Molecular orbital calculation device and program

Abstract

The present invention provides a molecular orbital calculation device and program capable of determining the set of natural bond orbitals and base orbitals localized for each atom in a molecule. [Solution] The present invention obtains the Fock matrix (F matrix) of the natural bond orbital basis based on the second-region localized molecular orbitals of the orthogonal atomic orbital basis of the active region, performs a cut process and a two-electron integral correction process on this F matrix to obtain the cut-corrected F matrix, determines the electron density of the active region based on the cut-corrected F matrix, and uses this as an initial value to determine the final electron density of the active region by the self-consistent field method. The cut process replaces the one-electron integral and the two-electron integral of the kinetic energy integral and the nuclear-electron attractive energy integral, respectively, with zero, depending on the cut position where the interaction is to be cut, and the two-electron integral correction process determines the two-electron integral of the active region based on the atomic orbitals of the frozen region.

Description

[Technical Field]

[0001] This invention relates to a molecular orbital calculation device and a molecular orbital calculation program for determining the electronic state of a molecule. [Background technology]

[0002] The physical properties of a molecule are closely related to the types of atoms that make up the molecule and their electronic states. Knowing the electronic state of a molecule allows for analytical analysis of its energy gradient (the so-called energy gradient method), enabling the determination of the stable structure where the molecule's energy is minimized, the structure of its transition state, and its normal vibrational frequency. Furthermore, by calculating the potential energy relative to the reaction coordinate in a molecular reaction, the equilibrium points of the reaction system, products, reaction intermediates, and transition state can be determined. Other properties such as vibrational spectra, electronic spectra, dipole moments, ionization potential, polarizability, and spin density can also be determined. Thus, knowing the electronic state of a molecule allows for the determination of various molecular properties.

[0003] Examples of analytical methods for determining the electronic state of such molecules include the TS / TB interaction analysis method and the elongation method (ELG method). The TS / TB interaction analysis method uses hybridized atomic orbitals as the basis set, replaces the integral elements corresponding to the interaction to be cut with integral elements using the concept of orbital contraction, sets up the so-called Hartree-Fock-Roturn equation (HFR equation), and determines the wave function of the molecule by solving this HFR equation. This method is disclosed, for example, in Patent Document 1, Non-Patent Document 1, and Non-Patent Document 2.

[0004] For example, the molecular orbital calculation device disclosed in Patent Document 1 is a computer-based device for determining the electronic state of a molecule using the HFR equation, comprising: an input unit for inputting the molecular structure data and cut information indicating interactions to be excluded; a normal integral storage unit for storing integral elements in the molecular orbital method calculated using basis functions with normal orbital indices as normal integral elements; a large integral storage unit for storing integral elements in the molecular orbital method calculated using basis functions with substantially infinitely increased orbital indices as large integral elements; and a normal integral storage unit for calculating the integral elements of the atomic orbital basis in the overlap integral, kinetic energy integral, nuclear-electron attractive energy integral, and two-electron integral in the molecular orbital method for the molecule in the structural data using basis functions with normal orbital indices, and storing them in the normal integral storage unit, as well as calculating the integral elements of the atomic orbital basis in the overlap integral, kinetic energy integral, nuclear-electron attractive energy integral, and two-electron integral in the molecular orbital method using basis functions with substantially infinitely increased orbital indices. The system includes: an integral calculation unit that calculates the integral elements of the child orbital bases as integral elements after treating each interaction within the molecule as having no interaction, and stores them in the large integral memory; a base conversion unit that converts the normal integral elements of the atomic orbital bases stored in the normal integral memory unit into integral elements of the natural hybrid orbital base or the natural bonded orbital base and stores them in the normal integral memory unit, and converts the large integral elements of the atomic orbital bases stored in the large integral memory unit into integral elements of the natural hybrid orbital base or the natural bonded orbital base and stores them in the large integral memory unit; an integral element replacement unit that replaces the integral elements of the natural hybrid orbital base or the natural bonded orbital bases stored in the normal integral memory unit with integral elements of the natural hybrid orbital base or the natural bonded orbital base stored in the large integral memory unit for the interaction corresponding to the cut information; an equation calculation unit that solves the HFR equation using the integral elements replaced by the integral element replacement unit; and an output unit that outputs the calculation results of the equation calculation unit.

[0005] The ELG method extends to the target polymer by sequentially adding monomers as adducts (fragments) while tracking the polymerization reaction of the polymer with respect to the oligomer as the starting material (starting cluster). Each time a fragment is added, the electronic state is calculated using region-localized molecular orbitals instead of canonical molecular orbitals, and the electronic state of the target polymer is calculated sequentially. For example, it is disclosed in Patent Document 2, Non-Patent Document 2, Non-Patent Document 3, etc.

