Design support device, design support method, and program

Abstract

This design support device comprises: a physical property calculation unit that calculates a statistical amount of physical property values of a substance on the basis of information indicating motion of each of a plurality of atoms included in the substance; and a contribution calculation unit that calculates a contribution ratio of each atom to the statistical amount on the basis of a displacement amount of the physical property value of each atom.

Description

Design Support Device, Design Support Method, and Program

[0001] The present disclosure relates to a design support device, a design support method, and a program.

[0002] Techniques for calculating the dipole moment based on molecular dynamics calculations are known. For example, Patent Document 1 discloses a simulation device that calculates time-series data of the dipole moment by molecular dynamics calculations and outputs a dielectric relaxation function based on the time-series data in a predetermined frequency band.

[0003] Japanese Patent Application Laid-Open No. 2024-111615

[0004] However, in the prior art, the contribution of each atom to the physical property value of a substance cannot be analyzed. For example, there may be a case where the total dipole moment, which is the sum of the dipole moments of the atoms contained in a substance, is calculated, and the movement of an atom with a large contribution to the dispersion of the total dipole moment is to be analyzed.

[0005] One aspect of the present disclosure aims to analyze the contribution of each atom to the physical property value of a substance.

[0006] The present disclosure includes the following configurations.

[0007] <1> A physical property calculation unit configured to calculate a statistic of the physical property value of the substance based on information indicating the movement of each of a plurality of atoms contained in the substance, and a contribution calculation unit configured to calculate the contribution rate of each of the atoms to the statistic based on the displacement amount of the physical property value of each of the atoms. A design support device comprising:

[0008] <2> The design support device according to <1> above, wherein the contribution calculation unit is configured to calculate the contribution rate of each of the atoms by performing singular value decomposition on a matrix generated based on the displacement amount.

[0009] <3> The design support device according to <1> or <2> above, wherein the statistic is the dispersion of the total dipole moment.

[0010] <4> The design support device according to <3> above, wherein the information indicating the motion includes the time change of the position of each of the atoms, and the physical property calculation unit is configured to calculate the variance of the total dipole moment based on the time average of the position of each of the atoms and the charge of the atoms.

[0011] <5> The design support apparatus according to any one of <1> to <4> above, further comprising a visualization unit configured to visualize molecules with large atomic motion.

[0012] <6> The design support device according to <5> above, wherein the visualization unit is configured to visualize at least one of the arrangement of the molecules, the structure of the molecules, the contribution rate of the atoms contained in the molecules, or the motion modes of the atoms contained in the molecules.

[0013] <7> A design support method that performs the following steps on a computer: a procedure for calculating statistical quantities of physical properties of a substance based on information indicating the motion of each of several atoms contained in the substance; and a procedure for calculating the contribution rate of each atom to the statistical quantities based on the displacement of each atom's physical properties.

[0014] <8> A program for causing a computer to perform the following steps: a procedure for calculating statistical quantities of physical properties of a substance based on information indicating the motion of each of several atoms contained in the substance; and a procedure for calculating the contribution rate of each atom to the statistical quantities based on the displacement of each atom's physical properties.

[0015] According to one aspect of this disclosure, the contribution of each atom to the physical properties of a substance can be analyzed.

[0016] Figure 1 is a block diagram showing an example of the overall configuration of a design support system. Figure 2 is a block diagram showing an example of the computer hardware configuration. Figure 3 is a block diagram showing an example of the functional configuration of a design support system. Figure 4 is a flowchart showing an example of a design support method. Figure 5 is a diagram showing an example of the visualization results.

[0017] Hereinafter, embodiments of this disclosure will be described with reference to the accompanying drawings. In this specification and the drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant descriptions will be omitted.

[0018] [Embodiment] One embodiment of the present disclosure is an example of an information processing system that supports the design of a material. The information processing system according to this embodiment is referred to as the "design support system". In this embodiment, the design support system has a function to calculate the physical properties of a material based on molecular dynamics calculations. Hereinafter, the material to be designed is referred to as the "target material". The target material may be an additive, a flame retardant, or an organophosphorus compound used in high-frequency substrate materials, for example.

[0019] Traditionally, it is sometimes necessary to calculate certain quantities using only the k (<m) dimension information from data of dimension m. As an example, consider molecular dynamics calculations. In molecular dynamics calculations, the coordinate data x (dimension 3N) of N atoms is evolved over time using a predetermined equation of motion. By multiplying the coordinate data of each atom by the partial charge of each atom, the dipole moment m (dimension 3N) of the N atoms can be obtained. Therefore, given the partial charge of each atom, the time evolution of the dipole moment of the N atoms can be calculated using molecular dynamics calculations.

[0020] The total dipole moment M (dimension 3) can be calculated by summing the dipole moments of N atoms over all atoms. Here, the variance of the total dipole moment is given by equation (1).

[0021]

[0022] However, M(t) is the total dipole moment at time t, and T is the simulation time.

