Storage medium, quantum chemical calculation method and quantum chemical calculation device

Abstract

Reducing the amount of calculations in quantum chemical calculations. The quantum chemical calculation device combines two molecular orbitals included in a plurality of molecular orbitals of a molecule as an object of quantum chemical calculation to generate a plurality of molecular orbital pairs. Next, the quantum chemical calculation device calculates the overlap integral values ​​between the included molecular orbitals for each of the plurality of molecular orbital pairs. Then, the quantum chemical calculation device determines the first molecular orbital to be included in the active space orbital group of the quantum chemical calculation based on the overlap integral values ​​of each of the plurality of molecular orbital pairs.

Description

Technical Field

[0001] The invention relates to a storage medium, a quantum chemical calculation method and a quantum chemical calculation device. Background Art

[0002] Quantum chemical calculations can be performed using either classical computers or quantum computers. Quantum chemical calculations accurately solve the Schrödinger equation that deals with atomic nuclei and electrons.

[0003] In quantum chemical calculations, in order to introduce electron correlation effects and perform high-precision calculations, for example, the configuration interaction method (CI) is used to solve the wave function by considering multiple electron configurations. In the CI method, for example, calculations are performed by considering multiple electron configurations created using molecular orbitals obtained by the Hartree-Fock method.

[0004] As a technology related to quantum chemical calculation, for example, a quantitative analysis system for quantitatively analyzing molecular orbital distribution has been proposed, and a calculation device for suppressing the amount of calculation when calculating the all-electron wave function has also been proposed.

[0005] Prior art literature

[0006] Patent Literature

[0007] Patent Document 1: U.S. Patent Application Publication No. 2016 / 0371467

[0008] Patent Document 2: Japanese Patent Application Publication No. 2018-152018 Summary of the invention

[0009] Problem that the invention aims to solve

[0010] When the scale of the system is small and the number of basis functions is small, the number of molecular orbitals (the number of basis functions) obtained by the Hartree-Fock method is also small. Therefore, it is also possible to perform calculations that take into account all available electronic configurations (Full-CI calculations). On the other hand, if the scale of the system becomes larger and the number of basis functions becomes larger, the number of molecular orbitals obtained by the Hartree-Fock method also increases, and Full-CI calculations become difficult.

[0011] In the case of Full-CI calculation difficulties, it is effective to select an electronic configuration that is as conducive to the electron correlation effect as possible and perform calculations taking into account the selected electronic configuration. The set of more than one molecular orbitals (molecular orbital group) that configure electrons in the electronic configuration considered at this time is called the active space orbital group. In order to suppress the calculation load and introduce more accurate calculations of electron correlation effects, it is important to select an appropriate active space orbital group.

[0012] However, there is no suitable molecular orbital selection criteria for performing more accurate calculations that introduce more electron correlation effects, and it is impossible to suppress the reduction in calculation accuracy caused by limiting the electron configuration destination to the active space orbital group. Therefore, when implementing quantum chemical calculations with high accuracy, Full-CI calculations have to be performed, which makes it difficult to reduce the amount of calculations.

[0013] In one aspect, the present invention aims to reduce the computational effort of quantum chemical calculations.

[0014] Means used to solve problems

[0015] In one embodiment, a quantum chemical calculation program is provided that causes a computer to execute the following processing.

[0016] The computer generates a plurality of molecular orbital pairs showing a variety of combinations of two molecular orbitals based on a plurality of molecular orbitals in a molecule that is the object of quantum chemical calculation. Next, the computer calculates the overlap integral values ​​between the included molecular orbitals for each of the plurality of molecular orbital pairs. Then, the computer determines the first molecular orbital to be included in the active space orbital group of quantum chemical calculation based on the overlap integral values ​​of each of the plurality of molecular orbital pairs.

[0017] Effects of the Invention

[0018] According to one embodiment, the amount of calculation required for quantum chemical calculations can be reduced.

[0019] The above and other objects, features and advantages of the present invention will become more apparent from the following description in conjunction with the accompanying drawings which illustrate exemplary preferred embodiments of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a diagram showing an example of the quantum chemical calculation method according to the first embodiment.

[0021] Figure 2 This is a diagram showing an example of computer hardware used for quantum chemical calculations.

[0022] Figure 3 It is a diagram showing an example of calculation of energy according to the state of a molecule.

[0023] Figure 4 This is a diagram showing a first example of the relationship between the overlap integral value between molecular orbitals included in the active space orbital group and the total energy value.

[0024] Figure 5 This is a diagram showing a second example of the relationship between the overlap integral value between molecular orbitals included in the active space orbital group and the total energy value.

[0025] Figure 6 This is a block diagram showing an example of a computer's function for quantum chemical calculations.

[0026] Figure 7 This is a diagram showing an example of calculation condition data.

[0027] Figure 8 This is a flowchart showing an example of the steps of quantum chemical calculation.

[0028] Fig. 9 : is a flowchart showing an example of the procedure of active space orbital group generation processing.

