JP4646064B2 - Molecular orbital calculation method and calculation apparatus - Google Patents

Description

  The present invention relates to a molecular simulation calculation, and more particularly to a calculation method and a calculation apparatus using a calculation algorithm of a first principle molecular orbital method.

As a strong demand from society for the current quantum chemistry field,
(1) Elucidation of the chemical reaction mechanism of biological enzymes,
(2) a priori design of molecular functional materials,
The following two points may be mentioned. In both cases, intramolecular and intermolecular electron interactions are closely related to their functionality, so first-principles electronic state calculations that take into account electronic correlation are required for functional analysis and molecular design. It becomes. For qualitative evaluation of functionality, HOMO (highest occupied molecular orbital), LUMO (lowest unoccupied molecular orbital) electronic correlation (ie, non-dynamical correlation) However, since quantitative numerical evaluation must be performed for a priori molecular design, dynamical electron correlation (dynamical excitation such as excitation from inner orbitals to virtual orbitals with high orbital energy) It is necessary to perform high-accuracy calculation that also considers correlation).

  FIG. 1 conceptually shows static electron correlation and dynamic electron correlation. As shown in the figure, the molecular orbitals have lower orbital energies, such as inner core orbitals that are strongly bound to nuclei, HOMO and LUMO, which are considered to be directly involved in the activity of molecules, etc. There are active orbits and virtual orbits with high orbital energy. The static electron correlation represents a phenomenon such as electron transition in or near the active orbit, as indicated by a white arrow in the figure. On the other hand, dynamic electron correlation is a phenomenon such as transition from inner shell orbit to LUMO, transition from HOMO to virtual orbit, and transition from inner orbit to virtual orbit as shown by the black arrow in the figure. Represents.

  It is desired to develop a first-principles molecular orbital method that can cover these static electron correlations and dynamic electron correlations at a low cost in a well-balanced manner and can calculate all physical quantities with high accuracy.

Conventionally, the first-principles molecular orbital calculation method used for general purposes is large,
(1) Wave function theory (WFT),
(2) Density functional theory (DFT)
It can be divided into two.

  Among them, wave function theory is a method of covering electron correlation by wave function expansion, CI (configuration Interaction) method, MCSCF (multiconfiguratin self-consistent-field) method, The CC (coupled-cluster) method, the MP (Moller-Pleset) method, and the like belong to this. In the wave function theory, generally, as the number of expansion terms increases, the accuracy of the description of the electron correlation becomes higher, but at the same time, the calculation cost becomes enormous. Therefore, various ideas have been made within the framework of wave function theory. In particular, in the CI method and the MCSCF method, a method in which all expansions are taken by limiting the active orbit near the valence orbit (Fermi level), that is, the CAS (complete-active-space) CI method and the CASSCF method, As a theory, it is one standard theory as a method capable of almost completely covering static electron correlation while having a relatively low calculation cost. The CASCI method and CASSCF method are collectively referred to as CAS method.

  The calculation of dynamic electron correlation in wave function theory requires excitation to a virtual orbit with a high energy level and higher-order wave function expansion, and for this purpose, it was obtained by CASCI / CASSCF method. MR (multiple arrangement reference) CI methods and MRMP methods have been developed that perform CI or MP operations using a wave function as a reference function. The MRCI method and the MRMP method have a feature that not only static electron correlation but also dynamic electron correlation can be calculated with high accuracy, and physical quantities other than energy can be obtained in the calculation of dynamic electron correlation. However, since the MRCI method and the MRMP method use a large number of terms for calculation and require a calculation amount proportional to the fifth power of the number of electrons N, the calculation cost of these methods is enormous and the application range is also a small molecule. It is limited to. It cannot be desired to apply the MRCI method or the MRMP method to calculations for biological enzymes or molecular functional materials. If the calculation cost is taken into account, it can be said that the wave function theory is not good at describing dynamic electron correlation.

