CN115938520A - Density matrix model method for electronic structure analysis - Google Patents

Density matrix model method for electronic structure analysis Download PDF

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CN115938520A
CN115938520A CN202211703463.5A CN202211703463A CN115938520A CN 115938520 A CN115938520 A CN 115938520A CN 202211703463 A CN202211703463 A CN 202211703463A CN 115938520 A CN115938520 A CN 115938520A
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density matrix
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CN115938520B (en
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姜小明
郭国聪
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Fujian Institute of Research on the Structure of Matter of CAS
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Fujian Institute of Research on the Structure of Matter of CAS
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Abstract

The invention belongs to the field of material subdivision, in particular to a density matrix model method for electronic structure analysis, which comprises the following steps: establishing parameters
Figure DDA0004025381780000011
The theoretical X-ray diffraction intensity of each diffraction point and the theoretical value of the Compton scattering profile of each momentum are calculated by the electron density matrix model; obtaining the experimental intensity I of each diffraction point through an X-ray single crystal diffraction experiment Experiment of (ii) a The Compton scattering profile J of each momentum is obtained through an X-ray Compton scattering experiment Experiment of (ii) a Establishing a difference function between theoretical intensity and experimental intensity; calculating the minimum value in the difference function by adopting a least square method, and finally obtaining the parameters of the optimal model
Figure DDA0004025381780000012
The refined electronic structure in the field of material analysis is obtained through the method; and the subsequent topology analysis and material design are more accurate according to the electronic structure.

Description

Density matrix model method for electronic structure analysis
Technical Field
The invention relates to the technical field of material analysis, in particular to a density matrix model method for electronic structure analysis.
Background
The material science is the foundation and the leader of modern science and technology, and the cognitive level of the material structure and the material structure relationship directly determines the research and development capability of new materials.
The microstructure of the material comprises atomic layer-level structures such as a crystal structure, a local structure, a defect structure and the like, and an electronic structure, wherein the electronic structure fundamentally determines the intrinsic performance of the material. At present, the experimental testing technology of the atomic layer structure of the material has been developed very mature, but the electronic structure experimental testing is always in the exploration stage, although the electronic structure can be obtained by the first theoretical calculation, the theoretical calculation adopts a large number of assumptions, the calculation result has deviation from the actual situation, and the design of the high-performance material is difficult to guide.
Thus, how to obtain experimental electronic structures of materials is a key scientific issue. The solution of the problem is beneficial to realizing the spanning of the experimental research of the material structure of China from atomic layer level to electronic level and accelerating the research and development process of a batch of national defense and civil key functional materials.
Fig. 1 is a schematic diagram of an experimental structure using X-rays in the prior art, where the X-rays are incident on a crystal to be measured, and the X-rays are diffracted after passing through the crystal to be measured, and the experimental electronic structure of the material can be obtained by obtaining high-precision and high-resolution X-ray single crystal diffraction data (position and intensity information), performing electronic structure refinement, and reversely deducing the experimental electronic structure of the material, so that the experimental electronic structure of the material under static and active conditions can be finally obtained, and the electronic structure can be described by using an electronic density, a density matrix, or an electronic wave function.
FIG. 2 is a schematic diagram of an experimental structure of X-ray Compton scattering from which experimental Compton scattering profile data for each scattering vector can be obtained.
Disclosure of Invention
The invention provides a density matrix model method for electronic structure analysis.
