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

Abstract

To reduce a processing time required for performing structural relaxation calculations.SOLUTION: An information processing apparatus 100 performs a structural relaxation calculation 110 in which a density functional theory calculation 111 for repeatedly updating electron density is performed a plurality of times. The information processing apparatus 100 performs, for example, the structural relaxation calculation 110 so as to repeatedly update the electron density until a first condition is satisfied in at least any one of the plurality of times of the structural relaxation calculation 110. Any one of the plurality of times is, for example, the first time. The first condition is that a rate of change of the total electron energy based on the last updated electron density is equal to or less than a first threshold value.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 material 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 the self-consistent field method. For example, the electron density is calculated by repeating a calculation for updating the electron density using a wave function by the density functional theory until it is determined that the electron density has converged. For example, if the number of atoms is N, the amount of calculation required to calculate the electron density by the density functional theory is O(N^3). In addition, there is a structural relaxation calculation that utilizes the density functional theory to find a stable structure of a molecule in which the total electronic energy is minimized. For example, the stable structure of a molecule is found by repeatedly performing the density functional theory while updating the three-dimensional structure of the molecule.

[0003] As a prior art, for example, there is a technique for determining a stable structure of a molecule corresponding to a first minimum point detected on the potential energy surface of the molecule based on a gradient from the molecular coordinates of the molecule. Also, for example, there is a technique for optimizing a charge allocation structure obtained by allocating a charge amount to each atom by a charge balance method in a schematic structure determined based on the chemical structural formula of a molecule or ion, using a molecular force field calculation method, and generating an initial structure for a structural optimization calculation of a quantum chemical calculation method. Also, for example, there is a technique for determining a multi-layer matrix of a multi-element crystal based on a layer of the multi-element crystal and a composition ratio of a transition metal contained in the multi-element crystal. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2021 / 117510 [Patent Document 2] JP 2012-032908 A [Patent Document 3] US Patent Application Publication No. 2017 / 0097310 Summary of the Invention [Problem to be solved by the invention]

[0005] However, in the conventional technology, the density functional theory may be utilized to perform a structural relaxation calculation, which may increase the processing time required for the calculation. For example, in a structural relaxation calculation, when the density functional theory for calculating the electron density is repeatedly performed while updating the three-dimensional structure of the molecule, the amount of calculation required for calculating the electron density increases, which may result in an increase in the processing time required for the structural relaxation calculation.

[0006] In one aspect, the present invention aims to reduce the processing time required for performing a structural relaxation calculation. [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 for performing a structural relaxation calculation in which density functional theory calculations in which electron density is repeatedly updated are performed multiple times, so that the electron density is repeatedly updated in at least any of the multiple times until a first condition is satisfied indicating that the rate of change of the total electronic energy based on the last updated electron density is equal to or less than a first threshold value. Effect of the Invention

[0008] According to one aspect, it is possible to reduce the processing time required for performing a structural relaxation calculation. [Brief description of the drawings]

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

[0010] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of an information processing program, an information processing method, and an information processing device according to the present invention will be described in detail with reference to the 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 a structural relaxation calculation. The information processing device 100 is, for example, a server or a PC (Personal Computer).

[0012] The structural relaxation calculation is, for example, a series of processes for obtaining a stable structure of a molecule. The structural relaxation calculation corresponds to, for example, an iterative solution. The iterative solution is, for example, a method of repeatedly performing a specific operation until it is determined that the solution has converged. The convergence is, for example, a state in which the calculated solution is equal to or less than a threshold. The structural relaxation calculation is, for example, a series of processes for calculating the electron density by implementing density functional theory, and calculating the magnitude of the force acting on the atom based on the electron density, while updating the three-dimensional structure of the molecule, and repeating the process until a convergence condition is satisfied, thereby obtaining a stable structure of the molecule. The convergence condition is a condition for determining that the solution has converged. The convergence condition is, for example, that the magnitude of the force acting on the atom calculated last is equal to or less than a threshold.

[0013] The density functional theory is, for example, a series of processes for calculating electron density. The density functional theory corresponds to, for example, an iterative solution method. The density functional theory calculates the electron density by, for example, repeatedly performing a process for updating the electron density until a convergence condition is satisfied. The density functional theory corresponds to, for example, a self-consistent field method. The density functional theory calculates the electron density of each point in a space by, for example, repeatedly performing a series of processes for updating the electron density of each point in a space using a wave function until a convergence condition is satisfied. The convergence condition is a condition for determining that the solution has converged. The convergence 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 threshold value.

[0014] Structural relaxation calculations may be used, for example, in the field of material development, when attempting to find a stable structure of a molecule that governs the properties of a substance. Specifically, structural relaxation calculations are used in the field of material development, when attempting to find a stable molecular structure and accumulate useful material data for materials informatics, which aims to shorten research time and reduce research costs. For structural relaxation calculations and density functional theory, see, for example, Reference 1 below.