[0006] The molecular orbital calculation device disclosed in this Patent Document 2 is a device for obtaining the electronic state of a molecule by the ELG method, which is configured by a computer. It includes an input unit for inputting the structural data of the starting cluster for the target polymer whose electronic state is to be calculated, an output unit for outputting the calculation result, a transformation matrix Y for converting the canonical molecular orbitals of the region-localized molecular orbitals CMO RLMO , the transposed matrix C of the matrix representing the canonical molecular orbitals of the region atomic orbitals RO CMO† , and a storage unit for storing a transformation matrix U for eliminating the elements in the off-diagonal block by the Jacobi method in the density matrix D of the region atomic orbitals RO . A molecular orbital calculation unit for obtaining the canonical molecular orbitals by the atomic orbital basis in the starting cluster by a predetermined molecular orbital calculation method, and a matrix representing the region-localized molecular orbitals of the atomic orbital basis as C AO RLMO , and when the matrix representing the canonical molecular orbitals of the atomic orbital basis is C AO CMO , Y CMO RLMO = C RO CMO† U, C AO RLMO = C AO CMO Y CMO RLMOThe system includes a region localization calculation unit that performs a localization process to convert the canonical molecular orbitals based on the atomic orbital basis in the starting cluster into region-localized molecular orbitals using the formula represented by , such that a frozen AO region is created on one end of the starting cluster such that the orbital phase is larger, and an active AO region is created on the other end of the starting cluster such that the orbital phase is larger. The system also includes a post-addition molecular orbital calculation unit that determines the molecular orbitals when a fragment is added to the starting cluster by solving the Fock matrix based on the region-localized molecular orbitals using the self-consistent field method, and if the result of adding the fragment to the starting cluster is not the target polymer, it sets the result of adding the fragment to the starting cluster as a new starting cluster, and if the result of adding the fragment to the starting cluster is the target polymer, it outputs the determined molecular orbitals as the calculation result to the output unit. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Patent No. 4870911 [Patent Document 2] Patent No. 4221351 [Non-patent literature]

[0008] [Non-Patent Document 1] R. Hoffmann, A. Imamura, W. J. Hehre, J. Am. Chem. Soc. 90, 1499 (1968) [Non-Patent Document 2] Yuuichi Orimoto, Yuriko Aoki “Pure Trough-Bond State in Organic Molecules for Analysis of the Relationship Between Intramolecular Interactions and Total Energy”, International Journal of Quantum Chemistry,Vol.92,355-366(2003) [Non-Patent Document 3] Akira Imamura, Yuriko Aoki, and Koji Maekawa “A theoretical synthesis of polymers by using uniform localization of molecular orbirals : Proposal of an elongation method”, J.Chem.Phys.,Vol.95,pp5419-5431(1991) [Non-Patent Document 4] Yuriko Aoki, “Project Research Content,” [online], Internet<ttp: / / aoki.cube.Kyushu-.ac.jp / text / contents / JST_project / JST_content_new.html> [Retrieved August 31, 2004] [Overview of the Initiative] [Problems that the invention aims to solve]

[0009] Incidentally, if the interactions between atoms in a molecule can be eliminated, it becomes possible to investigate the influence of these interactions on the molecular properties, and thus design molecular structures with desired properties. To do this, it is necessary to determine the set of orbitals based on naturally bonded orbitals localized for each atom in the molecule. In molecular orbitals obtained by the ELG method, regionally localized molecular orbitals in the frozen region and regionally localized molecular orbitals in the active region are obtained at the end of the sequential calculation, but although they are localized, some of the regionally localized molecular orbitals in the frozen region extend into the active region, so it is not possible to determine the set of orbitals based on naturally bonded orbitals localized for each atom in the molecule.

[0010] This invention was made in view of the above circumstances, and its purpose is to provide a molecular orbital calculation device and molecular orbital calculation program that can determine the set of natural bond orbitals and base orbitals localized for each atom in a molecule. [Means for solving the problem]

[0011] As a result of various studies, the inventors have found that the above objective can be achieved by the present invention as described below. That is, a molecular orbital calculation device according to one aspect of the present invention is a computer-based device for determining the electronic state of a molecule, comprising: a storage unit that stores structural data of the molecule to be calculated; a first-region localized molecular orbital of the orthogonal atomic orbital basis of the frozen region of the ELG method and a second-region localized molecular orbital of the orthogonal atomic orbital basis of the active region of the ELG method in the molecule to be calculated; and cut information indicating the cut position between atoms whose interactions to be cut in the active region; an NBO conversion processing unit that calculates the Fock matrix of the natural bond orbital basis based on the second-region localized molecular orbital of the orthogonal atomic orbital basis of the active region; and a function that calculates the Fock matrix obtained by the NBO conversion processing unit. The system comprises a first electron density processing unit that determines the electron density of the active region based on the Fock matrix after cut correction by performing a predetermined cut process and a predetermined two-electron integral correction process, and a second electron density processing unit that determines the final electron density of the active region by performing a self-consistent field method using the electron density obtained by the first electron density processing unit as an initial value, wherein the cut process is a process of replacing the one-electron integral and the two-electron integral of the kinetic energy integral and the nuclear-electron attractive energy integral, respectively, corresponding to the cut information, with zero, and the two-electron integral correction process is a process of determining the two-electron integral of the active region based on the atomic orbitals of the frozen region.