In order to achieve the purpose, the invention adopts the following technical scheme: a density matrix modeling method for electronic structure analysis, comprising: the method comprises the following steps: establishing parameters
Figure BDA0004025381760000021
Calculating the theoretical X-ray diffraction intensity of each diffraction point and the theoretical value of the Compton scattering profile of each momentum;
step two: obtaining the experimental intensity I of each diffraction point through an X-ray single crystal diffraction experiment Experiment of (ii) a The Compton scattering profile J of each momentum is obtained through an X-ray Compton scattering experiment Experiment of ；
Step three: establishing a difference function between theoretical intensity and experimental intensity;
step four: calculating the minimum value in the difference function by adopting a least square method to obtain the parameters of the optimal model
Figure BDA0004025381760000022
In the first step, a parameterized electron density matrix model function is established:
Figure BDA0004025381760000023
/>
P i,j is an m multiplied by m parameter matrix which is the parameter needed to be obtained by fine modification; phi is a i (r)，φ j (r') are the ith and jth basis functions (i, j =1,2,3, \8230;, m; m is the number of basis functions), respectively, which are known functions. Parameter matrix
Figure BDA0004025381760000024
And the density matrix Γ (r, r') may be written in two parts, one part consisting of diagonal elements, each denoted ^ er>
Figure BDA0004025381760000031
Γ (r, r' = r); the other part consists of elements not lying diagonally and are each designated as->
Figure BDA0004025381760000032
Γ(r,r'≠r)。
Namely:
Figure BDA0004025381760000033
Γ(r,r')＝Γ(r,r'＝r)+Γ(r,r'≠r)
the diagonal matrix element of the gamma (r, r ') is the electron density rho (r), namely rho (r) = gamma (r, r' = r), and the theoretical structure factor of each diffraction point can be calculated through the Fourier transform of the rho (r)
Figure BDA0004025381760000034
The experimental intensity I of each diffraction point can be obtained through an X-ray single crystal diffraction experiment Experimental values The structural factor is calculated based on the intensity of the diffraction spot>
Figure BDA0004025381760000035
From the off-diagonal elements of Γ (r, r' ≠ r), the theoretical compton scattering profile J (q) can be derived by fourier transformation, namely:
Figure BDA0004025381760000036
wherein q is the electron momentum; through the X-ray Compton scattering experiment, the experimental Compton scattering profile data of each scattering vector can be obtained
Figure BDA0004025381760000037
Wherein, the preferred scheme is as follows: obtaining the experimental intensity of each diffraction point kappa through an X-ray single crystal diffraction experiment
Figure BDA0004025381760000038
Further obtaining the structural factor of the experiment>
Figure BDA0004025381760000039
Meanwhile, experimental Compton scattering profile data of each scattering vector is obtained through an X-ray Compton scattering experiment
Figure BDA00040253817600000310
Wherein, the preferred scheme is as follows: defining a difference function of the difference between the theoretical value and the experimental value of the matrix density model as
Figure BDA00040253817600000311
Wherein the difference function of the difference between the theoretical and experimental values associated with diagonal bins of the density matrix is: />
Figure BDA0004025381760000041
The difference function of the difference between the theoretical and experimental values associated with the non-diagonal elements of the density matrix is: />
Figure BDA0004025381760000042
Namely:
Figure BDA0004025381760000043
wherein, the preferred scheme is as follows: calculating by least square method
Figure BDA0004025381760000044
Gets the optimal model parameter pick>
Figure BDA0004025381760000045
Wherein, the preferred scheme is as follows: calculated by least squares and using
Figure BDA0004025381760000046
Figure BDA0004025381760000047
Preset->
Figure BDA0004025381760000048
Performing a value operation, comprising: a: randomly selects two groups of parameter values>
Figure BDA0004025381760000049
And &>
Figure BDA00040253817600000410
Each group having m x m parameters to be combined>
Figure BDA00040253817600000411
Figure BDA00040253817600000412
Substitution into
Figure BDA00040253817600000413
Respectively obtain>
Figure BDA00040253817600000414
And &>
Figure BDA00040253817600000415
B according to the formula>
Figure BDA00040253817600000416
A is a step size factor, and the value is calculated>
Figure BDA0004025381760000051
I.e. n =3, wherein>
Figure BDA0004025381760000052
And will->
Figure BDA0004025381760000053
Substituted into>
Figure BDA0004025381760000054
Has been calculated>
Figure BDA0004025381760000055
A value; c: likewise in step B the formula for calculating &>
Figure BDA0004025381760000056
(i.e., n = 4) and similarly calculated @>
Figure BDA0004025381760000057
Circulating n steps until>
Figure BDA0004025381760000058
Less than a predetermined precision value, in which case>
Figure BDA0004025381760000059
Has reached a minimum, is taken up>
Figure BDA00040253817600000510
Is an optimum value; d: ->
Figure BDA00040253817600000511
Substituted into>
Figure BDA00040253817600000512
And obtaining a final experimental electron density matrix gamma, namely the refined electronic structure function.