[0029] Fig.10 : is a diagram showing an example of generation of an active space orbital group. DETAILED DESCRIPTION

[0030] Hereinafter, the present embodiment will be described with reference to the drawings. In addition, each embodiment can be implemented by combining a plurality of embodiments within a range where no contradiction occurs.

[0031] [First embodiment]

[0032] First, as a first embodiment, a quantum chemical calculation method that can reduce the amount of calculation in quantum chemical calculation will be described.

[0033] Figure 1 is a diagram showing an example of the quantum chemical calculation method according to the first embodiment. Figure 1 2 shows an example of a case where a quantum chemical calculation method capable of reducing the amount of calculation is performed using the quantum chemical calculation device 10. The quantum chemical calculation device 10 can perform the quantum chemical calculation method by, for example, executing a quantum chemical calculation program.

[0034] The quantum chemical calculation device 10 includes a storage unit 11 and a processing unit 12. The storage unit 11 is, for example, a memory or a storage device included in the quantum chemical calculation device 10. The processing unit 12 is, for example, a processor or a calculation circuit included in the quantum chemical calculation device 10.

[0035] The storage unit 11 stores, for example, molecular structure information 11a of a molecule to be calculated in quantum chemistry. The molecular structure information 11a includes information such as atoms included in the molecule, the bonding distance between atoms, and bonding accuracy.

[0036] The processing unit 12 performs quantum chemical calculation based on the molecular structure information 11a. For example, the processing unit 12 calculates a plurality of molecular orbitals 1a to 1d of a molecule to be calculated as a target of quantum chemical calculation based on the molecular structure information 11a.

[0037] When the plurality of molecular orbitals 1a to 1d of a molecule are known, information indicating the plurality of molecular orbitals 1a to 1d may be pre-stored in the storage unit 11 . In this case, the processing unit 12 acquires the information indicating the plurality of molecular orbitals 1a to 1d from the storage unit 11 .

[0038] Next, the processing unit 12 generates a plurality of molecular orbital pairs 2a to 2f showing various combinations of two molecular orbitals based on the plurality of molecular orbitals 1a to 1d. Figure 1 In the example of , six molecular orbital pairs 2a to 2f are generated based on four molecular orbitals 1a to 1d.

[0039] The processing unit 12 calculates the overlap integral values ​​(overlap integral values) between the included molecular orbitals for each of the plurality of molecular orbital pairs 2a to 2f. The overlap integral values ​​of each of the plurality of molecular orbital pairs 2a to 2f are set to S1 to S6. At this time, the magnitude relationship of the overlap integral values ​​S1 to S6 is S1>S5>S4>S2>S3>S6.

[0040] The processing unit 12 determines the first molecular orbital included in the active space orbital group 3 in the quantum chemical calculation based on the overlap integral values ​​S1 to S6 of each of the plurality of molecular orbital pairs 2a to 2f. For example, the processing unit 12 determines a predetermined number of molecular orbitals as the first molecular orbital in descending order of the overlap integral values ​​S1 to S6 with other molecular orbitals from the molecular orbitals. The number of molecular orbitals included in the active space orbital group 3 is a value less than the total number of the plurality of molecular orbitals 1a to 1d.

[0041] When the number of molecular orbitals included in the active space orbital group 3 is set to "3", the processing unit 12 first includes the molecular orbitals 1a and 1b included in the molecular orbital pair 2a having the largest overlap integral value in the active space orbital group 3. Next, the processing unit 12 includes the molecular orbital 1d, which is the molecular orbital that has not been included in the active space orbital group 3 among the molecular orbitals 1b and 1d included in the molecular orbital pair 2e having the second largest overlap integral value, in the active space orbital group 3. At this point, the number of molecular orbitals in the active space orbital group 3 reaches "3", and therefore, the generation of the active space orbital group 3 is completed.

[0042] The processing unit 12 calculates the energy of the molecule based on the electronic configuration for the first molecular orbital included in the active space orbital group 3. For example, the processing unit 12 calculates the total energy obtained by integrating the states of a plurality of electronic configurations showing a plurality of configuration patterns of electrons with respect to the active space orbital group 3. The processing unit 12 outputs the calculated energy value as a result of quantum chemical calculation.

[0043] According to such a quantum chemical calculation device 10, it is possible to include a molecular orbital with a large overlap integral value with other molecular orbitals in the active space orbital group 3. The molecular orbitals of the molecular orbital pair with a large overlap integral value also interact with each other greatly. By including the molecular orbitals with a large interaction with each other in the active space orbital group 3, the possibility of making an electronic state that reduces the total energy becomes greater, and high-precision calculation can be achieved. In other words, the calculation accuracy is maintained at a high precision and the Full-CI calculation can be omitted, thereby reducing the amount of calculation.

