydrides, or deuterium from metal-deuterium solutions.
A source of ener~y ho!~es com~rises a catalytic energy hole ma~erial 58, typically comprising ol~ctrochernical couples including the catalytic couples described in the Coulombic Annihilation Fusion Section. Thus, an 3~ exemplary fusion reaction mixture is molecular deuterium a salt of Pd2+

: . . .

WO 90/13126 PCI'/US90/01998 3 L~ rl 11 0 and a lithium+ salt. Palladium absorbs molecular deuterium and the Pd2+/Li+ catalytic system effect resonant shrinkage of deuterium to the point of fusion. In one embodiment, the lithium is 8Li in which case the neutrons released from fusion of deuterium effects the fusion of 6Li to 5 helium.
In other embodiments, the fusionable material is one of any element of the periodic chart, and the energy of the holes of the said source of energy holes is resonant with the Mills orbital shrinkage energy which is calculated using Mills mechanics of the present invention and described 10 for deuterium in Appendix Vl.
In the preferred embodiment, 2H, 3H, or 6Li is used as the fusionable material .
in all embodiments, the source of energy holes is one or more of an electrochemical, chemical, photochemical, thermal, free radical, sonic, or 15 nuclear reactions, inelastic photon or particle scattering reactions.
In the latter two cases, the present invention of a fusion reac~or comprises a particle and/or photon source to supply the said energy holes.
In ail reaction mixtures a selected external energy device 75, such as an electrode may be used to supply an electrostatic potential or a current 20 to decrease the activation energy of the resonant absorption of an energy hole.
In another embodiment the fusion mixture 54, further comprises a surface or material to absorb atoms and/or molecules of the fusionable material 56. Such surfaces or materials to absorb deuteriurn, or tritium 2 5- comprise transition elements and inner transition elements including iron, platinum, palladium, zirconium, vanadium, nickel, titanium, Sc, Cr, Mn, Co, Cu, Zn, Y, Nb, Mo, Tc, Ru, Rh, Ag, Cd, La, Hf, Ta, W, Re, Os, Ir, Au, Hg, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Oy, Ho, Er, Tm, Yb, Lu, Th, Pa, and U.
Experimental 30 S. Pons, et al, have demonstrated cold fusion with an electrochemical cell that electrolyzes deuterium oxide to deuterium at a palladium electrode with lithium as the counter ion. That excess heat is released and that some fusion of deuterium is detectabl0 is apparent by the present invention. Th~ third ionization energy of palladium is 32.93 eV and the 3 5 first ionization energy of lithium is 5.392 eV. This system can catalytically generate energy holes of WO 90/13126 PCI'/US90/01998 111 ` 2Q~5~

32.93 eV - 5.392 eV - 27.538 eV
The catalytic reaction is given in the Coulombic Annihilation Fusion Section. The quantum of energy needed to decrease a Mills orbital by aO( n1 - n2 ) is 27.21 eV. The energy difference between 27.538 eV and 5 27.21 eV is carried by a phonon or a translational or rotational mode. CAF
occurs at a slower rate when sodium or potassium is used as the electrolyte because the energy hole produced by the Pd2+/Na~ system is 27.791 eV and the energy hole of the Pd2+/K~ system is 28.589 eV.
The energy holes of the Pd2+/Li+ system are closer to the resonance 10 quantum of 27.21 eV. Thus, it is not surprising that lithium is a superior counter ion to effect CAF.
That cold fusion at a titanium electrode has been observed by S. E.
Jones et al to proceed a faster rate than with the Pd2+/ Li+ catalytic system is not surprising in that the catalytic reaction involves only one 1~ atom as the catalyst, and the third ionization energy of titanium is 27.491 eV which is close to the shrinkage quantum of 27.21 eV. The catalytic reaction appears in the Coulombic Annihilation Fusion Section.
27.21 eV of heat is released during a radius reducing cycle of the Mills orbital of the deuterium atom in the Pons and Jones systems.
20 Approximately 100 KeV of heat energy is released by the shrinkage process before the nuclei approach sufficiently for fusion to occur. This heat is unaccountable by both research groups. Interestingly, this unaccountable heat was observed in electrochemical cells with pailadium electrodes, Group I cation electrolytes, and aqueous solutions as long ago 25 as 1924 by Jirsa (Jirsa, F., Z. Physik, Chem., 113, 241 (1924)). Thus, Pons and Jones' observation of the phenomenon of heat release due to resonant Mills orbital shrinkage is not the first.
Furthermore, physicist Francesco Scaramuzzi effected cold fusion of deuterium gas using shavings of titanium; whereas, in 1973, Catlett, et 30 al., (Catlett, D. S., et al., The Journal of Chemical Physics, ~., p. 3432, ~1973)) diffused deuterium gas into palladium and measured no fusion products by sensitive mass spectroscopy. According to the present model of-the atom, CAF was catalyzed by Ti2+ in the former experiment, and CAF
was not possible in the latter due to the absence of the second element of 35 a two-element catalytic couple such as Li+ of the Pd2~/Li+ couple.

