CN107271468A - A kind of evaluation method of crystal electrons Density Distribution model and its application - Google Patents
A kind of evaluation method of crystal electrons Density Distribution model and its application Download PDFInfo
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Abstract
The invention provides a kind of evaluation method of crystal electrons Density Distribution model and its application.The evaluation method includes：S1. calculate the structural amplitude value of the correct electron density distribution model of crystal to be measured after the first perturbation is undergone, first perturbation cause the correct electron density distribution model of each atom in the crystal to be measured after experience perturbation in structure cell plus it is identical with the electron outside nucleus number of corresponding atom；S2. structural amplitude value of the Current electronic Density Distribution model of crystal to be measured after experience perturbation is calculated, the perturbation makes the low density area in Current electronic Density Distribution model change；S3. structural amplitude value and structural amplitude value in S1 in S2 are compared, to evaluate Current electronic Density Distribution model.The evaluation method of the present invention can be used for crystal structure analysis.Under lower data resolution condition, traditional evaluation method has failed, and the evaluation method that the present invention is provided is still effective.
Description
Technical field
The present invention relates to crystal structure analysis technical field, more particularly, to a kind of crystal electrons Density Distribution model
Evaluation method and its application.
Background technology
The physics of material, chemical property depend on its microstructure, therefore, obtain the structural information of material for understanding thing
The physics of matter, chemical property are particularly important.Current X-ray diffraction technology is that measure amorphous material structure is most important, most authoritative
Method, is also most widely used method.Also just because of the appearance of X-ray diffraction technology before more than 100 years, people are made to material
The understanding of structure has been deep into atom level, so as to change the ambits such as physics, chemistry, material, life science deeply
Looks, have greatly promoted technological progress, and then the deep looks for changing human lives.The original substantially of X-ray diffraction technology
Reason is that the X-ray incided in crystal can be by the electronics in electron density the institute diffraction, and crystal of periodic distribution in crystal
Density Distribution is exactly the inverse Fourier transform of crystal structure factor.Electron density distribution just represents the structure letter of crystal in crystal
Breath, as long as therefore measure the structure factor of crystal by X-ray diffraction technology, it is possible to easily obtain crystal structure letter
Breath.Unfortunately, X-ray diffraction technology is typically only capable to obtain diffracted intensity information, can be obtained from diffracted intensity information
The modulus value (commonly known as structural amplitude) of crystal structure factor, but the phase information of crystal structure factor can not be obtained, this is just
It is in X-ray crystallography famous " phase problem ".
People have had been developed that a variety of theories and experimental method for pushing away guiding structure factor phase, but these sides at present so far
Method all respectively has its limitation." direct method " of the Nobel Prize was for example once won, was only applicable in structure cell containing individual atoms
The situation of number less (usually less than 1000), and require that the resolution ratio of diffraction data is atom level (about 0.1 nanometer).Even if
Under the conditions of best, various push away draws the trial phase generally also simply recommended that the method for phase is provided, with correct phase
Remain larger gap.These trial phases are combined with the diffraction amplitudes that experiment measurement is obtained, it is possible to build
The model of electron density distribution in crystal.But whether the electron density distribution model being achieved in that is correct (i.e. with the reality in crystal
Border electron density distribution is consistent) also need to be further analyzed judgement.In diffraction data high resolution and electron density
Distributed model is correct or close in the case of correct, and atom level structural model can be gone out according to electron density distribution model construction,
Then the structural amplitude of crystal is calculated using atom level structural model, if the structural amplitude and the knot of experimental observation that calculate
Structure amplitude is consistent, then it is assumed that structural model is correct.
In this case, structural model is generally evaluated with the degree being actually consistent with following indexs：
Wherein, ∑hRepresent to it is all observe diffraction amplitudes add and, | Fobs| and | Fcal| represent that experiment is measured respectively
Diffraction amplitudes and the diffraction amplitudes that are calculated by structural model.RES (the commonly known as residual error factor) may not apply to can not
Construct the situation of atom level structural model.In 2004, Oszl á nyi andProposing electric charge inversion method parsing crystal knot
While structure, it is proposed that a R factor, for evaluating the quality of a current electron density distribution model.