[0044] In addition, the processing unit 12 can also generate multiple molecular orbital pairs by combining a second molecular orbital from multiple molecular orbitals 1a~1d, wherein the energy level of the second molecular orbital is above the first threshold value and below the second threshold value that is greater than the first threshold value. Molecular orbitals with energy levels lower than the first threshold value are processed as molecular orbitals that are always equipped with electrons, for example, in energy calculations. In addition, molecular orbitals with energy levels higher than the second threshold value are processed as molecular orbitals that are never equipped with electrons, for example, in energy calculations. By limiting the electronic orbitals included in the molecular orbital pair at the stage of generating the molecular orbital pair, the number of calculations of the overlap integral value can be reduced. As a result, the efficiency of the processing can be improved.

[0045] [Second embodiment]

[0046] Next, the second embodiment is described. In the second embodiment, a computer is made to execute quantum chemical calculations.

[0047] Figure 21 is a diagram showing an example of the hardware of a computer used in quantum chemical calculations. Computer 100 controls the entire device through processor 101. Memory 102 and multiple peripheral devices are connected to processor 101 via bus 109. Processor 101 can also be a multiprocessor. Processor 101 is, for example, a CPU (Central Processing Unit), an MPU (Micro Processing Unit), or a DSP (Digital Signal Processor). It is also possible that at least a part of the functions implemented by executing a program by processor 101 is implemented by electronic circuits such as ASIC (Application Specific Integrated Circuit), PLD (Programmable Logic Device), etc.

[0048] The memory 102 is used as a main storage device of the computer 100. The memory 102 temporarily stores at least a part of the OS (Operating System) program and the application program for the processor 101 to execute. In addition, the memory 102 stores various data used in the processing of the processor 101. As the memory 102, for example, a volatile semiconductor storage device such as a RAM (Random Access Memory) is used.

[0049] Peripheral devices connected to the bus 109 include a storage device 103 , a graphics processing device 104 , an input interface 105 , an optical drive device 106 , a device connection interface 107 , and a network interface 108 .

[0050] The storage device 103 writes and reads data to and from a built-in recording medium electrically or magnetically. The storage device 103 is used as an auxiliary storage device of a computer. The storage device 103 stores OS programs, application programs, and various data. In addition, as the storage device 103, for example, a HDD (Hard Disk Drive) or an SSD (Solid State Drive) can be used.

[0051] The monitor 21 is connected to the graphic processing device 104. The graphic processing device 104 displays an image on the screen of the monitor 21 according to a command from the processor 101. The monitor 21 may be a display device using an organic EL (Electro Luminescence), a liquid crystal display device, or the like.

[0052] The keyboard 22 and the mouse 23 are connected to the input interface 105. The input interface 105 transmits signals sent from the keyboard 22 and the mouse 23 to the processor 101. In addition, the mouse 23 is an example of a pointing device, and other pointing devices may also be used. As other pointing devices, there are touch panels, tablets, touch pads, trackballs, etc.

[0053] The optical drive device 106 uses laser light or the like to read data recorded on the optical disk 24 or write data to the optical disk 24. The optical disk 24 is a portable recording medium on which data is recorded in a manner that can be read by reflection of light. The optical disk 24 includes DVD (Digital Versatile Disc), DVD-RAM, CD-ROM (Compact Disc Read Only Memory), CD-R (Recordable) / RW (ReWritable), etc.

[0054] The device connection interface 107 is a communication interface for connecting peripheral devices to the computer 100. For example, the memory device 25 and the memory card reader / writer 26 can be connected to the device connection interface 107. The memory device 25 is a recording medium equipped with a communication function with the device connection interface 107. The memory card reader / writer 26 is a device for writing data to the memory card 27 or reading data from the memory card 27. The memory card 27 is a card-type recording medium.

[0055] The network interface 108 is connected to the network 20. The network interface 108 transmits and receives data with other computers or communication devices via the network 20. The network interface 108 is, for example, a wired communication interface connected to a wired communication device such as a switch or a router via a cable. In addition, the network interface 108 may also be a wireless communication interface that communicates with a wireless communication device such as a base station or an access point via radio waves.

[0056] The computer 100 can realize the processing functions of the second embodiment by the hardware described above. Figure 2 The computer 100 shown is implemented with the same hardware.

[0057] The computer 100 realizes the processing function of the second embodiment by, for example, executing a program stored in a computer-readable recording medium. The program that describes the processing content to be executed by the computer 100 can be recorded in advance on various recording media. For example, the program to be executed by the computer 100 can be stored in advance in the storage device 103. The processor 101 loads at least a part of the program in the storage device 103 into the memory 102 and executes the program. In addition, the program to be executed by the computer 100 can also be recorded in advance on a mobile recording medium such as an optical disk 24, a memory device 25, or a memory card 27. The program stored in the mobile recording medium can be executed after being installed in the storage device 103, for example, by control from the processor 101. In addition, the processor 101 can also read out and execute the program directly from the mobile recording medium.