, . , ' , WO 9û/13126 PCr/US90/01998 2 0 ~ 7 Further Applications Mills Mechanics, the present invention, is a means to derive a complete quantitative description of any atom, molecule, or material. The said descriptions can be used to device novel molecules, materials, and electronic devices; thus, they can eliminate much experimentation. And, they can be used to interpret the results of experimentation.
For any atom, the radii of all Mills orbitals are calculated using the balance of forces as described in the One Electron Section, the Two Electron Section, and the Three Electron Section. The orbital energies are 10 then calculated as described in the said sections to give the complete mathematical description of any atom or ion. Thus, with the selection rules, described in the Section Rules Section, together with the orbital energies and the principle of conservation of energy, all transitions are given.
Bonding is calculated by minimizing the total energy stored in the electric and magnetic fields of the participating atoms as described in the Nature of the Chemical Bond Section. The resulting minimum for all atoms describes ~xactly any molecule or material. The physical properties can then be calculated from the following parameters:
2 0 1.) coordinates of the nuclei and Mills orbitals;
2.) the bond and orbital energies 3.~ the bond energy as a function of said coordinates - 4.) population of Mills orbitals (e.g., unpaired electron or two spin paired electrons in a given orbital) 25 Furthermore, Mills mechanics is a means to calculate reaction coordinates as energy surfaces that describe the intermediates of a . reaction; thus, reaction mechanisms are given. With this knowledge, novel syntheses and products can be engineered, catalysts can be developed, and yields of the desired products increased. Also, phenomenon which occur 30 too rapidly to be observed or have yet to be discovered (recent examples are cold fusion and high transition temperature superconductors) are described exactty via Mills mechanics which provides a complete description of matter on the atomic and molecular level.

2 ~ 3 ~ ~ 9 7 Appenclix I
Proof that the condition for radiation by a charge density function is that it possesses components of its space-time Fourier Transform which are synehronous with waves traveling at the speed of light is given.
5 Charge obeys superposition; thus, only a point charge need be considered.
The proof starts with the Fourier components of the current produced by the moving charge. The electric field is found from the vector wave equation in Fourier space (k, ~ space). The inverse Fourier transform is carried over the magnitude of k. The resulting expression demonstrates 10 that ~he radiation field is proportional to Jl(c n ,CI~), where Jl(k,~) is the space-time Fourier transform of the current perpendicular to k and n ~ Ik ; thus, the necessary condition for radiation by the charge is that its space-time Fourier transform possesses components which travel at the speed of light.
15 ` Il. The Source and Its Fourier Transforms Consider a charged particle of charge q and position rO(t). The charge density of the particle is described by p( r, t) = qo[r - r o(t)] (2.1 ) where ~( r - rO ~ is the spatial unit irnpulse function. The current density 20 is J ( r, tj = qr O(t)o[r - r o(t)] (2.2) The spatial Fourier trarisform represents the current density as a superposition of spatial exponentials, exp -j k- r.
r J( k, t) = ¦ ¦ J d3 kqrO(t)o,[r - rO(t)] exp(-i k r) (2.3) = qrO(t) exp(-i k- rO) The full space time Fourier transform is of course, WO 90/13126 PCl'/US90/01998 2 ~ r~ 1 14 J( k, w) = ¦ ¦ ¦ J dtd3 k J(r,t) exp(-i k r) exp(i~t) (2.4) The inverse Fourier transform is J( r,t)= (2 ) ¦d~'~ ¦ ¦ J dk3J(k,cl3) exp(i k r) exp(-ic,~t) (2.5) Ill. The Electromagnetic Field The electric field obeys the vector wave equation V x ~V x E) ~ c2 ~jt2 = ~Il~t (3.1) The space-time Fourier transform of the vector wave equation is:
k x [ k x E(k,c~) ] + c2 E(k,c~ oJ(k,c~) (3.2) In the far-field, only the component perpendicular to k is of interest.
10 Concentrating on this component one has 1( l ) k2 C~21C2 with - k n Ikl (3.4) IV. The Inverse Spatial Fourier Transform 15 The inverse space-time Fourier transform involves the integrals .. ..
J 2--Jt exp(-ic,~t)(2 )3JJJd3kexp(ik-r ) We shall retain the Fourier transform with respect to time and thus not carry out the integration over ~o. But we shall foous on a spectral width d~ of the field and thus write down expressions for El(r,~)2 . We .

., WO 90tl3126 PCr/US90/01998 115 2~ 3 ~
! . ' : :;

separate the integrals into an integral over the magnitude of k, and into a double integral with respect to the angles ~ and ~ of k with respect to r.
E (r ~jdc~) = d~l) ( 1 )3JI d~d~sin~

Jic~ ok2dk k 2[ (2 / 2] e x p ( i k- r ) (4 .1 ) The last integral can be carried out by contour integration. For k r ~ 0, the contour must be closed into the negative imaginary half plane of k with the result d~ 1 2 ~2 Cd ~ d~d~sin~
El(r,~)2~ = (2~) c2 d(c)JJ 41~

~0 cnx[nxJ(c n,~)]exp(iC n-r) (4.2) ThiS expreSsion may be rewritten in a way that lends itself to an appealing interpretation. The density of (linearly polarized) modes per unit volume and unit solid angle, p(cd,Q), is ( Q) d dn 1 (_)2d(C~dn With this definition, one has El( r ~C~) 2 = 2 JP(~'Q)dC')dQ~

_ _ C3 -- ~
nx[nxJ(c n,c~)]exp(iC n-r) (4.4) The field El(r,c,))2 is propsrtional to -J(c n,cl)) namely, the Fourier component for whiCh k = co/C. Factors of ~D that multiply the Fourier component Of the Current are due to the density of modes per unit volume 20 and Unit solid angle. An unaccelerated charge does not radiate in free space, not because it experiences no acceleration, but because it has no - , ~ ~ ~ ,.............. . ' ' .