[0023] There are times when we want to analyze the motion of atoms that make a large contribution to the dispersion of the total dipole moment. However, since the total dipole moment M only contains three-dimensional information, it is not possible to directly analyze the magnitude of the contribution of 3N-dimensional atomic motion from the total dipole moment M or its dispersion.

[0024] As in the example above, when calculating some quantity z using only k (<m) dimensional information from m-dimensional data x, if there is a method that allows for the following (1) and (2), it becomes possible to understand the cause of quantity z using the m-dimensional data x. (1) Extract the components that have a large contribution to quantity z from the data x. (2) Numerically evaluate the magnitude of the contribution of the extracted components.

[0025] The design support system according to this embodiment aims to analyze the contribution of each of several atoms contained in a material. To this end, the design support system calculates statistical quantities of the material's physical properties based on information indicating the motion of each atom contained in the material, and calculates the contribution rate of each atom to the statistical quantities based on the displacement of each atom's physical properties.

[0026] In one aspect, this embodiment allows for the analysis of the contribution of each atom to the physical properties of a substance. In another aspect, this embodiment allows for the visualization of molecules with large atomic motion among multiple molecules contained in a substance. As a result, molecules that affect physical properties can be efficiently analyzed, and the design of materials with improved physical properties can be supported.

[0027] <Principle> In this embodiment, a method having the following two stages is used. The first stage is the stage of preparing data. The second stage is the stage of performing calculations based on the data.

[0028] In the first stage, the following two steps are performed. In the first step, a d × m complex-valued matrix X and a d × n complex-valued matrix Y are obtained. In the second step, an m × k complex-valued matrix P and an n × k complex-valued matrix Q are obtained, where d, m, n, and k are natural numbers and k ≤ m, n.

[0029] In the second stage, the following four steps are performed. In the first step, matrix PQ Ｔ Y Ｔ Calculate X. However, Ｔ is the Hermitian conjugate of matrix . In the second step, matrix PQ Ｔ Y Ｔ Perform singular value decomposition on X, UΛV Ｔ = PQ Ｔ Y ＴObtain the left singular vector \(U\), right singular vector \(V\), and singular value \(\Lambda\) that result in \(X\). In the third step, calculate the diagonal components of \(U\Lambda V\). Ｔ In the fourth step, based on the diagonal components of \(U\Lambda V\), evaluate the contribution magnitudes of the left singular vector \(U\) and right singular vector \(V\) respectively to \(tr(Q Ｔ Y Ｔ XP)\). Here, \(tr(\cdot)\) represents the trace of the matrix \(\cdot\) (the sum of diagonal components). Ｔ Regarding the quantity \(z\) defined by \(tr(Q

[0030] Y Ｔ XP)\), when \(Q Ｔ Y Ｔ XP\) is decomposed into singular values, at most the components that contribute significantly to the quantity \(z\) in a \(k\)-dimensional space will be analyzed. Here, like the above method, when \(PQ Ｔ Y Ｔ X\) is decomposed into singular values, the components that contribute significantly to the quantity \(z\) in a maximum \(m\)-dimensional space can be analyzed. Ｔ Specifically, regarding the quantity \(z\) defined by \(tr(Q

[0031] Y Ｔ XP)\), the left and right singular vectors \(U, V\) obtained by decomposing \(Q Ｔ Y Ｔ XP\) only provide information about the projected space, while the left and right singular vectors \(U, V\) obtained by decomposing \(PQ Ｔ Y Ｔ X\) provide information that also includes information about the space before projection with respect to the matrix \(X\). This is beneficial for extracting and analyzing the components that contribute significantly (i.e., the causes for increasing or decreasing the quantity \(z\)) in a form that includes information about the space before projection for the quantity \(z\) calculated based on the information about the projected space. Ｔ

[0032] <Mathematical Foundation> Hereinafter, all lowercase alphabets represent natural numbers (non-negative integers). Let \(X\in C ｄ×ｍ \) and \(Y\in F ｄ×ｎ \). Here, \(F\) is the complex number field. Let \(P\in ｍ×ｋ \) (where \(k\leq m\)) and \(Q\in ｎ×ｋ \) (where \(k\leq n\)) be projection operators, and \(P ｒｓ =\delta ｒｓ \), \(Q ｒｓ= δ ｒｓ Let δ ｒｓ This is the Kronecker delta defined by equation (2).

[0033]

[0034] The matrices that are unitarily equivalent to P and Q are: ｒｓ = δ ｒｓ Q ｒｓ = δ ｒｓ It is always possible to convert to this form. Here, we convert to this form for the sake of simplifying the later discussion, but this does not result in a loss of generality. Note that if necessary, P and Q may be multiplied by non-zero constants.

[0035] Let the quantity z be given by equation (3).

[0036]

[0037] Due to the properties of matrix tracing, equation (4) holds true.

[0038]

[0039] Using singular value decomposition, two unitary matrices U, V ∈ C satisfy equation (5). ｍ×ｍ and the rectangular diagonal matrix Λ∈F ｍ×ｍ This is obtained. However, Λ can generally be chosen such that it is positive semi-definite. Hereafter, we will assume that Λ is positive semi-definite.

