Active space determination program, active space determination method, and information processing device.

Abstract

The goal is to automate the determination of the active space, which is useful for quantum chemical calculations. [Solution] The active space determination program obtains occupancy data, which includes data showing the time-series changes in the number of electrons occupied in each of multiple molecular orbitals. Using the occupancy data as input, the program calculates the solution to a mathematical optimization model formulated with constraints that keep the sum of the number of electrons occupied in multiple molecular orbitals constant, and an objective function that gives a relatively higher evaluation to combinations of molecular orbitals whose time-series changes in the number of electrons occupied are negatively correlated with combinations whose time-series changes in the number of electrons occupied when selecting a subset from multiple molecular orbitals to be used in quantum chemical calculations, compared to combinations whose time-series changes in the number of electrons occupied are positively correlated. The program then has the computer execute the calculation and output the result.

Description

[Technical Field]

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

[0002] Molecular orbital theory is known as one of the approximation methods for quantum chemical calculations. In molecular orbital theory, the electron orbitals that extend throughout the entire molecule, so-called molecular orbitals, are approximately constructed by the linear combination of the electron orbitals of each atom, so-called atomic orbitals.

[0003] For example, the HF (Hartree-Fock) method allows us to determine the wave function and orbital energy of molecular orbitals using a successive approximation method. In the HF model, electrons are accommodated in orbitals in order of increasing orbital energy.

[0004] Of these, the orbital with the highest energy occupied by electrons is called the HOMO (Highest Occupied Molecular Orbital), while the empty orbital with the lowest energy is called the LUMO (Lowest Unoccupied Molecular Orbital).

[0005] In molecular orbital theory, to reduce computational complexity, instead of using the entire set of molecular orbitals in optimization methods such as variational calculus, a subset of molecular orbitals, known as the "active space," is sometimes specified for variational optimization.

[0006] One known method for specifying such active spaces is the "HOMO-m / LUMO+n type," which specifies m orbitals in descending order from the HOMO and n orbitals in ascending order from the LUMO. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Application Laid-Open No. 2003-012567 [Patent Document 2] International Publication No. 2022 / 097298 [Patent Document 3] Specification of US Patent Application Publication No. 2023 / 0377693 [Summary of the Invention] [Problems to be Solved by the Invention]

[0008] However, there are no clear rules for determining the above-mentioned active space, so it is left to the user's subjectivity. For this reason, the above-mentioned designation of the active space may not always be appropriate in terms of the accuracy and computational cost of quantum chemical calculations.

[0009] In one aspect, an object of the present invention is to provide an active space determination program, an active space determination method, and an information processing apparatus that can automate the determination of an active space useful for quantum chemical calculations. [Means for Solving the Problems]

[0010] An active space determination program according to one aspect acquires occupancy data including data indicating the time-series change of the occupancy number of electrons in each of a plurality of molecular orbitals, and uses the occupancy data as an input to make the sum of the occupancy numbers of electrons in the plurality of molecular orbitals constant. Calculate the solution of a mathematical optimization model in which a constraint condition and an objective function that gives a relatively high evaluation to a combination of molecular orbitals having a positive correlation in the time-series change of the occupancy number of electrons are formulated for the selection of a subset used for quantum chemical calculations from among the plurality of molecular orbitals, and output the result of the calculation, causing a computer to execute the process. [Effects of the Invention]

[0011] According to one embodiment, automation of the determination of an active space useful for quantum chemical calculations can be realized. [Brief Description of the Drawings]

[0012] [Figure 1] Figure 1 is a block diagram showing an example of the functional configuration of a server device. [Figure 2] Figure 2 is a schematic diagram illustrating an example of a molecular orbital. [Figure 3] Figure 3 is a schematic diagram illustrating an example of an active space. [Figure 4] Figure 4 is a flowchart showing the procedure for generating occupancy data. [Figure 5] Figure 5 is a flowchart showing the procedure for determining the active space. [Figure 6] Figure 6 shows an example of a hardware configuration. [Modes for carrying out the invention]

[0013] Hereinafter, embodiments of the active space determination program, active space determination method, and information processing apparatus relating to this disclosure will be described with reference to the attached drawings. It should be noted that these embodiments represent only one example or aspect, and such examples do not limit the structure, operation, function, properties, characteristics, methods, and applications relating to this disclosure. Furthermore, each embodiment can be appropriately combined as long as the processing content is not contradictory.