[0015] Reference 1: “Introduction to Density Functional Theory and its Applications”, DS Schul and JA Steckel, co-authored, Taizo Sasaki and Shigeru Suehara, Yoshioka Shoten, ISBN978-4842703657

[0016] Here, depending on the problem to be calculated, the time required to determine that the solution has converged may be long in density functional theory. For example, when density functional theory is implemented for the first time in structural relaxation calculations, the time required to determine that the solution has converged may be long in density functional theory. For example, when density functional theory is implemented for the first time in structural relaxation calculations, the number of times a series of processes for updating the electron density at each point in space is repeated may increase. This may lead to an increase in the processing time required to implement density functional theory for the first time, and an increase in the processing time required to implement structural relaxation calculations.

[0017] Specifically, when density functional theory is implemented for the first time, if a certain condition is satisfied and the total electronic energy transitions to a state of small fluctuation, the number of times a series of processes for updating the electron density at each point in space is repeated increases. The certain condition is that an atom exists whose position is relatively different between the initial structure of the molecule and the stable structure of the molecule. Specifically, the certain condition is that a point exists in the 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 the point to converge.

[0018] In this embodiment, an information processing method that can reduce the processing time required for performing a structural relaxation calculation utilizing density functional theory will be described. In the following description, density functional theory may be referred to as "DFT (Density Functional Theory) method."

[0019] In FIG. 1, the information processing device 100 stores a convergence condition for the structural relaxation calculation 110. The convergence condition is, for example, that the magnitude of the calculated force acting on the atom is equal to or less than a threshold. The information processing device 100 stores a first condition that can be a convergence condition for the density functional theory. The first condition is, for example, that the rate of change of the total electronic energy based on the last updated electron density is equal to or less than a first threshold. 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. 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 a structural relaxation calculation 110 in which a density functional theory calculation 111 for repeatedly updating the electron density is performed multiple times. For example, the information processing device 100 performs the structural relaxation calculation 110 so as to repeatedly update the electron density until a first condition is satisfied in at least one of the multiple times in the structural relaxation calculation 110. The one of the times is, for example, the first time. Specifically, the information processing device 100 performs the structural relaxation calculation 110 so as to repeatedly update the electron density until a first condition is satisfied in the first time of the multiple times in the structural relaxation calculation 110.

[0021] Specifically, the information processing device 100 performs the structural relaxation calculation 110 so as to repeatedly update the electron density until the first condition is satisfied in the first time among the multiple times, and to repeatedly update the electron density until the second condition is satisfied in each time other than the first time. Specifically, the information processing device 100 may perform the structural relaxation calculation 110 so as to repeatedly update the electron density until at least one of the first condition and the second condition is satisfied in the first time among the multiple times.

[0022] As a result, the information processing device 100 can reduce the processing time required to perform the density functional theory at least in the first time among the multiple times. Therefore, the information processing device 100 can reduce the processing time required to perform the structural relaxation calculation 110. For example, even if the total electronic energy transitions to a state of small fluctuation in the first time, the information processing device 100 can reduce the number of times to repeat a series of processes for updating the electron density, and can reduce the processing time required to perform the density functional theory. The information processing device 100 can easily perform the density functional theory with high accuracy in each time other than the first time among the multiple times, and can easily perform the structural relaxation calculation 110 with high accuracy.

[0023] When the convergence condition is satisfied in the structural relaxation calculation 110, the information processing device 100 outputs a stable structure of the molecule. The output format may be, for example, display on a display, printout on 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 stable structure of the molecule so that the user can refer to it. In this way, the information processing device 100 can make the stable structure of the molecule 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 the present invention is not limited to this. For example, the functions of the information processing device 100 may be realized by cooperation of a plurality of 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 the structural relaxation calculation. 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 convergence condition for the structural relaxation calculation. The convergence condition is, for example, that the magnitude of the calculated force acting on the atom is equal to or less than a threshold value.

[0029] The information processing device 100 sets a first condition that may be a convergence condition for the density functional theory. The first condition is, for example, that the fluctuation rate of the total electronic energy based on the last updated electron density is equal to or less than a first threshold. In addition to the first condition, the information processing device 100 sets a second condition that may be a convergence condition for the density functional theory. 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 a structural relaxation calculation based on the set convergence condition, the first condition, and the second condition.

[0030] The information processing device 100, for example, initializes the structure of the molecule. The information processing device 100, for example, refers to the structure of the molecule and performs a first density functional theory based on a first condition and a second condition. The information processing device 100 performs a second or subsequent density functional theory based on the second condition while updating the structure of the molecule until the convergence condition is satisfied, for example. In this way, the information processing device 100 identifies a stable structure of the molecule. When the convergence condition is satisfied in the structural relaxation calculation, the information processing device 100 transmits the stable structure of the molecule to the client device 202.

[0031] Here, the information processing device 100 may perform, for example, distributed processing of the structural relaxation calculation with the numerical calculation device 201. The information processing device 100 transmits a processing request for the structural relaxation calculation to the numerical calculation device 201. The information processing device 100 may receive a stable structure of a molecule 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.