The R factors are defined as follows：
Wherein ∑hWith | Fobs| it is identical with RES,It is specific micro- to apply one to Current electronic Density Distribution model
The calculated value of structural amplitude after disturbing.The good and bad principle of R factor evaluation crystal electrons Density Distributions model is：Differentiated in data
(i.e. the resolution ratio of diffraction data reaches atom level, about 0.1 nanometer), correct electron density distribution model in the case that rate is higher
Middle electron density will focus mainly in the region of the very little near atomic nucleus, and interatomic region is that flat electronics is low close
Spend area.Electron density distribution overall after one perturbation is applied to electronics low density area and changes very little, now | Fobs| with
Still closely, therefore, the R factors can for evaluate a Current electronic Density Distribution model quality：One less R
Factor values illustrate that Current electronic density model is correct or substantially correct.Compared with RES, the R factors can be used for remote because attempting phase
It is remote to deviate correct phase and the situation of atom level structural model be built.But then, the R factors are also only applicable to diffraction number
According to resolution ratio can reach the situation of atomic resolution.
With the deterioration of resolution ratio, in correct electron density model will have increasing electron density distribution exists
Region between atom, applies after a perturbation to correct electron density distribution model, and electron density will occur more notable
Change, now, | Fobs| withLarger difference will be had, the R factors can take a larger value, and the electronics of mistake is close
Degree distributed model is possible to that the smaller R factors can be obtained on the contrary.That is, in the case where resolution ratio is relatively low, the R factors are no longer
The quality of electron density distribution model can effectively be evaluated.
It is many times that can not obtain the diffraction data of atomic resolution, such as protein in X-ray diffraction
The resolution ratio of the diffraction data of macromolecule crystal can usually be inferior to 0.2 nanometer at present.How in relatively low diffraction data resolution ratio
Under the conditions of evaluate a Current electronic Density Distribution model quality, and how using low resolution diffraction data export
Correct electron density distribution model, which is always one, problem to be solved.
The content of the invention
The present invention provides a kind of crystal electrons density point for overcoming above mentioned problem or solving the above problems at least in part
The evaluation method of cloth model, including：
S1. structural amplitude value of the correct electron density distribution model of crystal to be measured after the first perturbation is undergone, institute are calculated
State the first perturbation so that in the crystal to be measured each atom correct electron density distribution model experience perturbation after in structure cell
Plus it is identical with the electron outside nucleus number of corresponding atom；
S2. structural amplitude value of the Current electronic Density Distribution model of crystal to be measured after experience perturbation is calculated, it is described micro-
Disturbing makes the low density area in Current electronic Density Distribution model change；
S3. structural amplitude value and structural amplitude value in S1 in S2 are compared, to evaluate Current electronic Density Distribution model.
Preferably, S1 includes：
Based on the imaginary crystal of lattice parameter identical with crystal to be measured, the correct electron density distribution of crystal to be measured is calculated
Model structural amplitude value after the first perturbation is undergone；
Wherein, the imaginary crystal only has an atom and at origin at structure cell origin, the species of the atom
One of atom with constituting the crystal to be measured is identical.
Preferably, S1 is specifically included：
S11. the electron density distribution after the first perturbation is applied based on the electron density distribution model to the imaginary crystal
Model, is calculated using Fourier transformation and obtains pseudoatom dispersion factor；
S12. the pseudoatom dispersion factor is based on, according to crystal diffraction kinematical theory, the correct of crystal to be measured is obtained
Structural amplitude value of the electron density distribution model after the first perturbation.
Preferably, S11 is specially：
S111. the structure factor based on the imaginary crystal, electron density distribution model is obtained using inverse Fourier transform；
S112. the first perturbation is applied to S111 electron density distribution model, obtains undergoing the electron density point after perturbation
Cloth model；
S113. based on the electron density distribution model after perturbation is undergone in S112, the electronics is obtained according to Fourier transformation
The pseudoatom dispersion factor of Density Distribution model.
Preferably, the acquisition of the structure factor of the imaginary crystal is based on the atomic scattering factor for constituting imaginary crystal.
Preferably, the S12 is specially：
Based on the pseudoatom dispersion factor, crystal experimental observation diffracted intensity value to be measured is modified, obtains to be measured
Structural amplitude value of the correct electron density distribution model of crystal after the first perturbation is undergone.
Preferably, structural amplitude value of the Current electronic Density Distribution model of crystal to be measured described in S2 after experience perturbation
Acquisition include：
Using the diffraction amplitudes and current phase of experimental observation, the Current electronic for building crystal to be measured is synthesized by Fourier
Density Distribution model；
Perturbation is applied to the Current electronic Density Distribution model, the low density area in model is changed, and utilize
Fourier transformation calculates the diffraction amplitudes value for obtaining Current electronic Density Distribution model after experience perturbation.