Wherein, the preferred scheme is as follows: step A acquisition
Figure BDA00040253817600000513
And &>
Figure BDA00040253817600000514
First, by combining->
Figure BDA00040253817600000515
And &>
Figure BDA00040253817600000516
Respectively substitute for
Figure BDA00040253817600000517
Get->
Figure BDA00040253817600000518
And &>
Figure BDA00040253817600000519
According to>
Figure BDA00040253817600000520
And &>
Figure BDA00040253817600000521
The diagonal portion of (r, r '= r) and ρ (r) = Γ (r, r' = r) are obtained { [ MEASURED } { (R) } in the corresponding location in the image>
Figure BDA00040253817600000522
And &>
Figure BDA00040253817600000523
According to >>
Figure BDA00040253817600000524
Counting/or>
Figure BDA00040253817600000525
And &>
Figure BDA00040253817600000526
According to>
Figure BDA00040253817600000527
Is calculated out>
Figure BDA00040253817600000528
And &>
Figure BDA00040253817600000529
And according to >>
Figure BDA00040253817600000530
And &>
Figure BDA00040253817600000531
Of the non-diagonal sections Γ (r, r' ≠ r) and
Figure BDA00040253817600000532
get->
Figure BDA00040253817600000533
And &>
Figure BDA00040253817600000534
According to>
Figure BDA00040253817600000535
Is calculated out>
Figure BDA00040253817600000536
And &>
Figure BDA00040253817600000537
By means of>
Figure BDA00040253817600000538
And &>
Figure BDA00040253817600000539
Acquire->
Figure BDA00040253817600000540
And &>
Figure BDA00040253817600000541
Wherein, the preferred scheme is as follows: the preset precision value is as follows: 0.1 or 0.01 or 0.001, the smaller the preset precision value is, the refined
Figure BDA0004025381760000061
The more accurate.
Compared with the prior art, the invention has the beneficial effects that:
calculating theoretical structure factor by establishing parameterized electron density matrix model gamma (r, r
Figure BDA0004025381760000062
And compton scatter profile->
Figure BDA0004025381760000063
Obtaining the intensity I of diffraction point by X-ray experiment Experiment of (ii) a And obtaining a Compton scattering profile->
Figure BDA0004025381760000064
The theoretical structural factor is calculated by the least square method>
Figure BDA0004025381760000065
And the experimental structural factor->
Figure BDA0004025381760000066
And the theoretical compton scattering profile->
Figure BDA0004025381760000067
And the experimental compton scattering profile>
Figure BDA0004025381760000068
The parameter value ^ of the electronic wave function model Γ (r, r') is deduced back with the smallest difference between>
Figure BDA0004025381760000069
Thereby obtaining the refined electronic structure in the field of material analysis; therefore, the subsequent topological analysis and material design according to the electronic structure are more accurate.
