JP4870911B2 - Molecular orbital calculation device, method, program and recording medium - Google Patents

Description

  The present invention relates to a molecular orbital calculation apparatus, a molecular orbital calculation method, a molecular orbital calculation program, and a recording medium that are suitable for analyzing transition states by incorporating electronic correlation.

  The physical properties of molecules are closely related to the types of atoms and electronic states that make up molecules. If the electronic state of a molecule is known, for example, a differential structure based on energy coordinates is analytically obtained (so-called energy gradient method), thereby performing a stable structure in which the molecular energy is minimized, a transition state structure, a normal vibration analysis, and the like. be able to. Further, for example, by calculating the potential energy with respect to the reaction coordinate in the reaction of the molecule, the reaction system, the generation system, the reaction intermediate, and the transition state are obtained as the equilibrium point. In addition, vibration spectrum, electron spectrum, dipole moment, ionization potential, polarizability, spin density, and the like can be obtained. Thus, if the electronic state of a molecule | numerator is known, the physical property of various molecules can be calculated | required.

  There is a molecular orbital method as an approximate method for obtaining the electronic state of this molecule based on quantum mechanics. The electronic state of a molecule is represented by a molecular orbital, and this molecular orbital is obtained by solving an equation called a Hartree-Fock-Lautern equation (hereinafter abbreviated as “HFR equation”). This HFR equation is an equation for finding a set of spin orbits that is the best approximation to the ground state when the wave function of the system is approximated by one slater determinant.

  In the molecular orbital method, depending on the degree of approximation used when solving the HFR equation, the empirical molecular orbital method typified by the Hückel method and the extended Huckel method are ignored, and certain terms of the two-electron integral are ignored as sufficiently small values. And semi-empirical molecular orbital methods that use measured values as calculation parameters, and ab initio molecular orbital methods that are all calculated from the first principle without using measured values except for physical constants. . The empirical molecular orbital method and the semiempirical molecular orbital method have the disadvantage that the calculation results depend on the approximation method and parameters, but are not reliable. The non-empirical molecular orbital method does not have such a disadvantage. Is excellent. Application programs for executing such ab initio molecular orbital methods include, for example, Gaussian 94/98 (manufactured by Gaussian Inc., USA) and GAMESS (manufactured by NRCC, USA).

  The NBO energy analysis method, which is one analysis method of the conventional molecular orbital method, is used to analyze a specific interaction at the stage of the calculated wave function when the analysis is performed with no specific interaction (cut) according to the analysis purpose. It was difficult to include an electron correlation. In particular, it has been difficult to analyze a transition state in which the effect of electron correlation becomes significant.

  On the other hand, when examining intramolecular and intermolecular interactions (hereinafter referred to as “molecular interactions”), they are explained using concepts called through-bond interactions and through-space interactions. There is a case. These concepts are the concepts proposed by Hoffmann, Imamura et al. In 1968 (for example, Non-Patent Document 1). Through Bond (Through Bond) interaction (hereinafter abbreviated as “TB interaction”) refers to interaction through bonds (Through Space) interaction (hereinafter referred to as “TS interaction”). Is abbreviated as “.” Refers to an interaction through a space without a bond. Conventionally, when examining molecular interactions, these concepts have been used to explain qualitatively, but cannot be explained quantitatively, and it has been desired to explain quantitatively.

  Therefore, the inventors incorporated the concepts of TB interaction and TS interaction into the ab initio molecular orbital method, and showed the relationship between activation energy and transition state stability and interorbital interactions such as stereoelectronic effects. A technique for quantitative analysis including electronic correlation (hereinafter referred to as “TS / TB interaction analysis method”) has been developed and disclosed in Non-Patent Document 2.

The TS / TB interaction analysis method disclosed in Non-Patent Document 2 uses a hybrid atom orbit (Hybridized Atomic Orbitals, hereinafter abbreviated as “HAO”) as a basis function (Basis Set), and is cut. This is a technique for obtaining a wave function of a molecule by replacing the integral element corresponding to the desired interaction with an integral element using the concept of orbital contraction, establishing an HFR equation, and solving the HFR equation.
R. Hoffmann, A. Imamura, WJHehre, J. Am. Chem. Soc. 90, 1499 (1968) Yuuichi Orimoto, Yuriko Aoki “Pure Trough-Bond State in Organic Molecules for Analysis of the Relationship Between Intramolecular Interactions and Total Energy”, International Journal of Quantum Chemistry, Vol. 92, 355-366 (2003)

By the way, in the conventional method, HAO is used for the basis function. HAO is only compatible with the minimum basis set STO-3G, and is not sufficient to represent the actual phenomenon in terms of accuracy and inability to create a hybrid orbit exceeding the sp ³ hybrid orbit. It was. In particular, when 4 or more bonds (interaction between atoms in a molecule) such as a transition state are expected, it cannot be applied.

  The present invention was made in view of the above circumstances, and recorded a molecular orbital calculation device, a molecular orbital calculation method, a molecular orbital calculation program, and a molecular orbital calculation program that can be analyzed by any large basis function system. An object is to provide a recording medium.

In order to achieve the above-described object, a molecular orbital calculation device for obtaining an electronic state of a molecule by the Hartree-Fock-Lautern equation according to the present invention, which is configured by a computer, is based on the structure data of the molecule and the mutual information to be excluded. An input unit for inputting cut information indicating the action, a normal integration storage unit for storing the integration element in the molecular orbital method calculated using a basis function having a normal orbital index as a normal integration element , and virtually infinite The molecular orbital method using the large integral storage unit that stores the integral element in the molecular orbital method calculated using the basis function having the orbital index increased to the large integral element and the basis function having the normal orbital index. Of atomic orbital bases in overlap integral, kinetic energy integral, nucleus-electron attractive energy integral and two-electron integral in With the element by calculating the said molecules of the structure data stored in the normal integral storage unit, by using the basis function having a track index has increased to substantially infinite, integral overlap of the molecular orbital method, kinetic energy The integral element of the atomic orbital basis in the integral, the nucleus-electron attractive energy integral and the two-electron integral is calculated as an integral element after each interaction in the molecule has no interaction, and is stored in the large integral storage unit. and integration unit that stores, stores in the normal integral storage unit by converting the normal integral element of the atomic orbital basis stored in the normal integration storage unit to the integral element of the natural hybrid orbital basis or natural bond orbital base with natural hybrid orbital basis or natural binding a large integral element of the atomic orbital basis stored in the large integral storage unit A basis conversion unit to be stored in the large integration memory unit converts the integral element of the orbital basis, the cut information in one of the integral element of the natural hybrid orbital basis or natural bond orbital basis is stored in the normal integral storage unit An integral element replacement unit that replaces the integral element of the interaction corresponding to に with the integral element of the natural hybrid orbital basis or the natural coupled orbital base stored in the large integral storage unit, and the integral replaced by the integral element replacement unit An equation calculation unit that solves the Hartree-Fock-Low-turn equation using elements and an output unit that outputs the calculation result of the equation calculation unit are provided.