[0032] The numerical calculation device 201 is a computer that shares the structural relaxation theory. The numerical calculation device 201 may perform structural relaxation calculation in response to receiving a processing request. The numerical calculation device 201 transmits a stable structure of a molecule to the information processing device 100. The numerical calculation device 201 is, for example, a server or a PC. The client device 202 is a computer that transmits a calculation instruction to the information processing device 100 based on an operation input by a user. When the client device 202 receives the stable structure of a molecule from the information processing device 100, it 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. In the following description, a case where the information processing device 100 operates independently will be mainly described.

[0033] (Application example of information processing device 100) The information processing device 100 may be applied, for example, in the field of material development, when structural relaxation calculations are performed to obtain stable structures of molecules that govern the properties of a substance. Specifically, the information processing device 100 may be applied to materials informatics, when structural relaxation calculations are performed to obtain stable molecular structures, and useful material data is accumulated.

[0034] (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.

[0035] Fig. 3 is a block diagram showing an example of a 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. In addition, each component is connected to each other via a bus 300.

[0036] Here, the CPU 301 is responsible for the overall control of the information processing device 100. The memory 302 has, for example, a read only memory (ROM), a random access memory (RAM), and a flash ROM. Specifically, for example, the flash ROM and the ROM store various programs, and the RAM is used as a work area for the CPU 301. The programs stored in the memory 302 are loaded into the CPU 301, causing the CPU 301 to execute the coded processes.

[0037] The network I / F 303 is connected to the network 210 through a communication line, and is connected to other computers via the network 210. The network I / F 303 manages an internal interface with the network 210, and controls input and output of data from other computers. The network I / F 303 is, for example, a modem or a LAN adapter.

[0038] The recording medium I / F 304 controls reading / writing data from / 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), a universal serial bus (USB) port, etc. 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, a USB memory, etc. The recording medium 305 may be detachable from the information processing device 100.

[0039] In addition to the above-mentioned components, the information processing device 100 may have, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, etc. Furthermore, the information processing device 100 may have a plurality of recording medium I / Fs 304 and recording media 305. Furthermore, the information processing device 100 may not have the recording medium I / Fs 304 and the recording media 305.

[0040] (Example of functional configuration of information processing device 100) Next, an example of a functional configuration of the information processing device 100 will be described with reference to FIG.

[0041] 4 is a block diagram showing an example of a functional configuration of the information processing device 100. The information processing device 100 includes a storage unit 400, an acquisition unit 401, a first calculation unit 402, a second calculation unit 403, and an output unit 404.

[0042] 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.

[0043] The acquiring unit 401 to the output unit 404 function as an example of a control unit. Specifically, the acquiring unit 401 to the output unit 404 realize their functions by, for example, 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 the network I / F 303. The processing results of each functional unit are stored in, for example, a storage area such as the memory 302 or the recording medium 305 shown in Fig. 3.

[0044] The storage unit 400 stores various information that is referred to or updated in the processing of each functional unit. The storage unit 400 stores, for example, convergence conditions related to structural relaxation calculations. The convergence condition is, for example, that the magnitude of the calculated force acting on an atom is equal to or less than a threshold value. The convergence condition is acquired, for example, by the acquisition unit 401. The convergence condition may be set, for example, by a user in advance.

[0045] The storage unit 400 stores, for example, a first condition that can be a convergence condition for density functional theory. The first condition is, for example, that the rate of change of the total electronic energy based on the last updated electron density 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. The first condition is, for example, acquired by the acquisition unit 401. The first condition may be, for example, set by a user in advance.

[0046] The storage unit 400 stores, for example, a second condition that may be a convergence condition for density functional theory. The second condition is that the difference between the last calculated electron density and the immediately preceding calculated electron density 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, for example, by a user in advance.

[0047] The acquisition unit 401 acquires various information used for processing by each functional unit. The acquisition unit 401 stores the acquired various information in the storage unit 400 or outputs it to each functional unit. The acquisition unit 401 may also output the various information stored in the storage unit 400 to each functional unit. The acquisition unit 401 acquires various information based on, for example, an operation input by a user. The acquisition unit 401 may receive various information from, for example, a device different from the information processing device 100.

[0048] The acquiring unit 401 acquires, for example, a convergence condition. Specifically, the acquiring unit 401 acquires the convergence condition by accepting an input of 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.

[0049] The acquiring unit 401 acquires, for example, a first condition. Specifically, the acquiring unit 401 acquires the first condition by accepting an 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.

[0050] The acquiring unit 401 acquires, for example, the second condition. Specifically, the acquiring unit 401 acquires the second condition by accepting an 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.

[0051] 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 an 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.

[0052] The acquisition unit 401 may receive a start trigger for starting processing of 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 for starting processing of the first calculation unit 402 and the second calculation unit 403.

[0053] The first arithmetic unit 402 performs a structural relaxation calculation. The structural relaxation calculation performs density functional theory calculation multiple times. The structural relaxation calculation performs density functional theory calculation multiple times, for example, by repeatedly performing density functional theory calculation until a convergence condition is satisfied. The structural relaxation calculation obtains a stable structure of a molecule, for example, by performing density functional theory calculation multiple times. The density functional theory calculation repeatedly updates the electron density. The multiple times are, for example, a variable value. For example, an upper limit may be set for the multiple times. For example, the multiple times may be a fixed value. For example, in the structural relaxation calculation, the first arithmetic unit 402 controls the second arithmetic unit 403 to perform density functional theory.