Drawings
FIG. 1 is a schematic diagram of an experimental structure using X-rays in the prior art;
FIG. 2 is a schematic diagram of a prior art X-ray Compton scattering experiment;
FIG. 3 is a flow chart of a density matrix modeling method for electronic structure analysis in accordance with the present invention;
FIG. 4 shows a non-linear optical crystal material LiB 3 O 5 The asymmetry of the cell structure diagram after the refinement of the invention;
FIG. 5 is a molecular structural diagram of a fluorescent material pyrene after being refined by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
FIG. 3 is a flow chart of a density matrix modeling method for electronic structure analysis according to the present invention, as shown in FIG. 3: the method comprises the following steps: the method comprises the following steps: establishing parameters
Figure BDA0004025381760000071
The theoretical intensity of each diffraction point is calculated by the electron density matrix model; step two: obtaining the experimental intensity I of each diffraction point through an X-ray single crystal diffraction experiment Experiment of (ii) a Step three: obtaining Compton scattering profile of each momentum by X-ray Compton scattering diffraction experiment>
Figure BDA0004025381760000072
Step four: establishing a difference function between the physical strength and the experimental strength; step five: calculating the minimum value in the difference function by adopting a least square method to obtain the parameter(s) of the optimal model>
Figure BDA0004025381760000073
The preferred scheme is as follows: further comprising: step four-way over least square method for calculating preset P n The value operation step includes: using by least square calculation
Figure BDA0004025381760000074
Preset->
Figure BDA0004025381760000075
The value operation step includes: a: randomly selects two groups of parameter values>
Figure BDA0004025381760000076
And &>
Figure BDA0004025381760000077
Each group having m × m parametersWill be
Figure BDA0004025381760000078
Figure BDA0004025381760000079
Substitution into
Figure BDA00040253817600000710
Are respectively obtained
Figure BDA00040253817600000711
And &>
Figure BDA00040253817600000712
B according to the formula>
Figure BDA00040253817600000713
Figure BDA00040253817600000714
A is a step size factor, and the value is calculated>
Figure BDA00040253817600000715
Wherein +>
Figure BDA0004025381760000081
I.e. n =3, and will ÷>
Figure BDA0004025381760000082
Substituted into>
Figure BDA0004025381760000083
Figure BDA0004025381760000084
Is calculated out>
Figure BDA0004025381760000085
A value;c: is likewise calculated according to the step B formula>
Figure BDA0004025381760000086
(i.e., n = 4) and similarly calculated @>
Figure BDA0004025381760000087
Cycling n steps until->
Figure BDA0004025381760000088
Less than a predetermined precision value, at which time L (P) n ) Has reached a minimum, is taken up>
Figure BDA0004025381760000089
Is an optimum value; d: ->
Figure BDA00040253817600000810
Substituted into>
Figure BDA00040253817600000811
And obtaining a final experimental electron density matrix gamma, namely the refined electronic structure function.
It obtains to realize step A
Figure BDA00040253817600000812
And &>
Figure BDA00040253817600000813
First, by combining->
Figure BDA00040253817600000814
And &>
Figure BDA00040253817600000815
Respectively substitute for
Figure BDA00040253817600000816
Get->
Figure BDA00040253817600000817
And &>
Figure BDA00040253817600000818
According to >>
Figure BDA00040253817600000819
And &>
Figure BDA00040253817600000820
The diagonal portion of (r, r '= r) and ρ (r) = Γ (r, r' = r) are obtained { [ MEASURED } { (R) } in the corresponding location in the image>
Figure BDA00040253817600000821
And &>
Figure BDA00040253817600000822
According to
Figure BDA00040253817600000823
Counting/or>
Figure BDA00040253817600000824
And &>
Figure BDA00040253817600000825
According to
Figure BDA00040253817600000826
Is calculated out>
Figure BDA00040253817600000827
And &>
Figure BDA00040253817600000828
And according to >>
Figure BDA00040253817600000829
And &>
Figure BDA00040253817600000830
And ≠ ≠ r ^ r) and ^ r>
Figure BDA00040253817600000831
Get->
Figure BDA00040253817600000832
And &>
Figure BDA00040253817600000833
According to>
Figure BDA00040253817600000834
Has been calculated>
Figure BDA00040253817600000835
And &>
Figure BDA00040253817600000836
By using
Figure BDA00040253817600000837
And &>
Figure BDA00040253817600000838
Acquire->
Figure BDA00040253817600000839
And &>
Figure BDA00040253817600000840
The preset precision value is 0.1 or 0.01 or 0.001, and the smaller the preset precision value is, the refined
Figure BDA0004025381760000091
The more accurate.
Below by LiB 3 O 5 For example, the analysis process of the density matrix model method for electronic structure analysis of the present invention is verified as follows:
first by X-ray single crystal diffraction experiments, see table 1: under index parameter κ (h, k, l), the index parameter here is understood to be: the position index k (h, k, l) of a certain diffraction spot of the selected X-ray in the whole X-ray detector.