Preferably, the evaluation method is applied to the crystal electrons Density Distribution model that resolution ratio is inferior to 0.2 nanometer.
Another aspect of the present invention, additionally provides application of the above-mentioned evaluation method in crystal structure analysis.
Also including the use of direct method and/or electric charge inversion method in the crystal structure analysis.
The evaluation method of crystal electrons Density Distribution model proposed by the present invention, exists according to Current electronic Density Distribution model
Undergo estimating for structural amplitude of the structural amplitude after specific perturbation with correct electron density distribution model after specific perturbation is undergone
The degree of agreement of calculation value evaluates the quality of Current electronic Density Distribution model, and overcome existing evaluation method can not be at low point
The deficiency of electron density distribution model quality is reliably evaluated under the conditions of distinguishing, method of the invention is applicable not only to possess atom level
The situation of resolution diffraction data, and the relatively low situation of diffraction data resolution ratio can be applied to.The evaluation method of the present invention
In the estimated value of structural amplitude of the correct electron density distribution model after specific perturbation is undergone can directly can by experiment measurement
The information export of acquisition.Evaluation method provided by the present invention can apply to crystallographic structural analysis work, include but is not limited to
It is combined, is selected out from electron density distribution model that is alternative or attempting with methods such as existing direct method, electric charge inversion methods
Correct model.
Brief description of the drawings
Fig. 1 is C in test case 1 of the present invention6Br6The electron density distribution figure of the nanometer resolution of crystal 0.25 is after perturbation
Structural amplitude calculated value (× represent) and estimated value (Represent)；
Fig. 2 a are R in test case 2 of the present inventiontianValue is with the variation diagram of different electron density distribution models；
Fig. 2 b be test case 2 of the present invention in RtianThe corresponding electron density model of minimum value；
Fig. 2 c are the correct electron density distribution figure of crystal in test case 2 of the present invention；
Fig. 3 is R and R in test case 3 of the present invention and contrast test example 1tianValue is with different electron density distribution models
Change curve.
Embodiment
With reference to the accompanying drawings and examples, the embodiment to the present invention is described in further detail.Implement below
Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
The invention provides a kind of evaluation method of crystal electrons Density Distribution model, this method includes：
S1. structural amplitude value of the correct electron density distribution model of crystal to be measured after the first perturbation is undergone, institute are calculated
State the first perturbation so that in the crystal to be measured each atom correct electron density distribution model experience perturbation after in structure cell
Plus it is identical with the electron outside nucleus number of corresponding atom；
S2. structural amplitude value of the Current electronic Density Distribution model of crystal to be measured after experience perturbation is calculated, it is described micro-
Disturbing makes the low density area in Current electronic Density Distribution model change；
S3. structural amplitude value and structural amplitude value in S1 in S2 are compared, to evaluate Current electronic Density Distribution model.
Wherein, when Current electronic Density Distribution model is correct, difference very little between the two.Difference is smaller between the two,
Illustrate Current electronic Density Distribution model closer to correct.
Present invention provides a kind of correct electron density using after data-evaluation perturbation that is measurable or obtaining in advance
The method of distributed model structural amplitude.
In the case where the structural amplitude of estimation can be substantial access to real structure amplitude, it is possible to use the structure of estimation is shaken
Amplitude is and consistent according between the two compared with the structural amplitude calculated value of the Current electronic Density Distribution model after perturbation
The quality of degree evaluation Current electronic Density Distribution model.
In the evaluation method of the present invention, it is possible to use the diffraction amplitudes of experimental observation and current phase of attempting pass through in Fu
The mode of leaf synthesis builds Current electronic Density Distribution model；Then, a perturbation is applied to Current electronic Density Distribution model,
The low density area in model is changed, and calculate the diffraction amplitudes of the electron density distribution after changing, perturbation herein is only
The low density area in model need to be made to change；Then, re-using experiment observation diffraction amplitudes and it is other can be advance
The crystal information of acquisition estimates structural amplitude of the correct electron density distribution after being disturbed by the first perturbation；Then, then investigate micro-
The diffraction amplitudes of correct electron density distribution figure after the diffraction amplitudes of Current electronic Density Distribution model after disturbing and disturbance
Matching degree.
That is the acquisition of structural amplitude value of the Current electronic Density Distribution model of crystal to be measured after experience perturbation can in S2
With including：
Using the diffraction amplitudes and current phase of experimental observation, the Current electronic for building crystal to be measured is synthesized by Fourier
Density Distribution model；
Perturbation is applied to Current electronic Density Distribution model, the low density area in model is changed, and using in Fu
Leaf transformation calculates the diffraction amplitudes value for obtaining Current electronic Density Distribution model after experience perturbation.