[0040]

[0041] The r-th column of U and V is the left and right singular vector for the (r,r)-th component of Λ (i.e., the r-th singular value). The r-th singular value is λ ｒ When expressed in this way, the quantity z can be expressed by equation (6).

[0042]

[0043] Here, σ is defined by equation (7) ｒ Based on this, the component with the largest (signed) contribution to quantity z is F. ｍ This makes it possible to analyze the data above.

[0044]

[0045] That is, for some r, σ ｒ If has a large positive value, then it can be seen that the r-th right singular vector makes a large positive contribution to the quantity z. Also, for some r, σ ｒ If the absolute value of is a large negative value, then it can be seen that the r-th right singular vector has a large negative contribution to the quantity z.

[0046] In a special case, if equation (8) or equation (9) holds and z ≠ 0, then ρ defined by equation (10) is used. ｒ This can be interpreted as the contribution rate of the r-th left-right singular vector to the quantity z. Therefore, by using the right singular vector with a large contribution rate, the component with a large contribution to the quantity z can be expressed as F ｍ This makes it possible to analyze the data above.

[0047]

[0048] However, it is important to note that even when Y = X and P = Q, equation (8) or equation (9) may not necessarily hold true. Regarding equation (5), V from the left side of both sides... Ｔ Multiplying by and then by V from the right, we obtain equation (11). Here, V is unitary (i.e., VV Ｔ = V Ｔ V = I, where I is the identity matrix).

[0049]

[0050] Considering the (s,s) component of equation (11), we obtain equation (12).

[0051]

[0052] The left-hand side of equation (12) can be decomposed as shown in equation (13).

[0053]

[0054] Substituting equation (13) into equation (12) yields equation (14).

[0055]

[0056] The first term on the left side of equation (14) is clearly non-negative, but the second term on the left side is not necessarily non-negative. Therefore, even when Y=X and P=Q, equation (8) or equation (9) does not necessarily hold. ρ is defined in equation (10). ｒ In order to interpret this as the rate of contribution to quantity z, it is necessary to confirm that equation (8) or equation (9) holds true.

[0057] <Overall Configuration> The overall configuration of the design support system in this embodiment will be explained with reference to Figure 1. Figure 1 is a block diagram showing an example of the overall configuration of the design support system.

[0058] As shown in Figure 1, the design support system 1000 includes a design support device 10 and a terminal device 50. The design support device 10 and the terminal device 50 are connected via a communication network N to enable data communication. The communication network N may include, for example, a LAN (Local Area Network), a VPN (Virtual Private Network), or the Internet.

[0059] The design support device 10 is an example of an information processing device that assists in the design of materials. The design support device 10 may be a computer such as a personal computer, workstation, or server.

[0060] The design support device 10 receives information about the target substance from the terminal device 50. The design support device 10 calculates statistical values ​​of the physical properties of the target substance and analyzes the contribution of each atom to the statistical values ​​of the physical properties. The design support device 10 also visualizes the molecules contained in the target substance and transmits the visualization results to the terminal device 50.

[0061] The terminal device 50 is an example of an information processing device operated by a user of the design support system 1000. The terminal device 50 may be a computer such as a personal computer, tablet terminal, or smartphone.

[0062] The terminal device 50 transmits information about the target substance to the design support device 10. The terminal device 50 receives the visualization results of molecules contained in the target substance from the design support device 10. The terminal device 50 presents the visualization results to the user. For example, the terminal device 50 may display the visualization results on the output device 505.

[0063] The overall configuration of the design support system 1000 shown in Figure 1 is just one example, and various system configurations are possible depending on the application and purpose. For example, one or more design support devices 10 and terminal devices 50 may be included in the design support system 1000. For example, the design support device 10 may be implemented using multiple computers, or it may be implemented as a cloud computing service. For example, the design support system 1000 may be implemented using a standalone computer. The classification of devices such as the design support device 10 and terminal device 50 shown in Figure 1 is just one example.

[0064] <Hardware Configuration> The hardware configuration of the design support system 1000 will be explained with reference to Figure 2. The design support device 10 and the terminal device 50 can be implemented using a computer. Figure 2 is a block diagram showing an example of the computer's hardware configuration.

[0065] As shown in Figure 2, the computer 500 includes a processor 501, memory 502, auxiliary storage device 503, input device 504, output device 505, communication device 506, and drive device 507. Each piece of hardware in the computer 500 is interconnected via a bus 508.

[0066] The processor 501 is an example of a computing device that implements the control and functions of the entire computer 500. The processor 501 may include, for example, at least one of a CPU (Central Processing Unit) or a GPU (Graphic Processing Unit). The processor 501 reads various programs installed in the auxiliary storage device 503 into the memory 502 and executes them.

[0067] Memory 502 is an example of a semiconductor memory (storage device) capable of holding programs and data. Memory 502 may include, for example, at least one of ROM (Read Only Memory) or RAM (Random Access Memory).