2~3~3~ ~
Fourier component.
_ ~ _ J(c n,~) Indeed, from (2.3) J (k,~) = rdtqv exp(-ik v t + ic,)t) = 2J~qv~ -v ) (4 5) The only nonzero Fourier components are for vcos6 c (4.6) where ~ is the angle between v and k. The reason for the radiation of an accelerated charge is that the Fourier decomposition of the current 10 acquires Fourier components that are "synchronous" with the light velocity, i.e. with the propagation constant Ikl = c . Thus, for example, an oscillating charge rO(t) = d sin~Ot (4 7) has a Fourier spectrum 15 J(k,c~) = 2 Jm(kCos~d){~[Ll~ - (m + 1)cl)o] + ~[c~ - (m - ~ )o]} (4.8) where the Jm's are Bessel functions of order m. These Fourier components can, and do, acquire phase velocities that are equal to the light velocity.
For small kd only m = 0 remains and is approximately independent of k, J( c co`s~d) ~ 1-V. Integration Over Angles Starting with (4.2), we note that ~he exponential is a strong function of ~ whereas the component n x [ n x J] varies much more slowly and thus can be pulled out from under the integration. We have to integrate an expression of the form -WO 90/131~6 PCI/US90/0199B

1 1 7 2 ~
"

2J~
r7~
1 C"2dC,~ I r d~d~sin~ ) d~
2~ c3 J J 4~ exp(iC cos~-r) = - 2 i c2r 2 exp(iC r) o o where the upper limit on ~ is ignored because of the rapid variation of the exponent. With this result introduced in (4.2) one has dcl) d~
El(r'~'~)2 = 2 4 '\1 ~0 cr nx[nxJ(C n,~)~ exp(iC- n r) (5.1) 5 Here, n is the direction of the radius vector r.We note now that a factor of CJ~ appears in front of the current. One may therefore interpret the source as containing the acceleration where ~ ) represents differentiation with respect to the time coordinate.
It seems more natural to attribute the factor to the integration over 10 all the modes, in particular because then Cherenkov radiation presents less of a mystery. Cherenkov radiation is produced by an unaccelerated particle, but since the velocity of light is less than c, the particle current can have Fourier components synchronous with c ~here ~ is the dielectric constant of the medium.
Appendix ll Space-time Fourier transform of Mills orbitals.
The space-time Fourier transform in three dimensions in polar coordinates is given as follows:

G(S,~ j ¦ g(r, ~ ), t)es~p (~ srlcos ~ cos O O
s3n ~3 sin ~3 cos(~ ]) r2 sin ~ dr d~ d~ dt with circular symmetry, 2 5 ~ ~11 G(S,~ - 2IEJ J g(r, ~3 ) JO 12~1sr sln ~1 sln ~) e~ sr cos O O
cos ~3) r2 sln ~ dr d~

... . . .
,~, .

. , .
~. ,.

.;

WO 90/13126 PCI'/US90/01998 J

with spherical symmetry.

r~
G(S) - 4~J g(r)slnc (2sr) r~ ~r O

For separable variables f(r) 9(~) h(~) k~t) ~ > F(s) 6~)) H(q~) K~) Mills orbitals are separable into a product of functions of independent variables, r, ~, ~, and t. The radial functions are delta functions. The time functions are of the form ei"t~ the angular functions are spherical 15 harmonics, sin or cosine trigonometric functions or sums of these functions, each raised to various powers. The space-~ime Fourier transform is derived of the separable variables for the angular space function of sin ~ and sin a. It follows from the space-time Fourier transform given below that other possible spherical harmonics angular 20 functions give the same form of result as the transform of sin ~ and sin ~.
The space Fourier transform of f(r) = ~(r-rO) is given as follows: ~
tOO
~(S) ~ 4~1 ~;(r - rl) slnc(2sr) r2dr J~

` ~(S) - 411rl2 slnc~2srl~
The space Fourier transform of y(~) - sin ~ is given as follows where there is no dependence on ~:

6(~) - 2J~¦ ¦ sln~3 Jc ~2~sr sin ~3 sin 0) exp (~ sr ~os (~ cos ~) O o sin ~ ~2 d~ dr WO 90~13126 PCI/US90/01998 2 ~
119 :.

G(~ 211~ r2sln~3Jo (2Ttsr sin ~) sln ~3) O O
cos (2~1sr cos (~) cos ~) d~3 dr 00 (_ 1 )n(~ )2n J~ (Z) ~ (LZ) ~ nl (~ ~2 ~ 13 z ~ 2~sr slnl~3 sln~3 G~)3 - 2~,1 ¦ r2sln2~ nl ~n ~1) cos~2~srcos~) cos~3) d~dr G(~ 2~1 Ir2l ~ r s~ 3 )211 sin~2(n~) O O n-~ nl (n ~1) 2 0 tos(2~srcos~) cos~3) d~dr ~ 1~ 217~ ~ t-l!n~ r sin(~ )2(n-l) 2n~3 cos~27~srcos~ cos~ dadr J~ k) ~ 2 - ~ cos(z cos~ ~sin2~ d~
rll~r~v~ 0 ~. ~,," ,.
'. '. ~ , .
2~34~7 120 Re (V) > -(l/2)~ Z ~ 271sr cos~) G(~ 211J r2 ~ r sinE~ )2(~
~ 1 0 l) r(l)r(~ sr coS~)o 2 2 sin2~3 cos(2TCsrcos~) cos~3) d~3dr (~r cos~))ur(l ) G(~ 2~ r2 (_1)v I(~rs~n~ )2 ~, ._ . ..
1 5 ~ V ~O - l )l r(2l)rl1~ 2 ) (~Isr cos~3?1) ¦ Sln2V~3 c0S(27~srco~ Cos~3)d~dr (~sr~s~ ) rll)rO~l) ~ 2 G(~ 2~1 r2 ~ r sln~3 )2(~1) O ~"g o 1) (1) ~l)r(~
J~(2~sr cos ~3) dr (~sr cos~

