Information processing program, information processing method, and information processing apparatus

Abstract

To reduce a processing time required for performing density functional theory calculation.SOLUTION: An information processing apparatus 100 stores a first condition that can be a convergence condition related to a density functional theory calculation 111. The first condition is, for example, that a difference ratio of a total electron energy based on an electron density updated last to a representative value of the total electron energy based on the electron density updated at an initial stage of the density functional theory calculation is equal to or less than a first threshold value. The information processing apparatus 100 performs the density functional theory calculation 111 of repeatedly updating the electron density. At this time, specifically, the information processing apparatus 100 repeatedly updates the electron density until the first condition is satisfied.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an information processing program, an information processing method, and an information processing device. [Background technology]

[0002] Conventionally, in the field of materials development, there is a technique for calculating electron density by a numerical analysis method. The numerical analysis method is, for example, density functional theory using a self-consistent field method. For example, there is a density functional theory calculation that calculates electron density by repeating a calculation to update electron density using a wave function according to density functional theory until it is determined that the electron density has converged.

[0003] Prior art techniques include, for example, using molecular orbitals of a structure relatively close to the target system among structures to which the self-consistent field method calculation process converges as the initial values ​​of the molecular orbitals of the target system. Other techniques include, for example, a technique for calculating microphase-separated structures using dynamic mean field approximation with a lattice constant optimization method. Another technique is, for example, a technique for calculating spin-polarized quantum transport in three-dimensional nanostructures under a finite computer bias and an external voltage. Another technique is, for example, a technique for numerically simulating at least one crystal structure by combining density functional theory calculations. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2008-210306 [Patent Document 2] Japanese Patent Application Laid-Open No. 2005-032058 [Patent Document 3] US Patent Application Publication No. 2008 / 0170338 [Patent Document 4] US Patent Application Publication No. 2007 / 0185695 Summary of the Invention [Problem to be solved by the invention]

[0005] However, conventional techniques can result in an increase in the processing time required for density functional theory calculations. For example, if the number of atoms is N, the amount of calculation required to calculate the electron density using density functional theory calculations is O(N^3).

[0006] In one aspect, the present invention aims to reduce the processing time required to perform density functional theory calculations. [Means for solving the problem]

[0007] According to one embodiment, an information processing program, an information processing method, and an information processing device are proposed that, in a density functional theory calculation in which electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that the difference ratio of the total electron energy based on the last updated electron density to a representative value of the total electron energy based on the initially updated electron density is equal to or less than a first threshold. [Effects of the Invention]

[0008] According to one aspect, it is possible to reduce the processing time required to perform density functional theory calculations. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 is an explanatory diagram illustrating an example of an information processing method according to an embodiment. [Figure 2] FIG. 2 is an explanatory diagram illustrating an example of an information processing system 200. As shown in FIG. [Figure 3] FIG. 3 is a block diagram showing an example of the hardware configuration of the information processing device 100. As shown in FIG. [Figure 4] FIG. 4 is a block diagram showing an example of the functional configuration of the information processing device 100. As shown in FIG. [Figure 5] FIG. 5 is an explanatory diagram (part 1) showing an example of the operation of the information processing device 100. [Figure 6]FIG. 6 is an explanatory diagram (part 2) showing an example of the operation of the information processing device 100. [Figure 7] FIG. 7 is an explanatory diagram (part 3) showing an example of the operation of the information processing device 100. [Figure 8] FIG. 8 is an explanatory diagram (part 4) showing an example of the operation of the information processing device 100. [Figure 9] FIG. 9 is an explanatory diagram (part 1) showing the results of comparison with the conventional method. [Figure 10] FIG. 10 is an explanatory diagram (part 2) showing the results of comparison with the conventional method. [Figure 11] FIG. 11 is a flowchart showing an example of the overall processing procedure. [Figure 12] FIG. 12 is a flowchart showing an example of a procedure for structural relaxation calculation processing. [Figure 13] FIG. 13 is a flowchart showing an example of a density functional theory processing procedure. DETAILED DESCRIPTION OF THE INVENTION

[0010] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an information processing device, an information processing method, and an information processing program according to embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[0011] (An example of an information processing method according to an embodiment) 1 is an explanatory diagram showing an example of an information processing method according to an embodiment. The information processing device 100 is a computer for reducing the processing time required to perform density functional theory calculations based on density functional theory. The information processing device 100 is, for example, a server or a PC (Personal Computer).

[0012] A density functional theory calculation is, for example, a series of calculation processes for calculating electron density. A density functional theory calculation corresponds to, for example, an iterative solution method. A density functional theory calculation calculates electron density by, for example, repeatedly performing a process of updating electron density until a convergence condition is satisfied. A density functional theory calculation corresponds to, for example, a self-consistent field method. A density functional theory calculation calculates electron density at each point in space by, for example, repeatedly performing a series of processes of updating electron density at each point in space using a wave function until a convergence condition is satisfied. The convergence condition is a condition for determining that a solution has converged. For example, the convergence condition is that the difference between the last calculated electron density and the electron density calculated immediately before is equal to or less than a threshold. For information on density functional theory, see, for example, Reference 1 below.

[0013] Reference 1: "Introduction to Density Functional Theory: Theory and Applications", co-authored by DS Schur and JA Steckel, co-translated by Taizo Sasaki and Shigeru Suehara, Yoshioka Shoten, ISBN978-4842703657

[0014] Depending on the problem to be calculated, the time required to determine that a solution has converged in density functional theory calculations may be long. For example, in density functional theory calculations, the number of times a series of processes for updating the electron density at each point in space must be repeated may increase. This may result in an increase in the processing time required to perform density functional theory calculations.

[0015] Specifically, if the total electron energy transitions to a state of slight fluctuation as a result of satisfying a predetermined condition, non-convergence and oscillation occur, leading to an increase in the number of times a series of processes for updating the electron density at each point in space is repeated. The predetermined condition is that atoms whose positions are relatively different between the initial structure of the molecule and the stable structure of the molecule exist. Specifically, the predetermined condition is that a point exists in space where the rate of fluctuation of the difference between the last calculated electron density and the electron density calculated immediately before is relatively small, making it difficult for the electron density at that point to converge. Specifically, the predetermined condition is that a point exists in space where the influence on the total electron energy is relatively small, making it difficult for the electron density at that point to converge.

[0016] Therefore, in this embodiment, an information processing method that can reduce the processing time required for performing density functional theory calculations will be described. In the following description, density functional theory may be referred to as the "DFT (Density Functional Theory) method."

[0017] 1, the information processing device 100 stores a first condition that can be a convergence condition for the density functional theory calculation 111. The first condition is, for example, that the difference ratio of the total electron energy based on the last updated electron density to the representative value of the total electron energy based on the electron density updated at the beginning of the density functional theory calculation 111 is equal to or less than a first threshold. The difference ratio is also referred to as, for example, RDE. The last condition is, for example, the point in time when the electron density is updated closest to the current point in the process of repeatedly updating the electron density in the density functional theory calculation 111.