[0054] Specifically, the first arithmetic unit 402 initializes the structure of the molecule by initializing the atomic positions, and then repeatedly performs a series of processes. The series of processes includes, for example, a process A for controlling the second arithmetic unit 403 based on the atomic positions in the structure of the molecule to perform density functional theory calculation. For example, the process A controls the second arithmetic unit 403 to set the first condition as the convergence condition when performing a specific density functional theory calculation among multiple calculations. The specific time is, for example, any one of multiple calculations of the density functional theory calculation. The specific time is, for example, the first time. The specific time may be, for example, the second time or later.

[0055] The process A may control the second arithmetic unit 403 to set the convergence condition to satisfy at least one of the first condition and the second condition when performing a density functional theory calculation in a specific number of times among the multiple times. The process A may control the second arithmetic unit 403 to set the convergence condition to the second condition when performing a density functional theory calculation other than the specific number of times among the multiple times.

[0056] The process A may control the second arithmetic unit 403 to set the first condition as the convergence condition when performing each density functional theory calculation before a specific time out of the multiple times. The process A may control the second arithmetic unit 403 to set the convergence condition to satisfy at least one of the first condition and the second condition when performing each density functional theory calculation before a specific time out of the multiple times. The process A may control the second arithmetic unit 403 to set the convergence condition to satisfy at least one of the first condition and the second condition when performing each density functional theory calculation after a specific time out of the multiple times.

[0057] The series of processes includes, for example, a process B performed after the process A, which calculates a total electronic energy based on the electron density at each point in the space calculated in the density functional theory calculation. The series of processes includes, for example, a process C performed after the process B, which determines whether or not the convergence condition is satisfied, and updates the atomic positions if the convergence condition is not satisfied. Specifically, the first arithmetic unit 402 repeatedly performs the series of processes so that, if the convergence condition is not satisfied when the series of processes is performed, the series of processes is performed again.

[0058] This allows the first calculation unit 402 to perform a structural relaxation calculation and obtain a stable molecular structure. When performing each of a plurality of density functional theory calculations, the first calculation unit 402 can control the second calculation unit 403 so that the second calculation unit 403 selectively uses the first condition and the second condition as the convergence condition. Therefore, the first calculation unit 402 can reduce the processing time required to perform a structural relaxation calculation, for example.

[0059] The second calculation unit 403 performs density functional theory calculations under the control of the first calculation unit 402. The second calculation unit 403 performs density functional theory calculations such that, for example, in a specific number of times among the multiple times the density functional theory calculations are performed, the electron density is repeatedly updated until a first condition is satisfied. The specific number of times is, for example, at least one of the multiple times the density functional theory calculations are performed. The specific number of times is, for example, the first number of times. The specific number of times may be, for example, the second number of times or later. The first condition indicates, for example, that the rate of change of the total electronic energy based on the last updated electron density is equal to or less than a first threshold value.

[0060] The fluctuation rate is calculated based on a representative value of the total electronic energy based on the electron density updated immediately before and the total electronic energy based on the electron density updated last. 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. The representative value may be, for example, any one of the total electronic energies based on the electron density updated immediately before. The fluctuation rate is, for example, an absolute value of a ratio of a difference between a representative value of the total electronic energy based on the electron density updated immediately before and the total electronic energy based on the electron density updated last to a representative value of the total electronic energy based on the electron density updated immediately before. This allows the second calculation unit 403 to reduce the processing time required for performing a specific density functional theory calculation, and to easily reduce the processing time required for performing a structural relaxation calculation.

[0061] The second arithmetic unit 403 may perform density functional theory calculations such that, for example, in at least a specific number of times among a plurality of times of performing density functional theory calculations, the electron density is repeatedly updated until at least one of the first condition and the second condition is satisfied. The second condition indicates, for example, 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. This allows the second arithmetic unit 403 to reduce the processing time required to perform a specific number of density functional theory calculations, and makes it easier to reduce the processing time required to perform structural relaxation calculations.

[0062] The second calculation unit 403 may perform density functional theory calculations such that, for example, in each of the multiple density functional theory calculations other than the specific number of times, the electron density is repeatedly updated until the second condition is satisfied. This allows the second calculation unit 403 to easily and accurately update the electron density when performing density functional theory calculations other than the specific number of times, and to easily and accurately obtain a stable structure of a molecule when performing a structural relaxation calculation.

[0063] The second arithmetic unit 403 may perform density functional theory calculations such that the electron density is repeatedly updated until at least one of the first condition and the second condition is satisfied in each of the times before the specific time, for example. This allows the second arithmetic unit 403 to reduce the processing time required for performing density functional theory calculations in each of the times before the specific time, and makes it easier to reduce the processing time required for performing structural relaxation calculations.