[0068] The processor 501 and the memory 502 form what is known as a computer (hereinafter also referred to as the "control unit"). The computer realizes various functions by having the processor 501 execute various programs read into the memory 502.

[0069] The auxiliary storage device 503 is an example of a non-volatile storage device that stores various programs and various data used by those programs. The auxiliary storage device 503 may include, for example, at least one of the following: an HDD (Hard Disk Drive) or an SSD (Solid State Drive). The programs stored in the auxiliary storage device 503 may include, for example, basic software (Operating System) or various applications.

[0070] The input device 504 is a device used by the user of the computer 500 to input various signals. The input device 504 may include, for example, an operating device such as a mouse, keyboard, or touch panel, or a sound collection device such as a microphone.

[0071] The output device 505 is a device that outputs the processing results of various processes performed by the computer 500. The output device 505 may include, for example, a display device such as a display or touch panel, or an audio device such as a speaker.

[0072] The communication device 506 is a communication device for communicating with external devices. For example, the communication device 506 may be a network interface that performs wired communication or wireless communication via the communication network N.

[0073] The drive device 507 is a device for setting the storage medium 509. The storage medium 509 may include, for example, a medium that stores electronic data optically or magnetically, such as a CD-ROM, DVD-ROM, flexible disk, or magneto-optical disk. The storage medium 509 may also include a medium such as a semiconductor memory that stores electronic data electrically, such as a flash memory.

[0074] The various programs to be installed in the auxiliary storage device 503 are installed, for example, when the distributed storage medium 509 is set in the drive device 507 and the various programs stored in the storage medium 509 are read by the drive device 507. Alternatively, the various programs to be installed in the auxiliary storage device 503 may be installed by downloading them from the communication network N via the communication device 506.

[0075] The computer 500 can perform various processes described later by having the hardware configuration shown in Figure 2. Note that the hardware configuration shown in Figure 2 is just one example, and the computer 500 may have other hardware configurations. For example, the computer 500 may have multiple processors 501 or multiple memory 502.

[0076] <Functional Configuration> The functional configuration of the design support system 1000 will be explained with reference to Figure 3. Figure 3 is a block diagram showing an example of the functional configuration of the design support system.

[0077] As shown in Figure 3, the design support device 10 comprises a motion calculation unit 110, a material properties calculation unit 120, a contribution calculation unit 130, and a visualization unit 140. The design support device 10 functions as the motion calculation unit 110, material properties calculation unit 120, contribution calculation unit 130, and visualization unit 140 when a pre-installed design support program is executed.

[0078] For example, the motion calculation unit 110, the physical property calculation unit 120, the contribution calculation unit 130, and the visualization unit 140 are realized by a process in which a program, which is loaded from the auxiliary storage device 503 shown in Figure 2 onto the memory 502, is executed by the processor 501.

[0079] The motion calculation unit 110 calculates the motion of each atom contained in the target substance. The motion calculation unit 110 may calculate the motion of each atom contained in the target substance by molecular dynamics calculation. The motion calculation unit 110 may also calculate the time change of the position of each atom as the motion of each atom.

[0080] The motion calculation unit 110 may calculate the motion of each atom contained in the target substance using quantum chemistry calculation software and molecular dynamics calculation software. For example, the quantum chemistry calculation software may be Gaussian 16 (registered trademark). For example, the molecular dynamics calculation software may be GROMACS v2018.8.

[0081] The physical property calculation unit 120 calculates the physical properties of the target substance. The physical property calculation unit 120 may also calculate statistical values ​​of the physical properties of the target substance. The physical property calculation unit 120 may also calculate the physical properties of the target substance based on the calculation results output by the motion calculation unit 110. In other words, the physical property calculation unit 120 may calculate statistical values ​​of the physical properties of the target substance based on information indicating the motion of each atom contained in the target substance.

[0082] The physical property value of the target substance may, for example, be the total dipole moment. The total dipole moment is the sum of the dipole moments of each atom contained in the target substance. The statistical quantity of the physical property value may, for example, be the variance (fluctuation) of the total dipole moment. The physical property calculation unit 120 may calculate the variance of the total dipole moment based on the time average of the position of each atom and the charge of the atom.

[0083] The contribution calculation unit 130 calculates information indicating the contribution of each atom to the physical properties of the target substance. The contribution calculation unit 130 may also calculate the contribution rate of each atom to the statistical quantities calculated by the physical property calculation unit 120. As an example, the contribution calculation unit 130 may calculate the contribution rate of each atom to the dispersion of the total dipole moment.

[0084] The contribution calculation unit 130 may calculate the contribution rate of each atom based on the displacement of the physical properties of each atom. The contribution calculation unit 130 may also calculate the contribution rate of each atom by singular value decomposition of the matrix generated based on the displacement. The displacement of the physical properties may be the displacement (difference) between the time average of the physical properties and the physical properties at each time point.