[0012] Another embodiment of the present invention is a molecular orbital calculation program that causes a computer to function as the molecular orbital calculation device described above. [Effects of the Invention]

[0013] The molecular orbital calculation device and molecular orbital calculation program according to the present invention obtain the Fock matrix of the natural bond orbital basis in the active region, and perform cut and correction processing. Therefore, it is possible to obtain a cut-corrected Fock matrix that takes into account the influence of the frozen region, and thus it is possible to determine the set of orbitals of the natural bond orbital basis that are localized for each atom in the molecule. [Brief explanation of the drawing]

[0014] [Figure 1] This is a block diagram showing the configuration of a molecular orbital calculation device in an embodiment. [Figure 2] This diagram schematically illustrates molecular orbitals to explain the molecular orbitals in each computational process. [Figure 3] This diagram schematically shows the Fock matrix of the molecule being operated on. [Figure 4] This flowchart shows the operation of the molecular orbital calculation device. [Modes for carrying out the invention]

[0015] Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. In each figure, components denoted by the same reference numerals are identified as identical components, and their descriptions are omitted where appropriate. In this specification, general reference numerals are used without subscripts, while individual components are indicated by subscripts.

[0016] The molecular orbital calculation device in this embodiment is a computer-based device for determining the electronic state of a molecule. This molecular orbital calculation device comprises a storage unit, an NBO processing unit, a first electron density processing unit, and a second electron density processing unit. The storage unit stores structural data of the molecule to be calculated and the first region localized molecular orbital C(A) of the orthogonal atomic orbital basis of the frozen region of the ELG method in the molecule to be calculated. OAO RLMO and the second-region localized molecular orbital C(B+C) of the orthogonal atomic orbital basis of the active region of the ELG method. OAO LCMO The NBO processing unit stores cut information indicating the cut position (B:C) between atoms whose interaction is to be cut in the active region. OAO LCMO Based on this, the Fock matrix F of the natural bond orbital basis NBO NBOThe first electron density processing unit obtains the Fock matrix F obtained in the NBO processing unit. NBO NBO The Fock matrix F' after cut correction is obtained by performing a predetermined cut process and a predetermined two-electron integral correction process on the Fock matrix F'. NBO NBO Based on this, the electron density D of the active region OAO The second electron density processing unit determines the electron density D obtained by the first electron density processing unit. OAO By performing the self-consistent field method with the initial value, the final electron density D of the active region is achieved. OAO The cut process is performed to obtain the one-electron integral H of the kinetic energy integral and the nuclear-electron attractive energy integral corresponding to the cut information. rs Core (T rs and V rs ) and two-electron integrals<rs|**> Coulomb and<r*|*s> Exchange , <**|rs> Coulomb and<*s|r*> Exchange This process replaces each of them with 0. The two-electron integral correction process is performed based on the atomic orbitals of the frozen region and the two-electron integral of the active region.<rs|tu> This is the process for determining the molecular orbital. Below, we will explain in more detail such a molecular orbital calculation device and the molecular orbital calculation program implemented therein.

[0017] Figure 1 is a block diagram showing the configuration of the molecular orbital calculation device in the embodiment. Figure 2 is a schematic diagram illustrating molecular orbitals to explain the molecular orbitals in each calculation process. Figure 2A is a schematic diagram of each molecular orbital in the frozen region and active region of the molecule to be calculated. Figure 2B is a schematic diagram showing the molecular orbitals in the active region represented by the orbitals of each atom. Figure 2C is a schematic diagram illustrating the correction of the active region by the frozen region. Figure 3 is a schematic diagram showing the Fock matrix of the molecule to be calculated.

[0018] The molecular orbital calculation device D in this embodiment includes, for example, a calculation processing unit 1, an input unit 2, an output unit 3, an interface unit (IF unit) 4, and a storage unit 5, as shown in Figure 1.

[0019] The input unit 2 is connected to the arithmetic processing unit 1 and is a device that inputs various data necessary for operating the molecular orbital calculation device D to the molecular orbital calculation device D, such as various commands such as commands to instruct the start of calculation, structural data of the molecule to be calculated, and region-localized molecular orbitals and cut information of the ELG method for the molecule to be calculated. For example, the input unit 2 is a keyboard, mouse, or multiple input switches to which predetermined functions are assigned. The output unit 3 is connected to the arithmetic processing unit 1 and is a device that outputs commands, data, and calculation results input from the input unit 2 according to the control of the arithmetic processing unit 1. For example, the output unit 3 is a display device such as a CRT display, LCD (liquid crystal display device), or organic EL display, or a printing device such as a printer.