Hankel transform formula:

~-~1/23 (rs)(1~23J~(rS) dr~ S~t/2) o Hankel transform relationship:

W0 90/13~26 Pcr/US90/01998 2 ~ 9 3J

~0 ~(X) <~ == => 9(y; V) ~ y)( ~ /2)J~ y) d~
o ~Im ~ ), m ~- 0, ~, 2.. <~ 9S~ y(l~2~ - O(~)ml ~(mtO-1/2)9(y; m~

r r~(~ (rS)~l/23 J~rs) ~r ~ s(l/2)~0( d )VI SU~O-l112) 1 0 ( ~ ~2) r1) 5(1/2) Jv(rs) dr ~ ~ ~ (dds)ul s21) ,00 .
J rV s(1/2) J~(rs) dr ~ S(l/2)-2v 21)1 sv, 201 5(1/2)-V
r S~~ 1 /2)s( 1 ~2)Jl~(r~) d~ " 2VI ~-V
oo ~ 00 5(~) - 2~ C sln~3 ~ J01~(~- 1)1 r~L,r",~1) 2 2 rl)J~I2~srCos ~3) dr (~s ~ost~

letr~- r dr... dr' 2~ Cos ~3 2R ~os oo 00 fi~ 2~ ~ ~ $1n~3 ~a 1~1J l)tO-l~
3 r~1)r~
? . 2 ~) J(sr') dr' (~s ens~) (2~ cosÇ3)'~
~o ~ 3) 2~ sln~ 3 V'l U (V - l)~

.

~ .
, WO 90/13126 PCI'/US90/01998 2 ~
r(l~r~
2 2 2~1 S V
111s c os~33Vt2~ tos~3)~ 1 Ol G(~ 2~t (~ sln~3 3 0~ 1 i3 (V - 1 ) 1 (7't c o s ~3)2l)~ 1 2~ V l The space Fourier transform of h(~) = sin ~ is given as follows where 10 there is no dependence on ~:
Apply change of variable to the Fourier transform of 9(~) = sin ~.

implies ~- - >~
H(~ sin~ ~2(1)-1~ r(l)rlv~l) S_2 0~1 V (V ~ os~3)Z~ol2Vtl 1)1 The time Fourier transform of K(t)~R~es~P(~ t~) is given as fo I lows:
f~
J cos~O t expf-K)t) d~ 8 ~ (C4~ 4 ~

The space-time Fourier transform of a Mills orbital is of the ~ollowing form:
~1(S, ~ F(S3 Gl~) H(~ K(O) WO 90/13126 PCI/US9~ 1998 ~ 0 ~
i~3 oo ~(S, ~4t~rl 2 slnt(2S~ sln~ !
r(l~r(u~l) 2~ 1 2V~ cos~2~

u-~ sin~ 2(0-l~ r(2)r(U 2) ?VI S-2V
0~) (V ~ 2~ cos~

The condit,on for radiation of a charge density function is given in Appendix 1. The space-time Fourier transform of the charge density function must not have waves synchronous with waves traveling at the 15 speed of light, that is synchronous with l~)n or synchronous with c ~where ~ is the dielectric constant of the medium. Given the angular veiocity, ~ = ~n. the space-time Fourier transform of the Mills orbital is zero for 20S = ~ when (11.1 ) 2~(nrl) = 27~rn = n~ n (11.2) where n = 1 2~ n=2,3,4, n = 2 3 is the allowed wavelength for n = 1 r1 is the allowed radius for n = 1 30 Thus, space-time harmonics of c = k or c ~= k do not exist.
Thus, radiation due to charge motion does not occur in any medium when this boundary condition is met.

':
2~ ~ fi97 124 Appendix lll The solution to the Schrodinger equation is a wave function ~ (x). An interpretation of ~y (x) is required. Schrodinger postulated that ~ (x) represents the amplitude of the particle in some sense, and because the 5 intensity of a wave is the square of the amplitude the ~intensity of the partic!e~ is proportional to ~ (x) ~Ir (x) [~y t(x) is the complex conjugate of (x)]. A controversy arose over the meaning of intensity. Schrodinger considered e ~ '(x) ~ (x) to be the charge density or e ~ t(x) ~ (x) to be the amount of charge between x and x + dx. Thus, he presumed the electron to 10 be spread all over the region.
The electron has kinetic energy and angular momentum and energy must be conserved; thus, the motion of an electron must be time harmonic.
It is demonstrated in Appendix I that emission of electromagnetic radiation occurs if the space-time Fourier transform possesses waves 15 that are light synchronous with waves traveling at the speed of light. It is demonstrated below that the Schrodinger wave equations have such components; thus, they must radiate. That no radiation is observed demonstrates the invalidity of ~hese equations as an accurate description of an electron.
20 The angular functions of Schrodinger wave equations are spherical harmonics and their space-time Fourier transform is given in Appendix ll as the transforms of 9(~), h(~), and k(t). The radial solutions are of the form of a r raised to a power times a negative exponential of r. The space-time Fourier transform of the radial function f(r) = re~r/~O follows:
~ OO
re~~r~o3 sinc(2sr) r2dr Jo ,~0 ¦ r3e-(r/~0) s!n 2~(2sr) dr Jû ~C2sr ,0~ .
(r2¢~(r/~o))/(2 Jls) sin 4~sr dr j.
.
, 2 0 ~
i25 Let r ~ r'/4~, dr' ~ (1/4J~ dr 1¦ r' 2 es~p ( ~~ ) 5In r's d~
4~ 0 ~ 2~s (4~)~o ~ne-a~ sln (xy) d~ ~ n~ ( 2 )n~l O C~, ~ y2 2 n ~ 2m 4 % ~ )m ( 2~ aJ
m~0 Let x - r, S - y, a ~ 1 /4~aO ~ n ~ 2 00 ' 1/4~1 - !? ~-(r/4Jl:~) sin rs dr ~ 1 _ O (4~r~)22~s (4~ 211s (21)(. (~.~4~o3 )3 ~/4~)2 ~ ~2 ~ . .
m2'0 ( 2m ~ /47~O) .