[0018] The difference ratio is, for example, a value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron density updated immediately before by the representative value of the total electron energy based on the initially updated electron density. The initial period is, for example, from the time when the electron density is first updated to the time when the electron density has been updated a predetermined number of times in the process of repeatedly updating the electron density in the density functional theory calculation 111. The initial period may be, for example, only the time when the electron density is first updated. The representative value is, for example, a statistical value. The statistical value is, for example, a maximum value, a minimum value, an average value, a mode value, or a median value.

[0019] The representative value of the total electron energy based on the electron density updated immediately before may be, for example, any one of the total electron energies based on the electron density updated immediately before. The representative value of the total electron energy based on the electron density updated initially may be, for example, any one of the total electron energies based on the electron density updated initially. In addition to the first condition, the information processing device 100 may store a second condition that can be a convergence condition for the density functional theory calculation 111. The second condition is that the difference between the last calculated electron density and the electron density calculated immediately before is equal to or less than a second threshold.

[0020] (1-1) The information processing device 100 performs density functional theory calculation 111 so as to repeatedly update the electron density until a first condition is satisfied. The information processing device 100 may perform density functional theory calculation 111 so as to repeatedly update the electron density until at least one of the first condition and the second condition is satisfied.

[0021] As a result, the information processing device 100 can reduce the processing time required to perform the density functional theory calculation 111. Since the information processing device 100 utilizes, for example, the first condition, it is possible to reduce the number of times a series of processes for updating the electron density is repeated even if the total electron energy transitions to a state of slight fluctuation. As a result, the information processing device 100 can reduce, for example, the processing time required to perform the density functional theory calculation 111. Furthermore, since the information processing device 100 utilizes the second condition, it is possible to easily perform the density functional theory calculation 111 with high accuracy.

[0022] Furthermore, since the information processing device 100 defines the difference ratio with respect to a representative value of the total electron energy based on the electron density updated at the beginning of the density functional theory calculation 111, a common value can be set for the first threshold to be compared with the difference ratio, regardless of the problem to be calculated. Therefore, the information processing device 100 can maintain the accuracy of determining whether or not the solution has converged in the density functional theory calculation 111, regardless of the problem to be calculated, thereby improving convenience.

[0023] When a convergence condition is satisfied in the density functional theory calculation 111, the information processing device 100 outputs the final electron density, the final total electron energy, etc. The output format may be, for example, display on a display, printout to a printer, transmission to an external device via a network I / F, or storage in a storage area. The information processing device 100 outputs the final electron density, the final total electron energy, etc. so that the user can refer to it. In this way, the information processing device 100 can make the final electron density, the final total electron energy, etc. available to the user.

[0024] Here, the case where the functions of the information processing device 100 are realized by a single computer has been described, but this is not limiting. For example, the functions of the information processing device 100 may be realized by cooperation of multiple computers. For example, the functions of the information processing device 100 may be realized on the cloud.

[0025] (An example of the information processing system 200) Next, an example of an information processing system 200 to which the information processing device 100 shown in FIG. 1 is applied will be described with reference to FIG.

[0026] 2 is an explanatory diagram showing an example of an information processing system 200. In FIG. 2, the information processing system 200 includes an information processing device 100, a numerical calculation device 201, and a client device 202.

[0027] In the information processing system 200, the information processing device 100 and the client device 202 are connected via a wired or wireless network 210. The network 210 is, for example, a local area network (LAN), a wide area network (WAN), the Internet, etc. In the information processing system 200, the information processing device 100 and the numerical calculation device 201 are connected via the wired or wireless network 210.

[0028] The information processing device 100 is a computer that manages density functional theory calculations. The information processing device 100 receives, for example, a calculation instruction from the client device 202. The calculation instruction specifies a problem to be calculated. The information processing device 100 sets a first condition that can serve as a convergence condition for the density functional theory calculation. The first condition is, for example, that the difference ratio of the total electron energy based on the last updated electron density to the representative value of the total electron energy based on the electron density updated initially in the density functional theory calculation is equal to or less than a first threshold. The difference ratio is, for example, a value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron density updated immediately before by the representative value of the total electron energy based on the electron density updated initially.

[0029] In addition to the first condition, the information processing device 100 sets a second condition that can serve as a convergence condition for the density functional theory calculation. The second condition is that the difference between the last calculated electron density and the electron density calculated immediately before is equal to or less than a second threshold. In response to a calculation instruction, the information processing device 100 performs the density functional theory calculation based on the set first and second conditions that can serve as convergence conditions for the density functional theory calculation. The information processing device 100 performs the density functional theory calculation so as to repeatedly update the electron density until, for example, at least one of the first and second conditions is satisfied. This allows the information processing device 100 to identify the final electron density. When at least one of the first and second conditions that can serve as convergence conditions for the density functional theory calculation is satisfied, the information processing device 100 transmits the final electron density to the client device 202.

[0030] Here, the information processing device 100 may perform, for example, distributed processing of density functional theory calculations with the numerical calculation device 201. The information processing device 100 transmits a processing request for density functional theory calculations to the numerical calculation device 201. The information processing device 100 may receive the final electron density from the numerical calculation device 201 and transmit it to the client device 202. The information processing device 100 is, for example, a server or a PC.

[0031] The numerical calculation device 201 is a computer that shares the density functional theory calculation. In response to receiving a processing request, the numerical calculation device 201 may perform the density functional theory calculation. The numerical calculation device 201 transmits the final electron density obtained as a result of performing the density functional theory calculation to the information processing device 100. The numerical calculation device 201 is, for example, a server or a PC.

[0032] The client device 202 is a computer that transmits calculation instructions to the information processing device 100 based on operational input from the user. Upon receiving the final electron density from the information processing device 100, the client device 202 outputs it so that the user can refer to it. The client device 202 is, for example, a PC, a tablet terminal, or a smartphone. The following description will mainly focus on the case where the information processing device 100 operates independently.

[0033] (Application example of information processing device 100) The information processing device 100 is considered to be applied, for example, in the field of materials development, when performing structural relaxation calculations in which density functional theory calculations are repeated multiple times to find stable structures of molecules that govern the properties of a substance. Specifically, the information processing device 100 is considered to be applied, for materials informatics, when performing structural relaxation calculations in which density functional theory calculations are repeated multiple times to find stable molecular structures and accumulate useful material data.