[0085] The visualization unit 140 visualizes the molecules contained in the target substance. The visualization unit 140 may visualize only the molecules in the target substance in which the motion of the atoms contained in that molecule is large. The visualization unit 140 may extract molecules in which the motion of atoms is large based on the norm of the vector that shows the time change of the position of each atom contained in the molecule. As an example, the visualization unit 140 may extract molecules in which the deviation value of the norm of the vector is greater than or equal to a threshold (for example, 60).

[0086] The visualization unit 140 may visualize the arrangement of molecules. The visualization unit 140 may visualize the structure of molecules. The visualization unit 140 may visualize the contribution rate of atoms contained in molecules. The visualization unit 140 may visualize the motion modes of atoms contained in molecules. The motion modes of atoms may include, for example, the motion mode of the dipole moment of atoms, or the motion mode of the position coordinates of atoms. The visualization unit 140 may visualize two or more of the following: the arrangement of molecules, the structure of molecules, the contribution rate of atoms, or the motion modes of atoms.

[0087] It should be noted that the functional configuration of the design support device 10 shown in Figure 3 is just one example, and there are various other functional configurations depending on the application and purpose. The division of processing units such as the motion calculation unit 110, material property calculation unit 120, contribution calculation unit 130, and visualization unit 140 shown in Figure 3 is just one example.

[0088] <Processing Procedure> The processing procedure for the design support method executed by the design support system 1000 will be explained with reference to Figure 4. Figure 4 is a flowchart showing an example of a design support method.

[0089] In step S1, the terminal device 50 accepts input of analysis conditions from the user. The analysis conditions include information about the target substance, and parameters related to quantum mechanics calculations and molecular dynamics calculations. The terminal device 50 transmits the input analysis conditions to the design support device 10. The design support device 10 receives the analysis conditions from the terminal device 50.

[0090] Information regarding the target substance may include, for example, identification information for the target substance. Identification information is information that can identify the substance. Identification information may include, as an example, the compound name, structural formula, SMILES (Simplified Molecular Input Line Entry System) information, ECFP (Extended Connectivity Circular Fingerprints) information, etc. Identification information is not limited to these, and any information that can identify the substance can be used.

[0091] Parameters for quantum mechanics calculations may include, for example, calculation conditions, atomic positions, information on bonding between atoms, or solvent information. Parameters for molecular dynamics calculations may include, for example, results calculated by quantum chemistry calculation software. Parameters for molecular dynamics calculations may include, as an example, information specifying structure optimization, charge calculation, force field, partial charge, ensemble, heat bath, pressure control, calculation time, temperature, pressure, electric field strength, or electric field period.

[0092] In step S2, the motion calculation unit 110 of the design support device 10 acquires the analysis conditions received by the design support device 10. Based on the acquired analysis conditions, the motion calculation unit 110 calculates the motion of each atom contained in the target substance. Specifically, the motion calculation unit 110 first inputs parameters related to quantum mechanics calculations into quantum chemistry calculation software and executes quantum chemistry calculations. Next, the motion calculation unit 110 inputs the results of the quantum chemistry calculations, including charge and optimized structural information, into molecular dynamics calculation software and executes molecular dynamics calculations. The quantum chemistry calculation software, as an example, optimizes the molecular structure of the target substance and calculates the charge. The molecular dynamics calculation software, as an example, calculates intermolecular interactions, response motion to external fields, molecular relaxation motion, vibration, translation, and rotation in a group of molecules of the target substance.

[0093] The motion calculation unit 110 outputs the calculation results of the motion of each atom. The calculation results output by the motion calculation unit 110 are sent to the material properties calculation unit 120 and the visualization unit 140. The calculation results output by the motion calculation unit 110 include information indicating the motion of each atom contained in the target substance. For example, the calculation results output by the motion calculation unit 110 may include a matrix in which the position information of each atom contained in the target substance is arranged in chronological order. The position information may, as an example, be xyz coordinates in a Cartesian coordinate system.

[0094] The calculation results output by the motion calculation unit 110 may include the matrix C defined by equation (15).

[0095]

[0096] However, m is the number of atoms in the system, and n is the number of time steps. For example, x ｉｊ represents the x-coordinate of the j-th atom at the i-th time step, where i ≤ n and j ≤ m.

[0097] In step S3, the physical property calculation unit 120 of the design support device 10 receives calculation results from the motion calculation unit 110. Based on the received calculation results, the physical property calculation unit 120 calculates statistical quantities of the physical properties of the target material. The physical property calculation unit 120 sends the calculated statistical quantities of physical properties to the contribution calculation unit 130.

[0098] In this embodiment, the physical property calculation unit 120 calculates the variance of the total dipole moment as an example. Specifically, the physical property calculation unit 120 first calculates the matrix ΔC defined by equation (16) based on the matrix C shown in equation (15). Matrix ΔC is a matrix in which the displacement amounts from the average value of the position of each of the m atoms are arranged in time series.

[0099]

[0100] However, <x ｊ > is the average x-coordinate of the j-th atom. <y ｊ > represents the average y-coordinate of the j-th atom. <z ｊ > represents the average z-coordinate of the j-th atom. <x ｊ >, <y ｊ >, <z ｊ > is defined by equation (17).