Selecting material LiB 3 O 5 The index parameter k (0, 1,0) (ii) a κ (0, -1, 0); κ (0, 1, -1); κ (0, 1); experimental intensity I of diffraction Point at κ (0, 1, -1) Experiment of (ii) a And obtaining LiB through X-ray Compton scattering diffraction experiment 3 O 5 Compton scatter profiles at momentums q of 1.023,1.133,1.205,1.369, and 1.488, respectively
Figure BDA0004025381760000092
It respectively is as follows: 3.111, 2.788, 2.356, 1.890 and 1.366.
TABLE 1 materials LiB 3 O 5 Experimental Strength at index K (h, k, l)
Figure BDA0004025381760000093
And an experimental structural factor>
Figure BDA0004025381760000094
And a compton scatter profile under momentum q>
Figure BDA0004025381760000095
Figure BDA0004025381760000096
TABLE 2 materials LiB 3 O 5 Is selected from the parameters
Figure BDA0004025381760000097
Based on the theoretical structural factor->
Figure BDA0004025381760000098
And compton scatter profile->
Figure BDA0004025381760000099
Figure BDA00040253817600000910
Figure BDA0004025381760000101
By comparing the data in Table 2
Figure BDA0004025381760000102
Into>
Figure BDA0004025381760000103
Get->
Figure BDA0004025381760000104
According to
Figure BDA0004025381760000105
Obtain = based on the diagonal portion Γ (r, r' = r) of (a) or (b)>
Figure BDA0004025381760000106
According to>
Figure BDA0004025381760000107
Counting/or>
Figure BDA0004025381760000108
At various indices κ (0, 1, 0); κ (0, -1, 0); κ (0, 1, -1); κ (0, 1); kappa (0, 1, -1) are the values: 1.1254, 0.9877, 15.2874, 13.1221 and 14.5059; based on the momentum q =1.023,1.133,1.205,1.369 and 1.488>
Figure BDA0004025381760000109
The values are respectively: 2.987, 2.011, 1.974, 1.669, 1.158; according to
Figure BDA00040253817600001010
Formula +>
Figure BDA00040253817600001011
According to the formula:
Figure BDA00040253817600001012
Figure BDA00040253817600001013
according to the formula>
Figure BDA00040253817600001014
Has->
Figure BDA00040253817600001015
Table 3 shows the material LiB 3 O 5 Is selected from the parameters
Figure BDA00040253817600001016
Based on the theoretical structural factor->
Figure BDA00040253817600001017
And compton scatter profile->
Figure BDA00040253817600001018
Figure BDA00040253817600001019
As shown in table 3: the following were calculated according to the same method as above:
Figure BDA00040253817600001020
such that the difference function:
Figure BDA0004025381760000111
in the present embodiment, the precision of λ is set to 0.001, and thus by a two-multiplication formula: />
Figure BDA0004025381760000112
Is calculated out>
Figure BDA0004025381760000113
The value of (a).
TABLE 4 materials LiB 3 O 5 Is selected from the parameters
Figure BDA0004025381760000114
Theoretical structural factor>
Figure BDA0004025381760000115
And compton scatter profile->
Figure BDA0004025381760000116
/>
Figure BDA0004025381760000117
As shown in table 4: by a two-multiplication formula:
Figure BDA0004025381760000118
wherein A takes a value of 0.01 and is based on an index parameter kappa (0, 1, 0)>
Figure BDA0004025381760000119
Figure BDA00040253817600001110
By analogy, get out>
Figure BDA00040253817600001111
Is taken and reused
Figure BDA00040253817600001112
Is calculated out>
Figure BDA00040253817600001113
Value,. Or>
Figure BDA00040253817600001114
Difference value->
Figure BDA00040253817600001115
Figure BDA00040253817600001116
In this embodiment, the predetermined accuracy of λ is set to 0.001, so that the two-multiplication value is still required until λ reaches 0.001, and then the value is greater than or equal to ^ 5>
Figure BDA00040253817600001117
TABLE 5 materials LiB 3 O 5 Selected parameter(s) of
Figure BDA00040253817600001118
Based on the theoretical structural factor->
Figure BDA00040253817600001119
And compton scatter profile->
Figure BDA00040253817600001120
Figure BDA00040253817600001121
Figure BDA0004025381760000121
Obtaining the parameter value of the refined electron density matrix model gamma
Figure BDA0004025381760000122
TABLE 6 materials LiB 3 O 5 Comparison with theoretical value after refinement by electron density model
Atom(s) Experimental value of valence state Theoretical calculation of first character
As shown in FIG. 3 as the B atom at the B1 position 2.530 2.570
As shown in FIG. 3 at the B2 position B atom 2.548 2.593
As shown in the B3 position B atom in FIG. 3 2.541 2.575
E.g. O atom in O1 position in FIG. 3 -1.728 -1.748
O atom in O2 position as in FIG. 3 -1.755 -1.787
As shown in the O3 position of FIG. 3 as the O atom -1.690 -1.707
O atom at O4 position in FIG. 3 -1.689 -1.710
O atom at O5 position as in FIG. 3 -1.694 -1.711
Such as Li atom in FIG. 3 0.938 0.934
TABLE 6 materials LiB 3 O 5 Comparing the refined electron density model with a theoretical value; and FIG. 4 is a finished LiB 3 O 5 The valence state experimental value of the electron wave function diagram is very close to the first theoretical calculated value, the feasibility of the method is proved, and the method is suitable for the nonlinear optical crystal material LiB 3 O 5 The use of (1).