[0058] The computer 100 solves the Schrödinger equation of a predetermined molecule by introducing Hartree-Fock calculation or electron-related calculation. When the molecule to be analyzed is in a stable state, the computer 100 usually arranges electrons in sequence from the molecular orbital with a low energy level, thereby obtaining a base state with minimum energy. However, when the electron configuration with minimum energy is to be obtained in a deformed state of the molecule, the accuracy of the calculation will deteriorate if the calculation introducing electron correlation is not performed.

[0059] Figure 3 It is a diagram showing an example of calculation of energy according to the state of a molecule. Figure 3 In FIG. 30, a calculation example of the energy value corresponding to the distance R between atoms of a LiH molecule is shown. The horizontal axis of FIG. 30 is the distance between atoms. The vertical axis represents energy (hartree). The dotted line in Graph 30 represents the energy value obtained by Hartree-Fock calculation, and the solid line represents the energy value obtained by calculation incorporating electron correlation.

[0060] When the distance R between atoms is short, there is basically no difference in energy value between the Hartree-Fock calculation and the calculation with the introduction of electron correlation. As the distance R becomes longer, the difference in energy value between the Hartree-Fock calculation and the calculation with the introduction of electron correlation becomes larger. In addition, it can be seen that the calculation with the introduction of electron correlation is a high-precision calculation. Therefore, when the distance R is shorter to a certain extent, if the calculation accuracy can be allowed, the Hartree-Fock calculation can also be used. However, when the distance R is longer than a certain extent and the calculation accuracy is deteriorated to an unacceptable level when the Hartree-Fock calculation is used, it is suitable to perform the calculation with the introduction of electron correlation (CI calculation).

[0061] For example, Figure 3In the case of the LiH molecule shown, the electron correlation effect becomes large In the region of the distance R above, calculations involving electron correlation are suitable. Here, when the scale of the system is small and the number of basis functions is small, such as in the case of the LiH molecule, the number of molecular orbitals (the number of basis functions) is also small, and therefore, Full-CI calculations that take into account all available electronic configurations can be performed. However, if the scale of the system becomes larger and the number of molecular orbitals also increases, Full-CI calculations become difficult.

[0062] Therefore, the computer 100 includes a part of the molecular orbitals in the active space orbital group, and performs CI calculations that limit the available electronic configurations to the active space orbital group. At this time, in order to suppress the calculation load and perform more accurate calculations that introduce more electron correlation effects, it is important to appropriately select the molecular orbitals to be included in the active space orbital group.

[0063] In addition, quantum computers can also be used to perform quantum chemical calculations. When using a quantum computer for quantum chemical calculations, the more molecular orbitals that are the destinations for the electrons to be configured, the more quantum bits are used in the calculation. In quantum computers (especially NISQ: Noisy Intermediate-Scale Quantum computer) where there are physical limitations on the number of quantum bits that can be used, in order to perform quantum chemical calculations efficiently, the number of molecular orbitals that can configure electrons has to be limited. Therefore, even for quantum chemical calculations using a quantum computer, it is very important to appropriately select the molecular orbitals to be included in the active space orbital group.

[0064] Conventionally, an active space orbital group is selected from a plurality of molecular orbitals near the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) obtained by the Hartree-Fock method, and then quantum chemical calculations are performed by considering the electronic configuration formed by the active space orbital group including the selected molecular orbital.

[0065] However, even if the molecular orbitals near HOMO and LUMO are selected, the best active space orbital group may not be obtained. Therefore, experience and intuition are mostly required when selecting the active space orbital group. In order to determine the best active space orbital group, quantum chemical calculations are performed on multiple active space orbital groups to confirm which active space orbital group has lower energy. In this way, if quantum chemical calculations are performed on multiple active space orbital groups, it will cost more calculation costs.

[0066] Here, as a selection criterion for appropriately selecting the molecular orbitals to be included in the active space orbital group, the magnitude of the interaction between the molecular orbitals is focused on. The magnitude of the interaction between the molecular orbitals is related to the magnitude of the overlap integral between the molecular orbitals. By including the molecular orbitals with a large overlap integral in the active space orbital group, the molecular orbitals with a large interaction can be included in the active space orbital group, and there is a possibility that the energy can be lowered by the influence of the interaction.

[0067] The reason why it is appropriate to include a molecular orbital having a large overlap integral in the active space orbital group will be qualitatively described below.

[0068] The CI method is used to describe complex electronic states (states that introduce electron correlation) that cannot be represented by only one electronic configuration (such as the Hartree-Fock electronic configuration). When the electron correlation is introduced by the CI method, more diverse electronic states are expressed by mixing multiple electronic configurations. In order to introduce more electron correlations, the greater the interaction between the molecular orbitals contained in the electronic configuration under consideration (that is, the greater the electron exchange between the orbitals), the more advantageous it is. The magnitude of the interaction between molecular orbitals is closely related to the magnitude of the overlap integral between the orbitals. The greater the overlap integral, the greater the interaction between the orbitals. Therefore, by including a molecular orbital with a large overlap integral with other molecular orbitals in the active space orbital group and setting it to be possible to configure electrons to the molecular orbital, the possibility of creating an electronic state that reduces the total energy becomes greater.