On the other hand, density functional theory is originally based on the Hohenberg-Kohn theorem that energy is given uniquely as a density functional and that the variational principle holds for that functional. It depends. The commonly used KS-DFT method is one possible theoretical form of DFT.
(1) The density is given by the density of a single Slater determinant,
(2) One electron orbit (called the Kohn-Sham orbit) composing the Slater determinant is based on the effective field (exchange correlation potential) reflecting the effect of electron correlation (exchange correlation term). One-electron problem, the solution of the Kohn-Sham equation,
These are two points. Considering N electrons with N as an even number, in the Kohn-Sham orbit, N / 2 orbitals are occupied by two electrons from the lower energy orbit, Tracks with more orbital energy are unoccupied tracks. In wave function theory, this corresponds to Hartree-Fock (HF) approximation, which is a technique that does not consider electron correlation. However, the KS-DFT method reflects the effect of electron correlation through an effective field (exchange correlation potential), and is a low-cost, high-performance electronic state theory that can consider electron correlation without expanding wave functions.

Incorporation of electron correlation in the KS-DFT method is a method of describing an electron correlation term (exchange correlation term) as a functional of local density (and density gradient). It is possible to simulate the short-range interaction of dynamic electron correlation without requiring higher-order wave function expansion or higher-order perturbation expansion. However, in the KS-DFT method, the density search range is limited to a set of densities of a single slater determinant,
(i) Atomic multiplet state,
(ii) molecular diradical dissociation (eg, homolysis),
(iii) It has been pointed out that the Kondo effect of dilute magnetic alloys cannot be described. These (i) to (iii) can be described by the CAS method, and are typical examples of static electron correlation. That is, the KS-DFT method is not good at describing static electron correlation.

As described above, the CAS method captures the static electron correlation almost completely but is not good at the dynamic electron correlation. The KS-DFT method covers the dynamic electron correlation well but is not good at the static electron correlation. And From the characteristics of these two methods, a method combining these two methods (hereinafter referred to as “CAS calculation + DFT correction method”) has been devised. This method is a method in which an energy correction value based on DFT is added to a CAS wave function obtained by the CAS method. At each stage of calculation of the CAS method and DFT correction, static electron correlation, dynamic Each electron correlation is reflected in energy. In addition, unlike the MRCI method and the MRMP method, the calculation amount is almost determined by the number of terms of the wave function expansion of the CAS method, so that the calculation cost can be made relatively small. A problem in the CAS calculation + DFT correction method is that double counting of electronic correlation, that is, electronic correlation is considered twice. For this,
(1) By calculating the orbital energy in k-space and defining the effective density for DFT correction, the correlation energy other than that covered by the CAS method can be calculated without excess or deficiency,
Or
(2) Coulomb term between two electrons of Hamiltonian is divided into contribution to static electron correlation and contribution to dynamic electron correlation using error function, and the former is CAS method (more generally wave function theory) Thus, it is proposed to remove the double count by using the method of covering the latter with the DFT correlation energy term. This proposed method has had some success in molecular system applications.

  However, in this existing CAS calculation + DFT correction method, since DFT correction is performed only on energy, a CAS wave function not subjected to DFT correction is obtained as a solution (wave function). This means that the physical quantity other than energy has no dynamic electron correlation effect. Therefore, the CAS operation + DFT correction method does not give a correct result for a physical quantity other than energy, such as a dipole moment or structure of a molecule.

  As described above, there is currently no known calculation method that is low in calculation cost and can accurately cover both static electron correlation and dynamic electron correlation. If we follow the method of covering static electron correlation with CAS and dynamic electron correlation with DFT, as described in the background section, the problem to be solved is to replace the CAS calculation + DFT correction method with the dynamic calculation. It is to obtain a theoretical form in which dynamic electron correlation is reflected in physical quantities other than energy.