WO 90/13126 PCl'/US90/01998 ~Q~4~

Thus, the complete space-time Fourier transform of a Schrodinger 5 wave equation is given as follows:

W(S ~ (21)(_(~/4~0~ )3~ )m 1 0 (47~)3 2~s (1/4~uo~2 ~ s2 m-~O
3 ) ( - ~ )2m 2m ~ 1 1 /4~nO

2~ cOs~3)2o~ ! 5-2t ~t(~sln~3 )2~ ) r~2~r~L, _ _ _ __ _ 2 2 0 ~
~u ~ cos~3)2U~l2~ 3 25 This transform has components c" = k which are not zero and are synchronous with waves traveling at the speed of light. Thus, a charge density function given by the Schrodinger wave equation must radiate in accordance with Maxwell's Equations.

. ~

WO 90~13126 P{~/US90/01998 1 2 7 ~ Q ~

Appendix IV
Derivation of the Orbital Energy Stored in the Magnetic Fields of Two Paired Electrons Derivation of the Magnetic Field Consider Figure 2; the magnetic fielcl must satisfy the following relationships:
V- H = 0 in free space (IV.1) n x (Ha - Hb ) = ~ (IV.2) n (Ha - Hb ) = (IV.3) H = - V ~ (IV.4) 2 Il.r 3 sin~ (IV.5) Ha~ - Hb~ = 2 ~r 3 sin~ (IV.6) To obtain H~ ,the derivative of Y' with respect to a must be taken, and this suggests that the ~ dependence of ~ be taken as cos ~ .The field is 15 finite at the origin and is zero at infinity; so, solutions of Laplace's equation in spherical coordinates are selected because they are consistent with these conditions.
~=C[r] Cs~; r<rn (IV.7) ~ r 1 Y' = A --~ 3 cos~; r > rn (IV.8) 2 0 The negative gradient of these potentials is H = r ~Ircos~ sin~) for r < rn (IV.g) H = rn [r--]3 (Ir 2 cos~ sin~) for r > rn (IV.10) The continuity conditions of Equations (IV.3), (IV.5), and (IV.6) and are applied to obtain the following relationships among the variables 2 5 -- = r ~ I V . 1 1 ) rn n rn rn = 2 ~rn3 (IV.12) Solving the variables algebraically gives the magnetic fields of an .

. .

WO 90/13126 PCr/US90/019~8 .
~ 128 2 ~
eiectron:
H = ~r 3 (~r cosl3 - l~ sin~) for r < rn (IV.13) H = 2~r3 (Ir 2 cos~ -13 sin~) for r > rn (IV.14) Derivation of the Energy 5 The energy stored in the magnetic field of two electrons is 2 ~
Emag =2 2 ~lo J J JH2r2sin~drd~d~ (IV.15) o o O
Emag,totai = Emag,externai + Emag.internai (IV.16) ¦ ~ oJ[ llrl3] ~ (IV. 17) 4~ 0e2~2 3IL2r13 (IV.18) 1 o J i [ 2~r3 ] (4cos~ + sin2~) r2sin~drd~d~

2~ oe2~2 3ll2r13 (IV.20) '4~,o~2~2 2~ oe2~2 Emag.total = 3~L2r13 + 31,l2r13 (IV.21 ) 2J~IlOe2fl2 Emag,total = ~2 r13 ( I V . 22) 129 20~97 Appendix V
The Hydrogen Molecule It can be shown easily that the internuclear distance for the dihydrogen, H2, is 0.748 A. Consider two hydrogen atoms, A and B, approaching each 5 other along the x-axis as shown in Figure 3. The radius of each Mills orbital is aO. The electrostatic energy is Einteraction= 2x 2 ~O J~2dv (v 1~
We define this energy as EjnteraCtjon Recall that the electric field is zero for r > aO. Until the orbitsphere penetrate the energy of interaction, 10 Einteraction, is zero.
As the atoms move closer, the Mills orbitals begin to penetrate. When the penetration is small, as shown in Figure 4, Ei~teraction decreaseS (is negative) because most of the electric field vectors from nucleus A in the overlap region are pointed in direct opposition to the B electric field 15 vectors from nucleus B.
As the atoms move closer and the overlap increases, the Einteraction will continue to decrease (become more negative). However, the decrease per unit volume will be smaller because a lower fraction of the A-vectors will be in direct opposition to the B-vectors. Figure ~ shows the two 20 radial vectors and the net electric field vector (EAg) for the point of intersection of the Mills orbitals.
We see that K

EA = E~ = ~a )2 (V.2) A A (aO)4 (V.3) 2 5 EXB a EXA (V.4) EAB = EyA + EyB = 2 EyA ~V.5) From the angle ~, y _~ EyA ~V.6) EyA = (a )3 (V.7) yK
EAB -- 2 (aO)3 (V.8) '.' ., WO 90/13126 PCr/US90/01998 2 0 3 ~ ~ ~ 7 1 3 0 Therefore, (EAg)2 will be less than [(EA)2 + (EB)2] when 4y2 K2 2K2 (aO)6 ' (aO)4 (V.9) y2 < (a2) or y < ~ (V.10) Thus, for y = O to y ~ aO/~r Ejnteractjon de~reases- For y > aO/~ Einteraction 5 Increases. And for y = aO/~, Ejnte~aCtjon is a minimum. When y = aJ~

RAB = xB = 2x ~ = ~ aO = 0.748A (V.11) - The experimental internuclear bond distance is 0.746 A

. .