[0014] <Example 1> Figure 1 is a block diagram illustrating an example of the functional configuration of the server device 10. Figure 1 illustrates a server device 10 that provides an active space determination function to automate the determination of the active space, which is useful for quantum chemical calculations.

[0015] <Explanation of Terms> Before describing the example of the functional configuration of the server device 10 shown in Figure 1, we will first explain some of the terms related to the above-mentioned active space determination function in the field of quantum chemistry.

[0016] (1)Molecular orbital method In the field of quantum chemistry, solving the Schrödinger equation inevitably becomes a many-body problem because the objects of interest are various compounds. Therefore, since finding an exact solution is impractical in some aspects, various approximation methods are introduced. Molecular orbital theory is one such system of approximation methods and is one of the fundamental concepts underlying current quantum chemical calculations.

[0017] In molecular orbital theory, the electron orbitals that extend throughout the entire molecule (molecular orbitals) are approximately constructed by the linear combination of the electron orbitals of each atom (atomic orbitals). In the most basic HF method, the wave function of the molecular orbital (φ i ) and orbital energy (ε i This can be determined using a successive approximation method. Note that "i" may refer to the index of the molecular orbital.

[0018] Figure 2 is a schematic diagram illustrating an example of a molecular orbital. For example, Figure 2 shows eight molecular orbitals i=1 to 8 corresponding to orbital energies (ε1) to (ε8) as an example. As shown in Figure 2, electrons are arranged in order of increasing orbital energy in each of the eight molecular orbitals i=1 to 8. Up to two electrons can be accommodated in each molecular orbital. In this case, the spin state when two electrons are present is limited to antiparallel by the Pauli exclusion ratio.

[0019] (2) Number of occupants The number of electrons in each molecular orbital is called the "occupation number." In the HF method model, the occupation number can be an integer value of 0, 1, or 2, and in the case of spin orbitals, it can be an integer value of 0 or 1. However, in post-HF models such as the CCSD (Coupled Cluster Singles and Doubles) method, a single molecular orbital can take a real value from 0 to 2, and in the case of spin orbitals, it can take a real value from 0 to 1.

[0020] (3) HOMO and LUMO In the HF model, electrons are accommodated in orbitals in order of increasing orbital energy. The orbital with the highest energy among those occupied by electrons is called the highest occupied orbital, or "HOMO." On the other hand, the empty orbital with the lowest energy is called the lowest unoccupied orbital, or "LUMO."

[0021] (4)Active space In molecular orbital theory, the expected values ​​of physical quantities such as orbital energy can be calculated using optimization techniques such as variational calculations. Strictly speaking, all molecular orbitals can be targeted for optimization, but often, due to computational cost considerations, only a subset of orbitals is selected. This selected subset of molecular orbitals is called the "active space."

[0022] Figure 3 is a schematic diagram illustrating an example of an active space. Similar to Figure 2, Figure 3 shows molecular orbitals corresponding to orbital energies (ε1) to (ε8). Furthermore, in Figure 3, the molecular orbitals corresponding to the active space are distinguished by hatching among the eight molecular orbitals.

[0023] As shown in Figure 3, of the eight molecular orbitals i=1 to i=8, electrons are located in the five molecular orbitals i=1 to i=5. Of these, the molecular orbital i=5, which has the highest orbital energy ε5, becomes the HOMO. On the other hand, of the three molecular orbitals i=6 to i=8, which do not have electrons, the one with the lowest orbital energy ε6 becomes the LUMO.