Further, in the molecular orbital computing device described above, the electron correlation effect on the computation result of the equation computation unit is expressed by the configuration interaction method ((Configuration Interaction, CI) method), perturbation method ((Mφller-Plesset perturbation theory, MPn) method) and a multi-configuration SCF method ((Multi Configurational Self Consistent Field, MCSCF) method) are further included, and the output unit outputs the calculation result of the electronic correlation calculation unit. It is characterized by outputting.

And, according to the present invention, the molecular orbital calculation method for calculating the electronic state of a molecule by the Hartree-Fock-Lautern equation, executed by a computer, includes the structure data of the molecule and the cut information indicating the interaction that should be absent. Using the input step to input and a basis function having a normal orbital index, the integral data of the atomic orbital basis in the overlap or integral in the molecular orbital method, the kinetic energy integral, the nucleus-electron attractive energy integral, and the two-electron integral are obtained as the structural data. Is used as a normal integral element of the atomic orbital basis, and by using a basis function having an orbital index substantially increased to infinity, an overlap integral, a kinetic energy integral, a nucleus − in the molecular orbital method are used. the integral element of atomic orbital basis in electronic attraction energy integral and two-electron integrals in the molecule And integral operation steps of the large integral element of each operation on atomic orbital basis as an integral element of after as no interaction for each interaction, the normal integral element of the atomic orbital basis which is calculated by the integral calculation step Is converted into an integral element of a natural hybrid orbital base or a natural coupled orbital base, and a large integral element of the atomic orbital base calculated in the integration operation step is converted into an integral element of a natural hybrid orbital base or a natural coupled orbital base Of the normal integration elements of the base conversion step and the natural hybrid orbital base or the natural coupling orbit base converted in the base conversion step, the interaction integration element corresponding to the cut information was converted in the base conversion step. integral element substitution step for replacing the large integral element of natural hybrid orbital basis or natural bond orbital base And an equation calculation step that solves the Hartree-Fock-Lautern equation using the integration element replaced in the integration element replacement step, and an output step that outputs the calculation result of the equation calculation step. .

Further, according to the present invention, the molecular orbital calculation program for causing a computer to obtain an electronic state of a molecule by the Hartree-Fock-Lautern equation and to cause the computer to execute the structure data and the cut information indicating the interaction to be eliminated And the integration element of the atomic orbital basis in the molecular orbital method in the overlap or integral, kinetic energy integration, nuclear-electron attractive energy integration and two-electron integration using the basis step having a normal orbital index Using the basis function with the orbital index increased to substantially infinite, using the basis function with the orbital index increased to infinity, by computing the molecule of the data, the overlap integral, kinetic energy integral, nuclear - the amount of the integral element of the atomic orbital basis in electronic attraction energy integral and two-electron integrals And integral operation steps of the large integral element of each operation on atomic orbital basis as an integral element of after as no interaction for each interaction of the inner, the atomic orbital basis of the normal calculated in the integral calculation step The integral element is converted into an integral element of a natural hybrid orbital base or a natural coupled orbital base, and the large integral element of the atomic orbital base calculated in the integral operation step is converted into an integral element of a natural hybrid orbital base or a natural coupled orbital base. Of the normal integration elements of the basis conversion step to convert and the natural hybrid orbital base or the natural coupling orbit base converted by the basis conversion step, the integration element of the interaction corresponding to the cut information is converted by the basis conversion step. spontaneous hybrid orbital basis or integral element replacement scan replacing the large integral element of natural bond orbital base And an equation calculation step for solving the Hartree-Fock-Lautern equation using the integration element replaced in the integration element replacement step, and an output step for outputting the calculation result of the equation calculation step. And

Further, in a computer-readable recording medium in which a molecular orbital calculation program for obtaining a computer to obtain an electronic state of a molecule by using a Hartree-Fock-Lautern equation is recorded, the molecular orbital calculation program includes the molecular structure data. Using an input step for inputting cut information indicating an interaction desired to be absent and a basis function having a normal orbital index, an overlap integral, a kinetic energy integral, a nucleus-electron attractive energy integral and a two-electron in the molecular orbital method The integration element of the atomic orbital basis in the integration is calculated for the molecule of the structure data to be the normal integration element of the atomic orbital basis, and the basis function having the orbital index increased to substantially infinite Overlap integration, kinetic energy integration, nucleus-electron attraction in orbital method Integral calculation step of the large integral element of each operation on atomic orbital basis as an integral element after the integral element of the atomic orbital basis in the energy integral and two-electron integrals was assumed without interaction for each interaction in the molecule And converting the normal integration element of the atomic orbital basis calculated in the integration calculation step into an integration element of a natural hybrid orbital base or a natural coupling orbital base, and the large of the atomic orbital base calculated in the integration calculation step. The cut information in the base conversion step of converting the integral element into the integral element of the natural hybrid orbital base or the natural coupled orbital base and the normal integral element of the natural hybrid orbital base or natural coupled orbital base converted in the basis conversion step natural hybrid trajectories of the integral element of interaction corresponding, converted by said base conversion step And the integral element replacement step of replacing the large integral element of the base or a natural bond orbital basis, and Equations calculating step of solving the Hartree-Fock-Roothaan equations using the integral element which is replaced by the integral element replacement step, the equation computing step And an output step for outputting the result of the calculation.

  In the molecular orbital calculation device, molecular orbital calculation method, molecular orbital calculation program, and molecular orbital calculation program having such a configuration, the basis function of the integration element is converted into a natural hybrid orbital or a natural bond orbit. It is possible to handle a large basis set system by replacing the integral element that has no interaction among the integral elements that have no interaction and replacing the integral element with no interaction. .

  Embodiments according to the present invention will be described below with reference to the drawings. In addition, the structure which attached | subjected the same code | symbol in each figure shows that it is the same structure, The description is abbreviate | omitted.

(Configuration of the embodiment)
FIG. 1 is a block diagram showing the configuration of the molecular orbital calculation apparatus. In FIG. 1, the molecular orbital calculation device 1 includes an arithmetic processing unit 11, an input unit 12, an output unit 13, an internal storage unit 14, an auxiliary storage unit 16, and a bus 18.