  Therefore, an object of the present invention is to provide a calculation method and a calculation apparatus that are low in calculation cost, can be applied to large-scale molecules, and can accurately cover both static electron correlation and dynamic electron correlation. There is.

For the above purpose, the present inventor proposed a new approach based on density functional theory (DFT), formulated the CAS-DFT method as such an approach, and completed the present invention.

  Although details will be described later, the CAS-DFT method proposed by the present inventors is a method for correctly incorporating dynamic electronic correlation into a wave function obtained by the CAS method. The first-principles molecular orbital calculation algorithm using the CAS-DFT method solves the operation of the self-consistent field (SCF) CASCI method using an iterative method based on an effective field based on density functional theory (DFT). It is. In other words, the method according to the present invention is a new electronic state theory method called DFT using a CAS wave function as a reference system.

Therefore calculation of molecular orbital method of the present invention, the computer is an input stage for receiving an input of the molecular structure and the number of electrons, the computer, on the basis of the input molecular structure and the number of electrons, Casci equation based on the one-electron orbitals The initial value calculation stage to obtain the energy and density matrix used as the initial value by solving the equation , the computer calculates the density from the density matrix , and based on the equation (16) described later, the effective potential based on the density functional theory The potential calculation stage for calculating V ^RC (r) , and the computer calculates the integral correlation potential term and the ab initio CAS Hamiltonian that reflect the residual correlation energy and includes the effective potential V ^RC (r) based on the effective potential. wherein the door, solve the effective CASCI equations represented by below formula (13), the energy and density And CASCI calculation step of obtaining a sequence, computer includes a determination step determines convergence by comparing the energy and density matrix obtained this time and energy and density matrix obtained last time, and the non-convergence at the decision step determines when the computer is potential calculation step by using the time determined energy and the density matrix, and iteratively performing CASCI calculation step and the decision step, if it is determined that the convergence in the determination step, the computer End the calculation.

Computing device of molecular orbital method of the present invention includes an input unit which molecular structure and the number of electrons are entered, on the basis of the input molecular structure and the number of electrons, by solving CASCI equation based on one-electron orbital, the initial value An initial value calculation unit for obtaining an energy and density matrix used as a potential calculation, and a potential calculation for calculating a density from the density matrix and calculating an effective potential V ^RC (r) based on a density functional theory based on the following equation (16) And the integral correlation potential term that reflects the residual correlation energy and includes the effective potential V ^RC (r) based on the effective potential and the ab initio CAS Hamiltonian and is expressed by the following equation (13) A CASCI calculator that solves an effective CASCI equation represented by the following equation (13) to obtain an energy and density matrix, and an energy and density matrix that was previously obtained And a determination unit that determines convergence by comparing the energy and density matrix obtained this time, and a potential calculation unit and CASCI calculation using the energy and density matrix obtained this time when the determination unit determines that convergence has not occurred. And a control unit that terminates the calculation when the determination unit determines that the calculation is converged.

  According to the present invention, the dynamic electron correlation can be correctly taken into the wave function obtained by the CAS method, so that the static electron correlation and the dynamic electron correlation can be correctly covered. It is possible to accurately evaluate the dynamic electron correlation, and to correctly determine the structure and dipole moment in various molecules. Further, the calculation cost is almost the same as that of the conventional CAS method, and the method of the present invention can be applied to a large-scale molecule.

  Table 1 shows a summary of the calculation cost and calculation accuracy of the method of the present invention and the existing first-principle molecular orbital calculation method evaluated in four stages (◎, ○, Δ, ×). ◎ indicates excellent, ○ indicates slightly superior, △ indicates slightly inferior, and × indicates inferior (or impractical).

  As shown in Table 1, according to the method of the present invention, highly accurate calculation (計算) can be performed for all types of electronic correlations at a relatively low cost (◯).

  Next, a preferred embodiment of the present invention will be described. First, the CAS-DFT method newly proposed by the present inventors will be described.