, .

WO 90/13126 PCrlUS90/01998 131 20~9 7 Appendix Vl Calculation of the Resonant Energy Hoie to Effect Shrinkage of the Radius of the Mills Orbital of the Deuteriurn Atom.
For the deuterium atom, the force relationship is given as follows:
llv2 ~2 r = 4~0r2 The boundary condition for nonradiative Mills orbitals derived in Appendix ll, 21lr= n~, gives:
v=--.
~lr Consider the case where the electron in the ground state losses kinetic 10 energy, 112 mv2, due to an inelastic collision for example, then the radius of the Mills orbital will shrink until the boundary condition is satisfied.
The amount of energy which must be carried away (i.e., the magnitude of the energy hole absorbed) is calculated as follows:
Let r1 = initial radius.
Let r2 = final radius.
The force balance is:

r = 4~0r2 Vo is introduced as a perturbation of the velocity and the magnitude of the velocity change of the electron from the initial to final Mills orbital is 2 0 calculated as follows:
r~ Lr - Vo)2 = ~2 r2( ~2r12 ,ur1 + ) 4~eor22 Vo2 2tl Vo + t~2 e2 ~Lr1 ~L2r1 2 47tEor2 V llrt ~ 2 l2r1 2 IL4~eOr22 Vo= tl ~
~r1 ~l4,l0r2 WO 90/13126 PCI/US90/01~98 2~5~ ~J~
- ; 1 32 e2 ~2 4~1~o ilao Vo= ~+~
ILr1 ~2aOr2 For the ground state, the radius of the Mills orbital was determined in the One Electron Atom Section to be aO. Thus, the boundary condition is 5 given as follows.
27~aO = ~
From the boundary condition, 21lr = n~, with r c aO, the radius of any shrunken state is an integer fraction of the radius of the ground state.
Thus, for the first shrunken state aO

r2= 2 ~ and in general - aO
r2-Substituting r1 = aO and r2= n into the relationship for Vo gives . .. .
Vo = tl +,~ i h2n ,uaO ~ ~2aO2 Vo =--~ ~--~aO~ ~aO
1 5 n=2,3,4 The angular velocity of the electron in ground state is a and the angular velocity in the first shrunken state is--.
~aO

Consider the velocity of the centripetal force equation:
r2 ( Il.r1 - Vo)2 = Fc 2 0 and the relationship resulting from the perturbation:
Vo = 11 i ~ ~ n=2,3,4 ~aO ~aO

In order to satisfy the boundary conditions, the first term of Vo, ~, WO 90/13126 PCI-/US90/0~998 133 20~97 must be negative so that it adds to the initial velocity a to give the final velocity a ~ and the kinetic energy due to the velocity component ~a must be removed to effect the shrinkage transition.
Ths magnitude of the energy hole which arises from this term is 5 calculated as follows:
E = 2 ~ V2 =
~2 E = 2 ILn 2 2 n=2,3,4.....
Thus, the absorbed energy hole which effects shrinkage is quantized.
10 For the shrinkage transition n = 1 to n = 2, the resonant energy loss to shrink a Mills orbital by aO ( n1 - n2 ) where n1 is the quantum number of the initial orbital and n2 is the quantum number of the final orbital is given as follows:
tl2 E=2n a2;n=2 1~ E ~2 (1.05459 X 10-34)2 ~LaO2 (9.109~3 X 10-3~)(5.29177 X 1o-11)2 E = 4.3598285 X 1 o-1 8J = 27.211 682eV
n Thus, shrinkage requires the electron to lose a resonance energy of 2 27.21 eV where n - 2, 3, 4,.....
Notice that absorption of an energy hole reduces the radius; whereas, 20 absorption of energy as a photon increases the radius. The former increases the coulombic force by the rnultiple of n; the latter decreases the coulombic force by the multiple of n where n is the integer of the transition; thus, the force balance,`and the boundary conditions for nonradiation are satisfied.

wo 90~13126 PC-/US90/01998 2 ~ ~3 ~ J 1 3 4 Appendix Vll Detailed Description of Figure 1. Mills Orbitals Mills orbitals are obtained by adding a constant sphere which is normalized to a spherical harmonic which is normalized. This function is 5 the charge density on the surface of the spherical delta function that comprises the Mills orbital. The former can be consider the base charge density whose current gives rise to ma~netic spin, and the latter can be considered a charge density function which creates modulation of the former and whose traveling wave of current gives rise to orbital angular 10 momentum. The total charge of the Mills orbital for an electron is e and the total mass is ~L.
The application entitled ENERGY/ MATTER CONVERSION METHODS AND
STRUCTURES filed April 21, 1989 is herein incorporated by reference.
These and further methods and embodiments arising from substitution 15 and modifications made by one of ordinary skill in the art are considered within the scope of the present invention. For instance, in the case of energy release through fusion according to the present invention, the fusion material may include more than one element or molecule, where corresponding energy holes are provided for each fusion element.
20 Therefore, the present invention is not limited except by the claims which follow.