[0069] Figure 4 : is a diagram showing the first example of the relationship between the overlap integral value and the total energy value between the molecular orbitals included in the active space orbital group. Figure 4 In the example of , it is assumed that quantum chemical calculation is performed based on molecular structure information 31 representing LiH molecules. The molecular orbitals of the LiH molecules are obtained by the Hartree-Fock method, thereby obtaining five molecular orbitals. Figure 4In the figure, each molecular orbital is represented by a horizontal line. Each molecular orbital is assigned a number (1) to (5) indicating the order of energy level from low to high. As examples of selection modes of molecular orbitals included in the active space orbital group, a first selection mode 32 in which molecular orbital (1) and molecular orbital (5) are selected and a second selection mode 33 in which molecular orbital (1) and molecular orbital (2) are selected are shown.

[0070] In the first selection mode 32, an electronic configuration in which two electrons are arranged in the molecular orbital (1) and an electronic configuration in which two electrons are arranged in the molecular orbital (5) are considered. In addition, the overlap integral value of the molecular orbital (1) and the molecular orbital (5) selected in the first selection mode 32 is "0.071981". Moreover, the total energy value obtained by the active space orbital group of the first selection mode 32 is "-7.87714 (Hartree)".

[0071] The wave function of a molecule to be calculated in quantum chemistry is represented by a linear combination of configuration state functions (CSFs) representing the configurations of each electron, and the total energy value is obtained by solving the Schrodinger equation for the wave function.

[0072] In the second selection mode 33, an electronic configuration in which two electrons are arranged in the molecular orbital (1) and an electronic configuration in which two electrons are arranged in the molecular orbital (2) are considered. In addition, the overlap integral value of the molecular orbital (1) and the molecular orbital (2) selected in the second selection mode 33 is "0.034635". Moreover, the total energy value obtained by the active space orbital group of the second selection mode 33 is "-7.863267 (Hartree)".

[0073] exist Figure 4 In the example shown, the overlap integral value of the first selection mode 32 in which the molecular orbital (1) and the molecular orbital (5) are set as the active space orbital group is larger than the overlap integral value of the second selection mode 33 in which the molecular orbital (1) and the molecular orbital (2) are set as the active space orbital group. In addition, the first selection mode 32 having a large overlap integral value has a lower total energy value than the second selection mode 33 having a small overlap integral value.

[0074] Figure 5 : is a diagram showing a second example of the relationship between the overlap integral value and the total energy value between the molecular orbitals included in the active space orbital group. Figure 5 In the example of , it is assumed that quantum chemical calculation is performed based on molecular structure information 34 representing H2O molecules. The molecular orbitals of the H2O molecules are obtained by the Hartree-Fock method, thereby obtaining a large number of molecular orbitals. Figure 5In the figure, the 4th to 6th molecular orbitals from low to high energy levels are indicated by horizontal lines. Each molecular orbital is assigned a number (4) to (6) indicating the order of energy levels from low to high. As examples of selection patterns of molecular orbitals included in the active space orbital group, a first selection pattern 35 in which molecular orbital (4) and molecular orbital (6) are selected, and a second selection pattern 36 in which molecular orbital (5) and molecular orbital (6) are selected are shown.

[0075] In the first selection mode 35, an electronic configuration in which two electrons are arranged in the molecular orbital (4) and an electronic configuration in which two electrons are arranged in the molecular orbital (6) are considered. In addition, the overlap integral value of the molecular orbital (4) and the molecular orbital (6) selected in the first selection mode 35 is "0.295985". In addition, the total energy value obtained by the active space orbital group of the first selection mode 35 is "-74.96970 (Hartree)".

[0076] In the second selection mode 36, an electronic configuration in which two electrons are arranged in the molecular orbital (5) and an electronic configuration in which two electrons are arranged in the molecular orbital (6) are considered. In addition, the overlap integral value of the molecular orbital (5) and the molecular orbital (6) selected in the second selection mode 36 is "0.235437". In addition, the total energy value obtained by the active space orbital group of the second selection mode 36 is "-74.966436 (Hartree)".

[0077] exist Figure 5 In the example shown, the overlap integral value of the first selection mode 35 in which the molecular orbital (4) and the molecular orbital (6) are set as the active space orbital group is larger than that of the second selection mode 36 in which the molecular orbital (5) and the molecular orbital (6) are set as the active space orbital group. In addition, the first selection mode 35 having a large overlap integral value has a lower total energy value than the second selection mode 36 having a small overlap integral value.

[0078] like Figure 4 , Figure 5 As shown, when a molecular orbital having a large overlap integral value with other molecular orbitals is included in the active space orbital group, a lower total energy value can be obtained. Therefore, when the computer 100 selects the active space orbital group in the quantum chemical calculation, the molecular orbital having a large overlap integral value with other molecular orbitals is preferentially included in the active space orbital group.