Wherein, the low density area in the model is made to change to what Current electronic Density Distribution model applied in S2
Perturbation be this area in have above-mentioned effect perturbation.
Preferably, the perturbation for putting on Current electronic Density Distribution model is
Wherein δcrystIt is preferred that with a real number close to 0 or equal to 0.
In the evaluation method of the present invention, in S1, the correct electron density distribution model of crystal to be measured, which undergoes, to be somebody's turn to do
The electron outside nucleus data of the correct electron density distribution model of each atom adding in structure cell and corresponding atom in crystal
The perturbation of identical first, as long as the perturbation that can meet above-mentioned condition can be as the first perturbation of the invention.
For example, correct electron density distribution figure of the crystal under a certain specified resolution is ρo, ρiIt is former for i-th in structure cell
Electron density distribution figure of the son under same resolution ratio, riIt is the coordinate of i-th of atom in structure cell, each atom in structure cell is applied
Plus perturbationObtainWherein δiIt is to change with the difference of atom.
δiBe one close to 0 real number.Wherein, δiSelection should meet and makeIt is in structure cell plus and with i-th it is former
The electron outside nucleus number of son is identical.To correct electron density distribution figure ρoThe perturbation of application isWherein, Vi(ri) be
From origin translation to riThe V at placei。
Wherein, the diffraction amplitudes of experimental observation are the crystal structure amplitude obtained by x-ray diffraction experiment measurement.
Wherein, the trial value that phase refers to the phase corresponding to the diffraction amplitudes of experimental observation is attempted.Trial value can root
Learn according to statistics or mathematical relationship such as direct method formula is provided.
Matching degree can be, but not limited to be represented with following quantification of targets：
Wherein, wherein ∑hWithIt is identical with implication in R,To apply one to correct electron density distribution figure
Structural amplitude value after specific perturbation.
In embodiments of the present invention, in order that evaluating more accurate, S1 includes：
Based on the imaginary crystal of lattice parameter identical with crystal to be measured, the correct electron density distribution of crystal to be measured is calculated
Structural amplitude value of the model after the first perturbation is undergone；
Wherein, imaginary crystal only has an atom and at origin at structure cell origin, and atomic species is to be measured with constituting
One of atom of crystal is identical.
Computational methods and principle it is as follows：
It is assumed that the diffraction amplitudes and lattice parameter of a crystal are had determined by X-ray diffraction measurement.In addition, composition is brilliant
The atomic species and number of body are also by known to chemical analysis or other approach.It is assumed that in structure cell i-th of atom atom
Dispersion factor is fi, then an imaginary crystal structure can be built, its lattice parameter and the crystal phase studied are same, in structure cell only
There is an atom and at origin, atomic scattering factor is fi。
In a preferred embodiment of the invention, S1 is specifically included：
S11. the electron density distribution mould after the first perturbation is applied based on the electron density distribution model to the imaginary crystal
Type, is calculated using Fourier transformation and obtains pseudoatom dispersion factor；
S12. above-mentioned pseudoatom dispersion factor is based on, according to crystal diffraction kinematical theory, the correct of crystal to be measured is obtained
Structural amplitude value of the electron density distribution model after the first perturbation.
Wherein, S11 is specifically as follows：
S111. the structure factor based on the imaginary crystal, electron density distribution model is obtained using inverse Fourier transform；
S112. the first perturbation is applied to S111 electron density distribution model, obtains undergoing the electron density point after perturbation
Cloth model；
S113. based on the electron density distribution model after perturbation is undergone in S112, the electronics is obtained according to Fourier transformation
The pseudoatom dispersion factor of Density Distribution model.
Wherein, in S111, the lattice parameter of imaginary crystal and the crystal phase studied are same, in structure cell only one of which atom and
At origin, atomic scattering factor is fi, its structure factor is then
Wherein,WithRespectively diffraction vector and position vector.
The electron density distribution of the imaginary crystal is then
ρi=IFT (FI, h)=IFT (fi)
Wherein, IFT represents inverse Fourier transform.Fourier's synthesis in above formula ends in the diffraction number with studying crystal
According to identical resolution ratio.
" the ending in " of the present invention refers to the resolution limit that Fourier space adds and ended in experimental diffraction amplitude, higher
The Fourier space item of spatial frequency is not comprised in Fourier space plus among.