[0020] The input unit 2 and output unit 3 may be configured as touch panels. In this configuration, the input unit 2 is a position input device that detects and inputs the operating position, such as a resistive or capacitive touch panel, and the output unit 3 is a display device. In this touch panel, a position input device is provided on the display surface of the display device, and one or more candidate input contents that can be input to the display device are displayed. When the user touches the display position that displays the input content they want to input, the position input device detects that position, and the display content displayed at the detected position is input to the molecular orbital calculation device D as the user's operation input. With such a touch panel, the user can easily understand the input operation intuitively, thus providing a user-friendly molecular orbital calculation device D.

[0021] The IF unit 4 is connected to the arithmetic processing unit 1 and, under the control of the arithmetic processing unit 1, is a circuit that inputs and outputs data to and from external devices, for example. Examples include an RS-232C serial communication interface circuit, an interface circuit using the Bluetooth® standard, and an interface circuit using the USB standard. Alternatively, the IF unit 4 may be a communication interface circuit that sends and receives communication signals to and from external devices, such as a data communication card or a communication interface circuit conforming to the IEEE 802.11 standard.

[0022] The memory unit 5 is connected to the arithmetic processing unit 1 and is a circuit that stores various predetermined programs and various predetermined data in accordance with the control of the arithmetic processing unit 1.

[0023] The various predetermined programs mentioned above include, for example, a control processing program, which includes, for example, a control program, an NBO processing program, a first electron density processing program, and a second electron density processing program. The control program controls each part 2 to 5 of the molecular orbital calculation device D according to the function of each part. The NBO processing program controls the second region localized molecular orbital (B+C) of the orthogonal atomic orbital basis in the active region. OAO LCMO Based on this, the Fock matrix F of the natural bond orbital basis NBO NBO This is a program to obtain the Fock matrix F obtained in the NBO processing program. NBO NBO The Fock matrix F' after cut correction is obtained by performing a predetermined cut process and a predetermined two-electron integral correction process on the Fock matrix F'. NBO NBO Based on this, the electron density D of the active region OAO This is a program to obtain the electron density D obtained by the first electron density processing program. OAO By performing the self-consistent field method with the initial value, the final electron density D of the active region is achieved. OAOThis is a program to find the value of LCMO. LCMO stands for Localized Canonical Molecular Orbital.

[0024] The various predetermined data mentioned above include, for example, structural data of the molecule to be calculated, and the first region localized molecular orbital C(A) of the orthogonal atomic orbital basis of the frozen region of the ELG method in the molecule to be calculated. OAO RLMO and the second-region localized molecular orbital C(B+C) of the orthogonal atomic orbital basis of the active region of the ELG method. OAO LCMO This includes data necessary for executing each of these programs, such as cut information, various calculation results during the calculation process, and the final calculation result.

[0025] Such a storage unit 5 may include, for example, a non-volatile memory element such as ROM (Read Only Memory) or a rewritable non-volatile memory element such as EEPROM (Electrically Erasable Programmable Read Only Memory). Furthermore, the storage unit 5 includes RAM (Random Access Memory) which serves as the working memory of the arithmetic processing unit 1, storing data generated during the execution of the predetermined program. The storage unit 5 may also be configured to include a hard disk drive or solid-state drive (SSD) with a relatively large storage capacity.

[0026] The memory unit 5 includes a structure data information storage unit 51 that stores structure data information representing the structure data of the molecule to be calculated, and the first region localized molecular orbital C(A) of the orthogonal atomic orbital basis of the frozen region of the ELG method in the molecule to be calculated. OAO RLMO and the second-region localized molecular orbital C(B+C) of the orthogonal atomic orbital basis of the active region of the ELG method. OAO LCMO The system functionally includes a molecular orbital information storage unit 52 that stores molecular orbital information, and a cut information storage unit 53 that stores cut information indicating the cut position (B:C) between atoms whose interaction is to be cut in the active region.

[0027] For the molecule to be analyzed, a coordinate system is determined, and based on this coordinate system, the coordinates of each atom in the molecule to be analyzed are determined, thereby generating the structural data of the molecule to be analyzed. For example, if there are nine atoms from the first to the ninth in the active region, and the interaction between the sixth and seventh atoms is cut, the cut position is between the sixth and seventh atoms, and the coordinate of the sixth atom is 6 and the coordinate of the seventh atom is 7, then the cut information is represented by enclosing a predefined code representing the cut position (e.g., -, / , :, etc.) at each coordinate of each atom, for example, "6:7".

[0028] The molecules to be calculated are not particularly limited as long as they are composed of multiple atoms. The state of the molecules to be calculated (e.g., solid, liquid, gas, etc.) is also not particularly limited. The molecules to be calculated may be, for example, ceramics, glass, metals, polymers, etc. Two molecules may be treated as a single molecule to be calculated, and the interaction between specific atoms in each molecule may be calculated. For example, two water molecules may be treated as a single molecule to be calculated, a metal and a molecule attached to the metal surface may be treated as a single molecule to be calculated, and nucleic acids or proteins and small molecules interacting by van der Waals forces, hydrogen bonds, ionic bonds, etc. may be treated as a single molecule to be calculated. One molecule and one atom may be treated as a single molecule to be calculated, and the interaction between the molecule and the atom may be calculated.