  The arithmetic processing unit 11 includes, for example, a microprocessor, and functionally includes an integration calculation unit 111, a basis conversion unit 112, an integral element replacement unit 113, an equation calculation unit 114, and an electronic correlation calculation unit 115. The input unit 12, the output unit 13, the internal storage unit 14, and the auxiliary storage unit 16 are controlled according to the control program.

  The integral calculation unit 111 calculates various integral elements of the atomic orbital basis in the molecular orbital method. The various integral elements are the overlap integral S, the kinetic energy integral T, the nucleus-electron attractive energy integral V, and the two-electron integral in the molecular orbital method. Various kinds of integral elements are disclosed together with these notations, for example, in “Mr. Kaeda,“ Chemical New Series, Molecular Orbital Method ”, Hankabo, April 30, 1999, first printing”.

  The basis conversion unit 112 converts the basis of various integration elements calculated by the integration calculation unit 111 into a natural hybrid orbit or a natural coupling orbit. The integral element replacement unit 113 replaces the integral element corresponding to the cut information among the integral elements whose basis has been converted by the basis conversion unit 112 with an integral element after having made no interaction. The cut information is information indicating an interaction (TB interaction, TS interaction) that is not artificially desired (to be cut). The equation calculation unit 114 solves the HFR equation using the integration element replaced by the integration element replacement unit 113. The electronic correlation calculation unit 115 calculates an electronic correlation effect on the calculation result of the equation calculation unit 114.

  The input unit 12 is a device that inputs various commands such as calculation start instructions of the molecular orbital calculation device 1 and various data such as structure data, cut information, and initial electron density to be described later to the molecular orbital calculation device 1, for example, Keyboard and mouse. The output unit 13 is a device that outputs the command and data input from the input unit 12, the calculation result of the molecular orbital calculation device 1, and the like, for example, a display device such as a CRT display, LCD, organic EL display, or plasma display, A printing device such as a printer;

  The internal storage unit 14 is a so-called working memory that reads the molecular orbital calculation program and control program executed by the arithmetic processing unit 11 from the auxiliary storage unit 16 and temporarily stores each data during execution of the molecular orbital calculation program. For example, a RAM (Random Access Memory) that is a volatile storage element is provided.

  The auxiliary storage unit 16 is a device for storing data and programs such as a non-volatile storage element such as a ROM and EEPROM, a hard disk, and the like, and includes a normal integration storage unit 161 and a large integration storage unit 162, and calculates molecular orbitals. Data (not shown) such as a control program for operating the molecular orbital calculation program and the molecular orbital calculation device 1, and data necessary for execution of each program such as an initial electron density D (0) described later (not shown) Etc.) are stored.

  The normal integration storage unit 161 calls various integration elements (referred to as “normal integration elements”) of each basis calculated using basis functions having normal orbital indices (referred to as “normal basis functions”). Memorize).

  Each base is an AO (Atomic Orbital) base, an NHO (Natural Hybrid Orbital) base, and an NBO (Natural Bond Orbital) base.

  NHO is a hybrid orbit based on a so-called Lewis structure that is made of an arbitrary basis function system and is easy to understand intuitively, and is a constituent unit of NBO. This NHO is disclosed in, for example, “J.P. Foster and F. Weinhold” Natural Hybrid Orbitals ”J. Am. Chem Soc. 1980, 102, 7211-7218”.

  NBO is an intelligible orbit localized at the bond or so-called lone pair orbital portion that is the basic unit of the molecular structure, and the number of occupied electrons can be a non-integer value. Orbit with a more natural picture. For this NBO, see, for example, “F. Weinhold, C. Landis” Natural Bond Orbitals and Extensions of Localized Bonding Concepts ”, Chemistry education research and practice in Europe. 2001, Vol. 2, No. 2, 91-104. It is disclosed.

  The large integral storage unit 162 uses each basis function having a trajectory index α increased to substantially infinity to cut the interaction (referred to as a “large basis function”). Various basic integration elements (referred to as “large integration elements”) are stored. In the NBO energy analysis method, a specific interaction is cut at the calculated wave function stage. In the present invention, a specific interaction (interaction related to the analysis purpose) is cut at the basis function stage. To do. Conventionally, it has been difficult to include the effect of electron correlation and analysis of the excited state, but by cutting a specific interaction at the basis function stage, the present invention includes the effect of electron correlation and excited state. Can be analyzed.

FIG. 2 is a diagram for explaining an artificial cut of interaction due to trajectory contraction. FIG. 2 (A) shows the case of an artificial cut of the AO-based interaction, and FIG. 2 (B) shows the artificial interaction of the NBO-based interaction in the ammonia-allyl bromide _SN 2 reaction transition state. The case of a simple cut is shown.

  First, an artificial cut of the interaction by the AO base will be described.

In FIG. 2A, artificially cutting the interaction between AOχr belonging to atom A and AOχs belonging to atom B shown on the left side of FIG. 2A completely eliminates the overlap between χr and χs. That is. This makes the absolute value of the orbital index α in the Gaussian function exp (−α × r ² ) corresponding to the interaction between χr and χs (L _AB is the distance between the atom A and the atom B) infinite. It corresponds to doing. That is, when the orbital index α is gradually increased from the state on the left side of FIG. 2A, χr and χs are localized in the nucleus A and the nucleus B to which the orbital index B belongs, and the orbital index α is substantially equal. When increasing to infinity, as shown on the right side of FIG. 2A, χr and χs are localized on the nucleus A and the nucleus B to which they belong (orbital contraction). As a result, the overlap between χr and χs is completely eliminated, and the interaction due to the spatial overlap between χr and χs is artificially cut.

Specifically, the non-relevance of χr and χs among integral elements (overlap integral S, kinetic energy integral T, nucleus-electron attractive energy integral V, and two-electron integral (rs | tu)) necessary for calculation of molecular orbitals. The diagonal component becomes zero. That is, each integral element changes as follows by the contraction of the trajectory.
a) Overlap integral Srs → 0
b) Kinetic energy integration Trs → 0
c) Nuclear-electron attractive energy integration Vrs → 0
d) (rs | **) type of 2-electron integral → 0
From another viewpoint, this state corresponds to the fact that the effect of delocalization of electrons between χr and χs is artificially suppressed. The subscript rs indicates that the integral element is a component of r rows and s columns in the matrix.