Wherein, in S112, to ρiApply after the first perturbation, electron density is changed into
Wherein ViIt is a perturbing function, it is defined as：
Wherein δiBe one close to 0 real number.
Wherein, in S113, the calculation of pseudoatom dispersion factor is specially：
Corresponding structure factor is
Wherein, FT represents Fourier transformation,Represent convolution, viIt is ViFourier transformation FT (Vi).It can be seen by above formula
Go out,Can be considered as a lattice parameter and studied crystal phase with and only there is the atomic scattering factor to be in structure cell originPseudoatom imaginary crystal electron density.
Obviously,And fi *All will be with δiValue it is different and change.According to the physical meaning of atomic scattering factor, atom
Value of the dispersion factor at θ=0 is the ectonuclear electron number of atom.The appropriate δ by choosingiIt can makeIn structure cell
Plus and it is identical with the electron outside nucleus number of i-th of atom, now, fi *With fiWill be basically identical in the range of low sin θ/λ, and only
More significant difference is produced in the range of high sin θ/λ.
The observation electron density distribution of studied crystal can regard as the electron density distributions of all atoms in structure cell by
The superposition carried out according to atom geometric position, i.e.,：
Wherein, ρi(ri) it is from structure cell origin translation to riThe ρ at placei, N is the atom number in structure cell.To ρoApply first
After perturbation, electron density distribution is changed into：
Wherein, Vi(ri) it is from origin translation to riThe V at placei.By selecting suitable δi, each atom V can be madej(rj)
=1 region is misaligned.
Have in this case
ρi(ri)×Vj(rj)=0fori ≠ j, then can obtain
The structure factor of this electron density distribution is
In S12, based on obtained pseudoatom dispersion factor, crystal experimental observation diffracted intensity value to be measured is repaiied
Just, the estimated value of structural amplitude of the correct electron density distribution model of crystal to be measured after the first perturbation is undergone is obtained.
According to crystal diffraction kinematical theory, the experimental observation diffracted intensity of a crystal is：
Wherein K is not dependent on the scale factor of diffraction angle.
Therefore, electron density distribution is in structure cellCrystal experimental observation diffracted intensity should be：
Wherein ki=fi*/fi,
If ki=kj, then can obtain：
As discussed above, δ is worked asiWhen taking appropriate value, fi *With fiIt is basically identical in the range of low angle of diffraction, this meaning
Taste k in the casei=kj=1 is approximately set up, therefore above formula is also approximately set up.
In high angle of diffraction scope, according to the Wilson Statistical Distributions of crystal diffraction intensity, have：
Wherein,<|Fobs|2>It is | Fobs|2In a certain sin specified2Average in the range of θ, K ' is not dependent on the angle of diffraction
The scale factor of degree.Correspondingly, it can obtain
Above-mentioned two formula of simultaneous, can be obtained
Therefore in high angle of diffraction scope, from the perspective of in the sense that statistical average, following formula is set up
Therefore we can beAsEstimated value, wherein all variables included are all
It can measure or precalculate what is obtained.
The estimated value can be measured retrievable information by experiment and directly be exported using above formula.
Quantizating index R can be calculated using above-mentioned estimated valuetian。
In conventional method, assessment structural model and the degree being actually consistent are come using residual error factor R ES,
That is,
Wherein, ∑hRepresent to it is all observe diffraction amplitudes add and, | Fobs| and | Fcal| represent that experiment is measured respectively
Diffraction amplitudes and the diffraction amplitudes that are calculated by structural model.
In the present invention, it is preferred to use RtianCome quantitatively evaluating electron density distribution model and the degree being actually consistent.
Wherein, ∑hRepresent to it is all observe diffraction amplitudes add and,For to Current electronic Density Distribution model
Apply the calculated value of the structural amplitude after a specific perturbation.
Wherein,Calculating process can be：Current electronic Density Distribution model ρ can utilize the reality of crystal to be measured
Test observation diffraction amplitudes combination trial phase to obtain by Fourier's synthesis, i.e.,
Wherein IFT represents inverse Fourier transform,To attempt phase value.
Apply after perturbation, Current electronic Density Distribution model is changed into ρ*,
ρ*=ρ × W
Wherein W is perturbing function,
Wherein δcrystIt is a real number close to 0 or equal to 0.Then,Can be by ρ*Fourier transformation obtain：
Of particular note is that only to Current electronic Density Distribution model and the application of correct electron density distribution figure
In the case of same perturbation, RtianThe contribution of electron density distribution model in itself is just only contained in value.In "current" model just
In the case of really, RtianIt will level off to zero.But derivingDuring, it has been assumed that to correct electron density distribution
Figure apply perturbation beTherefore, reply Current electronic Density Distribution model applies same perturbation and just can guarantee that
RtianThe contribution of model in itself is only contained in value.