[0064] The second calculation unit 403 may perform density functional theory calculations so as to repeatedly update the electron density in each round after a specific round until the second condition is satisfied, for example. This allows the second calculation unit 403 to easily and accurately update the electron density when performing each round of density functional theory calculations after a specific round, and to easily and accurately obtain a stable structure of a molecule when performing a structural relaxation calculation.

[0065] Specifically, the second calculation unit 403 updates the electron density by repeatedly performing a series of processes after setting the electron density to an initial state, and calculates the final electron density. The series of processes includes, for example, a process a for calculating and updating 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, a process b performed after the process a for calculating the difference between the electron density immediately before the update and the electron density immediately after the update. The series of processes includes, for example, a process c performed after the process b for calculating the total electron energy as a physical characteristic value based on the electron density immediately after the update and calculating the fluctuation rate of the total electron energy.

[0066] Specifically, the second arithmetic unit 403 repeats a series of processes so that if the convergence condition is not satisfied when a series of processes is performed, the series of processes is performed again. The convergence condition is, for example, a first condition in a specific density functional theory calculation. The first condition corresponds to, for example, the rate of change of the calculated total electronic energy being equal to or less than a first threshold value.

[0067] The convergence condition may be, for example, that at least one of the first condition and the second condition is satisfied in a specific density functional theory calculation. 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 is, for example, the second condition in density functional theory calculations other than the specific calculation.

[0068] The convergence condition may be, for example, the first condition in each density functional theory calculation before a specific time. The convergence condition may be, for example, that at least one of the first condition and the second condition is satisfied in each density functional theory calculation before a specific time. The convergence condition may be, for example, the second condition in each density functional theory calculation after a specific time. This allows the second arithmetic unit 403 to easily reduce the processing time required to perform the structural relaxation calculation, and to easily obtain a stable structure of a molecule with high accuracy.

[0069] The output unit 404 outputs the processing result of at least one of the functional units. The output format is, for example, display on a display, printout on 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 404 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.

[0070] The output unit 404 outputs, for example, the result of the structural relaxation calculation performed by the first calculation unit 402 so that the result can be referred to by a user. The output unit 404 may transmit, for example, the result of the structural relaxation calculation performed by the first calculation unit 402 to another computer. In this way, the output unit 404 can make the result of the structural relaxation calculation performed by the first calculation unit 402 externally accessible.

[0071] Specifically, the output unit 404 outputs the stable structure of the molecule obtained as a result of the structural relaxation calculation performed by the first calculation unit 402 so that the user can refer to it. Specifically, the output unit 404 outputs the stable structure of the molecule obtained as a result of the structural relaxation calculation performed by the first calculation unit 402 so that the user can refer to it. In this way, the output unit 404 can make the stable structure of the molecule accessible externally.

[0072] Specifically, the output unit 404 may output the total electronic energy obtained as a result of the structural relaxation calculation performed by the first calculation unit 402 so that the total electronic energy can be referred to by a user. Specifically, the output unit 404 may transmit the total electronic energy obtained as a result of the structural relaxation calculation performed by the first calculation unit 402 to another computer. In this way, the output unit 404 can make the total electronic energy available for external reference.

[0073] Specifically, the output unit 404 may output the final electron density obtained as a result of performing the structural relaxation calculation in the first calculation unit 402 so that the final electron density can be referred to by a user. Specifically, the output unit 404 may transmit the final electron density obtained as a result of performing the structural relaxation calculation in the first calculation unit 402 to another computer. In this way, the output unit 404 can make the electron density available for external reference.

[0074] (Operation example of information processing device 100) Next, an example of the operation of the information processing device 100 will be described with reference to FIGS.

[0075] 5 to 8 are explanatory diagrams showing an example of the operation of the information processing device 100. In Fig. 5 and Fig. 6, the information processing device 100 performs a structural relaxation calculation. When performing a first density functional theory calculation in the structural relaxation calculation, the information processing device 100 sets, as a convergence condition, that at least one of a first condition and a second condition is satisfied.

[0076] The first condition indicates that the fluctuation rate RCE of the total electron energy is equal to or less than a permissible value RCE_TH. The fluctuation rate RCE is, for example, an absolute value of a ratio of a difference between a representative value of the total electron energy based on the electron density calculated up to immediately before and a total electron energy based on the electron density calculated last, to a representative value of the total electron energy based on the electron density calculated up to immediately before. 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, or a median value related to the electron density calculated up to immediately before.

[0077] The representative value may be, for example, a total electron energy based on the electron density calculated at any timing up to the immediately preceding timing. The representative value may be, for example, a total electron energy based on the electron density calculated immediately before. The allowable value RCE_TH is, for example, set in advance by a user. RCE_TH is, for example, 1.0e-5.

[0078] 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 previously calculated 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 smaller than the Δρ tolerance value. The Δρ tolerance value is set in advance by the user, for example. The Δρ tolerance value is assumed to be 1.0, for example. The information processing device 100 performs the first density functional theory calculation by repeatedly performing the process of calculating the electron density until the convergence condition is satisfied.

[0079] 5 and 6, the timing for satisfying the second condition will be described. A graph 500 in FIG. 5 shows the relationship between Δρ(r i ) and indicates the timing when 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.