First, it is a feature of the KS-DFT method.
(1) The density is given by the density of a single Slater determinant,
(2) One-electron problem in the slater determinant (called the Kohn-Sham orbit), an one-electron problem with an effective field (exchange correlation potential) reflecting the effect of electron correlation (exchange correlation term), Kohn -Sham equation solution
These two points are rewritten as follows (formulation).

(A1) The density is given by the density of the CAS wave function;
(A2) The CAS wave function is a multi-electron problem, CASCI based on the effective field (correlation potential) reflecting the effect of the remaining electron correlation (correlation term).

Euler's equation in ordinary DFT is that density is ρ (r), DFT universal functional is F ^DFT [ρ (r)], nuclear attractive potential is V _Ne (r), and the number of electrons is constant. If the undetermined multiplier (Lagrange multiplier) under the conditions is μ,

It is. Therefore, in the present invention, the expression (1) is expanded based on the above formulation. As a result, a DFT Euler equation corresponding to the CAS-DFT method according to the present invention is obtained.

Here, F ^CAS-DFT [ρ (r)] is a universal functional in the CAS-DFT method, and instead of the “non-interacting reference system” in the conventional DFT, an “interacting reference system” is introduced. Is to do. E _RC [ρ (r)] is the residual correlation energy,
E _RC [ρ (r)] = F ^DFT [ρ (r)] − F ^CAS-DFT [ρ (r)] (3)
Defined by Here, if E _RC [ρ (r)] can be accurately determined, the equation (2) is equivalent to an accurate DFT Euler equation.

F ^CAS-DFT [ρ (r)] in equation (2) is given by equation (4).

Where Ψ represents the wave function,

Are respectively the kinetic energy term and the electron correlation term that can be covered by the CAS method. Regarding the electron correlation terms that can be covered by the CAS method,

It can be expressed as Here, Σ ^CAS indicates that a summation is obtained for the canonical orbit in the active space in the CAS operation function theory, and ρ ₁ (i, l; σ) and ρ ₂ (i, j, k, l; (σσ ′) is expressed as follows.

c _i σ, c ⁺ _i σ are generation and annihilation operators for the corresponding canonical orbital basis {φ _i σ}. Here, given the minimum energy,

By defining F ^CAS-DFT [ρ (r)] as expressed by equation (4) from the variational principle, the Euler equation (equation ( From 1)), it can be seen that the Euler equation in the CAS-DFT method based on the present invention shown in equation (2) is obtained.

  By the way, the energy in equation (2) is

Can be rewritten as Here, H _core (i, j, σ) is the core Hamiltonian of the (i, j) element, and is expressed by the following equation.

  When the orbit is fixed to the canonical orbit, δρ (r) is

It is represented by Therefore, in the steady state in the real system,

It becomes.

  Here, the effective multi-electron problem is expressed in accordance with (A2) in the above formulation.

It expresses like this. Equation (13) is an effective CASCI equation in the CAS-DFT method. here,

Are integral correlation potential terms reflecting ab initio CAS Hamiltonian and residual correlation energy, respectively.

Holds. V ^eff is used as an operator for taking in the electron correlation. In Expression (14), the second term on the right side is an explicit electron repulsion term in the CASCI method. When the integral correlation potential term is determined so that the solution of Equation (13) satisfies the stationary condition of Equation (2),

Is obtained. However, the effective potential (effective field) V ^RC (r) is the residual correlation energy E _RC [ρ (r)] corresponding to the dynamic electron correlation,

And depends on the electron number density n (ρ). Therefore, the wave function to be obtained in the present embodiment can be obtained by iteratively solving Equation (13) by the self-consistent field (SCF) method.