[0029] These structural data, first and second region-localized molecular orbitals, and cut positions are pre-input, for example, from the input unit 2, and stored in the structural data information storage unit 51, molecular orbital information storage unit 52, and cut information storage unit 53. Alternatively, for example, these structural data, first and second region-localized molecular orbitals are stored (recorded) on a storage medium such as a USB memory or SD card (registered trademark), or a recording medium such as a CD-R (Compact Disc Recordable) or DVD-R (Digital Versatile Disc Recordable), input to the molecular orbital calculation device D via the IF unit 4, and pre-stored in the structural data information storage unit 51 and molecular orbital information storage unit 52, while the cut positions are pre-input, for example, from the input unit 2, and stored in the cut information storage unit 53. Alternatively, for example, these structural data and first and second region-localized molecular orbitals are downloaded from the management server that manages them to the molecular orbital calculation device D via the IF unit 4 and stored in advance in the structural data information storage unit 51 and the molecular orbital information storage unit 52. The cut positions are input in advance, for example, from the input unit 2 and stored in the cut information storage unit 53. The cut positions may be input from the input unit 2 and stored in the cut information storage unit 53 each time the cut position is changed and the electron density is calculated.

[0030] The arithmetic processing unit 1 is a circuit that controls each of the parts 2 to 5 of the molecular orbital calculation device D according to the function of each part, in order to determine the molecular orbitals of the target molecule. The arithmetic processing unit 1 is configured, for example, with a CPU (Central Processing Unit) and its peripheral circuits. When the control processing program is executed, the control unit 11, the NBO conversion processing unit 12, the first electron density processing unit 13, and the second electron density processing unit 14 are functionally configured in the arithmetic processing unit 1.

[0031] The control unit 11 controls each of the molecular orbital calculation device D parts 2 to 5 according to the function of each part, and is responsible for the overall control of the molecular orbital calculation device D.

[0032] The NBO processing unit 12 determines the Fock matrix F of the natural bond orbital basis based on the second-region localized molecular orbital C(B+C) of the orthogonal atomic orbital basis in the active region. OAO LCMO Specifically, taking the Fock matrix F of the orthogonal atomic orbital basis in the active region as F OAO OAO , and diagonalizing the Fock matrix F RLMO RLMO with the region-localized molecular orbital in the active region as the basis, if the diagonal matrix with the eigenvalues (local orbital energies) as the diagonal terms is E, then the following equation 1 holds.

[0033] More specifically, taking the Fock matrix F of the orthogonal atomic orbital basis in the active region as F OAO OAO , and diagonalizing the Fock matrix F RLMO RLMO with the region-localized molecular orbital in the active region as the basis, if the diagonal matrix with the eigenvalues (local orbital energies) as the diagonal terms is E, then the following equation 1 holds. OAO OAO Taking the Fock matrix F of the orthogonal atomic orbital basis in the active region as F OAO OAO , and diagonalizing the Fock matrix F RLMO RLMO with the region-localized molecular orbital in the active region as the basis, if the diagonal matrix with the eigenvalues (local orbital energies) as the diagonal terms is E, then the following equation 1 holds. RLMO RLMO If the eigenvalues (local orbital energies) obtained by diagonalizing the Fock matrix F RLMO RLMO with the region-localized molecular orbital in the active region as the basis are used as the diagonal terms of the diagonal matrix E, then the following equation 1 holds. Equation 1; C OAO LCMO F OAO OAO C LCMO OAO = E

[0034] Taking the transformation matrix for converting atomic orbitals to natural bond orbitals as T and the identity matrix as I, if this transformation matrix T is a unitary matrix, then the following equation 2 holds, equation 1 can be transformed into equation 3, and using equation 2, it can be further transformed into equation 4. Equation 2; T NBO OAO T OAO <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ T in this equation 4 OAO NBO† F OAO OAO T NBO OAO This is the Fock matrix F of the natural bond orbital basis. NBO NBO Therefore, T OAO NBO† F OAO OAO T NBO OAO By performing the calculation, the Fock matrix F of the natural bond orbital basis is obtained. NBO NBO The following is required: A transformation matrix T that converts orthogonal atomic orbital basis to natural bond basis. OAO NBO This can be determined by known, conventional methods (e.g., JP Foster and F. Weinhold, "Natural Hybrid Orbitals," J. Am. Chem. Soc. 1980, 102, 7211-7218). Fock matrix F OAO OAO This is the first-region localized molecular orbital C of the atomic orbital basis of the frozen region in the target molecule, calculated by the ELG method. AO RLMO and the second-region localized molecular orbital C of the atomic orbital base of the active region. AO LCMO It is required when seeking.