[0080] 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 i Δρ(r i) is the electron density ρ(r i ) is relatively large at r i Δρ(r i ), it is difficult for Δρ to become smaller than the allowable value. Therefore, as shown in table 600, the number of times N for repeating the process of calculating the electron density until the second condition is satisfied tends to be a relatively large number, specifically, 7.

[0081] Next, we move on to the explanation of Figures 7 and 8 to explain the timing at which the first condition is satisfied. Graph 700 in Figure 7 shows the change in RCE when the process of calculating electron density is repeated, and shows 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 RCE. 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.

[0082] 8 shows specific values ​​of RCE 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, RCE is likely to be smaller than the allowable value RCE_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.

[0083] 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, so that the number of times the process of calculating the electron density is repeated can be reduced when the first density functional theory calculation is performed. For example, the information processing device 100 can suppress the number of times the process of calculating the electron density is repeated to M times instead of N times. Therefore, the information processing device 100 can reduce the processing time required when performing the first density functional theory calculation.

[0084] 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 number of times the process of calculating the electron density is repeated is N times. Therefore, the conventional method leads to an increase in the processing time required for performing the first density functional theory calculation. Compared to the conventional method, the information processing device 100 can reduce the processing time required for performing the first density functional theory calculation, and can reduce the processing time required for performing the structural relaxation calculation.

[0085] In the structural relaxation calculation, the information processing device 100 preferably sets the second condition as the convergence condition when performing the second or subsequent density functional theory calculation. As a result, the information processing device 100 does not set the first condition as the convergence condition, so that it is easy to calculate the electron density with high accuracy when performing the second or subsequent density functional theory calculation. Therefore, the information processing device 100 can accurately obtain a stable structure of the molecule when performing the structural relaxation calculation.

[0086] (Effects of the information processing device 100) Next, an example of an effect achieved by the information processing device 100 will be described with reference to FIGS.

[0087] 9 and 10 are explanatory diagrams showing the results of comparison with the conventional method. In FIG. 9 and FIG. 10, it is assumed that the information processing device 100 performs a structural relaxation calculation using VASP (Vienna Ab initio Simulation Package) software. The VASP software is a non-empirical quantum molecular dynamics calculation program using pseudopotentials and a plane wave basis. It is assumed that the information processing device 100 specifically performs a structural relaxation calculation for an ammonia catalyst.

[0088] Table 900 in FIG. 9 shows a comparative 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 a convergence condition, but uses only the second condition. As shown in table 900, the conventional method calculates total electron energy=-372.89573691 eV. In the conventional method, the number of steps when performing a structural relaxation calculation is 88 steps. In the conventional method, the number of iterations in the first density functional theory calculation is 41. The number of iterations is the number of times the process of calculating the electron density is repeated. In the conventional method, the elapsed time when performing a structural relaxation calculation is 1039.316 (seconds).

[0089] On the other hand, the information processing device 100 sets the tolerance RCE_TH=1.0e-5. The information processing device 100 calculates the total electron energy=-372.89481001 eV. In the information processing device 100, the number of steps when performing the structural relaxation calculation is 74 steps. In the information processing device 100, the number of iterations in the first density functional theory calculation is 24. The number of iterations is the number of times the process of calculating the electron density is repeated. In the information processing device 100, the elapsed time when performing the structural relaxation calculation is 892.714 (seconds). In this way, the information processing device 100 can speed up the structural relaxation calculation by 1.16 times compared to the conventional method.

[0090] A graph 1000 in FIG. 10 shows a comparative example of the speed-up rate between the information processing device 100 and the conventional method. As shown in FIG. 10, the speed-up rate of the information processing device 100 is 1.16 times when the conventional method is set as the standard: 1. The information processing device 100 can speed up the structural relaxation calculation compared to the conventional method, and can suppress an increase in the processing time required for performing the structural relaxation calculation. The information processing device 100 can reduce the number of steps when performing the structural relaxation calculation by about 16% compared to the conventional method, for example. The information processing device 100 can reduce the number of times the process of calculating the electron density is repeated in the first density functional theory calculation by about 41% compared to the conventional method, for example. The information processing device 100 can accurately calculate the total electron energy with a difference of less than 0.001 eV compared to the conventional method, for example.

[0091] (Overall processing procedure) Next, 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.

[0092] Fig. 11 is a flowchart showing an example of the overall processing procedure. In Fig. 11, the information processing device 100 sets a convergence condition for the structural relaxation calculation (step S1101). The information processing device 100 performs a structural relaxation calculation process 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. Thereby, the information processing device 100 can make the stable structure of the molecule accessible to the user.

[0093] (Structural relaxation calculation procedure) Next, an example of a procedure of 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.

[0094] 12 is a flowchart showing an example of a procedure for a structural relaxation calculation process, in which the information processing device 100 initializes the atomic positions to thereby initialize the molecular structure (step S1201).

[0095] 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 electronic 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).

[0096] The information processing device 100 is i It is determined whether |≦|F| is satisfied (step S1205). |F| is set in advance by a user, for example. Here, for all |F i Not |≦|F|, but at least one of |F i If |>|F| is satisfied (step S1205: No), the information processing device 100 proceeds to the process of step S1206.