  Since Equation (13) is formulated to satisfy Equation (2), the solution of Equation (13)

The density ρ (r) is the solution of the Euler equation (equation (2)). As a result, the validity problem is re-formulated from the one-electron problem of the KS-DFT method to the multi-electron problem of the CAS-DFT method. In the present embodiment, it is possible to obtain a wave function that reflects the influence of dynamic electron correlation, which was not obtained by the CAS calculation + DFT correction method. This makes it possible to calculate physical quantities other than energy that reflect the effects of dynamic electron correlation, such as molecular structure and dipole moment.

In the method according to the present embodiment, if E _RC [ρ (r)] is configured as described above, a double counting problem in electronic correlation occurs, equivalent to the case of the existing CAS calculation + DFT correction method. . Therefore, in order to remove double counting, as in the case of the existing CAS calculation + DFT correction method,
(1) By calculating the effective energy density for DFT correction by mapping the orbital energy into k-space, the correlation energy other than that covered by the CAS method can be calculated without excess or deficiency, or
(2) Coulomb term between two electrons of Hamiltonian is divided into contribution to static electron correlation and contribution to dynamic electron correlation using error function, and the former is CAS method (more generally wave function theory) Thus, any of the methods of covering the latter with the DFT correlation energy term can be employed as it is.

By the way, V ^eff (i, j; σ) in equation (14) is

Therefore, from Equation (14), the Hamiltonian in the CAS-DFT method of this embodiment is practically

It is expressed as Therefore, instead of performing the iterative operation based on the equation (13), iterative calculation may be performed using the Hamiltonian of the equation (18).

  Next, a specific calculation procedure using the above-described calculation method will be described. FIG. 2 is a flowchart showing a calculation procedure in the present embodiment.

First, in step 101, calculation conditions such as the molecular structure, the number of electrons, and the threshold of SCF are set. In step 102, the CASCI equation is solved based on one electron orbit such as a canonical orbit, and initial value setting is performed. Calculate initial energy, initial one-electron reduced density matrix. Next, in step 103, the density is calculated from the one-electron contraction density matrix, and in step 104, the effective potential V ^RC (r) is obtained from the equation (16) using the density obtained in step 103. , The effective CASCI equation (formula (13)) is solved using the effective potential obtained in step 104, and in step 106, the energy and one-electron reduced density matrix are calculated from the result of solving the effective CASCI equation. Next, in step 106, the energy and one-electron contraction density matrix calculated in the previous cycle is compared with the energy and one-electron contraction density matrix calculated this time, and the difference between them is set in step 101. Determine if it is below threshold. If it is equal to or less than the threshold value, it is assumed that the iterative calculation has converged, and the calculation is completed. In step 107, the result is output. Return.

  By performing the SCF iterative CASCI calculation as described above, the dynamic electron correlation can be correctly incorporated into the wave function obtained by the CAS method, and the wave function accurately covers the static electron correlation and the dynamic electron correlation. Based on the energy value and the electron density matrix can be calculated.

  FIG. 3 shows a configuration of a computing device that executes the above-described computation. The calculation device 10 includes an input unit 11 for inputting calculation conditions such as a molecular structure, the number of electrons, and an SCF threshold, an initial value calculation unit 12 for calculating an initial value by solving a CASCI equation, and a one-electron contraction density. A potential calculator 13 for calculating the density and effective potential from the matrix; a CASCI calculator 14 for solving the effective CASCI equation (13) using the effective potential; and a storage 15 for storing data and calculation results during the calculation. The comparison unit 16 that compares the energy and one-electron contraction density matrix calculated in the previous cycle with the energy and one-electron contraction density matrix calculated this time, and the calculation result (energy, one-electron contraction density matrix, etc.) An output unit 17 that outputs data and a control unit 18 that controls the entire computing device are provided. In the calculation apparatus 10, the control unit 18 controls the calculation units 12 to 14, the storage unit 15, and the comparison unit 16, so that the processes of steps 101 to 107 described above are performed.

