JP7358801B2 - How to search for diffusion routes - Google Patents

Description

The present invention relates to a diffusion route search method.

With the aim of further improving the performance of various materials, the search for new materials and the search for substitution elements that replace some of the elements constituting substances are actively being conducted.

As mentioned above, when searching for new materials and substitution elements, it is important to consider the routes through which atoms that affect the desired reaction, function, etc. move and diffuse within the crystal of the desired substance. It is preferable to know exactly what to do.

However, the elements inside the crystal are often tightly packed, and there appear to be only small gaps between the atoms that make up the crystal. For this reason, if you estimate the size of an atom whose diffusion path you want to investigate using its atomic radius or van der Waals radius, you can identify the diffusion path of the atom by comparing the sizes of multiple gaps in the crystal. was difficult.

In view of the problems of the above-mentioned conventional techniques, one aspect of the present invention aims to provide a method for searching for diffusion paths that can efficiently search for diffusion paths of atoms within a crystal.

According to one aspect of the present invention to solve the above problems,
The computer is
an initial structure setting step of setting the positions of multiple atoms included in the crystal used for diffusion route search;
a calculation step of performing molecular dynamics calculations using the plurality of atoms whose positions were set in the initial structure setting step;
an analysis step of performing principal component analysis on the coordinate data of the plurality of atoms obtained in the calculation step and determining a direction in which the plurality of atoms are likely to move;
a structural model creation step of creating a plurality of structural models in which the plurality of atoms are located in directions where they are likely to move, based on the results of the analysis step;
A diffusion path search method is provided, which performs a diffusion path search step of searching for an atomic diffusion path from the plurality of structural models created in the structural model creation step.

According to one aspect of the present invention, it is possible to provide a method for searching for diffusion paths that can efficiently search for diffusion paths of atoms within a crystal.

FIG. 2 is a schematic diagram showing the initial structure of LiMn ₂ O ₄ in which the diffusion path was searched in Example 1. FIG. FIG. 2 is a schematic diagram showing the diffusion path of Li atoms in LiMn ₂ O ₄ determined in Example 1.

Hereinafter, modes for carrying out the present invention will be described. However, the present invention is not limited to the following embodiments, and various modifications and variations may be made to the following embodiments without departing from the scope of the present invention. Substitutions can be added.

The diffusion route search method of this embodiment can include the following steps.
Initial structure setting step to set the positions of multiple atoms included in the crystal used for diffusion route search.
A calculation process in which molecular dynamics calculations are performed using multiple atoms whose positions were set in the initial structure setting process.
An analysis process that performs principal component analysis on the coordinate data of multiple atoms obtained in the calculation process to determine the direction in which multiple atoms tend to move.

A structural model creation process in which multiple structural models are created based on the results of the analysis process, in which multiple atoms are positioned in directions where they are likely to move.
Diffusion path search step to search for atomic diffusion paths from multiple structural models created in the structural model creation step.

The inventor of the present invention has conducted extensive studies on an efficient method for searching for the diffusion path of atoms within a crystal. As a result, from the results of the molecular dynamics method, principal component analysis is used to derive the directions in which multiple atoms within the crystal tend to move, and by searching for diffusion paths from a structural model in which atoms are arranged in the directions in which they are easy to move, The present invention was completed by discovering that it is possible to efficiently derive a diffusion path.

Each step will be explained below.
(Initial structure setting process)
In the initial structure setting step, the positions of a plurality of atoms included in the crystal used for diffusion route searching can be set. That is, it is possible to set the initial coordinates of the crystal used in the calculation process.

In the initial structure setting step, a specific method for setting the positions of a plurality of atoms included in the crystal used for diffusion route search is not particularly limited. For example, the atomic arrangement of each atom can be set based on the crystal structure of the crystal, which has been experimentally determined or disclosed in literature, etc., and can be used as an initial structure.

The initial structure set in the initial structure setting step may or may not contain diffusion atoms, which are atoms that search for diffusion paths. That is, it may be only a skeletal structure excluding diffused atoms. In the diffusion route search method of this embodiment, the diffusion route is searched based on the size of the space formed by the movement of atoms other than the diffusing atoms. This is because there is no big difference in the results.
(calculation process)
In the calculation step, molecular dynamics calculations can be performed using a plurality of atoms whose positions were set in the initial structure setting step.

Molecular dynamics calculation is a computer simulation method of the physical movement of atoms, and by numerically solving Newton's equation of motion, it is possible to determine the evolution of the position of atoms over time. Therefore, by performing the calculation step, it is possible to obtain time-series changes in the coordinates of a plurality of atoms set in the initial structure setting step.

In molecular dynamics calculations, information about atoms and interactions between atoms is represented by a functional form for describing potential energy and its parameter set (force field).