[0036] As a result, the Fock matrix F of the orthogonal atomic orbital basis spanning the entire active region shown in Figure 2A OAO OAO This is the Fock matrix F of the natural bonding orbital basis for each atom, as shown in Figure 2B. NBO NBO This is required.

[0037] The first electron density processing unit 13 processes the Fock matrix F obtained by the NBO processing unit 12. NBO NBO The Fock matrix F' after cut correction is obtained by performing a predetermined cut process and a predetermined two-electron integral correction process on the Fock matrix F'. NBO NBO Based on this, the electron density D of the active regionOAO This is what we are looking for.

[0038] The aforementioned cut process involves the one-electron integral H of the kinetic energy integral and the nuclear-electron attractive energy integral corresponding to the cut information. rs Core (T rs and V rs ) and two-electron integrals<rs|**> Coulomb and<r*|*s> Exchange , <**|rs> Coulomb and<*s|r*> Exchange This process replaces each of them with 0. Note that * is an arbitrary coordinate value of the active region in the structural data of the molecule to be operated on. For example, if there are 9 first to 9 atoms in the active region, as in the example above, * is an integer value from 1 to 9. If the cut information is, for example, "6:7" as described above, then the one-electron integral H 67 Core (T 67 and V 67 ) is set to 0, <67|**> Coulomb and<6*|*7> Exchange It is set to 0, <**|67> Coulomb and<*7|6*> Exchange This is set to 0. Various integral elements, along with their notation, are disclosed, for example, in "Minoru Hirota, 'New Series on Chemistry: Molecular Orbital Method,' Shokabo, first printing April 30, 1999."

[0039] For example, among the Fock matrices F of the molecule to be operated on, schematically shown in Figure 3, AA This becomes the Fock matrix corresponding to the frozen region, F AB F AC F BA F CA This is the part of the interaction between the frozen region and the active region, F BB F BC F CB F CC This is the Fock matrix corresponding to the active region. BC F CBThis cuts out the interaction between region B and region C, so all matrix elements become 0. Therefore, the cut process is effectively F BB F CC In contrast, the cut process (replacement with 0) is performed as described above, and the following two-electron integral correction process is essentially F BB F CC Then, as described later, we perform a process to calculate the two-electron integral.

[0040] The two-electron integral correction process is a process of determining the two-electron integral of the active region based on the atomic orbitals of the frozen region. More specifically, the two-electron integral correction process is a process of determining the two-electron integral of the active region based on the atomic orbitals of the frozen region so that it is not an independent two-electron integral of the active region alone, but rather the correct two-electron integral of the active region as part of the entire system including the frozen region. This is because the two-electron integral consists of atomic orbitals with four indices, for example, the Fock matrix F in the active region whose elements are atomic orbitals μ and ν. μν When calculating this, the summation with respect to other atomic orbitals σ and λ is included via the two-electron integrals (μν|σλ) and (μλ|σν), and by including the atomic orbitals σ and λ that exist in the frozen region in this summation, the correct Fock matrix F is obtained. μν Therefore, the correct Fock matrix F in the entire system in the active region is obtained. μν In order to create the above, corrections by (μν|σλ) and (μλ|σν), which include the atomic orbitals σ and λ of the frozen region, cannot be ignored.

[0041] Furthermore, molecular orbitals are represented as a linear combination of atomic orbitals, and atomic orbitals are inherent in molecular orbitals. Formula 5;F μν =H μν CORE +G μν =H μν CORE +ΣΣD σλ ×(2(μν|σλ)-(μλ|σν)) Here, μ, ν, σ, and λ represent specific elements of orthogonal atomic orbitals (OAO), the first Σ in ΣΣ is an operator that calculates the sum up to n for σ, and the second Σ is an operator that calculates the sum up to n for λ. F μν H is the matrix element of the μ row and ν column in the Fock matrix F, and μν CORE This is the electron core Hamiltonian, and G μν This is the two-electron integral part. In the examples shown in Figures 2 and 3, D σλ This is given by equation 6 below. Formula 6;D σλ =ΣC σi C λi =Σ(C σi (A) + C σi (B))(C λi (A) + C λi (B)) Here, Σ is the operator that calculates the sum of i up to n / 2. σi (A) is a coefficient on the σ of the i-th orbital in region A of the frozen region, and C σi (B) is a coefficient on the σ of the i-th orbital in the B region of the active region, and C λi (A) is a coefficient on the λ of the i-th orbital in region A of the frozen region, and C λi (B) is a coefficient on λ of the i-th orbital in the active region B. As can be seen from equations 5 and 6, even if μ and ν belong to the active region B, the atomic orbital of the frozen orbital is F μν This affects the two-electron integral correction process. For example, when calculating the electron density on r(↑) that belongs to region B, since it is the electron density on the r-th atom, C ri (A) + C ri (B) must be used for the calculation.