[0079] Figure 6 1 is a block diagram showing an example of functions of a computer for quantum chemical calculations. The computer 100 includes a storage unit 110 , a molecular orbital calculation unit 120 , an overlap integral unit 130 , an active space orbital group generation unit 140 , and an energy calculation unit 150 .

[0080] The storage unit 110 stores calculation condition data 111, which includes: molecular structure information indicating the structure of a molecule to be calculated as a quantum chemical calculation object; and conditions for quantum chemical calculation of the molecule. For example, a part of the storage area of ​​the memory 102 or the storage device 103 is used as the storage unit 110.

[0081] The molecular orbital calculation unit 120 calculates the molecular orbital of the molecule to be subjected to quantum chemical calculation based on the calculation condition data 111. For example, the molecular orbital calculation unit 120 calculates the molecular orbital by the Hartree-Fock method.

[0082] The overlap integral unit 130 calculates the overlap integral value between molecular orbitals. For example, the overlap integral unit 130 calculates the energy level of each of the plurality of molecular orbitals. The overlap integral unit 130 selects molecular orbitals whose energy level is greater than or equal to a predetermined lower limit value and less than or equal to a predetermined upper limit value as selection candidates. The overlap integral unit 130 generates a combination of two molecular orbitals among the selection candidates and calculates the overlap integral value for each combination.

[0083] The active space orbital group generation unit 140 selects the molecular orbitals in descending order of the overlap integral values ​​with other molecular orbitals, and includes the selected molecular orbitals in the active space orbital group. If the number of molecular orbitals included in the active space orbital group reaches a predetermined number, the active space orbital group generation unit 140 ends the selection of the molecular orbitals included in the active space orbital group.

[0084] The energy calculation unit 150 calculates the total energy value of the molecule as the object of quantum chemical calculation based on the generated active space orbital group. The energy calculation unit 150 outputs the calculated total energy value as the result of quantum chemical calculation. For example, the energy calculation unit 150 stores the calculated total energy value in the memory 102 or the storage device 103. In addition, the energy calculation unit 150 can also display the calculated total energy value on the monitor 21.

[0085] in addition, Figure 6 The functions of the elements shown can be realized, for example, by causing a computer to execute a program module corresponding to the element. Calculation condition data 111 for performing quantum chemical calculations are input into the computer 100 in advance by a user and stored in the storage unit 110 .

[0086] Figure 7 FIG. 1 is a diagram showing an example of calculation condition data. Figure 7Calculation condition data 111 representing the structure of the LiH molecule is shown in FIG. The STO-3G basis function is used in the calculation condition data 111. The STO-3G basis function is a minimum basis function system that fits three original Gaussian orbitals to a single Slater-type orbital (STO). In addition, the distance between Li-H atoms is set in the calculation condition data 111. The value in the case of .

[0087] The meanings of the items in the calculation condition data 111 are as follows. "method" indicates the calculation method used in quantum chemical calculation. Figure 7 In the example, the Hartree-Fock method is specified as the calculation method. "basis" indicates the basis function system to be applied. "charge" indicates the total charge of the molecule. "spin multiplicity" indicates the spin multiplicity. "geometry" indicates the coordinates of each atom that constitutes the molecule. Information related to the molecular structure, such as the distance between atoms (bonding distance) and bond angle, is determined based on the coordinates of each constituent atom. "Energy level minimum" indicates the minimum value of the energy level (E min ). “Energy level maximum” indicates the maximum value of the energy level considered in the overlap integral calculation (E max ).

[0088] Next, the steps of quantum chemical calculation are explained.

[0089] Figure 8 is a flowchart showing an example of the steps of quantum chemical calculation. Figure 8 The processing shown in FIG. 1 is described.

[0090] [Step S101 ] The molecular orbital calculation unit 120 acquires the calculation condition data 111 . For example, the molecular orbital calculation unit 120 receives input of the calculation condition data 111 designating a molecule to be the target of quantum chemical calculation from a user, and reads the designated calculation condition data 111 from the storage unit 110 .

[0091] [Step S102 ] The molecular orbital calculation unit 120 obtains molecular orbitals using the Hartree-Fock method. The molecular orbital calculation unit 120 assigns molecular orbital numbers in ascending order starting from 1 to the obtained one or more molecular orbitals. The molecular orbital calculation unit 120 sends information indicating the molecular orbitals to the overlap integration unit 130 .

[0092] [Step S103 ] The overlap integration unit 130 sets an initial value “0” (i=0) to a variable i indicating a molecular orbital number to be examined for energy levels.

[0093] [Step S104 ] The overlap integration unit 130 adds 1 to the variable i (i=i+1).

[0094] [Step S105] The overlap integration unit 130 determines whether the energy level of the i-th molecular orbital is at the minimum energy level (E min ) and the maximum value of the energy level (E max ). For example, if the energy level of the molecular orbital is E min Above and E max Then, the overlap integration unit 130 advances the process to step S106. min or greater than E max In the case of , the overlap integration unit 130 advances the process to step S107.