The type of force field used in the molecular dynamics calculation in the calculation process is not particularly limited, and various force fields can be used. For example, metal/alloy systems include EAM and MEAM, inorganic compound systems include Buckingham, BKS, Clay-FF, CVFF_aug, etc., semiconductor systems include Tersoff, and organic compound systems include PCFF, Compass, MMFF, OPLS-AA, AMBER, CHARMM, etc. UFF etc. can be used. In addition, forces selected from existing force fields such as polarization force fields such as X-Pol, AMBER polarization force field, and CHARMM polarization force field, and reaction force fields such as ReaxFF, as well as force fields created by yourself as necessary. You can use the field.

Existing force fields may not specify the charge of the target atom. In that case, RESP (Restrained ElectroStatic Potential) charges, AM1-BCC (Bond Charge Correction) charges, etc. can also be used.

The program (software) used for molecular dynamics calculations is not particularly limited, but may be selected from existing programs such as LAMMPS, DL_POLY, Gromacs (Groningen Machine for Chemical Simulations), AMBER, CHARMM, NAMD, or self-made programs. A program can be used.

The setting environment for performing molecular dynamics calculations can be, for example, vacuum or periodic boundary conditions if a solvent is included.

The numerical integration method for solving Newton's equation of motion when performing molecular dynamics calculations is not particularly limited, but may be selected from, for example, the Berlet method, the velocity Berlet method, the Leap-frog method, the predictor-modifier method, etc. Other methods can be used.

Although the time span for performing molecular dynamics calculations is not particularly limited, it is preferably selected so that the directions in which the plurality of atoms constituting the crystal tend to move can be grasped and calculation costs can be suppressed. The time width for performing the molecular dynamics calculation can be, for example, 0.5 fs or more and 2 fs or less.

Further, the temperature control method is not particularly limited, but may be selected from, for example, the rate scaling method, the Nose-Hoover hot bath method, the Nose-Hoover chain method, the Berendsen hot bath method, the Andersen hot bath method, the Langevin kinetic method, etc. Other methods can be used.

The method of controlling the pressure under periodic boundary conditions is not particularly limited either, but for example, a method selected from the Berendsen method, the Parinello-Rahman method, etc. can be used.

A cutoff method can be used to calculate long-range interactions such as electrostatic interactions and van der Waals interactions. In particular, the Particle-Mesh Ewald method, the multipole expansion method, etc. can be used to calculate electrostatic interactions under periodic boundary conditions.

Molecular dynamics calculation in the calculation process uses, for example, a CPU (Central Processing Unit), a RAM (Random Access Memory), various storage media such as a hard disk, an output device such as a display, an input device such as a keyboard, various peripheral devices, etc. It can be carried out using a conventional computer system equipped with a computer system. Note that examples of the computer system include a network server, a workstation, a personal computer, and the like.

Specifically, for example, a program for the molecular dynamics calculation described above is stored in a storage medium, and the program is executed by a CPU, and an input device such as a keyboard or the like is stored in a storage medium such as a RAM. This can be achieved by reading the initial structure and conditions input from .
(Analysis process)
In the analysis step, principal component analysis is performed on the coordinate data of the plural atoms obtained in the calculation step, and the direction in which the plural atoms tend to move can be determined.

Here, principal component analysis is a multivariate analysis aimed at extracting features and compressing the dimensions of data.

In principal component analysis, first, the first principal component is set in the direction that best represents the data, that is, the direction in which the variance of the data is maximized. The larger the variance, which is the dispersion of values in the axial direction, the larger the amount of information, so by using the information of the first principal component, you can suppress missing information and reduce the number of variables compared to the original data. , enables highly accurate data processing.

Then, the second principal component is set within a space orthogonal to the first principal component in a direction that can best express data fluctuations that cannot be expressed by the first principal component. In addition, when expanding to N (≧2) dimensions or more, the axis of the Nth principal component can be set under the constraint that it is orthogonal to all axes below the (N-1)th principal component. .

The coordinate data of each atom obtained in the calculation process can be projected onto the axis of the principal component newly set as described above, and the coordinates can be converted.

In the calculation step, as described above, time-series changes in the coordinates of a plurality of atoms can be determined. However, such data on time-series changes in the coordinates of a plurality of atoms is data set in advance, for example, data associated with x, y, and z axes. For this reason, sufficient information is not necessarily included in any one of the x, y, and z axes, and usually the data obtained in the calculation process is used to calculate the number of atoms set in the initial structure setting process. It is difficult to directly grasp the direction in which a person is likely to move. Therefore, by using the principal component analysis as described above, it is possible to acquire data in which the variance is maximized in order from the first principal component. In other words, it becomes possible to use appropriate information for processing, and the direction in which each atom is likely to move can be derived from data on time-series changes in the coordinates of multiple atoms obtained in the calculation process.