  When the molecular structure, the number of electrons, the SCF threshold value, etc. are input to the input unit 11, the threshold value is set in the comparison unit 16, and the molecular structure, the number of electrons, etc. are stored in the storage unit 15. The process of step 101 is executed. First, the initial value calculation unit 12 solves the CASCI equation based on one electron orbit such as a canonical orbit, based on the molecular structure, the number of electrons, etc. stored in the storage unit 15 as the processing of step 102, An initial energy and an initial one-electron contraction density matrix are calculated and stored in the storage unit 15.

The potential calculation unit 13 calculates the density from the latest one-electron reduced density matrix stored in the storage unit 15 as the processing of steps 103 and 104, and uses the density to calculate the effective potential V from Equation (16). ^RC (r) is obtained, and the effective potential is stored in the storage unit 15. The CASCI calculation unit 14 solves the effective CASCI equation (formula (13)) using the latest effective potential stored in the storage unit 15 as the process of step 105, and from the result, the energy and the one-electron contraction density are calculated. The matrix is calculated and stored in the storage unit 15. The comparison unit 16 refers to the storage unit 15 as the process of step 106, compares the energy and one-electron contraction density matrix calculated in the previous cycle with the energy and one-electron contraction density matrix calculated this time, It is determined whether or not the difference is equal to or less than a set threshold value. Based on the determination result, the control unit 18 restarts the potential calculation unit 13 and the CASCI calculation unit 14 in order to re-execute the processing from step 103, or stores it in the storage unit 15 as processing in step 107. On the other hand, control is performed so that the output unit 17 outputs the result.

  The computing device described above can also be realized by causing a computer program such as a personal computer or a supercomputer to read the computer program for realizing it and executing the program. The program causes the computer to execute the SCF repetitive CASCI operation based on the CAS-DFT method described above, and is read into the computer by a recording medium such as a magnetic tape or a CD-ROM or via a network. In such a computer, the read program is stored in the hard disk device of the computer, and the program stored in the hard disk device is executed by the CPU of the computer to function as a computing device.

FIG. 4 is a graph showing a comparison between the calculation result obtained by the method according to the present invention (CAS-DFT method) and the calculation result obtained by an existing calculation method for the potential surface of the fluorine molecule (F ₂ ). The horizontal axis indicates the interatomic distance of fluorine atoms, and the vertical axis indicates the total energy. In the figure, large square marks indicate actual measurement values. Among the existing methods, the CAS-PT2 method is an attempt to incorporate dynamic electronic correlation as a second-order perturbation term in the existing CAS method.

  As can be seen from the figure, in the conventional CAS method, the dynamic electron correlation is not taken in, so a result deviating greatly from the actually measured value (total energy about 0.35% larger than the actually measured value) is obtained. Even with the CAS-PT2 method, a total energy of about 0.1% larger than the actually measured value is obtained. On the other hand, according to the method of the present invention, since the dynamic electron correlation is correctly taken in, a result almost coincident with the actually measured value is obtained.

  According to the calculation method and the calculation apparatus of the present invention, accurate molecular orbital calculation that covers static electron correlation and dynamic electron correlation can be performed with low calculation cost. Therefore, by using the present invention, quantitative evaluation can be performed in fields such as elucidation of the chemical reaction mechanism of biological enzymes and a priori design of molecular functional materials. And useful for the design and synthesis of new useful substances. Furthermore, the computing device of the present invention can be used in an ASP (Application Service Provider) specialized in the bioinfomatics field. Such ASPs are equipped with computer resources (hardware and software) that can efficiently process the calculation algorithms according to the present invention, and each customer accesses the ASP's calculation center via the network to obtain the desired The molecular orbital calculation will be executed.