Claims (40)

What is claimed is:

1. A method of releasing energy, comprising the steps of:
selecting a first element of matter having a nucleus and at least one electron orbital;
selecting a second element of matter having a nucleus and, at least one electron orbital;
determining the resonance shrinkage energy levels of the electron orbitals of said first and second elements of matter;
providing two energy holes substantially equal to each of the resonance shrinkage energy levels of said first and second elements of matter;
juxtaposing said first and second elements of matter and said energy holes, wherein;
fusion of said first and second elements of matter is produced when the energy of said first and second elements of matter is removed by said energy holes from said electron orbitals to permit forces from each nucleus of said first and second element of matter to be attractive to form a common nucleus, providing the release of energy.

2. The method of claim 1, wherein:
said first and second elements of matter comprise the same element of matter.

3. The method of claim 1, wherein said step of providing an energy hole for each fusionable element comprises the step of selecting a third element of matter having an ionization energy substantially equal to the resonance shrinkage energy of said first and second elements of matter.

4. The method of claim 3, further comprising the step of transferring energy between said juxtaposed first and second elements of maker and external energy apparatus, said energy hole to control the rate of fusion according to the relative equivalence of said energy hole and transferred energy to the energy levels of said first and second elements of matter.

5. The method of claim 1, wherein the step of providing an energy hole comprises the steps of:
selecting a plurality of elements of matter, each having an ionization energy, wherein each of said plurality of elements of matter are selected to produce a difference in ionization energies substantially equal to the energy resonance shrinkage energy of said first element of matter.

6. The method of claim 1, wherein said first and second elements of matter comprise different elements of matter.

7. The method of claim 6, wherein said step of providing an energy hole for each of said first and second elements comprises the step of:
selecting a third and fourth element of matter each having an ionization energy substantially equal to the resonance shrinkage energy of the respective first and second elements.

8. The method of claim 6, wherein said step of providing an energy hole for each of said first and second elements comprising the step of:
selecting a plurality of elements providing a difference in ionization energies substantially equal to at least one of the resonance shrinkage energy of said first and second elements.

9. The method of claim 8, wherein the step of providing an energy hole includes the step of:
selecting an additional element providing an ionization energy equal to the other resonance shrinkage energy of said first and second element.

10. The method of claim 5, further comprises the step of transferring energy between said juxtaposed first and second elements of matter and external energy apparatus, said energy hole to control the rate of fusion according to the relative equivalence of said energy hole and transferred energy to the resonance shrinkage energy levels of said first and second elements of matter.

11. The method of claim 10, wherein the transfer of energy is provided by one of an externally applied electric, magnetic field, or heat transfer and acoustic energy.

12. The method of claim 1, wherein the step of determining the resonance shrinkage energy comprises the step of calculating the said energy of the electron orbitals.

13. The method of claim 12, wherein the step of calculating comprises the steps of:
equating the sum of the magnetic and coulombic forces with the centripetal force;
introducing an energy hole into the centripetal force as a velocity deficit; and determining the energy hole by solving for the energy in the velocity deficit where the boundary conditions of Mills orbital, 2.pi.r = n.lambda. is observed.

14. The method of claim 1, wherein:
said first and second elements of matter have an atomic number of 26 or less.

15. The method of claim 1, wherein the step of providing an energy hole comprises:
providing a catalytic system.

16. The method of claim 15, wherein the step of providing a catalytic system comprises:
providing an electrochemical reactant comprising at least one of a cation and an anion.

17. Apparatus for providing the release of energy, comprising:
means for providing a first and second element of matter in a selected volume, each of said first and second elements having a nucleus and at least one electron at an orbital having a respective resonance shrinkage energy level; and a substance introduced into said selected volume for providing an energy hole in juxtaposition with said first and second elements of matter, said energy hole having a magnitude substantially equal to said resonance shrinkage energy, wherein:
fusion of said first and second elements of matter is produced when the orbitals of said first and second elements of matter are reduced due to removal of orbital energy by said energy hole permitting forces from each nucleus of said first and second elements of matter to form a common nucleus, providing the release of energy.

The apparatus of claim 17, wherein said substance comprises at least a third element of matter having an ionization energy substantially equal to the resonance shrinkage energy of each of said first and second elements of matter.

19. The apparatus of claim 18, wherein said substance further comprises at least an additional element of matter having an ionization energy, which in combination with the ionization energy of said third element produce said energy hole substantially equal to the resonance shrinkage energy of at least one of said first and second elements of matter.

20. The apparatus of claim 18, wherein:
said first and second elements of matter are the same elements.

21. The apparatus of claim 20, wherein:
said first and second elements of matter have an atomic number of 26 or less.

22. The apparatus of claim 18, wherein:
said first and second elements of matter comprises one of 2H, 3H, 6Li; and said third element comprises Ti2+.

23. The apparatus of claim 22, wherein said first and second elements of matter comprise deuterium and said third element comprises one of:
single-ion capable of producing energy holes for shrinking deuterium atoms. The number following the atomic symbol (n) is the nth ionization energy of the atom. That is for example, Ti2+ + 27.49 eV = Ti3+ + e-.

n = 16 (resonance shrinkage energy is given by ? 27.21; with n = 16, the resonance shrinkage energy is 217.68)

24. The apparatus of claim 20, wherein:
said first and second elements of matter comprises 2H and 3H; and said third and said additional element comprise Pd2+ and Li+.