[0034] The structural relaxation calculation is, for example, a series of processes for determining a stable molecular structure. The structural relaxation calculation corresponds, for example, to an iterative solution. The iterative solution is, for example, a method of repeatedly performing a specific calculation until it is determined that a solution has converged. Convergence, for example, refers to a state in which the calculated solution is equal to or less than a threshold. The structural relaxation calculation, for example, performs a density functional theory calculation to calculate electron density, and then calculates the magnitude of the force acting on atoms based on the electron density. This process is repeated while updating the three-dimensional structure of the molecule until a convergence condition is satisfied, thereby determining a stable molecular structure. The convergence condition refers to a condition for determining that the solution has converged. For example, the convergence condition refers to the last calculated magnitude of the force acting on the atom being equal to or less than a threshold. In this case, the information processing device 100 may selectively use the first condition and the second condition for each of the multiple density functional theory calculations.

[0035] (Example of hardware configuration of information processing device 100) Next, an example of the hardware configuration of the information processing device 100 will be described with reference to FIG.

[0036] Fig. 3 is a block diagram showing an example of the hardware configuration of the information processing device 100. In Fig. 3, the information processing device 100 has a CPU (Central Processing Unit) 301, a memory 302, a network I / F (Interface) 303, a recording medium I / F 304, and a recording medium 305. Furthermore, each component is connected to each other by a bus 300.

[0037] Here, CPU 301 is responsible for overall control of information processing device 100. Memory 302 includes, for example, a read-only memory (ROM), a random access memory (RAM), and a flash ROM. Specifically, for example, the flash ROM or ROM stores various programs, and RAM is used as a work area for CPU 301. The programs stored in memory 302 are loaded into CPU 301, causing CPU 301 to execute coded processes.

[0038] The network I / F 303 is connected to the network 210 via a communication line, and is connected to other computers via the network 210. The network I / F 303 manages the internal interface with the network 210 and controls the input and output of data from other computers. The network I / F 303 is, for example, a modem or a LAN adapter.

[0039] The recording medium I / F 304 controls reading and writing of data from and to the recording medium 305 under the control of the CPU 301. The recording medium I / F 304 is, for example, a disk drive, a solid state drive (SSD), or a universal serial bus (USB) port. The recording medium 305 is a non-volatile memory that stores data written under the control of the recording medium I / F 304. The recording medium 305 is, for example, a disk, a semiconductor memory, or a USB memory. The recording medium 305 may be detachable from the information processing device 100.

[0040] In addition to the components described above, the information processing device 100 may also include, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, etc. The information processing device 100 may also include a plurality of recording medium I / Fs 304 and recording media 305. The information processing device 100 may also not include the recording medium I / Fs 304 and recording media 305.

[0041] (Example of hardware configuration of the numerical calculation device 201) An example of the hardware configuration of the numerical calculation device 201 is similar to the example of the hardware configuration of the information processing device 100 shown in FIG. 3, and therefore a description thereof will be omitted.

[0042] (Example of hardware configuration of client device 202) An example of the hardware configuration of the client device 202 is similar to the example of the hardware configuration of the information processing device 100 shown in FIG. 3, and therefore a description thereof will be omitted.

[0043] (Example of functional configuration of information processing device 100) Next, an example of the functional configuration of the information processing device 100 will be described with reference to FIG.

[0044] 4 is a block diagram showing an example of the functional configuration of the information processing device 100. The information processing device 100 includes a storage unit 400, an acquisition unit 401, a calculation unit 402, and an output unit 403.

[0045] The storage unit 400 is realized by, for example, a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3. In the following, a case where the storage unit 400 is included in the information processing device 100 will be described, but this is not limiting. For example, the storage unit 400 may be included in a device different from the information processing device 100, and the stored contents of the storage unit 400 may be accessible from the information processing device 100.

[0046] The acquiring unit 401 to the output unit 403 function as an example of a control unit. Specifically, the acquiring unit 401 to the output unit 403 realize their functions by causing the CPU 301 to execute a program stored in a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3, or by using the network I / F 303. The processing results of each functional unit are stored in a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3, for example.

[0047] The storage unit 400 stores various information that is referenced or updated in the processing of each functional unit. The storage unit 400 stores, for example, a first condition that can be a convergence condition for density functional theory calculations. The first condition is, for example, that the difference ratio of the total electron energy based on the last updated electron density to the representative value of the total electron energy based on the electron density updated at the beginning of the density functional theory calculation is equal to or less than a first threshold. The electron density is, for example, the electron density at each point in a specified space.

[0048] The difference ratio is, for example, a value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron densities updated immediately before by the representative value of the total electron energy based on the initially updated electron density. The difference ratio is, for example, the absolute value of the value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron densities updated immediately before by the representative value of the total electron energy based on the initially updated electron density.

[0049] The initial period may be, for example, from the time when the electron density is first updated to the time when the electron density has been updated a predetermined number of times. The initial period may be, for example, only the time when the electron density is first updated. The representative value may be, for example, a statistical value. The statistical value may be, for example, a maximum value, a minimum value, an average value, a mode, or a median. The representative value of the total electron energy based on the electron density updated up to the immediately preceding time may be, for example, any one of the total electron energies based on the electron density updated up to the immediately preceding time. The representative value of the total electron energy based on the electron density updated initially may be, for example, any one of the total electron energies based on the electron density updated initially.

[0050] The difference ratio is, for example, a value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron density updated immediately before by the representative value of the total electron energy based on the first updated electron density. Specifically, the difference ratio is the absolute value of the value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron density updated immediately before by the representative value of the total electron energy based on the first updated electron density. The first condition is, for example, acquired by the acquisition unit 401. The first condition may, for example, be set in advance by a user.

[0051] The storage unit 400 stores, for example, a second condition that can be a convergence condition for density functional theory calculations. The second condition is that the difference between the last calculated electron density and the electron density calculated immediately before is equal to or less than a second threshold. The second condition is acquired, for example, by the acquisition unit 401. The second condition may be set in advance by a user, for example.

[0052] The storage unit 400 may store, for example, convergence conditions for structural relaxation calculations that utilize density functional theory calculations. The convergence condition for structural relaxation calculations is, for example, that the magnitude of the calculated force acting on an atom is equal to or less than a threshold. The convergence conditions are acquired, for example, by the acquisition unit 401. The convergence conditions may be set in advance by a user, for example.

[0053] The acquisition unit 401 acquires various types of information used in processing by each functional unit. The acquisition unit 401 stores the acquired various types of information in the storage unit 400 or outputs it to each functional unit. The acquisition unit 401 may also output the various types of information stored in the storage unit 400 to each functional unit. The acquisition unit 401 acquires various types of information based on, for example, a user's operation input. The acquisition unit 401 may also receive various types of information from, for example, a device different from the information processing device 100.

[0054] The acquiring unit 401 acquires, for example, a first condition. Specifically, the acquiring unit 401 acquires the first condition by accepting input of the first condition based on an operation input by a user. Specifically, the acquiring unit 401 acquires the first condition by receiving it from another computer.

[0055] The acquiring unit 401 acquires, for example, the second condition. Specifically, the acquiring unit 401 acquires the second condition by accepting input of the second condition based on an operation input by a user. Specifically, the acquiring unit 401 acquires the second condition by receiving it from another computer.

