JP4827444B2 - A method for experimentally determining electrostatic potential by MEM structural analysis of X-ray diffraction data of crystalline materials - Google Patents

Description

The present invention relates to a method for experimentally obtaining the electrostatic potential, electric field, and electric field gradient based on X-ray diffraction data of a crystalline substance.
That is, according to the present invention, an electrostatic potential can be obtained from a highly accurate electron density distribution obtained by performing MEM structural analysis on the X-ray diffraction data of the substance. Therefore, the present invention is widely used as a tool for elucidating the functions from advanced materials such as ferroelectrics, which are advanced materials, to research on high-molecular substances such as proteins.

The above MEM (Maximum Entropy Method) structural analysis, by methods that have been developed in information theory are used in various fields as one method of estimating the information remaining information lacking any for some reason .

  As a method for experimentally determining the electrostatic potential of a substance based on X-ray diffraction data, a method of expanding the electron density distribution to multipole has been used. In this method, the electron density distribution given as a superposition of plane waves is developed as a superposition of spherical waves centered on the atomic position, and the electrostatic potential is calculated from the result.

  However, in this method, there is an arbitrary nature such as how much the expansion order is taken and how to redistribute the electron density that could not be taken in by the expansion. There is also a problem of accuracy due to the limited number of diffraction data obtained experimentally.

In the present invention, these problems are solved by using the maximum entropy method (MEM) (Non-Patent Documents 1, 2 and 3).
M. Sakata and M. Sato, Acta Cryst. 46, 66 (1990) M. Sakata, E. Nishibori, and M. Sato, Z. Kristallogr. 216, 71 (2001) H. Tanaka, M. Takata, E. Nishibori, K. Kato, T. Iishi, and M. Sakata, J. Appl.Crystallogr. 35, 282 (2002)

  In recent years, a method for analyzing the X-ray diffraction data of the above substances using the maximum entropy method (MEM) and obtaining the detailed electron density distribution has been proposed in recent years and has been successfully applied to various systems. Recently, parallel processing has made it possible to apply to polymers such as proteins. Therefore, we applied the electron density obtained by MEM structural analysis to the calculation of electrostatic potential. The parallel processing is to perform high-speed data processing by performing processing in parallel (simultaneously) using a computer having a plurality of CPUs or a plurality of computers.

  The present invention is a new calculation that uniquely obtains a precise electrostatic potential by using MEM when calculating the electrostatic potential of a crystalline material based on experimentally obtained X-ray diffraction data. An algorithm is provided.

  That is, when MEM structural analysis is performed on X-ray diffraction data, a detailed electron density distribution can be obtained. When the obtained electron density distribution is subjected to inverse Fourier transform, X-ray diffraction data that is not observed is predicted. be able to. Therefore, if there is X-ray diffraction that complements the electron density distribution obtained by performing MEM structural analysis on the X-ray diffraction data and the data that has not been observed, it is possible to The electric potential can be calculated. In the conventional method (method not using MEM structure analysis), the analysis is arbitrary and different electrostatic potentials are derived from the same data. In the present invention, the parameter that can be changed according to the intention of the analyst is uniquely obtained instead of the principle.

  The above-mentioned Ewald's method is that the Coulomb interaction is a long-range force, and the electrostatic potential represented by the sum does not converge when calculated in real space (real three-dimensional space) (almost infinitely far away) It is a method to calculate the Coulomb interaction well, by calculating the Coulomb interaction in both real space and reciprocal lattice space. can do.

  The above-mentioned reciprocal space is expressed by the coordinates (x, y, z) in the real space because a material having a periodic structure such as a crystal material often performs Fourier transform and considers things in the reciprocal space. When the Fourier transform is performed, the variable shifts from x, y, z to a variable (Gx, Gy, Gz) in the reciprocal lattice space.

In addition, by using the method of the present invention, it is possible to simultaneously obtain the detailed electron density of the crystalline substance and the corresponding electrostatic potential under the same algorithm.
That is, conventionally, the electron density and the electrostatic potential have been obtained by different methods. In addition, the conventional method has arbitraryness as described above. On the other hand, in the method of the present invention, the electron density and the electrostatic potential are obtained by the same method, and when the electron density is determined, the electrostatic potential is uniquely and simultaneously determined.

Therefore, the present invention obtains the most probable electron density distribution by performing MEM structural analysis based on the X-ray diffraction data of the crystal substance, estimates the crystal structure factor not measured from the distribution, and calculates the crystal by calculation. Obtain the electrostatic potential of a substance, calculate the electric field of the crystalline substance from the electrostatic potential thus obtained, and further obtain the electric field gradient from the gradient, thereby elucidating the state of polarization at the atomic and molecular level of the crystalline substance Is the method.
That is, the positively charged part of the polarized molecule or the cation is attracted to a place with a high electrostatic potential, and the negatively charged part of the polarized molecule or the anion is an electrostatic potential. Although attracted to a low place, the electric field indicates the direction of the force that molecules and ions receive at that time. Therefore, if the electric field is known, it is possible to predict the reaction path of molecules and ions. In some cases, the electric field gradient in the crystal can be experimentally measured. In this case, the analysis result of the present invention can be compared with the experimental result, which is useful for crystal analysis.

  Various aspects such as structural phase transitions of ferroelectrics, photoinduced structural phase transitions of organic materials, bonding of atoms and molecules to solid surfaces, bonding of molecules, reactions and catalysis of organic substances, protein reactions and information transmission And electrostatic potential plays an important role. If the method of the present invention is used, the electrostatic potential can be determined experimentally, and the state of polarization can be examined in detail at the atomic / molecular level.