  The localized orbital χ forms a point charge on the nucleus A and the nucleus B. This means that the negatively charged point charge formed by the orbital χ has the effect of shielding the positive charge of the nucleus, so that the electrostatic interaction between atoms is also cut simultaneously. Therefore, when the interaction is cut, there is an effect that it is not necessary to consider the balance of each term contributing to the total energy of internuclear repulsion, interelectron repulsion, and nucleus-electron attraction.

Specifically, each integral element changes as follows by the contraction of the trajectory.
e) The diagonal component Vrr ^B between the nucleus B and the orbit χr and the diagonal component Vss ^A between the nucleus A and the orbit χs in the nuclear-electron attractive energy integral Vrs are respectively the classical Coulomb attractive forces. Become energy. If the distance between the nucleus A and the nucleus B (distance between nuclei) is L _AB and the charge of the electron is e,
Vrr ^B → −e ² / L _AB , Vss ^A → −e ² / L _AB
It is.
f) The (rr | ss) type of the two-electron integral becomes the classical Coulomb repulsion energy.
(Rr | ss) → e ² / L _AB

  Here, when it is desired to estimate only the interaction due to delocalization of electrons (for example, steric electron effect, electron transfer reaction, etc.), the above-described a) to d) interaction is artificially cut. What will be described later may be performed. On the other hand, when it is desired to estimate the effect of the steric repulsion including all the interactions between atoms such as the electronic interaction and the interaction between nuclei, the above-mentioned interaction a) to f) is artificial. It is only necessary to perform an after-mentioned calculation with a simple cut. The effect of steric repulsion plays an important role in the problem of rotation barriers.

The artificial cut of the interaction by the NBO base and the artificial cut of the interaction by the NBO base can be considered similarly to the artificial cut of the interaction by the AO base. However, since the NBO base is described by a linear combination of a plurality of AOs, one NBO extends over a plurality of nuclei, and thus becomes complicated. The case where the σ-π ^* interaction is cut in the S _N 2 reaction between ammonia and allyl bromide handled in the examples will be specifically described below.

The σ orbit corresponds to NBOφr belonging to the nitrogen atom N1 straddling N—C—Br and φs belonging to the carbon atom C2 and bromine atom Br3, and the π ^* orbital corresponds to φt belonging to the carbon atom C4 and carbon atom C5. Corresponds. Here, N, C, and Br are element symbols of nitrogen, carbon, and bromine, respectively, and the subscript is a number assigned to each atom in allyl bromide as shown on the left side of FIG. .

First, the above-described processes a) to d) are performed. The cutting of the σ-π ^* interaction corresponds to cutting the interaction between φr and φt and between φs and φt. That is, the overlap between φr and φt and the overlap between φs and φt are artificially eliminated by the contraction of the trajectory (see the right side of FIG. 2B). For this reason, the absolute value of the orbital exponent of the Gaussian function in the integral element of the AO base constituting the integral element of the NBO base corresponding to these interactions is made substantially infinite.

  In addition, as a result of localization, the orbit forms a point charge on the nucleus in the same manner as described above. Since one orbit belongs to a plurality of nuclei in the NBO base, Processing corresponding to e) and f) is performed.

  In the case of the NBO base as in the case of the AO base, if only the interaction due to the delocalization of electrons is to be estimated, the above-described a) to d) interaction is artificially cut. What will be described later may be performed. On the other hand, when it is desired to estimate the effect of solid repulsion, an artificial cut of the above-described interactions a) to f) may be performed and the calculation described later may be performed.

  Returning to FIG. 1, the arithmetic processing unit 11, the input unit 12, the output unit 13, the internal storage unit 14, and the auxiliary storage unit 16 are respectively connected to the bus 18 so that data can be exchanged with each other.

  If necessary, the molecular orbital computing device 1 may further include an external storage unit 15 and a communication interface unit 17 indicated by broken lines in FIG.

  The external storage unit 15 stores data with a recording medium such as a flexible disk, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Compact Disc Recordable), and a DVD-R (Digital Versatile Disc Recordable). An apparatus that performs reading and / or writing, such as a flexible disk drive, a CD-ROM drive, a CD-R drive, and a DVD-R drive. The communication interface unit 17 is connected to a communication network and is a device for transmitting and receiving communication signals to and from other client devices via the communication network.

  If each program is not stored, it may be configured to be installed in the auxiliary storage unit 16 via the external storage unit 15 from a recording medium on which these programs are recorded, and a server computer that manages these programs Each program may be downloaded from a communication network and communication interface unit 17 (not shown). In addition, the data to be input to the molecular orbital calculation device 1 in calculating the molecular orbital may be configured to be input to the molecular orbital calculation device 1 via the external storage unit 15 by a recording medium storing this data. In addition, the molecular orbital calculation device 1 may be configured to be input from the client device via the communication network and the communication interface unit 17.

  Next, the operation of this embodiment will be described.

(Operation of the embodiment)
First, the structure of the object to be calculated is determined. Next, a coordinate system is determined, and structure data of the operation target is created based on the determined coordinate system. Then, the structure data and the cut information are input to the molecular orbital calculation device 1 via the input unit 12. The structure data is coordinates based on the determined coordinate system of each atom in the molecule of the calculation object. In the present embodiment, an interaction through a bond (bond) between adjacent neighbors is defined as a TB interaction, and an interaction other than that is defined as a TS interaction. It is not necessary to define the action as a TB interaction and the other as a TS interaction. For example, an interaction through a neighboring bond in addition to a neighboring bond is defined as a TB interaction, and other interactions are defined. What is necessary is just to define according to the analysis objective, such as defining an action as TS interaction.

  FIG. 3 is a flowchart showing the operation of the molecular orbital calculation device. In FIG. 3, when structure data and cut information are input from the input unit 12 (S11), the integration calculation unit 111 of the calculation processing unit 11 uses a basis function (normal basis function) having a normal orbital index α. Various AO-based integration elements (hereinafter referred to as “AO normal integration elements”) are calculated, and the calculation results are stored in the normal integration storage unit 161 (S12).

  Further, the integral calculation unit 111 uses various basis elements (large basis functions) having an orbital index α (for example, α → ∞) increased so as to cut the interaction. (Hereinafter referred to as “AO large integration element”) is calculated for each interaction in the calculation object, and the calculation result is stored in the large integration storage unit 162 (S13). That is, according to the analysis purpose, the above-described artificial cut of the interaction a) to d) or the artificial cut of the above-described interaction a) to f) is performed for each interaction in the calculation object. Do. Thus, by previously calculating and storing each AO large integral element for each interaction, it is possible to quickly cope with a change in the interaction to be cut in the calculation object.