[0056] The acquiring unit 401 may acquire, for example, a convergence condition related to the structural relaxation calculation. Specifically, the acquiring unit 401 acquires the convergence condition by receiving the convergence condition based on an operation input by a user. Specifically, the acquiring unit 401 acquires the convergence condition by receiving it from another computer.

[0057] The acquisition unit 401 acquires, for example, a calculation instruction. The calculation instruction specifies a problem to be calculated. Specifically, the acquisition unit 401 acquires the calculation instruction by accepting input of the calculation instruction based on an operation input by a user. Specifically, the acquisition unit 401 acquires the calculation instruction by receiving it from another computer.

[0058] The acquisition unit 401 may receive a start trigger to start processing by any of the functional units. The start trigger may be, for example, a predetermined operation input by a user. The start trigger may be, for example, reception of predetermined information from another computer. The start trigger may be, for example, output of predetermined information by any of the functional units. The acquisition unit 401 receives the acquisition of a calculation instruction as a start trigger to start processing by the calculation unit 402.

[0059] The calculation unit 402 performs density functional theory calculations. The calculation unit 402 performs density functional theory calculations so as to repeatedly update the electron density until, for example, a first condition is satisfied. The first condition is, for example, that the difference ratio of the total electron energy based on the last updated electron density to the representative value of the total electron energy based on the electron density updated at the beginning of the density functional theory calculations is equal to or less than a first threshold.

[0060] The difference ratio is, for example, a value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron densities updated immediately before by the representative value of the total electron energy based on the initially updated electron density. Specifically, the difference ratio is the absolute value of the value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron densities updated immediately before by the representative value of the total electron energy based on the initially updated electron density.

[0061] The initial period may be, for example, from the time when the electron density is first updated to the time when the electron density has been updated a predetermined number of times. The initial period may be, for example, only the time when the electron density is first updated. The representative value may be, for example, a statistical value. The statistical value may be, for example, a maximum value, a minimum value, an average value, a mode, or a median. The representative value of the total electron energy based on the electron density updated up to the immediately preceding time may be, for example, any one of the total electron energies based on the electron density updated up to the immediately preceding time. The representative value of the total electron energy based on the electron density updated initially may be, for example, any one of the total electron energies based on the electron density updated initially.

[0062] The difference ratio is a value obtained by, for example, dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron densities updated immediately before by the representative value of the total electron energy based on the first updated electron density. Specifically, the difference ratio is the absolute value of the value obtained by dividing the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron densities updated immediately before by the representative value of the total electron energy based on the first updated electron density.

[0063] The calculation unit 402 terminates the density functional theory calculation when, for example, the first condition is satisfied. This allows the calculation unit 402 to reduce the processing time required to perform the density functional theory calculation. Furthermore, because the calculation unit 402 defines the difference ratio with respect to a representative value of the total electronic energy based on the electron density updated at the beginning of the density functional theory calculation, a common value can be set for the first threshold to be compared with the difference ratio, regardless of the problem being calculated. Therefore, the calculation unit 402 can maintain the accuracy of determining whether a solution has converged in the density functional theory calculation, regardless of the problem being calculated, thereby improving convenience.

[0064] The calculation unit 402 may perform density functional theory calculations by repeatedly updating the electron density until, for example, at least one of a first condition and a second condition is satisfied. The second condition, for example, indicates that the difference between the last updated electron density and the electron density updated immediately before is equal to or less than a second threshold. The calculation unit 402 terminates the density functional theory calculations when, for example, at least one of the first condition and the second condition is satisfied. This allows the calculation unit 402 to reduce the processing time required to perform density functional theory calculations.

[0065] The calculation unit 402 may perform density functional theory calculations so as to repeatedly update the electron density until the second condition is satisfied, without referring to the first condition. The calculation unit 402 may terminate the density functional theory calculations when the second condition is satisfied, for example. This allows the calculation unit 402 to easily update the electron density with high accuracy when performing density functional theory calculations.

[0066] The calculation unit 402 may selectively use the first condition and the second condition during the density functional theory calculation, for example. Specifically, the calculation unit 402 performs the density functional theory calculation so as to repeatedly update the electron density at the beginning of the density functional theory calculation unless the second condition is satisfied. Specifically, the calculation unit 402 terminates the density functional theory calculation when the second condition is satisfied.

[0067] Specifically, the calculation unit 402 performs density functional theory calculations such that, if the second condition is not satisfied at the beginning of the density functional theory calculations, the electron density is repeatedly updated after the beginning of the density functional theory calculations unless the first condition is satisfied. Specifically, the calculation unit 402 may terminate the density functional theory calculations if the first condition is satisfied. This allows the calculation unit 402 to reduce the amount of processing.

[0068] More specifically, the calculation unit 402 sets the electron density to an initial state, and then updates the electron density by repeatedly performing a series of processes to calculate a final electron density. The series of processes includes, for example, process a, which calculates and updates the electron density using a one-electron wave function derived by solving the Kohn-Sham equation based on the current electron density. The series of processes includes, for example, process b, which is performed after process a. Process b includes calculating the difference between the electron density immediately before the update and the electron density immediately after the update.

[0069] The series of processes includes process c, which is performed after process b. Process c includes calculating total electron energy as a physical property value based on the electron density immediately after updating. Process c includes calculating a difference between total electron energy based on the electron density immediately after the current update and a representative value of total electron energy based on the electron density updated immediately before the current update. The electron density immediately after the current update corresponds to the last updated electron density described above. The electron density updated immediately before the current update corresponds to the electron density updated immediately before the current update. Process c includes calculating a difference ratio by dividing the calculated difference by the representative value of total electron energy based on the electron density updated initially. The initial period is, for example, the first time. The initial period may be, for example, from the first time to a predetermined time.

[0070] Specifically, when a convergence condition for density functional theory calculations is not satisfied after a series of processes, the calculation unit 402 repeats the series of processes by repeating the series of processes again. The convergence condition for density functional theory calculations is, for example, a first condition. The first condition corresponds to, for example, the calculated difference ratio being equal to or less than a first threshold.

[0071] The convergence condition for the density functional theory calculation may be, for example, satisfying at least one of a first condition and a second condition. The second condition is, for example, that the difference between the last calculated electron density and the electron density calculated immediately before is equal to or less than a second threshold. The immediately calculated electron density is, for example, the electron density immediately before updating. The last calculated electron density is, for example, the electron density immediately after updating. The second condition corresponds to, for example, that the difference between the electron density immediately before updating and the electron density immediately after updating is equal to or less than a second threshold. The convergence condition for the density functional theory calculation may be, for example, the second condition.