Perturbing functionIn contained the information of atomic coordinates, therefore be can not be predetermined.Cause
This, can use such a perturbing functions of W to substitute perturbing function
Obviously, in this case, RtianValue will depend not only upon Current electronic Density Distribution model, also rely on
δcryst.It is correct in Current electronic Density Distribution model, and W close toWhen, RtianIt is intended to minimum.It is actual
On, under the conditions of certain data resolution, when Current electronic Density Distribution model is correct, W withBoth are micro-
The effect for disturbing mode is close.Therefore, RtianCan be for effectively evaluating the quality of electron density model.
Evaluation method disclosed in this invention goes for the crystal electrons density that resolution ratio as little as (is inferior to) 0.2 nanometer
Distributed model.
In one aspect of the invention, application of the above-mentioned evaluation method in crystal structure analysis is additionally provided.
Above-mentioned application includes but is not limited to be combined with methods such as existing direct method, electric charge inversion methods, from alternative or taste
Correct model is selected out in the crystal electrons Density Distribution model of examination.
Embodiment 1
The present embodiment is used to illustrate electron density distribution model evaluation method provided by the present invention and its in crystal structure
Application in parsing.
Diffraction data is originated：Correct electron density distribution model corresponding to the diffraction data obtained by real crystal measurement
It can not know exactly, so lacking strict in the quality of the electron density distribution model obtained in evaluating crystallographic structural analysis
Normative reference.To overcome this difficult, simulated diffraction data are used in the present embodiment, simulated diffraction data are reported in document
Known crystal structure calculate obtain.Known crystal structure in the present embodiment is quoted from document：
Wu,J.S.,Spence,J.C.H.,O’Keeffe,M.&Groy,T.L.(2004).Acta.Cryst.A60,326-
330。
Related crystalline structured data is as follows：
Molecular formula：C6Br6, space group：P21/ n, lattice parameter：A=0.8381 nanometers, b=0.40192 nanometers, c=
1.53939 nanometers, β=92.674 °, the molecular formula number (Z) in each structure cell：2.
The crystallography coordinate of each individual atoms refers to above-mentioned document.
Calculated according to crystal structural data and obtain structure factor, then remove the phase information of structure factor, only retain knot
The modulus value (structural amplitude) of the structure factor is used as simulated diffraction data.The resolution setting of simulated diffraction data is 0.25 nanometer.
(1) pseudoatom dispersion factor is calculatedWith
Imaginary crystal, the lattice parameter and C of imaginary crystal are built first6Br6The lattice parameter of crystal is identical, but only in crystalline substance
There are a C atom or Br atoms at born of the same parents' origin.All structure factors of the imaginary crystal in the range of 0.25 nanometer resolution are calculated,
And the electron-density map ρ under 0.25 nanometer resolution is obtained using inverse Fourier transformCAnd ρBr.Respectively to ρCAnd ρBrApply micro-
Disturb, perturbation has following functional form：
Suitable δ values are selected, so that the electronics respectively more than or equal to δ in the structure cell of C and the Br imaginary crystal constituted is close
Spend sum identical with C or Br electron outside nucleus number.In the present embodiment, δCAnd δBrRespectively 0.0024 He
Determine after perturbing function, electron-density map ρ is obtained after calculating perturbation respectivelyC *And ρBr *.Then utilize's
Relation calculates pseudoatom dispersion factorWith
(2) C is estimated6Br6Correct structural amplitude of the electron density distribution figure after perturbation
Utilize what is obtained in (1)WithAnd relational expression
Calculate C6Br6Correct structural amplitude estimated value of the electron density model after perturbation.
(3) structural amplitude of the Current electronic Density Distribution model after crystal perturbation is calculated
First to C6Br6Any Current electronic Density Distribution model ρ apply perturbation, perturbing function has following form：
Then, the electron density distribution model after perturbation is calculated：ρ*=ρ × W, then electron density distribution figure after perturbation
Structural amplitude can be obtained by Fourier transformation：
(4) R is calculatedtian
Utilize what is obtained in (2)(3) obtained inR can be then calculated according to following formulatian
Value：
(5) relatively more a series of different crystal electrons Density Distribution models, corresponding to RtianIt is worth smaller and RtianTake minimum
The electron density model of value is then the correct crystal electrons Density Distribution model in certain accuracy rating.