  Next, the base conversion unit 112 of the arithmetic processing unit 11 causes the conversion matrix U (AO → NBO) for conversion from the AO base to the NBO base to act on the AO normal integration element obtained in step S12 (formula (1A), ( 1B)), a normal integration element based on the NBO base (hereinafter referred to as “NBO normal integration element”) is obtained. Then, the basis conversion unit 112 stores the obtained NBO normal integration element in the normal integration storage unit 161 (S14).

  Next, the basis conversion unit 112 causes the transformation matrix U (AO → NBO) to act on the AO large integration element obtained in step S13 (see equations (1A) and (1B)), and performs large integration with the NBO basis as the basis. An element (hereinafter referred to as “NBO large integral element”) is obtained. Then, the basis conversion unit 112 stores the obtained NBO large integration element in the large integration storage unit 162 (S15).

U ⁺ is a complex conjugate of the transformation matrix U (AO → NBO).

  Here, the conversion from the AO base to the NBO base of the two-electron integral having a complicated operation will be specifically described.

FIG. 4 is a diagram illustrating a target system of a specific example in which a two-electron integral is converted from an AO base to an NBO base. As shown in FIG. 4, it is assumed that NBOφ _r in the target system of the specific example consists of AOχ ₁ belonging to atom A and AOχ ₂ belonging to atom B, while NBOφ _s consists of AOχ ₃ belonging to atom C. This can be expressed as a matrix as shown in Equation 2.

Here, N is a normalization constant, and Equation 3 is a transformation matrix U (AO → NBO).

  Considering the case where the two-electron integral (rr | ss) of the NBO basis becomes a classical Coulomb repulsion energy in the case of a large integral element, according to the equation (1B), among the terms mixed into (rr | ss), It is the expressions (4A) and (4B) that the transformation matrix U (AO → NBO) and the AO basis integral element are not zero.

  Further, although the AO basis integral element does not become zero, the transformation matrix U (AO → NBO) becomes zero according to Expression (5).

Here, L _ij is the interatomic distance between atom i and atom j (i, j = A, B, C).

Since the two-electron integrals of other AO bases are all zero in the large integral element, (rr | ss) is eventually N ² (e ² / L _AC + e ² / L _AC ), and only the Coulomb repulsion energy remains. .

  Next, considering terms mixed in the (rs | rs) term, the transformation matrix U (AO → NBO) does not become zero in terms of the equations (6A) and (6B), but (13 | 13) Since (23 | 23) are both zero, the terms of these equations (6A) and (6B) are zero. Similarly, in the other terms, either the transformation matrix U (AO → NBO) or the term of the integral element becomes zero, so that the (rs | rs) term eventually becomes zero.

  Returning to FIG. 3, the integration element replacement unit 113 of the arithmetic processing unit 11 selects the NBO normal integration element of the interaction corresponding to the cut information among the NBO normal integration elements corresponding to each interaction in the operation target. Replace with NBO large integral element (S16). Thereby, a new integration element for TS / TB analysis according to the present invention (hereinafter referred to as “integration element for TS / TB analysis”) is created.

Next, the equation calculation unit 114 of the calculation processing unit 11 obtains the electronic state of the molecule using the integration element for TS / TB analysis in the process S16 (S17). That is, an approximate solution of the wave function ψ and total energy E of the electron that satisfies Equation 7 is obtained. H is a Hamilton operator.
Hψ = Eψ (7)

  More specifically, first, the equation calculation unit 114 creates a Fock matrix (hereinafter abbreviated as “F matrix”) based on Expression (8) using the TS / TB analysis integration element in the process S16. (S17-1).

H _rs ^Core is called a core integral, and consists of a kinetic energy integral T and a nucleus-electron attractive integral V.

Next, the equation calculation unit 114 substitutes the initial electron density D (0) for Put in Expression (8) and diagonalizes the F matrix to obtain a new electron density function D (n) (S17-2). That is, the eigenvalue problem | F _rs −εS _rs | = 0 is solved. Note that D (n) indicates the electron density obtained by the nth calculation. Moreover, (epsilon) shows orbital energy.

  Next, the equation calculation unit 114 determines whether or not the newly obtained electron density D (n) matches the previous electron density D (n−1) (S17-3). As a result of the determination, if they do not match (No), the equation calculation unit 114 returns the processing to S17-1 to obtain a new electron density again, and if they match (Yes), the equation calculation unit 114 obtains the new electron density. The electron wave function and total energy are obtained from the measured electron density. That is, the equation calculation unit 114 repeats until the newly obtained electron density D (n) matches the previous electron density D (n−1) and solves the F matrix. Such a solution is generally called a self-consistent field method. Since the initial electron density D (0) is a value that serves as a starting point for this repeated calculation, it may be an arbitrary value, for example, 0.

In the solution method using the F matrix, a Hamilton operator related to one electron is assumed, and therefore, the molecular orbital obtained by such an operation takes into account only a part of the electron correlation effect . Therefore, the arithmetic processing unit 11 outputs to the output unit 13 whether or not to consider the electronic correlation effect (S18), and when an instruction to consider the electronic correlation effect is input by the operator, The electronic correlation calculation unit 115 of the processing unit 11 calculates the electronic correlation effect (S19). The calculation method considering the electron correlation effect includes, for example, CI (Configuration Interaction) (configuration interaction method), MPn (Mφller-Plesset perturbation theory) method (perturbation method), and MCSCF (Multi Configurational Self Consistent Field) method ( Multi-configuration SCF method) is known.

  And the arithmetic processing part 11 outputs a calculation result from the output part 13 (S20).

  Here, in the above-described embodiment, the method for obtaining the molecular orbitals in a state where a specific interaction by the NBO base is cut has been described. However, instead of the expressions (1A) and (1B) in the processes S14 and S15, the expressions By using (9A) and formula (9B), the electronic state in a state where a specific interaction by the NHO base is cut can be obtained by the same procedure.

  By operating as described above, the molecular orbital computing device 1 can obtain a molecular wave function and total energy in a state in which a specific interaction is cut with a large basis function system.

  In the conventional NBO energy analysis method (hereinafter abbreviated as “conventional analysis method”), a specific interaction is cut at the stage of the calculated wave function. For this reason, in order to consider the electron correlation in the conventional analysis method, it is necessary to cut the interaction for various multi-electron excitation arrangements, which has not been realized in the conventional analysis method. On the other hand, in the molecular orbital calculation method according to the present invention (hereinafter referred to as “TS / TB interaction analysis method”), the interaction is cut at the integration element stage as described above. The effect of cutting the interaction can be automatically introduced to various excitation electron configurations including the electron configuration, and the electron correlation can be taken into consideration. From this, the TS / TB interaction analysis method according to the present invention can quantitatively analyze the effect of the interaction cut in the excited state.