[0072] The calculation unit 402 may have a function to perform some kind of calculation processing utilizing density functional theory calculation, for example. The some kind of calculation processing is, for example, structural relaxation calculation. The structural relaxation calculation is performed by performing density functional theory calculation multiple times. Below, a case where the calculation unit 402 performs structural relaxation calculation will be described, but this is not limiting. For example, the calculation unit 402 may perform some kind of calculation processing other than structural relaxation calculation utilizing density functional theory calculation.

[0073] Specifically, the calculation unit 402 performs density functional theory calculations so as to repeatedly update the electron density until the first condition is satisfied in a specific iteration among the multiple iterations of the density functional theory calculations. The specific iteration is, for example, at least one of the multiple iterations of the density functional theory calculations. The specific iteration is, for example, the first iteration. The specific iteration may be, for example, the second iteration or later. The specific iteration may be, for example, each of the multiple iterations.

[0074] This allows the calculation unit 402 to reduce the processing time required to perform a specific density functional theory calculation, making it easier to reduce the processing time required to perform a structural relaxation calculation. Furthermore, because the calculation unit 402 defines the difference ratio with respect to a representative value of the total electronic energy based on the electron density updated at the beginning of the density functional theory calculation, a common value can be set for the first threshold to be compared with the difference ratio, regardless of the problem being calculated. Therefore, the calculation unit 402 can maintain the accuracy of determining whether a solution has converged in the density functional theory calculation, regardless of the problem being calculated, thereby improving convenience.

[0075] Specifically, the calculation unit 402 may perform the density functional theory calculation so as to repeatedly update the electron density until at least one of the first condition and the second condition is satisfied at least in a specific number of times among the multiple times the density functional theory calculation is performed. This allows the calculation unit 402 to reduce the processing time required to perform the specific number of density functional theory calculations, and makes it easier to reduce the processing time required to perform the structural relaxation calculation.

[0076] The calculation unit 402 may perform the density functional theory calculation so as to repeatedly update the electron density until the second condition is satisfied, without referring to the first condition, in each of the density functional theory calculations other than a specific one among multiple density functional theory calculations. This allows the calculation unit 402 to easily update the electron density with high accuracy when performing the density functional theory calculations other than the specific one, and to easily obtain a stable molecular structure with high accuracy when performing a structural relaxation calculation.

[0077] The calculation unit 402 may perform the density functional theory calculation so as to repeatedly update the electron density until at least one of the first condition and the second condition is satisfied in each of the density functional theory calculations up to a specific number of times among the plurality of times the density functional theory calculations are performed. This allows the calculation unit 402 to reduce the processing time required to perform each of the density functional theory calculations up to the specific number, and facilitates reducing the processing time required to perform the structural relaxation calculation.

[0078] The calculation unit 402 may perform the density functional theory calculation so that, for example, in each of the density functional theory calculations performed after a specific number of times, the calculation unit 402 repeatedly updates the electron density until the second condition is satisfied without referring to the first condition. This allows the calculation unit 402 to easily update the electron density with high accuracy when performing the density functional theory calculations after the specific number of times, and to easily obtain a stable molecular structure with high accuracy when performing a structural relaxation calculation.

[0079] Specifically, the calculation unit 402 initializes the molecular structure by initializing the atomic positions, and then repeatedly performs a series of processes. The series of processes includes, for example, process A, which performs density functional theory calculations based on the atomic positions in the molecular structure. Process A, for example, sets a first condition as a convergence condition for the density functional theory calculation when performing a specific density functional theory calculation among multiple calculations. The specific calculation is, for example, any one of multiple calculations in which the density functional theory calculation is performed. The specific calculation is, for example, the first calculation. The specific calculation may be, for example, the second calculation or later. The specific calculation may be, for example, each of the multiple calculations.

[0080] For example, when performing a specific number of density functional theory calculations among multiple calculations, the process A may set a convergence condition for the density functional theory calculation to satisfy at least one of a first condition and a second condition. For example, when performing a density functional theory calculation other than the specific number of calculations among multiple calculations, the process A may set a second condition for the convergence condition for the density functional theory calculation.

[0081] For example, when performing each density functional theory calculation before a specific number of times among the multiple times, the process A may set a first condition as a convergence condition for the density functional theory calculation. For example, when performing each density functional theory calculation before a specific number of times, the process A may set the convergence condition for the density functional theory calculation to satisfy at least one of a first condition and a second condition. For example, when performing each density functional theory calculation after a specific number of times among the multiple times, the process A may set a second condition as a convergence condition for the density functional theory calculation.

[0082] The series of processes includes, for example, process B, which is performed after process A. Process B includes calculating the total electronic energy based on the electron density at each point in space calculated in the density functional theory calculation. The series of processes includes, for example, process C, which is performed after process B. Process C includes determining whether or not the convergence condition for the structural relaxation calculation is satisfied. Process C includes updating the atomic positions when the convergence condition for the structural relaxation calculation is not satisfied. Specifically, when performing the series of processes, if the convergence condition for the structural relaxation calculation is not satisfied, the calculation unit 402 performs the series of processes again, thereby repeatedly performing the series of processes.

[0083] This allows the calculation unit 402 to perform a structural relaxation calculation and determine a stable molecular structure. When performing each of a plurality of density functional theory calculations, the calculation unit 402 can selectively use the first condition and the second condition as the convergence condition for the density functional theory calculation. This allows the calculation unit 402 to reduce the processing time required to perform a structural relaxation calculation, for example.

[0084] The output unit 403 outputs the processing result of at least one of the functional units. The output format is, for example, display on a display, printout to a printer, transmission to an external device via the network I / F 303, or storage in a storage area such as the memory 302 or the recording medium 305. In this way, the output unit 403 can notify the user of the processing result of at least one of the functional units, thereby improving the convenience of the information processing device 100.

[0085] Specifically, the output unit 403 may output the final electron density or the final total electronic energy obtained as a result of the density functional theory calculation performed by the calculation unit 402 so that the user can refer to it. Specifically, the output unit 403 may transmit the final electron density or the final total electronic energy obtained as a result of the density functional theory calculation performed by the calculation unit 402 to another computer. In this way, the output unit 403 can make the electron density or the total electronic energy available for external reference.

[0086] The output unit 403 may output, for example, the results of the structural relaxation calculation performed by the calculation unit 402 so that the results can be referenced by a user. The output unit 403 may also transmit, for example, the results of the structural relaxation calculation performed by the calculation unit 402 to another computer. In this way, the output unit 403 can make the results of the structural relaxation calculation performed by the calculation unit 402 externally accessible.

[0087] Specifically, the output unit 403 may output, so that a user can refer to, the stable structure of the molecule obtained as a result of performing the structural relaxation calculation in the calculation unit 402. Specifically, the output unit 403 outputs, so that a user can refer to, the stable structure of the molecule obtained as a result of performing the structural relaxation calculation in the calculation unit 402. In this way, the output unit 403 can make the stable structure of the molecule available for external reference.