[0097] In step S1206, the information processing device 100 updates the atomic positions to update the molecular structure (step S1206), and returns to the process of step S1202. i If |≦|F| is satisfied (step S1205: Yes), the information processing device 100 ends the structural relaxation calculation process. In this way, the information processing device 100 can obtain a stable structure of the molecule.

[0098] (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.

[0099] 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 a space, the information processing device 100 sets the electron density ρ(r) of each point. For example, in the first setting, the information processing device 100 sets an initial value of the electron density ρ(r). For example, in the second or subsequent setting, the information processing device 100 sets the electron density ρ(r) by some method. Specifically, in 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.

[0100] The information processing device 100 solves the Kohn-Sham equation based on the electron density ρ(r) to obtain a one-electron wave function φ i For example, when there are a plurality of points in the space, the information processing device 100 calculates a one-electron wave function φ 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.

[0101] 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 the space, the information processing device 100 calculates the difference Δρ(r) between each point. The information processing device 100 calculates the total electron energy as a physical characteristic value based on the electron density ρ'(r) (step S1305). The information processing device 100 calculates the rate of change RCE of the total electron energy (step S1306).

[0102] The information processing device 100 determines whether the difference Δρ(r)≦Δρ tolerance (step S1307). For example, when there are multiple points in the space, the information processing device 100 determines whether the difference Δρ(r) of all points≦Δρ tolerance. Here, if the difference Δρ(r) of all points≦Δρ tolerance (step S1307: Yes), the information processing device 100 ends the density functional theory processing. On the other hand, if the difference Δρ(r) of at least any point>Δρ tolerance (step S1307: No), the information processing device 100 proceeds to the processing of step S1308.

[0103] In step S1308, the information processing device 100 determines whether or not RCE≦RCE_TH (step S1308). If RCE≦RCE_TH is not satisfied (step S1308: No), the information processing device 100 returns to the process of step S1301. On the other hand, if RCE≦RCE_TH is satisfied (step S1308: Yes), the information processing device 100 ends the density functional theory process. This allows the information processing device 100 to perform density functional theory calculations.

[0104] The density functional theory processing shown in Fig. 13 realizes, for example, the first density functional theory calculation performed by the information processing device 100. 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.

[0105] Here, the information processing device 100 may change the order of the processes of some 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 steps in the flowcharts of Figures 11 to 13.

[0106] As described above, the information processing device 100 can store a first condition indicating that the rate of change of the total electronic energy based on the last updated electron density is equal to or less than a first threshold. The information processing device 100 can perform a structural relaxation calculation in which density functional theory calculations are performed multiple times, such that the electron density is repeatedly updated until the first condition is satisfied in at least one of the multiple times. This allows the information processing device 100 to reduce the processing time required to perform density functional theory calculations and reduce the processing time required to perform structural relaxation calculations.

[0107] According to the information processing device 100, 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 value can be stored. According to the information processing device 100, a structural relaxation calculation can be performed such that the electron density is repeatedly updated until at least one of the first condition and the second condition is satisfied in at least one of the times. This allows the information processing device 100 to reduce the processing time required to perform density functional theory calculations and reduce the processing time required to perform structural relaxation calculations.

[0108] According to the information processing device 100, in each of the multiple times before a specific time, the electron density can be repeatedly updated until at least one of the first condition and the second condition is satisfied. According to the information processing device 100, in each of the multiple times after a specific time, the electron density can be repeatedly updated until the second condition is satisfied. Thereby, the information processing device 100 can reduce the processing time required to perform density functional theory calculations and can reduce the processing time required to perform structural relaxation calculations. Furthermore, the information processing device 100 can perform structural relaxation calculations with high accuracy.

[0109] According to the information processing device 100, the fluctuation rate can be calculated based on a representative value of the total electronic energy based on the electron density updated up to the last time and the total electronic energy based on the electron density updated last time. This allows the information processing device 100 to accurately calculate the fluctuation rate, facilitates determining whether the first condition is satisfied, and accurately determines whether to end the density functional theory calculation.

[0110] 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. In this way, the information processing device 100 can realize density functional theory calculations.

[0111] 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. This makes it possible for the information processing device 100 to be applied to cases where multiple points exist in the specified space.

[0112] According to the information processing device 100, in each of the multiple times except one of the multiple times, the structural relaxation calculation can be performed so as to repeatedly update the electron density until the second condition is satisfied. This allows the information processing device 100 to perform the structural relaxation calculation with high accuracy.

[0113] According to the information processing device 100, the structural relaxation calculation can be performed so that the electron density is repeatedly updated until the first condition is satisfied at least in the first of the multiple calculations. This allows the information processing device 100 to reduce the processing time required to perform the density functional theory calculation and to reduce the processing time required to perform the structural relaxation calculation. Furthermore, the information processing device 100 can perform the structural relaxation calculation with high accuracy.

[0114] 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 is 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.

[0115] The following supplementary notes are further disclosed regarding the above-described embodiment.