[0042] Therefore, in the two-electron integral correction process, the two-electron integral of the active region is calculated according to equations 5 and 6 described above.<rs|tu> This is what is required. For example, the 1x1 matrix element F11 in the corrected Fock matrix corresponding to the active region is given by the following equation 7. Formula 7;F 11 =H 11 CORE +G 11 =H 11 CORE +ΣΣD σλ ×(2(11|σλ)-(1λ|σ1))

[0043] As a result, as shown in Figure 2C, the influence of the frozen region on the active region is taken into account because some of the region-localized molecular orbitals in the frozen region extend into the active region, and the corrected Fock matrix F' takes this influence into account. NBO NBO This is required.

[0044] Fock matrix F' after cut correction NBO NBO Based on this, the electron density D of the active region OAO To obtain this, the first electron density processing unit 13 first calculates the corrected Fock matrix F' NBO NBO Eigenvector B' that diagonalizes the matrix. NBO LCMO We find the eigenvector B' by the following equation 8. NBO LCMO This is required. Formula 8;B' NBO LCMO F" NBO NBO B' LCMO NBO =E' Here, E' is the local eigenvalue after the interaction has been cut in the active region.

[0045] Next, the first electron density processing unit 13 processes the eigenvector B' obtained in this diagonalization process. NBO LCMO and the transformation matrix T that transforms orthogonal atomic orbital basis to natural bond basis. OAO NBO Based on the cut correction, the third-region localized molecular orbital C' of the orthogonal atomic orbital basis in the active region. OAO LCMOTo determine the third-region localized molecular orbital C' of the atomic orbital basis in the active region after cut correction. AO LCMO This can be calculated using equation 9 below. Formula 9;B' NBO LCMO T OAO NBO =C' AO LCMO

[0046] Next, the first electron density processing unit 13 processes the third-region localized molecular orbital C' of the orthogonal atomic orbital basis of the active region after cut correction. OAO LCMO Based on electron density D OAO We will find the electron density D'. OAO If the diagonal occupancy matrix is ​​d, it can be obtained by the following equation 10. Formula 10;C' OAO LCMO dC' LCMO OAO =D' OAO Here, the diagonal occupation matrix d is a diagonal matrix that shows the occupation of electrons in each orbital.

[0047] The second electron density processing unit 14 processes the electron density D obtained by the first electron density processing unit 13. OAO By performing the Self-Contradictory Field (SCF) method with the initial value, the final electron density D of the active region is achieved. OAO This method aims to find the electron density D. The SCF method first obtains a new electron density by diagonalizing the Fock matrix using the initial electron density. Then, it obtains the next new electron density by diagonalizing the Fock matrix using this new electron density as the initial electron density. This process is repeated until the electron density obtained by diagonalizing the Fock matrix approximately matches the electron density obtained by using the initial electron density. Through this procedure, the SCF method solves the F matrix to obtain the final electron density D. AO This is required.

[0048] Then, the control unit 11 processes the final electron density D obtained by the SCF processing unit 19. OAOThe output unit 3 outputs the final electron density D, which is then made recognizable to the user (operator) by the output unit 3. OAO The output is as follows. The control unit 11 then sends the final electron density D” to an external device via the IF unit 4. OAO You may output this.

[0049] These arithmetic processing unit 1, input unit 2, output unit 3, IF unit 4, and storage unit 5 can be configured using, for example, a desktop or notebook computer.

[0050] Next, the operation of this embodiment will be described. Figure 4 is a flowchart showing the operation of the molecular orbital calculation device.

[0051] When the molecular orbital calculation device D with this configuration is powered on, it performs the initialization of each necessary part and starts operating. The calculation processing unit 1 is functionally configured with a control unit 11, an NBO conversion processing unit 12, a first electron density processing unit 13, and a second electron density processing unit 14 through the execution of its control processing program.

[0052] In Figure 4, the molecular orbital calculation device D first uses the NBO processing unit 12 of the calculation processing unit 1 to determine the second-region localized molecular orbital C(B+C) of the orthogonal atomic orbital basis of the active region. OAO LCMO Based on this, the Fock matrix F of the natural bond orbital basis NBO NBO The result is calculated and stored in memory unit 5 (S1).

[0053] Next, the molecular orbital calculation unit D uses the first electron density processing unit 13 of the calculation processing unit 1 to calculate the Fock matrix F obtained in the NBO processing unit 12. NBO NBO The Fock matrix F' after cut correction is obtained by performing a predetermined cut process and a predetermined two-electron integral correction process on the Fock matrix F'. NBO NBO Based on this, the electron density D of the active region OAO The result is calculated and stored in memory unit 5 (S2).

[0054] Next, the molecular orbital calculation device D uses the second electron density processing unit 14 of the calculation processing unit 1 to calculate the electron density D obtained by the first electron density processing unit 13. OAO By performing the Self-Contradictory Field (SCF) method with the initial value, the final electron density D of the active region is achieved. OAO The result is calculated and stored in memory unit 5 (S3).