[0088] Specifically, the output unit 403 may output the total electronic energy obtained as a result of the structural relaxation calculation performed by the calculation unit 402 so that the user can refer to it. Specifically, the output unit 403 may transmit the total electronic energy obtained as a result of the structural relaxation calculation performed by the calculation unit 402 to another computer. In this way, the output unit 403 can make the total electronic energy available for external reference.

[0089] Here, the case where the information processing device 100 includes the acquisition unit 401, the calculation unit 402, and the output unit 403 has been described, but the present invention is not limited to this. For example, the information processing device 100 may not include any of the functional units. Specifically, the information processing device 100 may cooperate with another computer that includes any of the functional units. The other computer is, for example, a numerical calculation device 201.

[0090] (Example of operation of information processing device 100) Next, an example of the operation of the information processing device 100 will be described with reference to FIGS.

[0091] 5 to 8 are explanatory diagrams showing an example of the operation of the information processing device 100. In Fig. 5 to Fig. 8, the information processing device 100 performs density functional theory calculations. When performing density functional theory calculations, the information processing device 100 sets, as convergence conditions for the density functional theory calculations, that at least one of a first condition and a second condition is satisfied.

[0092] The first condition indicates that the difference ratio RDE of the total electron energy is equal to or less than a tolerance value RDE_TH. The difference ratio RDE is, for example, the absolute value of the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron density updated immediately before, divided by the representative value of the total electron energy based on the initially updated electron density.

[0093] The allowable value RDE_TH is set in advance by the user, for example. RDE_TH is assumed to be 1.0e-5, for example. The representative value is, for example, a statistical value. The statistical value is, for example, the maximum value, minimum value, average value, mode, or median value of the electron density calculated up to the last time. The initial period is, for example, the first time. The initial period may be, for example, from the first time to a predetermined number of times.

[0094] The representative value of the total electron energy based on the electron density updated immediately before may be, for example, any one of the total electron energies based on the electron density updated immediately before.The representative value of the total electron energy based on the electron density updated immediately before may be, for example, a total electron energy based on the electron density calculated at any timing immediately before.

[0095] The representative value of the total electron energy based on the initially updated electron density may be, for example, any one of the total electron energies based on the initially updated electron density. The representative value of the total electron energy based on the initially updated electron density may be, for example, a total electron energy based on the electron density calculated at any initial timing.

[0096] The second condition is that for each point r in space i For all of the electron densities, the final calculated electron density ρ'(r i ) and the electron density ρ(r i ) and the absolute difference Δρ(r i )=|electron density ρ(r i )-electron density ρ'(r i )| is equal to or less than the Δρ tolerance value. The Δρ tolerance value is set in advance by, for example, a user. The Δρ tolerance value is assumed to be 1.0, for example. The information processing device 100 performs density functional theory calculations by repeatedly performing the process of calculating the electron density until a convergence condition for the density functional theory calculations is satisfied.

[0097] 5 and 6, the timing at which the second condition is satisfied will be described. A graph 500 in FIG. 5 shows the relationship between Δρ(r i ) and indicates the timing at which the second condition is satisfied. The horizontal axis of the graph 500 indicates, for example, the number of repetitions. The number of repetitions is the number of times the process of calculating the electron density is repeated. The vertical axis of the graph 500 indicates Δρ(r i ) As shown in the graph 500, the number of times the process of calculating the electron density is repeated until the second condition is satisfied is N. N is relatively close to the upper limit of the number of times the process of calculating the electron density is repeated.

[0098] Table 600 in FIG. 6 shows the results of Δρ(r i ) and the timing at which the second condition is satisfied. As shown in Table 600, the electron density ρ(r i ) is relatively small at point r i Δρ(r i ) is the electron density ρ(r i ) is relatively large at point r i Δρ(r i ), it is difficult for the Δρ to become smaller than the allowable value. Therefore, as shown in Table 600, the number of times N to repeat the process of calculating the electron density until the second condition is satisfied tends to be a relatively large number, specifically, 7.

[0099] Next, referring to FIGS. 7 and 8, the timing at which the first condition is satisfied will be described. Graph 700 in FIG. 7 shows changes in RDE when the process of calculating electron density is repeated, indicating the timing at which the first condition is satisfied. The horizontal axis of graph 700 indicates, for example, the number of repetitions. The number of repetitions is the number of times the process of calculating electron density is repeated. The vertical axis of graph 700 represents RDE. As shown in graph 700, the number of times the process of calculating electron density is repeated until the first condition is satisfied is M. M is equal to or less than N and is relatively far from the upper limit of the number of times the process of calculating electron density is repeated.

[0100] 8 shows specific values ​​of RDE when the process of calculating electron density is repeated, and indicates the timing at which the first condition is satisfied. As shown in table 800, RDE is likely to become smaller than the allowable value RDE_TH. Therefore, as shown in table 800, the number of times M to repeat the process of calculating electron density until the first condition is satisfied is specifically 5. M is a value smaller than N.

[0101] As a result, the information processing device 100 sets the convergence condition to satisfy at least one of the first condition and the second condition, thereby reducing the number of times the process of calculating the electron density is repeated when performing density functional theory calculations. For example, the information processing device 100 can reduce the number of times the process of calculating the electron density is repeated to M times instead of N times. As a result, the information processing device 100 can reduce the processing time required when performing density functional theory calculations.

[0102] For example, a conventional method may be considered in which the first condition is not used as the convergence condition, but only the second condition is used. In this conventional method, the process of calculating the electron density is repeated N times. This results in an increase in the processing time required to perform density functional theory calculations. Compared to the conventional method, the information processing device 100 can reduce the processing time required to perform density functional theory calculations.

[0103] (Effects of the information processing device 100) Next, an example of the effect achieved by the information processing device 100 will be described with reference to FIGS.

[0104] 9 and 10 are explanatory diagrams showing the results of comparison with conventional methods. In FIGS. 9 and 10, it is assumed that the information processing device 100 performs density functional theory calculations using VASP (Vienna Ab initio Simulation Package) software. The VASP software is an ab initio quantum molecular dynamics calculation program using pseudopotentials and a plane wave basis. Specifically, it is assumed that the information processing device 100 performs density functional theory calculations on an ammonia catalyst.

[0105] Table 900 in FIG. 9 shows a comparison example of calculation results between the information processing device 100 and a conventional method. The conventional method, for example, does not use the first condition as the convergence condition, but uses only the second condition. As shown in Table 900, the conventional method calculates a total electron energy of -370.02990719 eV. In the conventional method, the number of iterations in the density functional theory calculation is 42. The number of iterations is the number of times the process of calculating the electron density is repeated.

[0106] On the other hand, the information processing device 100 sets the tolerance RDE_TH=1.0e-5. The information processing device 100 calculates a total electron energy of −370.02900027 eV. In the information processing device 100, the number of iterations in the density functional theory calculation is 23. The number of iterations is the number of times the process of calculating the electron density is repeated. In this way, the information processing device 100 can speed up the density functional theory calculation by 1.66 times compared to the conventional method.