In the second embodiment of the present invention, an organic fluorescent material pyrene (molecular formula: C16H 10) is taken as an example;
table 7 shows the experimental intensity of organic fluorescent material under pyrene index kappa (h, k, l)
Figure BDA0004025381760000123
And an experimental structural factor->
Figure BDA0004025381760000124
And a compton scatter profile under momentum q>
Figure BDA0004025381760000125
Figure BDA0004025381760000131
Table 8 shows the selection parameters of organic fluorescent pyrene
Figure BDA0004025381760000132
Based on the theoretical structural factor->
Figure BDA0004025381760000133
And compton scatter profile->
Figure BDA0004025381760000134
Figure BDA0004025381760000135
TABLE 8 data passage of organic fluorescent Material pyrene
Figure BDA0004025381760000136
Is selected and substituted into>
Figure BDA0004025381760000137
To obtain
Figure BDA0004025381760000138
According to>
Figure BDA00040253817600001316
Gets ÷ based on the diagonal portion Γ (r, r' = r)>
Figure BDA0004025381760000139
According to >>
Figure BDA00040253817600001310
Calculate->
Figure BDA00040253817600001311
At different indices κ (8, 2, -6); kappa (8, -2, -6); kappa (-8, -2, 6); kappa (-8,2,6); the values at kappa (-8, 2, 5) were 17.1181, 17.2120, 13.5345, 16.8664, 11.9503, respectively. />
Figure BDA00040253817600001317
The values at different momentums q are respectively: 3.1885, 3.0924, 2.778, 2.8755, 2.2218; according to>
Figure BDA00040253817600001312
Formula->
Figure BDA00040253817600001313
Is/are>
Figure BDA00040253817600001314
According to the formula: />
Figure BDA00040253817600001315
Figure BDA0004025381760000141
According to the formula>
Figure BDA0004025381760000142
Has->
Figure BDA0004025381760000143
TABLE 9 selection parameters for organic fluorescent pyrene
Figure BDA0004025381760000144
Based on the theoretical structural factor->
Figure BDA0004025381760000145
And compton scattering profile>
Figure BDA0004025381760000146
Figure BDA0004025381760000147
As shown in table 9: the following were calculated according to the same method as above:
Figure BDA0004025381760000148
such difference function:
Figure BDA0004025381760000149
in the present embodiment, the precision of λ is set to 0.01, and thus by a two-multiplication formula: />
Figure BDA00040253817600001410
Is calculated out>
Figure BDA00040253817600001411
The value of (c).