Embodiment 2
The present embodiment is used to illustrate electron density distribution model evaluation method provided by the present invention and its in crystal structure
Application in parsing.
Diffraction data is originated：Based on the reason for same as Example 1, simulated diffraction data are still used in the present embodiment,
Simulated diffraction data are calculated by known crystal structure reported in the literature and obtained.Known crystal structure in the present embodiment is quoted certainly
Document：
Czugler,M.,Weber,E.,Parkanyi,L.,Korkas,P.P.&Bombicz,P.(2003)
.Chem.Eur.J.,9,3741-3747.
Related crystalline structured data is as follows：
Molecular formula：C252H324O18·H2O, space group：P1, lattice parameter：A=1.6909 nanometers, b=1.8772 nanometers, c
=2.1346 nanometers, α=111.46 °, β=103.38 °, γ=107.74 °.Molecular formula number (Z) in each structure cell：1.
The crystallography coordinate of each individual atoms refers to pertinent literature.
The method for obtaining simulated diffraction data (structural amplitude) from crystal structure is same as Example 1, and H atom does not include
Among calculating.The resolution ratio of simulated diffraction data is again set at 0.25 nanometer.
Step (1)-(5) are substantially the same manner as Example 1, and difference is only that the atomic species being related to is different.In the present embodiment
In, involved atomic species is C and O.
Test case 1
This test case is used for the structural amplitude for illustrating the correct electron density distribution figure after perturbation provided by the present invention
The test of evaluation method reliability.
Calculate C in embodiment 16Br6Electron-density map ρ of the crystal under 0.25 nanometer resolutiono, and perturbation is applied to it,
Electron density distribution figure after perturbation is
WhereinFor perturbing function, riFor the coordinate of C and Br atoms, perturbing function VC、VBrWith in embodiment 1
The perturbing function for putting on imaginary crystal is identical.The structural amplitude of electron-density map after perturbation is：
WillCompared with the estimated value obtained in the step of embodiment 1 (2), it can be seen that both coincide very much, see
Fig. 1.This explanation correct electron density distribution figure of estimation provided by the present invention is by the method for the structural amplitude after perturbation 0.25
It is effective under the resolution ratio of nanometer.
Test case 2
This test case is used for the survey for illustrating crystal electrons Density Distribution model evaluation method validity provided by the present invention
Examination.
According to the methods described of embodiment 1, in step (5), for each diffraction amplitudes in simulated diffraction data, point
Not Fu Yu a random phase, utilize these diffraction amplitudes and random phase to build initiating electron Density Distribution model ρ0, then
The electron density model for making a new round isAgain to ρi+1Fourier transformation is done, is obtained
The phase of structure factor retains, and the trial phase as a new round is combined with the observation of structural amplitude, produces a new round
Electron density distribution model, said process is constantly repeated, right until adding up to generate 300 different electron density distribution models
In each electron density distribution model, corresponding R is calculatedtianValue, acquired results are shown in Fig. 2 a.With RtianMinimum value
Corresponding electron density distribution model is shown in Fig. 2 b, and correct electron density distribution is shown in Fig. 2 c, wherein, Fig. 2 b and Fig. 2 c are
C6Br6Along the perspective view in [010] direction.In order to clear, only show and be higher than in figureElectron density.Can from Fig. 2
To find out, RtianMinimum electron density distribution model closely, has had revealed that out just with correct electron density distribution figure
The principal character of true electron density distribution figure, can determine whole heavy atom Br position.
Test case 3
This test case is used for the test for illustrating electron density distribution model evaluation method validity provided by the present invention.
This test case is directed to the simulated diffraction data progress obtained by embodiment 2.Method of testing and the basic phase of test case 2
Together, differ only in and assign correct electron density distribution figure as initiating electron Density Distribution model.Correct electron density distribution figure
Obtained using diffraction amplitudes and correct phase by Fourier's synthesis.The corresponding R of each electron density distribution modeltianValue
As shown in Figure 3.It can be seen that in 400 electron density distribution models of trial, correct electron density distribution figure institute
Corresponding RtianValue is minimum.
Contrast test example 1
This test case is used for the test for illustrating the electron density distribution model evaluation method validity of reference.