[0107] Graph 1000 in FIG. 10 shows a comparative example of the speed-up rate between the information processing device 100 and a conventional method. As shown in FIG. 10, when the conventional method is set as a reference of 1, the speed-up rate of the information processing device 100 is 1.66 times. Compared to the conventional method, the information processing device 100 can speed up density functional theory calculations and suppress an increase in the processing time required to perform density functional theory calculations. The information processing device 100 can accurately calculate the total electron energy with a difference of less than 0.001 eV, for example, compared to the conventional method.

[0108] Next, various processing procedures when the information processing device 100 performs structural relaxation calculations utilizing density functional theory calculations will be described with reference to Figures 11 to 13. In this case, the information processing device 100 specifically executes the overall processing described later in Figure 11.

[0109] (Overall processing procedure) First, an example of an overall processing procedure executed by the information processing device 100 will be described with reference to Fig. 11. The overall processing is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0110] Fig. 11 is a flowchart showing an example of the overall processing procedure. In Fig. 11, the information processing device 100 sets convergence conditions for structural relaxation calculations (step S1101). The information processing device 100 performs structural relaxation calculation processing, which will be described later in Fig. 12 (step S1102). The information processing device 100 outputs a stable structure of the molecule (step S1103). The information processing device 100 ends the overall processing. This allows the information processing device 100 to make the stable structure of the molecule available to the user.

[0111] (Structural relaxation calculation procedure) Next, an example of a procedure for a structural relaxation calculation process executed by the information processing device 100 will be described with reference to Fig. 12. The structural relaxation calculation process is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0112] 12 is a flowchart showing an example of a procedure for structural relaxation calculation processing. In FIG. 12, the information processing device 100 initializes the atomic positions to thereby initialize the molecular structure (step S1201).

[0113] The information processing device 100 performs density functional theory processing, which will be described later in FIG. 13, based on the atomic positions (step S1202). The information processing device 100 calculates the total electron energy based on the electron density at each point in space (step S1203). The information processing device 100 calculates the Force|F i | is calculated (step S1204).

[0114] The information processing device 100 is i It is determined whether |≦|F| is satisfied (step S1205). |F| is set in advance by the user, for example. Here, all |F i Not |≦|F|, but at least one |F i If |>|F| is satisfied (step S1205: No), the information processing apparatus 100 proceeds to the process of step S1206.

[0115] In step S1206, the information processing device 100 updates the atomic positions to update the molecular structure (step S1206), and returns to the processing of step S1202. i If |≦|F| is satisfied (step S1205: Yes), the information processing device 100 ends the structural relaxation calculation process. This enables the information processing device 100 to obtain a stable structure of the molecule.

[0116] (Density Functional Theory Procedure) Next, an example of a density functional theory processing procedure executed by the information processing device 100 will be described with reference to Fig. 13. The density functional theory processing is realized by, for example, the CPU 301, storage areas such as the memory 302 and the recording medium 305, and the network I / F 303 shown in Fig. 3.

[0117] FIG. 13 is a flowchart showing an example of a density functional theory processing procedure. In FIG. 13, the information processing device 100 sets the electron density ρ(r) (step S1301). For example, when there are multiple points in space, the information processing device 100 sets the electron density ρ(r) of each point. For example, if this is the first setting, the information processing device 100 sets an initial value of the electron density ρ(r). For example, if this is the second or subsequent setting, the information processing device 100 sets the electron density ρ(r) by some method. Specifically, if this is the second or subsequent setting, the information processing device 100 sets the electron density ρ(r) to the electron density ρ'(r) calculated immediately before.

[0118] The information processing device 100 solves the Kohn-Sham equation based on the electron density ρ(r) to obtain the one-electron wave function φ i For example, when there are multiple points in space, the information processing device 100 calculates the one-electron wave function φ for each point. i The information processing device 100 derives the one-electron wave function φ i The information processing device 100 calculates the electron density ρ'(r) using (r) (step S1303). For example, when there are multiple points in the space, the information processing device 100 calculates the electron density ρ'(r) of each point.

[0119] The information processing device 100 calculates the difference Δρ(r)=electron density ρ(r)−electron density ρ'(r) (step S1304). For example, when there are multiple points in space, the information processing device 100 calculates the difference Δρ(r) for each point. The information processing device 100 calculates the total electron energy as a physical property value based on the electron density ρ'(r) (step S1305). The information processing device 100 calculates the difference ratio RDE of the total electron energy (step S1306).

[0120] The information processing device 100 determines whether the difference Δρ(r)≦Δρ allowable value (step S1307). For example, when there are multiple points in the space, the information processing device 100 determines whether the differences Δρ(r) of all points≦Δρ allowable value. Here, if the differences Δρ(r) of all points≦Δρ allowable value (step S1307: Yes), the information processing device 100 ends the density functional theory processing. On the other hand, if the differences Δρ(r) of at least any point are greater than Δρ allowable value (step S1307: No), the information processing device 100 proceeds to the processing of step S1308.

[0121] In step S1308, the information processing device 100 determines whether RDE≦RDE_TH (step S1308). If RDE≦RDE_TH is not satisfied (step S1308: No), the information processing device 100 returns to the processing of step S1301. On the other hand, if RDE≦RDE_TH is satisfied (step S1308: Yes), the information processing device 100 ends the density functional theory processing. This allows the information processing device 100 to perform density functional theory calculations.

[0122] 13 realizes, for example, the first density functional theory calculation performed by the information processing device 100. It is considered that the second and subsequent density functional theory calculations performed by the information processing device 100 may be realized by the density functional theory processing shown in FIG. 13 from which the processing of step S1308 is deleted, for example.

[0123] The information processing device 100 may independently perform only the density functional theory processing shown in Fig. 13 without performing the overall processing shown in Fig. 11. In other words, the information processing device 100 may independently perform only the density functional theory calculation without performing the structural relaxation calculation.

[0124] Here, the information processing device 100 may change the order of the processes of some of the steps in the flowcharts of Figures 11 to 13. For example, the order of the processes of steps S1304 and S1305 may be changed. Furthermore, the information processing device 100 may omit the processes of some of the steps in the flowcharts of Figures 11 to 13.

[0125] As described above, the information processing device 100 can calculate the difference ratio of the total electron energy based on the last updated electron density to the representative value of the total electron energy based on the initially updated electron density in density functional theory calculations that repeatedly update the electron density. The information processing device 100 can repeatedly update the electron density until the calculated difference ratio satisfies a first condition indicating that it is equal to or less than a first threshold. This allows the information processing device 100 to reduce the processing time required to perform density functional theory calculations.