TABLE 10 parameters of the organic fluorescent Material pyrene
Figure BDA00040253817600001412
Based on the theoretical structural factor->
Figure BDA00040253817600001413
And compton scatter profile->
Figure BDA00040253817600001414
Figure BDA00040253817600001415
/>
See table 10, by the multiplication formula of two:
Figure BDA00040253817600001416
wherein A is 0.01, and an index parameter κ (8, 2, -6) is selected>
Figure BDA00040253817600001417
Figure BDA0004025381760000151
By analogy, get out>
Figure BDA0004025381760000152
Is taken and then is reused>
Figure BDA0004025381760000153
Calculate out
Figure BDA0004025381760000154
Value,. Or>
Figure BDA0004025381760000155
Difference value->
Figure BDA0004025381760000156
In this example, the essence of λThe degree is set to 0.01, so the multiplication continues until λ reaches 0.01, until ^ in table 11 is reached>
Figure BDA0004025381760000157
TABLE 11 selection parameters for the organic fluorescent Material pyrene
Figure BDA0004025381760000158
Based on the theoretical structural factor->
Figure BDA0004025381760000159
And Compton scattering profile
Figure BDA00040253817600001510
Figure BDA00040253817600001511
Finally, obtaining the parameter value of the refined electron density matrix model gamma of the organic fluorescent material pyrene
Figure BDA00040253817600001512
Table 12 and fig. 5 show: the valence experimental value obtained after the refining of the method is similar to the first theoretical calculated value, which indicates that the method is feasible.
TABLE 12 is a comparison graph of the experimental value of the valence state of pyrene and the theoretical calculation value of the first character
Figure BDA00040253817600001513
/>
Figure BDA0004025381760000161
The invention has the beneficial effects that: with LiB 3 O 5 And organic fluorescent material pyrene, by electron densityComparing the refined model with a theoretical value, and the valence state experimental value is very close to the first theoretical calculated value, so that the feasibility of the method is proved, and the LiB is obtained 3 O 5 And the refined electronic structure of the organic fluorescent material pyrene provides a better basis for subsequent topological analysis and material design according to the electronic structure.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (9)

1. A density matrix modeling method for electronic structural analysis, characterized by: the method comprises the following steps:
the method comprises the following steps: establishing parameters
Figure FDA0004025381750000011
Calculating the theoretical X-ray diffraction intensity of each diffraction point and the theoretical value of the Compton scattering profile of each momentum;
step two: obtaining the experimental intensity I of each diffraction point through an X-ray single crystal diffraction experiment Experiment of (ii) a The Compton scattering profile J of each momentum is obtained through an X-ray Compton scattering experiment Experiment of the invention ；
Step three: establishing a difference function between theoretical intensity and experimental intensity;
step four: calculating the minimum value in the difference function by adopting a least square method to obtain the parameters of the optimal model
Figure FDA0004025381750000012
2. The method of a density matrix model for electronic structure analysis according to claim 1, wherein in step one, a parameterized electron density matrix model Ψ:
Figure FDA0004025381750000013
P i,j is an m multiplied by m parameter matrix which is the parameter needed to be obtained by fine modification; phi is a i (r)，φ j (r') are the ith and jth basis functions (i, j =1,2,3, \ 8230;, m; m is the number of basis functions) respectively,
the basis functions are known functions.
3. The density matrix modeling method for electronic structure analysis according to claim 2, wherein: the parameter matrix
Figure FDA0004025381750000014
And the density matrix Γ (r, r') may both be written in two parts, one part consisting of the diagonal elements, denoted respectively by
Figure FDA0004025381750000015
Γ (r, r' = r); the other part consists of elements on the off-diagonal line, which are respectively marked as->
Figure FDA0004025381750000016
Γ (r, r' ≠ r), i.e.:
Figure FDA0004025381750000017
Γ (r, r ') = Γ (r, r ' = r) + Γ (r, r ' ≠ r), the diagonal matrix element of Γ (r, r ') is the electron density ρ (r), i.e., ρ (r) = Γ (r, r ' = r), and the theoretical structure factor = Γ of each diffraction point can be calculated through fourier transform of ρ (r)>
Figure FDA0004025381750000021