  That is, when the electron density distribution is low, the electrostatic potential is low in the heart, and the electrostatic potential is high at high places. For this reason, when the electron density distribution is biased (polarization) (when there is a shift between the position of the nucleus and the center of gravity of the electron density distribution), a change appears in the electrostatic potential. Since polarization works with the integrated value of charge density, it is difficult to understand the state of polarization even if only the charge distribution is observed, but it can be clearly understood from the electrostatic potential.

  In addition, in the case of polymers and proteins, it is possible to identify the reaction activation site and predict the chemical reaction pathway. For these reasons, the present invention contributes to the field of novel material design and drug discovery.

  That is, the reaction activation site is that most of organic substances are polarized, and therefore, one molecule has a positively charged portion and a negatively charged portion, and two molecules react there. When they are bonded, the charged parts are opposite to each other, and the high potential part is connected to the negatively charged part of the molecule. Such a portion that is easily bound is a reaction activation site.

  In addition, the above reaction path is a path through which molecules move during the reaction. In this case, if the potential is known, it is predicted what path the molecules will move to the reaction activation site. it can.

  FIG. 1 shows a comparison of the estimated crystal structure factor with the experimental value by analyzing the MEM structure in the X-ray diffraction data of the Si crystal obtained from the experiment. That is, FIG. 1 is a diagram showing a comparison between a crystal structure factor (electron density distribution) estimated from MEM structure analysis and a crystal structure factor (electron density distribution) obtained from experiments. From this figure, it can be seen that MEM structural analysis quantitatively reproduces experimental values up to higher-order crystal structure factors.

  In the algorithm of the present invention, first, the most probable electron density distribution is obtained by analyzing the MEM structure based on the X-ray diffraction data of the crystal substance, and the crystal structure factor that has not been measured is estimated from the result. (2) The electrostatic potential of the crystalline material is calculated by the formula. The electrostatic potential thus obtained corresponds to the electron density distribution of the same crystalline material obtained by MEM structural analysis.

  If the electrostatic potential is obtained, the electric field of the crystalline material can be calculated by calculating the gradient. Furthermore, the electric field gradient can be obtained by calculating the gradient.

Here, an example applied to PbTiO3, which is one of the ferroelectric materials, is shown. Fig. 2 is a diagram showing the contour map of the electron density of PbTiO3 obtained by MEM structural analysis on the (100) plane. The distribution of the electron density obtained by MEM structural analysis on the (100) plane is shown in blue. It is expressed by the color change from red to red. The red part has a high electron density and corresponds to each atomic position. FIG. 2 shows that the electron density decreases in the order of red, yellow, green, and blue (this is also true in FIGS. 3 and 4 below).
On the other hand, FIG. 3 is a diagram showing a contour map of the electrostatic potential of the PbTiO3 obtained by the method of the present invention on the (100) plane. The strength of the electrostatic potential on the (100) plane is shown from blue. It is expressed by the color change up to red. It can be seen that the electrostatic potential is increased corresponding to the polarization of Pb atoms and the accumulation of positive charges on the upper side (the electrostatic potential tends to increase at higher electron densities).

  FIG. 4 is a diagram showing the strength of the electrostatic potential on the isoelectronic density surface of PbTiO3 by the color change from blue to red, that is, the isoelectronic density surface of PbTiO3 (connecting the points with the same electron density). The surface made of is colored by the strength of the electrostatic potential. The electron density surface corresponding to Pb atoms changes from blue to red, indicating that the atoms are polarized. It can also be seen that O atoms are polarized, though not as much as Pb atoms. On the other hand, Ti atoms have almost no polarization because there is no color change.

Industrial application fields

  In accordance with the present invention, structural phase transitions of ferroelectrics, photoinduced structural phase transitions of organic materials, atomic / molecular bonds to solid surfaces, molecular bonds, organic reaction / catalysis, protein reactions and information transmission, etc. In various aspects, it is possible to experimentally determine their electrostatic potential based on X-ray diffraction data, and as a result, the state of polarization can be examined in detail at the atomic and molecular level. In addition, in the case of polymers and proteins, it is possible to identify the reaction activation site and predict the chemical reaction pathway. For these reasons, the present invention contributes to the field of novel material design and drug discovery.

It is a figure which shows the comparison of the crystal structure factor estimated from MEM structural analysis, and the crystal structure factor obtained from experiment. It is a figure which shows the contour map in (100) plane of the electron density of PbTiO3 obtained by MEM structural analysis. It is a figure which shows the contour map in (100) plane of the electrostatic potential of PbTiO3 obtained by the method of this invention. It is the figure which expressed the strength of the electrostatic potential on the isoelectronic density surface of PbTiO3 by the change of the color from blue to red.

Claims (4)

From experimentally-obtained X-ray diffraction data, predicts the diffraction data that is not observed by X-ray diffraction using the maximum entropy method (MEM), was obtained the experimentally in the predicted diffraction data A method for obtaining an electrostatic potential based on X-ray diffraction data , wherein the electrostatic potential is calculated by an Ewald method using X-ray diffraction data obtained by complementing the X-ray diffraction data .   The calculation method which calculates | requires an electric field by calculating the gradient of the electrostatic potential obtained by Claim 1.   The calculation method which calculates | requires an electric field gradient by calculating the gradient of the electric field obtained by Claim 2. A method for elucidating the state of polarization at the atomic / molecular level of a crystalline substance by calculating the electrostatic potential by a method for obtaining the electrostatic potential based on the X-ray diffraction data according to claim 1.

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