[0116] (Additional Note 1) In a structural relaxation calculation in which a density functional theory calculation in which an electron density is repeatedly updated is performed a plurality of times, the structural relaxation calculation is performed so as to repeatedly update the electron density until a first condition is satisfied in at least one of the plurality of times, the first condition indicating that a fluctuation rate of a total electronic 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.

[0117] (Appendix 2) The process to be performed is as follows: the structural relaxation calculation is performed so as to repeatedly update the electron density until at least one of the first condition and a second condition indicating that a difference between the last updated electron density and the electron density updated immediately before is equal to or less than a second threshold is satisfied, at least in any one of the times.

[0118] (Appendix 3) The process to be performed is as follows: the structural relaxation calculation is performed such that, in each of the multiple calculations before a specific calculation, the electron density is repeatedly updated until at least one of the first condition and the second condition is satisfied, and, in each of the multiple calculations after the specific calculation, the electron density is repeatedly updated until the second condition is satisfied.

[0119] (Appendix 4) The information processing program according to appendix 3, characterized in that the fluctuation rate is calculated based on a representative value of the total electron energy based on the electron density updated up to the immediately preceding time and the total electron energy based on the electron density updated last.

[0120] (Appendix 5) The information processing program according to appendix 3, characterized in that the density functional theory calculation is a process of repeatedly updating the electron density using the Kohn-Sham equation that enables calculation of a one-electron wave function.

[0121] (Supplementary Note 6) The information processing program according to any one of Supplementary Notes 1 to 5, wherein the density functional theory calculation is a process of repeatedly updating the electron density at each point in a specified space.

[0122] (Appendix 7) The process to be performed is as follows: the structural relaxation calculation is performed such that, in each of the multiple calculations other than any one of the multiple calculations, the electron density is repeatedly updated until a second condition is satisfied, the second condition indicating that a difference between the last updated electron density and the electron density updated immediately before is equal to or less than a second threshold value.

[0123] (Supplementary Note 8) The information processing program according to any one of Supplementary Notes 1 to 5, wherein the one of the times is the first time.

[0124] (Appendix 9) In a structural relaxation calculation in which a density functional theory calculation in which an electron density is repeatedly updated is performed a plurality of times, the structural relaxation calculation is performed so as to repeatedly update the electron density until a first condition indicating that a fluctuation rate of a total electronic energy based on the last updated electron density is equal to or less than a first threshold is satisfied in at least one of the plurality of times. An information processing method characterized in that the processing is executed by a computer.

[0125] (Appendix 10) In a structural relaxation calculation in which a density functional theory calculation in which an electron density is repeatedly updated is performed a plurality of times, the structural relaxation calculation is performed so as to repeatedly update the electron density until a first condition indicating that a fluctuation rate of a total electronic energy based on the last updated electron density is equal to or less than a first threshold is satisfied in at least one of the plurality of times. An information processing device comprising a control unit. [Explanation of symbols]

[0126] 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 Interface 304 Recording media I / F 305 Recording media 400 Storage section 401 Acquisition Department 402 1st calculation section 403 2nd calculation section 404 Output section 500,700,1000 graphs 600,800,900 tables

Claims

1. In a structural relaxation calculation in which a density functional theory calculation in which an electron density is repeatedly updated is performed a plurality of times, the structural relaxation calculation is performed so as to repeatedly update the electron density until a first condition indicating that a fluctuation rate of a total electronic energy based on the last updated electron density is equal to or less than a first threshold value is satisfied in at least any one of the plurality of times. An information processing program that causes a computer to execute a process.

2. The process to be performed is 2. The information processing program according to claim 1, wherein the structural relaxation calculation is performed so as to repeatedly update the electron density 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 in at least one of the times.

3. The process to be performed is 3. The information processing program according to claim 2, wherein the structural relaxation calculation is performed such that, in each of the multiple calculations before a specific calculation, the electron density is repeatedly updated until at least one of the first condition and the second condition is satisfied, and, in each of the multiple calculations after the specific calculation, the electron density is repeatedly updated until the second condition is satisfied.

4. 4. The information processing program according to claim 3, wherein the fluctuation rate is calculated based on a representative value of the total electron energy based on the electron density updated up to the immediately preceding time and the total electron energy based on the electron density updated last.

5. 5. The information processing program according to claim 1, wherein the one of the times is a first time.

6. In a structural relaxation calculation in which a density functional theory calculation in which an electron density is repeatedly updated is performed a plurality of times, the structural relaxation calculation is performed so as to repeatedly update the electron density until a first condition indicating that a fluctuation rate of a total electronic energy based on the last updated electron density is equal to or less than a first threshold value is satisfied in at least any one of the plurality of times. An information processing method characterized in that the processing is executed by a computer.

7. In a structural relaxation calculation in which a density functional theory calculation in which an electron density is repeatedly updated is performed a plurality of times, the structural relaxation calculation is performed so as to repeatedly update the electron density until a first condition indicating that a fluctuation rate of a total electronic energy based on the last updated electron density is equal to or less than a first threshold value is satisfied in at least any one of the plurality of times. An information processing device comprising a control unit.

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