[0101]

[0102] Next, the physical property calculation unit 120 generates a matrix Q defined by equation (18) based on the partial charge of each atom contained in the target substance.

[0103]

[0104] For example, q ｊ q is the partial charge of the j-th atom, where j ≤ m. That is, the 3j-2, 3j-1, and 3j diagonal elements of matrix Q are the partial charge q of the j-th atom. ｊ It is a square diagonal matrix.

[0105] Next, the material properties calculation unit 120 calculates the matrix X defined by equation (19) based on the matrix ΔC defined by equation (17) and the matrix Q defined by equation (18). Matrix X is a matrix obtained by dividing the dipole moment of each atom into components along the x, y, and z axes and arranging them in time series.

[0106]

[0107] Next, the material properties calculation unit 120 generates a projection operator P defined by equation (20). Note that the projection operator P may also be normalized by multiplying each row vector by 1 / √m instead of 1 / √n.

[0108]

[0109] Next, the material properties calculation unit 120 calculates the matrix XP defined by equation (21) based on the matrix X defined by equation (19) and the projection operator P defined by equation (20). Matrix XP is a matrix in which the displacements from the average value of the total dipole moments are arranged in time series.

[0110]

[0111] Then, the physical property calculation unit 120 calculates the quantity z defined by equation (22) based on the matrix X defined by equation (19), the projection operator P defined by equation (20), and the matrix XP defined by equation (21). That is, the physical property calculation unit 120 calculates P Ｔ X Ｔ The trace of XP is calculated. The quantity z is the variance of the total dipole moment.

[0112]

[0113] In step S4, the contribution calculation unit 130 receives statistical quantities of physical properties from the physical property calculation unit 120. The contribution calculation unit 130 calculates the contribution rate of each atom to the received statistical quantities of physical properties. In this embodiment, the contribution calculation unit 130 calculates the contribution rate of each atom by singular value decomposition of a matrix generated based on the displacement of the physical properties.

[0114] Specifically, the contribution calculation unit 130 calculates the matrix PP Ｔ X Ｔ By performing singular value decomposition on X, we calculate the singular value Λ, the left singular vector U, and the right singular vector V. The singular value Λ, the left singular vector U, and the right singular vector V satisfy equation (23).

[0115]

[0116] The contribution calculation unit 130 calculates matrix P Ｔ X Ｔ X may be subjected to singular value decomposition. Matrix PＴ X Ｔ Even if X undergoes singular value decomposition, the matrix PP remains the same. Ｔ X Ｔ Even if X is subjected to singular value decomposition, the resulting right singular vector V is the same, and the resulting left singular vector U is essentially the same except that it has a different dimension. From the perspective of computational cost, matrix P Ｔ X Ｔ It is preferable to perform singular value decomposition on X.

[0117] Then, the contribution calculation unit 130 calculates the value σ defined by equation (7) based on the left singular vector U and the right singular vector V. ｒ Calculate the value σ. ｒ This is the contribution rate of the r-th atom to the amount z.

[0118] Furthermore, the contribution calculation unit 130 may identify the motion mode of the dipole moment of each atom based on the contribution rate of each atom. Specifically, the contribution calculation unit 130 first multiplies the right singular vector V by the inverse matrix of the matrix Q defined by equation (18). That is, the contribution calculation unit 130 multiplies the matrix Q －１ Calculate V. Note that if matrix Q is not an invertible matrix, you may multiply by the generalized inverse of Moore-Penrose.

[0119] Next, the contribution calculation unit 130 calculates matrix Q －１ By normalizing each column vector of V, the motion mode of the position coordinates of each atom is analyzed. The motion mode of the position coordinates corresponds to the motion mode of the dipole moment. Therefore, the contribution calculation unit 130 can analyze the motion mode of the dipole moment of each atom.

[0120] The contribution calculation unit 130 sends the analysis results to the visualization unit 140. The analysis results may include, for each atom, the contribution rate of the total dipole moment to the dispersion, and information indicating the motion mode of the dipole moment. The analysis results may further include the singular value Λ, the left singular vector U, and the right singular vector V obtained by singular value decomposition.

[0121] In step S5, the visualization unit 140 of the design support device 10 receives calculation results from the motion calculation unit 110 showing the motion of each atom. The visualization unit 140 also receives analysis results from the contribution calculation unit 130 showing the motion mode of the dipole moment of each atom. Based on the calculation results from the motion calculation unit 110 and the analysis results from the contribution calculation unit 130, the visualization unit 140 visualizes the molecules contained in the target substance.

[0122] Specifically, the visualization unit 140 first generates a vector showing the time change of the position within each of the multiple molecules contained in the target substance, based on the matrix C defined by equation (15). Next, the visualization unit 140 calculates the norm of the vector corresponding to each molecule. Then, based on the calculated vector norm, the visualization unit 140 extracts molecules with large atomic motion. In this embodiment, molecules with a deviation value of 60 or more of the vector norm are extracted.