25. The apparatus of claim 20, wherein said first and second elements of matter comprise deuterium and said third and fourth elements of matter comprise on of the following two-ion couples:
Two-ion couples capable of producing energy holes for shrinking deuterium atoms. The number in the column following the ion, (n), is the nth ionization energy of the atom. That is for example, Pd2 + 32.93 eV = Pd3+ + e- and Li+ + e- = Li + 5.39 eV.

n = 16 (resonance shrinkage energy is given by ? 27.21 eV; with n = 16, the resonance shrinkage energy is 217.68) Atom n nth ion- Atom n nth ion- Energy n = 54 (resonance shrinkage energy is given by ? 27.21 eV; with n= 54, the resonance shrinkage energy is 734.67) Two-ion couples capable of producing energy holes for shrinking deuterium atoms involving cations and anion. The number in the column following the ion, (n), is the nth ionization energy of the atom. For example, Ga2+ + 30.71 eV = Ga3+ + e- and H + e- = H- +
3.08 eV.

Cations and anions with n = 16 (resonance shrinkage energy is given by ? 27.21; with n = 16, the resonance shrinkage energy is 217.68) Cations and anions with n = 54 (resonance shrinkage energy is given by ? 27.21; with n - 54, the resonance shrinkage energy is 734.67) Some representative couples comprising a cation and a molecule capable of producing enrgy holes for shrinking deuterium atoms where the molecule is reduced. The number in the column following the ion or molecule, (n), is the nth ionization ergy of the atom or molecule. For example, Ga2+ + 30.71 eV = Ga3+ + e- and BF3 + e- =
BF3 + 2.65 eV.
Cations and molecular anions with n = 54 (resonance shrinkage energy is given by ? 27.21 with n - 54, the resonance shrinkage energy is 734.67)

26. The apparatus of claim 19, wherein said energy hole is provided by one of the following three-ion couples:
Na 1 5.139

27. The apparatus of claim 17, further including:
external energy apparatus;
means for providing a transfer of energy between said juxtaposed first and second elements of matter and said substance, and said external energy apparatus for controlling the rate of said fusion according to the relative equivalence of said energy hole and resonance shrinkage energy transferred to said first and second elements of matter.

28. The apparatus of claim 27, wherein said means for providing a transfer of energy comprises means for applying one of an electric, a magnetic field, transfer of heat and acoustic energy to said selected volume.

29. The apparatus of claim 17, further comprising:
means for receiving said release of energy from said volume; and means for transferring the received released energy to external load apparatus for dissipation and production of work.

30. The apparatus of claim 29, wherein:
said means for receiving comprises heat exchanger means for providing a flow of heat in a selected medium; and said means for transferring comprises turbine means for receiving said heat flow and providing one of electrical and mechanical power therefrom.

31. A method of determining the energy levels of the electron orbitals of an element of matter, comprising the steps of:
determining the centripetal force of each electron orbital;
determining the gradient of said electrostatic potential of said element of matter;
determining the radius of each electron orbital shell according to the centripetal force and the gradient of said electrostatic potential; and determine the energy level according to the radius of said electron orbital .

32. The method of claim 31, further providing the step of providing relativistic corrections of the determined energy.

33. The method of claim 31, where the steps of determining the gradient comprises:

and the step of determining the energy level according to the radius comprises:

34. The method of claim 31, further including the steps of:
determining the gradient of the angular momentum of each said electron;
determining the radius of each Mills electron orbital shell according to the centripetal force, gradient of said electrostatic potential and the gradient of said angular momentum;
determining the electrostatic energy of each electron orbital according to the radius of each Mills electron orbital shell;
determining the magnetic energy of each electron orbital according to the radius of each electron orbital shell; and adding the electrostatic and magnetic energy to provide said electron orbital energy level.

35. The method of claim 34, further including the step of providing relativistic correction of the determined energy.

36. A method of determining the internuclear distance of a chemical bond, comprising the steps of:
determining the decrease in electron electrostatic energy as internuclear distance 2y decreases;
determining the increase in nuclear repulsive energy as internuclear distance 2y decreases; and determining the distance 2y at which point the change in electrostatic energy and nuclear repulsive energy are substantially equal, to provide the internuclear distance of a chemical bond, wherein the total energy stored in the resulting electric field is a minimum.

37. For use in the production of coulombic annihilation fusion, an energy hole of energy E, comprising a rst element of matter selected according to a corresponding ionization potential; and at least one second element of matter selected according to a corresponding ionization potential, wherein the combination of the ionization potentials provides a net positive ionization potential substantially equal to E.

38. An apparatus of claim 22, wherein the source of an energy hole is a single cation, neutral atom, or anion or a single molecule which is a cation, neutral molecule or anion, or is a combination of said species wherein the said energy hole is substantially equivalent to n/2 27.21 eV
where n = 2, 3, 4,....

39. A method of releasing energy, comprising the steps of:
selecting a first element of matter having a nucleus and at least one electron orbital;
selecting a second element of matter having a nucleus and at least one electron orbital;
determining the resonance shrinkage energy levels of the electron orbitals of said first and second elements of matter;
providing two energy holes substantially equal to each of the resonance shrinkage energy levels of said first and second elements of matter;
juxtaposing said first and second elements of matter and said energy holes, wherein;
a non-fusion release of energy is produced when the energy of said electron orbitals is removed by said energy holes.

40. A composition of matter, comprising:
a transition element, m, having a large population of electrons receptive of energy from one of an electric and magnetic field to urge formation of Cooper electron pairs; and a plurality of materials, A, B, C, and D having strong bond energies and a lattice of two of less dimensions, wherein A, B, C, and D each are of different atoms, different oxidation states of the same atom, and different oxidation states of different atoms, in a cell arrangement, , having superconductor properties.