This contrast test example is directed to the simulated diffraction data progress obtained by embodiment 2.Method of testing and test case 3 are basic
Identical, it is no longer R to differ only in corresponding to the calculating of each electron density distribution modeltianBut R values.Each electronics
The corresponding R values of Density Distribution model display that in figure 3 in order to RtianValue compares.It can be seen that tasting
In 400 electron density distribution models of examination, the R values corresponding to correct electron density distribution figure are not only not minimum value, on the contrary
It is maximum.Therefore, in this case, minimum value can not have been taken to identify correct electron density distribution model according to R.
On the contrary, RtianValue is still a kind of evaluation index of effective crystal electrons Density Distribution model, can be for identifying just
True electron density model.
Finally, method of the invention is only preferably embodiment, is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements made etc. should be included in the protection of the present invention
Within the scope of.
Claims (10)
1. a kind of evaluation method of crystal electrons Density Distribution model, including：
S1. the structural amplitude value of the correct electron density distribution model of crystal to be measured after the first perturbation is undergone is calculated, described the
One perturbation cause the correct electron density distribution model of each atom in the crystal to be measured after experience perturbation in structure cell plus
It is identical with the electron outside nucleus number of corresponding atom；
S2. structural amplitude value of the Current electronic Density Distribution model of crystal to be measured after experience perturbation is calculated, the perturbation makes
Low density area in Current electronic Density Distribution model changes；
S3. structural amplitude value and structural amplitude value in S1 in S2 are compared, to evaluate Current electronic Density Distribution model.
2. evaluation method according to claim 1, it is characterised in that S1 includes：
Based on the imaginary crystal of lattice parameter identical with crystal to be measured, the correct electron density distribution model of crystal to be measured is calculated
The structural amplitude value after the first perturbation is undergone；
Wherein, the imaginary crystal only has an atom and at origin at structure cell origin, the species and structure of the atom
One of atom into the crystal to be measured is identical.
3. evaluation method according to claim 2, it is characterised in that S1 is specifically included：
S11. the electron density distribution model after the first perturbation is applied based on the electron density distribution model to the imaginary crystal,
Calculated using Fourier transformation and obtain pseudoatom dispersion factor；
S12. the pseudoatom dispersion factor is based on, according to crystal diffraction kinematical theory, the correct electronics of crystal to be measured is obtained
Structural amplitude value of the Density Distribution model after the first perturbation.
4. evaluation method according to claim 3, it is characterised in that S11 is specially：
S111. the structure factor based on the imaginary crystal, electron density distribution model is obtained using inverse Fourier transform；
S112. the first perturbation is applied to S111 electron density distribution model, obtains undergoing the electron density distribution mould after perturbation
Type；
S113. based on the electron density distribution model after perturbation is undergone in S112, the electron density is obtained according to Fourier transformation
The pseudoatom dispersion factor of distributed model.
5. evaluation method according to claim 4, it is characterised in that the acquisition of the structure factor of the imaginary crystal is based on
Constitute the atomic scattering factor of imaginary crystal.
6. evaluation method according to claim 3, it is characterised in that the S12 is specially：
Based on the pseudoatom dispersion factor, crystal experimental observation diffracted intensity value to be measured is modified, crystal to be measured is obtained
Correct electron density distribution model undergo the first perturbation after structural amplitude value.
7. the evaluation method according to any one of claim 1-6, it is characterised in that crystal to be measured is current described in S2
The acquisition of structural amplitude value of the electron density distribution model after experience perturbation includes：
Using the diffraction amplitudes and current phase of experimental observation, the Current electronic density for building crystal to be measured is synthesized by Fourier
Distributed model；
Perturbation is applied to the Current electronic Density Distribution model, the low density area in model is changed, and using in Fu
Leaf transformation calculates the diffraction amplitudes value for obtaining Current electronic Density Distribution model after experience perturbation.
8. the evaluation method according to any one of claim 1-7, it is characterised in that the evaluation method is applied to differentiate
Rate is inferior to 0.2 nanometer of crystal electrons Density Distribution model.
9. application of the evaluation method any one of claim 1-8 in crystal structure analysis.
10. application according to claim 9, it is characterised in that also including the use of direct method in the crystal structure analysis
And/or electric charge inversion method.
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| CN115239999A (en) * | 2022-07-22 | 2022-10-25 | 水木未来(北京)科技有限公司 | Protein electron density map processing method, device, electronic apparatus and storage medium |
| CN115938519A (en) * | 2022-12-29 | 2023-04-07 | 中国科学院福建物质结构研究所 | Novel method for refining model of electronic structure |
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