[0055] Then, the molecular orbital calculation device D, controlled by the control unit 11 of the calculation processing unit 1, calculates the final electron density D" obtained in the process S3. OAO The output unit 3 outputs the final electron density D (S4), and the output unit 3 makes it recognizable to the user (operator). OAO The output is displayed, and this process ends.

[0056] The user compares the electron density before the interaction is cut off with this final electron density D. OAO By comparing this, the effect of interaction cuts on the molecule under calculation can be investigated. The user can, if necessary, adjust this final electron density D OAO Based on this, the charge distribution within the molecule, the dipole moment, the total energy of the system, and the energy gradient used for structural optimization can be determined using known and conventional methods.

[0057] As described above, the molecular orbital calculation device D and the molecular orbital calculation program implemented therein in the embodiment calculate the Fock matrix of the natural bond orbital basis in the active region, and perform cut processing and correction processing. Therefore, it is possible to obtain a Fock matrix after cut correction that takes into account the influence of the frozen region, and thus it is possible to determine the set of natural bond orbital basis orbitals localized for each atom in the molecule.

[0058] To illustrate the present invention, the embodiments have been adequately and fully described above with reference to the drawings. However, those skilled in the art should recognize that it is easy to modify and / or improve upon the embodiments described above. Therefore, unless such modifications or improvements implemented by those skilled in the art fall outside the scope of the claims, such modifications or improvements shall be considered to be included within the scope of the claims. [Industrial applicability]

[0059] This invention relates to a molecular orbital calculation device and molecular orbital calculation program that can determine the set of natural bond orbitals and ground orbitals localized for each atom in a molecule, and the final electron density D OAO Based on this, the charge distribution within the molecule, the dipole moment, the total energy of the system, and the energy gradient used for structural optimization can be determined using known and conventional methods.

[0060] Therefore, the present invention can contribute to the establishment of guidelines for the development of new optical, electrical, and magnetic functions by clarifying the fundamental physical properties (dielectric constant, refractive index, band structure, magnetism, etc.) of organic electronics and photonic materials and devices, nonlinear optical glasses, and heteronanostructures, which are expected to be important players in the next-generation information industry, and can provide guidelines for the development of next-generation materials.

[0061] This invention can serve as a guideline for drug discovery and development in the pharmaceutical field by elucidating and screening interactions between nucleic acids, proteins, and small molecules. By creating a database of the electronic states of various polymers and nanostructures, and the functions designed based on them, this invention can provide valuable information to researchers engaged in materials design and synthesis. By creating a database of amino acid sequence structures, DNA / RNA base sequences, and electronic state information obtained through this invention, it becomes possible to perform so-called molecular-level data mining, which involves extracting specific factors from sequences and information with high accuracy.

[0062] Machine learning generally requires large datasets for accurate predictions, but actual experimental data alone is often insufficient in terms of both quality and quantity. However, by using the present invention, it becomes possible to generate a large amount of high-quality sample data under various conditions, making it suitable for use in materials informatics, including the application of artificial intelligence (AI).

[0063] Therefore, the present invention has high potential for industrial application. [Explanation of Symbols]

[0064] D Molecular orbital calculation device 1. Processing Unit 2 Input section 3. Output section 4. Interface section (IF section) 5 Storage section 11 Control Unit 12 NBO Processing Unit 13. First Electron Density Processing Unit 14. Second Electron Density Processing Unit 51 Structure data information storage unit 52 Molecular orbital information storage unit 53 Cut Information Storage Unit

Claims

1. A molecular orbital calculation device, configured using a computer, for determining the electronic state of molecules, A storage unit that stores structural data of the molecule to be calculated, the first region localized molecular orbital of the orthogonal atomic orbital base of the frozen region of the ELG method and the second region localized molecular orbital of the orthogonal atomic orbital base of the active region of the ELG method in the molecule to be calculated, and cut information indicating the cut position between atoms whose interactions to be cut in the active region, An NBO processing unit that determines the Fock matrix of the natural bond orbital basis based on the second-region localized molecular orbitals of the orthogonal atomic orbital basis of the active region, A first electron density processing unit determines the electron density of the active region based on the Fock matrix after cut correction by performing a predetermined cut process and a predetermined two-electron integral correction process on the Fock matrix obtained in the NBO processing unit, The system comprises a second electron density processing unit that determines the final electron density of the active region by performing a self-consistent field method using the electron density obtained by the first electron density processing unit as an initial value, The aforementioned cut process is a process that replaces the one-electron integral and the two-electron integral of the kinetic energy integral and the nuclear-electron attractive energy integral, respectively, corresponding to the cut information, with zero. The aforementioned two-electron integral correction process is a process that determines the two-electron integral of the active region based on the atomic orbitals of the frozen region. Molecular orbital calculation device.

2. A molecular orbital calculation program for causing a computer to function as a molecular orbital calculation device according to claim 1.

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