[0095] [Step S106 ] The overlap integration unit 130 adds the i-th molecular orbital to the overlap integral calculation orbital list.

[0096] [Step S107] The overlap integration unit 130 determines whether the inspection of the energy levels of all molecular orbitals is completed. If the inspection of all molecular orbitals is completed, the overlap integration unit 130 advances the process to step S108. If there are uninspected molecular orbitals, the overlap integration unit 130 advances the process to step S104.

[0097] [Step S108] The overlap integral unit 130 obtains the overlap integral values ​​of the molecular orbitals in the overlap integral calculation orbital list. For example, the overlap integral unit 130 generates all possible combinations of molecular orbital pairs by selecting two molecular orbitals from the overlap integral calculation orbital list. The overlap integral unit 130 calculates the overlap integral values ​​for all the generated molecular orbital pairs. The overlap integral value S between the i-th molecular orbital and the j-th molecular orbital can be calculated by the following formula: ij .

[0098] [Formula 1]

[0099]

[0100] In formula (1), Ψ i * (r) is the complex conjugate of the atomic orbital function of the ith molecular orbital. j (r) is the atomic orbital function of the jth molecular orbital. The greater the overlap of the two molecular orbitals, the greater the value of formula (1). When there is no overlap between the two molecular orbitals, the overlap integral value is "0", and when the two molecular orbitals completely overlap, the overlap integral value is "1".

[0101] [Step S109] The active space orbital group generation unit 140 generates an active space orbital group based on the overlap integral value of each molecular orbital pair. This process will be described in detail later (see Fig. 9 ).

[0102] [Step S110 ] The energy calculation unit 150 solves the Schrödinger equation based on the electron configuration for the active space orbital group in consideration of electron correlation, thereby obtaining the total energy value of the molecule.

[0103] [Step S111 ] The energy calculation unit 150 outputs the total energy value of the molecule as a result of quantum chemical calculation.

[0104] Fig. 9 is a flowchart showing an example of the steps of the active space orbital group generation process. Fig. 9 Processing shown.

[0105] [Step S121 ] The active space orbital group generation unit 140 selects molecular orbital pairs in descending order of overlap integral values.

[0106] [Step S122 ] The active space orbital group generating unit 140 adds the molecular orbitals included in the selected molecular orbital pair, which are not included in the active space orbital group, to the active space orbital group.

[0107] [Step S123] The active space orbital group generation unit 140 determines whether the number of molecular orbitals in the active space orbital group has reached a predetermined number. If the number of molecular orbitals has reached a predetermined number, the active space orbital group generation unit 140 ends the active space orbital group generation process. If the number of molecular orbitals is less than the predetermined number, the active space orbital group generation unit 140 advances the process to step S121.

[0108] In this way, the molecular orbitals are added to the active space orbital group in descending order of the overlap integral values ​​with other molecular orbitals.

[0109] Fig.10 is a diagram showing an example of the generation of active space orbital groups. When the generated molecular orbitals are arranged according to energy levels, the energy level ratio of the minimum value (E min ) is an orbital that always contains electrons. max ) is an orbital with no electrons. min ) and the maximum value (E max ) are the molecular orbitals in which electrons can be possibly configured.

[0110] exist Fig.10 In the example, the energy levels of the 4th to 6th molecular orbitals are at their minimum (Emin ) and the maximum value (E max ). In this case, an overlap integral calculation orbital list 40 including the fourth to sixth molecular orbitals is generated. Then, three molecular orbital pairs 41 to 43 are generated from the molecular orbitals included in the overlap integral calculation orbital list 40.

[0111] The overlap integral values ​​are calculated for the molecular orbital pairs 41 to 43 respectively. Fig.10 In the example, the overlap integral value of the molecular orbital pair 41 is S1, the overlap integral value of the molecular orbital pair 42 is S2, and the overlap integral value of the molecular orbital pair 43 is S3. Here, it is assumed that the magnitude relationship of the overlap integral values ​​is "S2>S1>S3". In this case, first, the 4th molecular orbital and the 6th molecular orbital included in the molecular orbital pair 42 are included in the active space orbital group 50.

[0112] If the number of molecular orbitals included in the active space orbital group 50 is "2", a plurality of electronic configurations are determined based on the active space orbital group 50 including two molecular orbitals. min ) are always configured in molecular orbitals with low electrons, and electrons that cannot be configured in these molecular orbitals are configured in any molecular orbital in the active space orbital group. Moreover, the total energy value is obtained by solving the Schrödinger equation related to the following wave function, which is represented by a linear combination of the configuration state functions of multiple electronic configurations.

[0113] In this way, by including a molecular orbital having a large overlap integral value with other molecular orbitals in the active space orbital group 50, a high-precision calculation in which a large amount of electron correlation effect is introduced can be performed more efficiently.