[0123] The visualization unit 140 visualizes molecules in which the motion of extracted atoms is large. The visualization unit 140 may also visualize the arrangement of the extracted molecules. The visualization unit 140 may also visualize the structure of each extracted molecule. The visualization unit 140 may also visualize the contribution rate of each atom contained in each extracted molecule. The visualization unit 140 may also visualize the motion mode of the dipole moment of each atom contained in each extracted molecule.

[0124] The visualization unit 140 may non-dimension the contribution rate of each atom. For example, the visualization unit 140 may non-dimension the contribution rate by multiplying it by the value defined by equation (24).

[0125]

[0126] However, ε ０ k is the permittivity of vacuum, Ｂ is the Boltzmann constant, T is the average absolute temperature during the simulation, and V ｃｅｌｌ This is the average volume of the simulation cells.

[0127] The visualization unit 140 transmits the visualization results to the terminal device 50. The terminal device 50 receives the visualization results from the design support device 10. The terminal device 50 presents the visualization results to the user. For example, the terminal device 50 displays the visualization results on the output device 505.

[0128] Figure 5 shows an example of the visualization results. As shown in Figure 5, the visualization result 400 shows atoms contained in the target substance arranged in space 410, which represents the system subjected to molecular dynamics calculations. In space 410, atoms contained in molecules with large atomic motion from the target substance, which is composed of approximately 30,000 atoms, are visualized and arranged. Each atom may be placed in time-averaged position coordinates. Each atom placed in space 410 is associated with information that allows for the identification of the molecule in which that atom is contained. Therefore, it can be said that the arrangement of molecules and the structure of each molecule are visualized in space 410.

[0129] Figure 5 shows a magnified view of a single molecule 420 arranged in space 410. The molecule 420 contains one or more atoms 421. A kinetic mode 422 is associated with each atom 421. Note that in Figure 5, only representative atoms are labeled for clarity.

[0130] Atom 421 is displayed in a manner corresponding to its contribution rate. In this embodiment, atom 421 is displayed in a color corresponding to the magnitude of its contribution rate. However, the manner in which the contribution rate is displayed is not limited to the example in Figure 5, and it is sufficient if it is displayed in a manner that makes the magnitude of the contribution rate visually apparent.

[0131] Motion mode 422 indicates the motion mode of the dipole moment. In this embodiment, motion mode 422 is represented as an arrow indicating the direction and strength of the dipole moment. However, the display method of the motion mode is not limited to the example in Figure 5, and it is sufficient to display the motion mode of the dipole moment in a way that is visually apparent.

[0132] Users of the design support system 1000 may refer to the visualization results displayed on the output device 505 of the terminal device 50 and use them in the development of the target substance. For example, users may analyze molecules that affect the physical properties of the target substance based on the arrangement of molecules that are considered to have a large influence on the dispersion of the dipole moment, the structure of the molecules, the motion modes of the atoms contained in the molecules, etc. Users may also manufacture the target substance developed based on the visualization results, or manufacture products containing the target substance. Specifically, this can lead to changes in atomic species or substructures that have a large influence on the dispersion of the dipole moment, or to the design of molecules that take stereochemistry into consideration.

[0133] According to this embodiment, the accuracy of predicting the physical properties of materials, such as their elastic modulus and plasticity, can be improved, making material design and optimization more efficient.

[0134] Other possible applications include the following:

[0135] • Understanding transport properties: By analyzing the influence of fillers on the transport properties of molecules in the matrix, such as diffusion coefficient and thermal conductivity, from the perspective of individual molecules, it is possible to clarify how the size, shape, and dispersion state of the fillers affect these properties. Specifically, the influence of nanofillers on the diffusion properties of polymers can be explained from the behavior of individual molecules.

[0136] • Interaction Details: By analyzing the interactions between fillers and molecules in the matrix at the individual molecular level, it is possible to clarify which interactions contribute to the mechanical properties. For example, it is possible to investigate how interactions with fillers affect the intermolecular distances and orientation of the matrix, which can lead to the selection of raw materials that improve properties such as the strength and elasticity of the material.

[0137] • Structural stability: The effect of fillers on the structural stability of the matrix can be evaluated through changes in the arrangement and bonding state of individual molecules. For example, insights can be gained into how the type of filler and its dispersion state relate to the crystallinity and thermal stability of the polymer.

[0138] Understanding Phase Separation Phenomena: In complex many-body systems, the influence of fillers on phase separation phenomena can be understood at the individual molecular level. In particular, clarifying how fillers change their dispersion from nonpolar to polar phases enables material design that optimizes interface properties and interactions.