Principal component analysis can be performed, for example, for each atom in the crystal set in the initial structure setting structure, or can be performed for the same type of atoms all at once. Therefore, by selecting only atoms that are considered to be important or atoms that have large movements, and making them the targets of analysis, the analysis time can be shortened.
(Structural model creation process)
In the structural model creation process, it is possible to create multiple models of structures in which multiple atoms are located in directions where they can easily move, based on the results of the analysis process.

Specifically, for example, a structural model in which the coordinates of multiple atoms set in the initial structure setting process are changed in the direction in which each atom can easily move, calculated in the analysis process, is can be created.
(Diffusion route search process)
In the diffusion route searching step, it is possible to search for the diffusion route of the atom whose diffusion route is being searched, that is, the diffusion route of the diffusing atom, from the plurality of structural models created in the structure creation step. Specifically, for example, by comparing multiple structural models that have been created, it is possible to identify as the diffusion route the part where the interatomic distance is wider than the atomic radius of the diffusing atoms for atoms that make up the crystal other than the diffusing atoms. can.

According to the diffusion path search method of this embodiment described above, the direction in which atoms are likely to move is derived using principal component analysis based on the results of molecular dynamics calculation, and the structural model in which the atoms are moved in that direction is used. We are searching for the diffusion route. Therefore, it is possible to efficiently search for diffusion paths that are difficult to find from static crystal structures obtained through experiments in which atoms exist at average positions.

Furthermore, as described above, diffusion paths are searched using a structural model that reflects atomic fluctuations based on molecular dynamics calculation results, making it possible to search for diffusion paths in a structure that is closer to reality.

Hereinafter, the present invention will be described in more detail with reference to Examples. However, the present invention is not limited to the following examples.
[Example 1]
The following procedure was used to search for the diffusion route of Li atoms in LiMn ₂ O ₄ .
(Initial structure setting process)
The initial structure of LiMn ₂ O ₄ was set. Specifically, as shown in FIG. 1, an initial structure 10 of LiMn ₂ O ₄ in which lithium atoms 11, manganese atoms 12, and oxygen atoms 13 were arranged was set in the cell. In addition, in FIG. 1, atoms with the same hatching indicate atoms of the same type.
(calculation process)
Next, using molecular dynamics calculation, time-series changes in the coordinates of the lithium atom 11, the manganese atom 12, and the oxygen atom 13 whose positions were set in the initial structure setting step were determined.

Molecular dynamics calculations were performed using LAMMPS as software and a force field developed by Ishizawa et al. of Nagoya University. Then, the coordinates of each atom were entered to set the environment in the crystal.

In addition, the velocity Berlet method was used as a velocity calculation method when performing molecular dynamics calculations, and the time width was set to 1 fs. The Nose-Hoover chain method was used as a temperature control method, and the set temperature was 300K.

The Particle-Mesh Ewald method was used to calculate long-range interactions.

Molecular dynamics calculations were performed for 10 nanoseconds under the above conditions.
(Analysis process)
Principal component analysis was performed on changes in the coordinates of multiple atoms obtained during the calculation process, and the directions in which multiple atoms tend to move were determined.
(Structural model creation process)
From the results of the analysis process, the coordinates of multiple atoms set in the initial structure setting process are calculated in the analysis process. Created.
(Diffusion route search process)
We searched for diffusion paths of diffusing atoms from multiple structures created in the structure creation process.

FIG. 2 shows the diffusion paths of the diffused atoms obtained in the diffusion path search step.

As shown in FIG. 2, diffusion paths 211 to 214 were found as diffusion paths for lithium atoms. These diffusion paths connect the lithium atoms 11A (see FIG. 1) located in the center of the cell and the lithium It is formed so as to connect the lithium atoms arranged around the atom 11A.

These diffusion paths 211 to 214 match the previously reported diffusion paths of lithium atoms in LiMn ₂ O ₄ , and the method of searching for diffusion paths used in this example is based on actual phenomena. I was able to confirm that.

Claims (1)

The computer is
an initial structure setting step of setting the positions of multiple atoms included in the crystal used for diffusion route search;
a calculation step of performing molecular dynamics calculations using the plurality of atoms whose positions were set in the initial structure setting step;
an analysis step of performing principal component analysis on the coordinate data of the plurality of atoms obtained in the calculation step and determining a direction in which the plurality of atoms are likely to move;
a structural model creation step of creating a plurality of structural models in which the plurality of atoms are located in directions where they are likely to move, based on the results of the analysis step;
A method for searching for a diffusion path, comprising : a diffusion path searching step of searching for an atomic diffusion path from the plurality of structural models created in the structural model creation step.

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