[0114] That is, calculations involving electron correlations such as methods for inter-configuration interactions are usually performed using the results of Hartree-Fock calculations as a starting point. When performing a Hartree-Fock calculation, only one overlap integral value calculation is required, and the calculation time for the overlap integral value calculation is negligible compared to the calculation time required for the calculation involving electron correlation. In the second embodiment, an active space orbital group containing a large molecular orbital of an overlap integral is preselected for calculation. The calculation time in this case is much shorter than when there is no information related to the overlap integral value, for example, for M types (M is an integer greater than 2) of active space orbital groups (for example Figure 4 , Figure 5 The calculation of each selected mode) is shortened to about 1 / M.

[0115] In addition, the energy level ratio (E min ) is lower than the maximum value (Emax ) are excluded from the overlap integral calculation orbital list 40. Thus, the number of molecular orbital pairs to be calculated for overlap integral values ​​is reduced, thereby reducing the amount of calculation.

[0116] [Other implementation methods]

[0117] In the second embodiment, an example of using a classical computer 100 to perform an overall quantum chemical calculation is shown, but quantum chemical calculations can also be performed using a quantum computer. For example, a quantum computer can be used to implement the process of solving the Schrödinger equation. When a quantum computer is used, the number of molecular orbitals contained in the active space orbital group 50 is small, thereby reducing the number of quantum bits used in the calculation. As shown in the second embodiment, for quantum computers (especially NISQ) where there are physical limitations on the number of quantum bits that can be used, it is a very useful technology to appropriately reduce the number of molecular orbitals contained in the active space orbital group 50.

[0118] The above content is only to illustrate the principle of the present invention. Furthermore, those skilled in the art can make a lot of modifications and changes. The present invention is not limited by the accurate structure and application examples shown and described above, and all corresponding modifications and equivalents are deemed to be based on the scope of the present invention of the attached claims and their equivalents.

[0119] Description of Reference Numerals

[0120] 1a, 1b, 1c, 1d molecular orbitals

[0121] 2a, 2b, 2c, 2d, 2e, 2f molecular orbital pairs

[0122] 3 Active space orbital groups

[0123] 10 Quantum Chemical Calculation Device

[0124] 11 Storage

[0125] 11a Molecular structure information

[0126] 12 Processing Department

Claims

1. A computer-readable storage medium storing a quantum chemical calculation program, wherein the quantum chemical calculation program causes a computer to perform the following processing: Based on a plurality of molecular orbitals in a molecule to be calculated by quantum chemistry, a plurality of molecular orbital pairs showing various combinations of two molecular orbitals are generated. For the plurality of molecular orbital pairs, respectively calculating the overlap integral values ​​between the included molecular orbitals, Based on the overlap integral values ​​of each of the plurality of molecular orbital pairs, a predetermined number of molecular orbitals are determined as first molecular orbitals to be included in the active space orbital group for the quantum chemical calculation in descending order of overlap integral values ​​with other molecular orbitals.

2. The computer-readable storage medium according to claim 1, wherein: The generating includes generating the plurality of molecular orbital pairs by combining a second molecular orbital having a first energy level from among the plurality of molecular orbitals, wherein the first energy level is greater than a first threshold and less than a second threshold, wherein the second threshold is greater than the first threshold.

3. The computer-readable storage medium according to claim 1, wherein: The processing also includes: The energy of the molecule is calculated based on the electronic configuration of the first molecular orbital included in the active space orbital group.

4. A quantum chemical calculation method, wherein: The computer performs the following processing: Based on a plurality of molecular orbitals in a molecule to be calculated by quantum chemistry, a plurality of molecular orbital pairs showing various combinations of two molecular orbitals are generated. For the plurality of molecular orbital pairs, respectively calculating the overlap integral values ​​between the included molecular orbitals, Based on the overlap integral values ​​of each of the plurality of molecular orbital pairs, a predetermined number of molecular orbitals are determined as first molecular orbitals to be included in the active space orbital group for the quantum chemical calculation in descending order of overlap integral values ​​with other molecular orbitals.

5. The quantum chemical calculation method according to claim 4, wherein: The generating includes generating the plurality of molecular orbital pairs by combining a second molecular orbital having a first energy level from among the plurality of molecular orbitals, wherein the first energy level is greater than a first threshold and less than a second threshold, wherein the second threshold is greater than the first threshold.

6. The quantum chemical calculation method according to claim 4, wherein: The processing also includes: The energy of the molecule is calculated based on the electronic configuration of the first molecular orbital included in the active space orbital group.

7. A quantum chemical calculation device, comprising a processing unit, the processing unit performing the following processing: Based on a plurality of molecular orbitals in a molecule to be calculated by quantum chemistry, a plurality of molecular orbital pairs showing various combinations of two molecular orbitals are generated. For the plurality of molecular orbital pairs, respectively calculating the overlap integral values ​​between the included molecular orbitals, Based on the overlap integral values ​​of each of the plurality of molecular orbital pairs, a predetermined number of molecular orbitals are determined as first molecular orbitals to be included in the active space orbital group for the quantum chemical calculation in descending order of overlap integral values ​​with other molecular orbitals.

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