Further, regarding the cut of the two-electron integral, for example, when considering the case where the interaction between the trajectories χ ₁ -χ ₂ is cut, in the conventional analysis method, F ₁₂ corresponding to the interaction in the matrix element Frs of the F matrix. And F ₂₁ is replaced with 0 and the F matrix is diagonalized only once. That is, referring to equation (8), in the conventional analysis method, F ₁₂ = 0 means that H _rs ^Core and the Coulomb term (12 | tu) of the two-electron integral and the exchange term (1u | t2) are set to 0. means. In the matrix element Frs of the F determinant excluding F ₁₂ and F ₂₁ , (rs | 12) of the Coulomb term, which is a term that secondarily represents the interaction between the orbits χ ₁ -χ _2, and the exchange term (R2 | 1s) remains without being 0. For this reason, in the conventional analysis method, the cut of the two-electron integral is incomplete. The TS / TB interaction analysis method according to the present invention, since the cutting of the interaction by the above-described trajectory shrinkage at the stage of the integral element, which primarily included in F _{12 (12} | tu) and (1u | t2 ) And (rs | 12) and (r2 | 1s) included in other matrix elements automatically converge to 0. For this reason, in the TS / TB interaction analysis method according to the present invention, the two-electron integral cut is complete.

  Next, a specific example to which the TS / TB interaction analysis method according to the present invention is applied will be described.

(First specific example)
FIG. 5 is a diagram schematically showing the molecular structure of aminomethanol. FIG. 5A shows the case of Anti-periplanar, and FIG. 5B shows the case of Perpendicular. Moreover, the figure seen from the nitrogen atom N to the direction of the carbon atom C is shown on the right side of each figure.

The first specific example is an analysis of the steric electronic effect in aminomethanol. The Lone pair orbital [n (N)] of nitrogen atom N and the antibonding orbital between C—O (between carbon and oxygen atoms) [ The model [Anti-periplanar (APP)] (see FIG. 5A) whose relation to σ ^* (C−O)] is opposite to the same plane and the model [Perpendicular (PPD)] which becomes vertical (see FIG. 5B) ) in each of the reference), by C-O bond length is to compare to that extended the standard ones (1.43 Å) (1.63 Å), n-sigma ^* interacts with C-O The relationship between the ease of bond dissociation was analyzed. Note that the TS / TB interaction analysis method according to the present invention was incorporated into GAMESS, and the analysis of the first specific example and the second and third specific examples described later were performed.

Tables 1 and 2 show the results. Table 1 shows HF level total energy change ΔE (HF), internuclear repulsion term change ΔE (N−N), total when all interactions including all intramolecular interactions are considered (Full interaction). Electron energy term change ΔE ₀ and MP2 perturbation total energy change ΔE (MP2). The calculation was performed at the MP2 (Frozen Core) / 6-31G * level.

  The energy difference ΔE is the difference between the energy E (1.63) in the case of 1.63 Å and the energy E (1.43) in the case of 1.43 Å, that is, ΔE = E (1.63). -E (1.43). DIFF. Is the difference between the energy difference ΔE (APP) for APP and the energy difference ΔE (PPD) for PPD, ie, DIFF. = ΔE (APP) −ΔE (PPD). Advantage (advantage) indicates which conformation of APP and PPD is advantageous for C—O dissociation.

As can be seen from Table 1, in the case of full interaction, the APP model having a small ΔE (HF) is more advantageous for CO bond dissociation than the PPD model. It can also be seen that the effect of the electron correlation works to further increase the advantage of the APP model. This result shows that when the Lone pair orbit and σ ^* orbit are in the opposite coplanar relationship, the n-σ ^* electron movement is promoted, and the electrons flow into the σ ^* orbit and the bonds are easily dissociated. It supports the general concept of effects.

However, considering only the result of Full interaction in Table 1, this advantage of APP is interpreted not to be from ΔE ₀ but to the relaxation of ΔE (N−N), and the stereoelectronic effect is reduced. It is a denial.

Therefore, Table 2 shows the case where the n-σ ^* interaction is cut by the TS / TB interaction analysis method according to the present invention. Table 2 shows HF level total energy change ΔE (HF), internuclear repulsion change ΔE (N−N), total when n-σ ^* interaction is cut (Cut off n-σ ^* interaction). It is the change ΔE _{0 in the} electron energy term and the total energy change ΔE (MP2) in the MP2 level.

As can be seen from Table 2, in the case of Cut off n−σ ^* interaction, ΔE (HF) was almost equal between the APP model and the PPD model. This is interpreted to be due to the APP advantage at ΔE (N−N) being offset by the disadvantage at ΔE ₀ . In other words, the n-σ ^* interaction has the role of eliminating the disadvantages in APP (the role that causes an advantage of about -0.005 au to APP). As a result, in the case of Full interaction It can be concluded that only the ΔE (N−N) advantage of APP emerges, and that APP has an advantage for bond dissociation for all energies. That is, it was confirmed that the stereoelectronic effect (n-σ ^* interaction) indirectly controls the elimination reaction.

Furthermore, in order to investigate the behavior of the total electron energy in detail, the contribution of the n−σ ^* interaction to ΔE ₀ , that is, the difference between the full interaction and the cut off n−σ ^* interaction is The results are shown in Table 3, which are divided into a change in repulsion term ΔE (ee), a change in nuclear-electron attractive term ΔE (Ne), and a change in kinetic energy term ΔE (Kinetic). Table 3 shows the contribution of n-σ ^* interaction to the total electron energy change ΔE ₀ .

  As can be seen from Table 3, APP is advantageous for ΔE (N−e) and ΔE (Kinetic) corresponding to the resonance integral, and ΔE (ee), a secondary term, is PPD. Work in favor of. Therefore, it can be seen that the steric electronic effect in aminomethanol arises from the term corresponding to the resonance integral.

  Next, another specific example will be described.

(Second specific example)
FIG. 6 is a diagram showing the molecular structures of allyl bromide and propyl bromide and the activation energy of the S _N 2 reaction. FIG. 6 (A) shows allyl bromide, FIG. 6 (B) shows propyl bromide, and FIG. 6 (C) shows the activation energy of the S _N 2 reaction. In FIGS. 6A and 6B, carbon C and hydrogen H in the allyl group and the propyl group are omitted. FIG. 6C schematically shows the relationship between reaction coordinates and energy (the left side shows allyl bromide and the right side shows propyl bromide).