[0126] The information processing device 100 can repeatedly update the electron density until at least one of the first condition and the second condition indicating that the difference between the last updated electron density and the immediately preceding updated electron density is equal to or less than the second threshold is satisfied, thereby enabling the information processing device 100 to reduce the processing time required for performing density functional theory calculations.

[0127] The information processing device 100 can calculate the difference between the total electron energy based on the most recently updated electron density and the representative value of the total electron energy based on the electron density updated immediately before. The information processing device 100 can calculate the difference ratio by dividing the calculated difference by the representative value of the total electron energy based on the initially updated electron density. This allows the information processing device 100 to accurately calculate the difference ratio, making it easier to determine whether the first condition is satisfied and accurately determining whether to terminate the density functional theory calculation.

[0128] The information processing device 100 can calculate the difference between the total electron energy based on the last updated electron density and the representative value of the total electron energy based on the electron density updated immediately before. The information processing device 100 can calculate the difference ratio by dividing the calculated difference by the representative value of the total electron energy based on the first updated electron density. This allows the information processing device 100 to accurately calculate the difference ratio, making it easier to determine whether the first condition is satisfied and accurately determining whether to terminate the density functional theory calculation.

[0129] According to the information processing device 100, it is possible to perform density functional theory calculations so as to repeatedly update the electron density using the Kohn-Sham equation that enables calculation of a one-electron wave function. This allows the information processing device 100 to appropriately realize density functional theory calculations.

[0130] According to the information processing device 100, it is possible to perform density functional theory calculations so as to repeatedly update the electron density at each point in a specified space, which makes the information processing device 100 applicable to cases where multiple points exist in the specified space.

[0131] According to the information processing device 100, when performing a structural relaxation calculation in which density functional theory calculations are performed multiple times, the electron density can be repeatedly updated in at least one of the multiple density functional theory calculations until the first condition is satisfied. This allows the information processing device 100 to perform a structural relaxation calculation that utilizes density functional theory calculations. The information processing device 100 can reduce the processing time required to perform the structural relaxation calculation.

[0132] The information processing method described in this embodiment can be realized by executing a prepared program on a computer such as a PC or a workstation. The information processing program described in this embodiment is recorded on a computer-readable recording medium and executed by being read from the recording medium by the computer. The recording medium may be a hard disk, a flexible disk, a CD (Compact Disc)-ROM, an MO (Magneto Optical disc), a DVD (Digital Versatile Disc), or the like. The information processing program described in this embodiment may also be distributed via a network such as the Internet.

[0133] The following additional notes are provided regarding the above-described embodiment.

[0134] (Supplementary Note 1) In a density functional theory calculation in which an electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that a difference ratio of a representative value of a total electron energy based on the initially updated electron density to a total electron energy based on the last updated electron density is equal to or less than a first threshold value. An information processing program that causes a computer to execute a process.

[0135] (Appendix 2) The updating process is The information processing program according to claim 1, wherein the electron density is repeatedly updated until at least one of the first condition and a second condition indicating that the difference between the last updated electron density and the immediately preceding updated electron density is equal to or less than a second threshold is satisfied.

[0136] (Appendix 3) The information processing program according to appendix 1 or 2, characterized in that the difference ratio is obtained by dividing the difference between the total electron energy based on the electron density last updated and the representative value of the total electron energy based on the electron density updated up to the immediately preceding time by the representative value of the total electron energy based on the electron density initially updated.

[0137] (Appendix 4) The information processing program according to appendix 1 or 2, characterized in that the difference ratio is obtained by dividing the difference between the total electron energy based on the electron density last updated and the representative value of the total electron energy based on the electron density updated up to the immediately preceding time by the representative value of the total electron energy based on the electron density first updated.

[0138] (Appendix 5) The information processing program according to appendix 1 or 2, characterized in that the density functional theory calculation is a process of repeatedly updating the electron density using the Kohn-Sham equation, which enables calculation of a one-electron wave function.

[0139] (Appendix 6) The information processing program according to appendix 1 or 2, wherein the density functional theory calculation is a process of repeatedly updating the electron density at each point in a specified space.

[0140] (Appendix 7) The updating process is 3. The information processing program according to claim 2, wherein, when performing a structural relaxation calculation in which the density functional theory calculation is performed a plurality of times, the electron density is repeatedly updated in at least one of the plurality of density functional theory calculations until the first condition is satisfied.

[0141] (Supplementary Note 8) In a density functional theory calculation in which an electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that a difference ratio of a representative value of a total electron energy based on the initially updated electron density to a total electron energy based on the last updated electron density is equal to or less than a first threshold value. An information processing method characterized in that the processing is executed by a computer.

[0142] (Supplementary Note 9) In a density functional theory calculation in which an electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that a difference ratio of a representative value of a total electron energy based on the initially updated electron density to a total electron energy based on the last updated electron density is equal to or less than a first threshold value. An information processing device comprising a control unit. [Explanation of symbols]

[0143] 100 Information processing device 110 Structural relaxation calculation 111 Density Functional Theory Calculations 200 Information Processing Systems 201 Numerical Calculation Device 202 Client device 210 Network 300 Bus 301 CPU 302 memory 303 Network I / F 304 Recording Media I / F 305 Recording Media 400 Storage section 401 Acquisition Department 402 Arithmetic section 403 Output section 500, 700, 1000 graphs 600,800,900 tables

Claims

1. In a density functional theory calculation in which an electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that a difference ratio of a representative value of a total electron energy based on the initially updated electron density to a total electron energy based on the last updated electron density is equal to or less than a first threshold value. An information processing program that causes a computer to execute a process.

2. The updating process includes:

2. The information processing program according to claim 1, wherein the electron density is repeatedly updated until at least one of the first condition and a second condition indicating that a difference between the last updated electron density and the immediately preceding updated electron density is equal to or less than a second threshold is satisfied.

3. 3. The information processing program according to claim 1, wherein the difference ratio is obtained by dividing the difference between the total electron energy based on the electron density last updated and the representative value of the total electron energy based on the electron density updated up to the immediately preceding time by the representative value of the total electron energy based on the electron density initially updated.

4. 3. The information processing program according to claim 1, wherein the difference ratio is obtained by dividing the difference between the total electron energy based on the electron density last updated and the representative value of the total electron energy based on the electron density updated up to the immediately preceding time by the representative value of the total electron energy based on the electron density first updated.

5. In a density functional theory calculation in which an electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that a difference ratio of a representative value of a total electron energy based on the initially updated electron density to a total electron energy based on the last updated electron density is equal to or less than a first threshold value. An information processing method characterized in that the processing is executed by a computer.

6. In a density functional theory calculation in which an electron density is repeatedly updated, the electron density is repeatedly updated until a first condition is satisfied, which indicates that a difference ratio of a representative value of a total electron energy based on the initially updated electron density to a total electron energy based on the last updated electron density is equal to or less than a first threshold value. An information processing device comprising a control unit.

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