Figure FDA0004025381750000022
4. Root of herbaceous plantsThe method of density matrix modeling for electronic structure analysis according to claim 1, wherein the experimental intensity for each diffraction point κ is obtained by X-ray single crystal diffraction experiment
Figure FDA0004025381750000023
Further obtaining the structural factor of the experiment
Figure FDA0004025381750000024
Simultaneously, through an X-ray Compton scattering experiment, the experimental Compton scattering profile data of each scattering vector is obtained>
Figure FDA0004025381750000025
5. The method of claim 1, wherein in step three, a difference function defining the difference between theoretical and experimental values of the matrix density model is defined as
Figure FDA0004025381750000026
Wherein the difference function of the difference between the theoretical value and the experimental value on the diagonal of the density matrix is:
Figure FDA0004025381750000027
the difference function of the difference between theoretical and experimental values on the non-diagonal lines of the density matrix is: />
Figure FDA0004025381750000028
I.e. is>
Figure FDA0004025381750000029
6. The density matrix modeling method for electronic structure analysis as set forth in claim 5Characterized in that the least square method is adopted for calculation
Figure FDA00040253817500000210
Gets the optimal model parameter pick>
Figure FDA00040253817500000211
7. The method of claim 6, wherein the calculating is performed by least squares and utilizes
Figure FDA00040253817500000212
Figure FDA0004025381750000031
Preset>
Figure FDA0004025381750000032
Performing a value operation, comprising:
a: randomly selecting two sets of parameter values
Figure FDA0004025381750000033
And &>
Figure FDA0004025381750000034
Each group having m x m parameters, will
Figure FDA0004025381750000035
Substitution into
Figure FDA0004025381750000036
Respectively obtain->
Figure FDA0004025381750000037
And &>
Figure FDA0004025381750000038
B according to the formula
Figure FDA0004025381750000039
A is a step size factor, and the value is calculated>
Figure FDA00040253817500000310
Wherein it is present>
Figure FDA00040253817500000311
I.e. n =3, and will ÷>
Figure FDA00040253817500000312
Substituted into>
Figure FDA00040253817500000313
Is calculated out>
Figure FDA00040253817500000314
A value;
c: also according to the formula of step B
Figure FDA00040253817500000315
(i.e. n = 4) and similarly calculated ÷ based on>
Figure FDA00040253817500000316
Repeating the step n until
Figure FDA00040253817500000317
Less than a predetermined precision value, at which time L (P) n ) Has reached a minimum, is taken up>
Figure FDA00040253817500000318
Is an optimum value;
D:
Figure FDA00040253817500000319
substituted into>
Figure FDA00040253817500000320
And obtaining a final experimental electron density matrix gamma, namely the refined electronic structure function.
8. The method of claim 7, wherein step a obtains the density matrix model
Figure FDA00040253817500000321
And &>
Figure FDA00040253817500000322
First, by combining->
Figure FDA00040253817500000323
And &>
Figure FDA0004025381750000041
Respectively substituted into>
Figure FDA0004025381750000042
To obtain
Figure FDA0004025381750000043
And &>
Figure FDA0004025381750000044
According to>
Figure FDA0004025381750000045
And &>
Figure FDA0004025381750000046
The diagonal sections Γ (r, r '= r) and ρ (r) = Γ (r, r' = r) of (f) obtain ÷ r>
Figure FDA0004025381750000047
And &>
Figure FDA0004025381750000048
According to>
Figure FDA0004025381750000049
Calculate->
Figure FDA00040253817500000410
And
Figure FDA00040253817500000411
according to>
Figure FDA00040253817500000412
Is calculated out>
Figure FDA00040253817500000413
And &>
Figure FDA00040253817500000414
And according to
Figure FDA00040253817500000415
And &>
Figure FDA00040253817500000416
The non-diagonal parts Γ (r, r' ≠ r) and +>
Figure FDA00040253817500000417
Get->
Figure FDA00040253817500000418
And &>
Figure FDA00040253817500000419
According to>
Figure FDA00040253817500000420
Is calculated out>
Figure FDA00040253817500000421
And
Figure FDA00040253817500000422
by means of>
Figure FDA00040253817500000423
And &>
Figure FDA00040253817500000424
Figure FDA00040253817500000425
Acquire->
Figure FDA00040253817500000426
And &>
Figure FDA00040253817500000427
9. The method of claim 8, wherein the predetermined precision value is 0.1 or 0.01 or 0.001, and the smaller the predetermined precision value is, the refined
Figure FDA00040253817500000428
The more accurate. />
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