For example, according to “Kirby, AJStereoelectronic Effects; Oxford University, Oxford, 1996”, the S _N 2 reaction of allyl bromide (the nucleophile is NPhMe ₂ ) is 100 times the S _N 2 reaction of ethyl bromide. It is known to react faster than this, but no analysis has been performed at the molecular orbital level.

Therefore, the second specific examples are allyl bromide (CH ₂ ═CH—CH ₂ —Br) (see FIG. 6A) and propyl bromide (CH ₂ —CH ₂ —CH ₂ —Br) (FIG. 6). (B)) is analyzed for the difference in the S _N 2 reaction (the nucleophile is ammonia NH ₃ ).

First, the activation energy (reaction of the S _N 2 reaction) was calculated by calculating the energy of the HF / 6-31G ^* level without considering the electron correlation (the structural optimization was performed by calculating the HF / 6-31G ^* level). The difference between the energy of the intermediate on the product side and the energy of the transition state) was determined for each model. As a result, allyl bromide was 35.8 kcal / mol and propyl bromide was 35.9 kcal / mol. Indicated.

On the other hand, according to the present invention, the activation energy of the S _N 2 reaction was determined for each model by MP2 / 6-31G ^* level energy calculation taking into account the electron correlation. As a result, allyl bromide was found to be 34.5 kcal / mol (see FIG. 6 (C) left solid line), and propyl bromide was 37.0 kcal / mol (see right solid line in FIG. 6C).

  This indicates that allyl bromide has a lower activation energy by 2.5 kcal / mol than propyl bromide and has high reactivity, and supports the above-mentioned fact. In addition, since significant difference in activation energy is not seen unless electron correlation is taken into account, this system requires analysis including electron correlation and cannot be analyzed by the conventional analysis method.

Next, the activation energy of allyl bromide in a state where the σ-π ^* interaction was cut using the TS / TB interaction analysis method according to the present invention at the MP2 / 6-31G level was calculated. 7 kcal / mol (see the broken line on the left side of FIG. 6C).

From the above facts, the activation energy of allyl bromide is reduced by 37.7-34.5 = 3.2 kcal / mol due to the contribution of σ-π ^* interaction, and as a result, the transition state is stabilized. It can be said that. The activation energy (37.7 kcal / mol) of allyl bromide from which the σ-π ^* interaction is cut approximates the activation energy (37.0 kacl / mol) of propyl bromide having no π orbitals. It can be said that.

  This result shows that the hypothesis derived from the experimental fact of “stabilization of transition state by steric electronic effect involving π orbital” is based on quantitative discussion including electron correlation by the TS / TB interaction analysis method according to the present invention. It means that it has been proved.

  Next, another specific example will be described.

(Third example)
The third specific example is an analysis on which position in the reaction coordinates the σ-π ^* interaction in allyl bromide becomes maximum.

FIG. 7 is a diagram showing the energy difference between before (FULL) and after (CUT) the σ-π ^* interaction in allyl bromide by the TS / TB interaction analysis method according to the present invention. The horizontal axis in FIG. 7 is the reaction coordinate, and the vertical axis is the energy difference expressed in au units. FIG. 8 is a diagram showing a shift of the transition state position due to the solvent effect. The horizontal axis in FIG. 8 is reaction coordinates, and the vertical axis is energy expressed in au units.

the energy difference between the previous (FULL) and after (CUT) to cut the sigma-[pi ^* interaction is an energy contribution of sigma-[pi ^* interactions, as can be seen from Figure 7, σ-π ^* mutual The energetic contribution of the action is slightly on the reactant side, not in the transition state.

Here, the above analysis is in the gas phase and does not consider the effect of the solvent at all. Accordingly, FIG. 8 shows the result of obtaining the transition state and the intrinsic reaction coordinates in the same manner by using a PCM (Polarizable continuum model) method that can take in the effect of the solvent by considering the dielectric constant. As can be seen from FIG. 8, by introducing the solvent effect, the position of the transition state is shifted (moved) to the reactant side, and the maximum value of the contribution of σ-π ^* interaction is the transition state in which the solvent effect is added. Match the position of.

  In the above-described embodiment, the AO large integral element obtained by cutting each interaction in the calculation target one by one is calculated and stored in advance for each interaction, but the above-described processing S13 is performed. May be omitted, and only the AO large integral element of the interaction to be cut in step S16 may be calculated, and this may be converted into an NBO basis by applying a transformation matrix U (AO → NBO).

  In the above-described embodiment, the case where the transformation matrix U (AO → NBO) and the transformation matrix U (AO → NHO) are obtained in advance and incorporated into the molecular orbital computing device 1 according to the present invention has been described. When the present invention is incorporated in software, the transformation matrix U (AO → NBO) and the transformation matrix U (AO → NHO) may not be directly known from existing software. In such a case, the AO basis function, the NBO basis function, and the NHO basis function are once obtained using existing software, and then the transformation matrix U (AO → NBO) is obtained using the AO basis function and the NBO basis function. Alternatively, the transformation matrix U (AO → NHO) may be obtained using the AO basis function and the NHO basis function.

It is a block diagram which shows the structure of a molecular orbital calculating apparatus. It is a figure for demonstrating the artificial cut of the interaction by orbital contraction. It is a flowchart which shows operation | movement of a molecular orbital calculating apparatus. It is a figure which shows the object system of the specific example converted from the AO base of 2 electron integration to the NBO base. It is a figure which shows typically the molecular structure of aminomethanol. It is a figure which shows the molecular structure and activation energy of S _N2 reaction of allyl bromide and propyl bromide. It is a figure which shows the energy difference of before (FULL) and after (CUT) cutting the (sigma) -pi ^* interaction in allyl bromide by the TS / TB interaction analysis method based on this invention. It is a figure which shows the shift of the transition state position by a solvent effect.