It is a figure explaining a static electron correlation and a dynamic electron correlation. It is a flowchart explaining the process by the calculation method of one Embodiment of this invention. It is a block diagram which shows the structure of the calculation apparatus of one Embodiment of this invention. It is a graph which shows the result of having calculated the potential surface of the fluorine molecule by each of the method based on this invention, and the conventional method.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 Input part 12 Initial value calculation part 13 Potential calculation part 14 CASCI calculation part 15 Storage part 16 Comparison part 17 Output part 18 Control part 101-107 Step

Claims (5)

Computer, and an input stage for receiving an input of the molecular structure and electron number,
An initial value calculation step in which the computer obtains an energy and density matrix to be used as initial values by solving a CASCI equation based on one electron orbital based on the input molecular structure and the number of electrons;
The computer calculates the density from the density matrix , the residual correlation energy corresponding to the dynamic electron correlation is E _RC [ρ (r)], the electron number density is n (r),

A potential calculation stage for calculating an effective potential V ^RC (r) based on density functional theory based on
The computer includes an ab initio CAS Hamiltonian and an integral correlation potential term that reflects the residual correlation energy and includes the effective potential V ^RC (r), respectively.

And then, the wave function and [psi, energy as E ^eff, on the basis of the effective potential V ^RC (r),

A CASCI calculation stage to solve the effective CASCI equation represented by
The computer determines the convergence by comparing the energy and density matrix obtained last time with the energy and density matrix obtained this time;
Has, when it is determined that the non-convergence at the determination step, the computer, the potential calculation step by using the time determined energy and density matrix, and repeating the CASCI calculation step and the decision step The calculation method of the molecular orbital method is executed, and the computer ends the calculation when it is determined that convergence has occurred in the determination step. The calculation method according to claim 1 , wherein the density matrix is a one-electron reduced density matrix. An input unit for the molecular structure and the number of electrons are entered,
An initial value calculation unit for obtaining an energy and density matrix used as initial values by solving a CASCI equation based on one electron orbital based on the input molecular structure and the number of electrons;
The density is calculated from the density matrix , the residual correlation energy corresponding to the dynamic electron correlation is E _RC [ρ (r)], the electron number density is n (r),

A potential calculation unit for calculating an effective potential V ^RC (r) based on density functional theory ,
ab initio CAS Hamiltonian and integral correlation potential term that reflects the residual correlation energy and includes the effective potential V ^RC (r)

And then, the wave function and [psi, energy as E ^eff, on the basis of the effective potential V ^RC (r),

A CASCI calculator that solves the effective CASCI equation represented by
A determination unit that determines convergence by comparing the energy and density matrix obtained last time with the energy and density matrix obtained this time,
When the determination unit determines that convergence has not occurred, the potential calculation unit and the CASCI calculation unit repeat the calculation using the energy and density matrix obtained this time, and the determination unit determines convergence Includes a control unit for terminating the calculation, and
A molecular orbital calculation device. The calculation apparatus according to claim 3 , wherein the density matrix is a one-electron reduced density matrix. Computer
Input means for the molecular structure and the number of electrons are entered,
An initial value calculation means for obtaining an energy and density matrix used as initial values by solving a CASCI equation based on one electron orbital based on the input molecular structure and the number of electrons,
The density is calculated from the density matrix , the residual correlation energy corresponding to the dynamic electron correlation is E _RC [ρ (r)], the electron number density is n (r),

A potential calculation means for calculating an effective potential V ^RC (r) based on density functional theory based on
ab initio CAS Hamiltonian and integral correlation potential term that reflects the residual correlation energy and includes the effective potential V ^RC (r)

And then, the wave function and [psi, energy as E ^eff, on the basis of the effective potential V ^RC (r),

CASCI calculation means for solving the effective CASCI equation represented by
A determination means for determining convergence by comparing the energy and density matrix obtained last time with the energy and density matrix obtained this time,
When the determination means determines that the convergence has not occurred, the potential calculation means and the CASCI calculation means repeat the calculation using the energy and density matrix obtained this time, and the determination means determines that the convergence has occurred. Control means for terminating the calculation,
A program that functions as

Images