[0139] <Effects of the Embodiment> Conventionally, the properties of a substance have been analyzed by calculating a target substance containing a large number of molecules using molecular dynamics calculations. Such property analysis using molecular dynamics calculations is inherently statistical, and the influence of molecular structure on the properties of the substance is averaged out. As a result, the influence of molecular structure on the properties of the substance is not easily seen. In other words, the physical properties of a substance are characterized by the statistical behavior of the molecular group, and analysis focusing on the structure of individual molecules is not possible. According to this embodiment, analysis focusing on the structure of individual molecules can be performed. For example, when calculating the total dipole moment, which is the sum of the dipole moments of the atoms contained in the substance, atoms that make a large contribution to the dispersion of the total dipole moment can be extracted, and the characteristics of the dipole moment can be applied to a single molecule containing those atoms, thereby clarifying the influence of molecular structure on the properties of the substance.

[0140] In this embodiment, the design support device 10 calculates statistical quantities of the material's physical properties based on information indicating the motion of each atom contained in the material, and calculates the contribution rate of each atom to the statistical quantities based on the displacement of each atom's physical properties.

[0141] In one aspect, this embodiment allows for the analysis of the contribution of each atom to the physical properties of a substance. In another aspect, this embodiment allows for the visualization of molecules with large atomic motion among multiple molecules contained in a substance. As a result, molecules that affect physical properties can be efficiently analyzed, and the design of materials with improved physical properties can be supported.

[0142] The design support device 10 may calculate the contribution rate of each atom by performing singular value decomposition on the matrix generated based on the displacement. In one aspect, according to this embodiment, the contribution rate of each atom to the material properties can be calculated.

[0143] The statistical quantity may also be the variance of the total dipole moment. In one aspect, according to this embodiment, the contribution of each atom to the variance of the total dipole moment can be analyzed.

[0144] The information describing the motion may include the time evolution of the position of each atom. The design support device 10 may calculate the variance of the total dipole moment based on the time average of the position of each atom and the charge of the atom. In one aspect, according to this embodiment, the variance of the total dipole moment can be calculated.

[0145] The design support device 10 may visualize molecules with large atomic motion. In one aspect, according to this embodiment, molecules with large atomic motion can be visually identified among the molecules contained in the target substance.

[0146] The design support device 10 may visualize at least one of the molecular arrangement, molecular structure, contribution rate of atoms contained in the molecule, or motion mode of atoms contained in the molecule. In one aspect, according to this embodiment, the arrangement or structure of molecules with large atomic motion, or the contribution rate or motion mode of atoms contained in the molecule, can be visually identified.

[0147] [Supplement] Each function of the embodiments described above can be realized by one or more processing circuits. Hereinafter, "processing circuit" in this specification includes processors programmed to execute each function by software, such as processors implemented by electronic circuits, as well as devices such as ASICs (Application Specific Integrated Circuits), DSPs (Digital Signal Processors), FPGAs (Field Programmable Gate Arrays), and conventional circuit modules designed to execute each function described above.

[0148] While embodiments of the present disclosure have been described in detail above, the embodiments disclosed herein are illustrative and not restrictive in all respects. The embodiments can be modified and improved in various ways without departing from the scope and spirit of the appended claims. The features described in the above embodiments can be combined in any way that is not contradictory.

[0149] This application claims priority to Japanese Patent Application No. 2025-24467, filed with the Japan Patent Office on 18 February 2025, which is incorporated herein by reference to its entire contents.

[0150] 10: Design support device 50: Terminal device 110: Motion calculation unit 120: Material properties calculation unit 130: Contribution calculation unit 140: Visualization unit 1000: Design support system

Claims

1. A design support device comprising: a physical property calculation unit configured to calculate a statistical quantity of the physical property values ​​of a substance based on information indicating the motion of each of several atoms contained in the substance; and a contribution calculation unit configured to calculate the contribution rate of each atom to the statistical quantity based on the displacement of the physical property values ​​of each atom.

2. The design support device according to claim 1, wherein the contribution calculation unit is configured to calculate the contribution rate of each atom by singular value decomposition of a matrix generated based on the displacement amount.

3. The design support device according to claim 1 or 2, wherein the statistic is the variance of the total dipole moment.

4. The design support device according to claim 3, wherein the information indicating the motion includes the time change of the position of each of the atoms, and the physical property calculation unit is configured to calculate the variance of the total dipole moment based on the time average of the position of each of the atoms and the charge of the atoms.

5. The design support apparatus according to any one of claims 1 to 4, further comprising a visualization unit configured to visualize molecules with large atomic motion.

6. The design support device according to claim 5, wherein the visualization unit is configured to visualize at least one of the arrangement of the molecules, the structure of the molecules, the contribution rate of the atoms contained in the molecules, or the motion modes of the atoms contained in the molecules.

7. A design support method that performs the following steps on a computer: a procedure for calculating statistical quantities of physical properties of a substance based on information indicating the motion of each of several atoms contained in the substance; and a procedure for calculating the contribution rate of each atom to the statistical quantities based on the displacement of each atom's physical properties.

8. A program for causing a computer to perform the following steps: a procedure for calculating statistical quantities of physical properties of a substance based on information indicating the motion of each of several atoms contained in the substance; and a procedure for calculating the contribution rate of each atom to the statistical quantities based on the displacement of each atom's physical properties.

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