DESCRIPTION OF SYMBOLS 1 Molecular orbital calculation apparatus 11 Operation processing part 12 Input part 13 Output part 16 Auxiliary storage part 111 Integral operation part 112 Basis conversion part 113 Integration element substitution part 114 Equation calculation part 115 Electronic correlation calculation part 161 Normal integration storage part 162 Large integral storage Part

Claims (5)

In a molecular orbital computing device that calculates the electronic state of a molecule using the Hartree-Fock-Lautern equation,
An input unit for inputting cut information indicating the structure data of the molecule and an interaction to be absent;
A normal integral storage unit that stores integral elements in the molecular orbital method calculated using basis functions having ordinary orbital indices as normal integral elements ;
A large integral storage unit for storing the integral element in the molecular orbital method calculated using a basis function having an orbital index increased substantially to infinity as a large integral element ;
Using the basis function having the normal orbital index, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral in the molecular orbital method, and the atomic orbital basis integral element in the two-electron integral are calculated for the molecule of the structural data. the stores in the normal integral storage unit, by using the basis function having a track index has increased to substantially infinite, integral overlap of the molecular orbital method, kinetic energy integration, nuclear Te - electron attractive energy integration and 2 electrons An integration operation unit that calculates the integration element of the atomic orbital basis in the integration as an integration element after each interaction in the molecule has no interaction, and stores the integration element in the large integration storage unit ;
Converting the normal integration element of the atomic orbital basis stored in the normal integration storage unit into an integration element of a natural hybrid orbital basis or a natural coupling orbital base and storing it in the normal integration storage unit, and the large integration storage unit A base conversion unit that converts the large orbital basis element of the atomic orbital basis stored in a natural hybrid orbital basis or the natural orbital basis integration element and stores it in the large integration storage unit ;
Of the integration elements of the natural hybrid orbital basis or the natural coupled orbital base stored in the normal integration storage unit, the interaction component corresponding to the cut information is stored in the large integration storage unit. An integration element replacement unit that replaces an integration element of an orbital basis or a natural coupled orbital basis ;
An equation calculation unit that solves the Hartree-Fock-Lautern equation using the integration element replaced by the integration element replacement unit;
A molecular orbital calculation device comprising: an output unit that outputs a calculation result of the equation calculation unit. For the calculation result of the equation calculation unit, an electron correlation effect is obtained by using a configuration interaction method ((Configuration Interaction, CI) method), a perturbation method ((Mφller-Plesset perturbation theory, MPn) method) and a multi-configuration SCF method ( (Multi Configurational Self Consistent Field, MCSCF) method)
The molecular orbital computing device according to claim 1, wherein the output unit outputs a calculation result of an electron correlation calculation unit. In a molecular orbital calculation method for calculating an electronic state of a molecule by the Hartree-Fock-Lautern equation executed by a computer ,
An input step of inputting the structure data of the molecule and cut information indicating an interaction to be absent;
Using the basis function having the normal orbital index, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral in the molecular orbital method, and the atomic orbital basis integral element in the two-electron integral are calculated for the molecule of the structural data. Using the basis function having the orbital index increased to substantially infinite while using the normal integral element of the atomic orbital basis, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral and 2 in the molecular orbital method are used. An integration operation step of calculating an atomic orbital basis integral element in electron integration as an integral element after making each interaction in the molecule non- interacting to be a large integral element of atomic orbital basis ;
The normal integration element of the atomic orbital basis calculated in the integration calculation step is converted into an integration element of a natural hybrid orbital basis or a natural coupling orbital base, and the atomic orbital basis large integration element calculated in the integration calculation step A basis transformation step for transforming into an integral element of a natural hybrid orbital basis or a natural coupled orbital basis;
Among the natural hybrid orbital bases or natural coupled orbital base normal integral elements transformed in the basis transformation step, the interaction integral elements corresponding to the cut information are converted into the natural hybrid orbital bases transformed in the basis transformation step or An integral element replacement step for replacing the natural integral orbital basis with a large integral element;
Equation calculation step for solving the Hartree-Fock-Lautern equation using the integration element replaced in the integration element replacement step;
A molecular orbital calculation method comprising: an output step of outputting a calculation result of the equation calculation step. In the molecular orbital calculation program for computer to calculate the electronic state of the molecule by the Hartree-Fock-Lautern equation,
An input step of inputting the structure data of the molecule and cut information indicating an interaction to be absent;
Using the basis function having the normal orbital index, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral in the molecular orbital method, and the atomic orbital basis integral element in the two-electron integral are calculated for the molecule of the structural data. Using the basis function having the orbital index increased to substantially infinite while using the normal integral element of the atomic orbital basis, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral and 2 in the molecular orbital method are used. An integration operation step of calculating an atomic orbital basis integral element in electron integration as an integral element after making each interaction in the molecule non- interacting to be a large integral element of atomic orbital basis ;
The normal integration element of the atomic orbital basis calculated in the integration calculation step is converted into an integration element of a natural hybrid orbital basis or a natural coupling orbital base, and the atomic orbital basis large integration element calculated in the integration calculation step A basis transformation step for transforming into an integral element of a natural hybrid orbital basis or a natural coupled orbital basis;
Among the natural hybrid orbital bases or natural coupled orbital base normal integral elements transformed in the basis transformation step, the interaction integral elements corresponding to the cut information are converted into the natural hybrid orbital bases transformed in the basis transformation step or An integral element replacement step for replacing the natural integral orbital basis with a large integral element;
Equation calculation step for solving the Hartree-Fock-Lautern equation using the integration element replaced in the integration element replacement step;
A molecular orbital calculation program comprising: an output step for outputting a calculation result of the equation calculation step. In a computer-readable recording medium on which a molecular orbital calculation program for causing a computer to execute is obtained, which calculates the electronic state of a molecule by the Hartree-Fock-Lautern equation,
The molecular orbital calculation program is:
An input step of inputting the structure data of the molecule and cut information indicating an interaction to be absent;
Using the basis function having the normal orbital index, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral in the molecular orbital method, and the atomic orbital basis integral element in the two-electron integral are calculated for the molecule of the structural data. Using the basis function having the orbital index increased to substantially infinite while using the normal integral element of the atomic orbital basis, the overlap integral, kinetic energy integral, nucleus-electron attractive energy integral and 2 in the molecular orbital method are used. An integration operation step of calculating an atomic orbital basis integral element in electron integration as an integral element after making each interaction in the molecule non- interacting to be a large integral element of atomic orbital basis ;
The normal integration element of the atomic orbital basis calculated in the integration calculation step is converted into an integration element of a natural hybrid orbital basis or a natural coupling orbital base, and the atomic orbital basis large integration element calculated in the integration calculation step A basis transformation step for transforming into an integral element of a natural hybrid orbital basis or a natural coupled orbital basis;
Among the natural hybrid orbital bases or natural coupled orbital base normal integral elements transformed in the basis transformation step, the interaction integral elements corresponding to the cut information are converted into the natural hybrid orbital bases transformed in the basis transformation step or An integral element replacement step for replacing the natural integral orbital basis with a large integral element;
Equation calculation step for solving the Hartree-Fock-Lautern equation using the integration element replaced in the integration element replacement step;
An output step for outputting the calculation result of the equation calculation step.

Images