[0024] For example, in the example shown in Figure 3, the active space is defined as a subset of four molecular orbitals, i=4 to i=7, which is the range obtained by combining one molecular orbital in descending order from the HOMO (i=4) and one molecular orbital in ascending order from the LUMO (i=7).

[0025] <One aspect of the problem> As explained in the background technology section above, there are no clear rules for determining the active space, so it is left to the user's discretion. For this reason, the specification of the active space may not always be appropriate in terms of the accuracy and computational load of quantum chemical calculations.

[0026] In other words, the user is left to decide which molecular orbitals, arranged in descending order from the HOMO, have a significant impact on the accuracy of quantum chemical calculations, and which molecular orbitals, arranged in ascending order from the LUMO, also have a significant impact on the accuracy of quantum chemical calculations.

[0027] However, due to constraints such as computational resources and computation time, the acceptable range of (m,n) can only be determined empirically, and even experts find it difficult to determine which molecular orbitals, obtained through HF calculations, have a significant impact on the accuracy of quantum chemical calculations.

[0028] For example, even if experts use various information about molecular orbitals obtained from tools that visualize molecular orbitals or from HF calculations to predict interactions between molecular orbitals, it is difficult to determine the influence that individual molecular orbitals have on quantum chemical calculations.

[0029] Active spaces specified under such subjective user criteria may not always be appropriate in terms of the accuracy and computational complexity of quantum chemical calculations.

[0030] <One aspect of a problem-solving approach> Therefore, in this embodiment, in order to realize the automation of determining the active space which is useful for quantum chemical calculations, the following problem-solving approach is adopted. That is, the approach is to determine the active space by applying a quadratic 0-1 integer programming to the pre-convergence data of the molecular orbital method.

[0031] Thus, since the selection of the active space targeted in this embodiment belongs to a type of combinatorial optimization problem, we will explain it by giving an example of applying a 0-1 integer quadratic program, which is widely used as a means of solving combinatorial optimization problems, as merely one example of a mathematical optimization model.

[0032] <Formalization of mathematical optimization models> For example, in this embodiment, a mathematical optimization model is formulated based on a constraint that the sum of electron occupations (total number of electrons) is constant, and an objective function that highly values ​​the selection of orbitals in which the time-series change of occupations is negatively correlated when selecting a subset from all orbitals.

[0033] In such mathematical optimization models, the input may include occupation data that includes the time series of the optimization process of the occupation vectors corresponding to the occupation numbers of each of the multiple molecular orbitals.

[0034] As merely an example, the occupation data mentioned above may be pre-convergence data obtained during the process of variational optimization in molecular orbital methods. This is because variational calculations have energy minimization as their objective function, and even during convergence, they inherently contain characteristic changes that align with that objective. While variational calculations are used as an example here, optimization may also be applied to calculations other than variational calculations. Therefore, the term "variational calculations, etc." may be used to include variational calculations and similar calculations used for optimization.

[0035] In other words, for low-energy occupied orbitals and high-energy unoccupied orbitals, the occupation number is unlikely to change from 2 or 0. On the other hand, orbitals closer to the HOMO / LUMO boundary have similar energy values, resulting in frequent changes in occupation numbers and thus temporal variations in occupation numbers.

[0036] For example, data points x = (x1, x2, ..., x p Let's assume a scenario where the occupation numbers of p orbitals are arranged in the row direction of the occupation vector, and a sequence of n data points obtained from pre-convergence data of molecular orbital method is arranged in the column direction of the occupation vector.

[0037] For the matrix \(X\in\mathbb{R}\) corresponding to such occupancy data n×p it is expressed as shown in the following formula (1). Furthermore, in the following formula (2), an example in which numerical values are assigned to each element of the following formula (1) is given. For example, in the elements of the rows of the matrix \(X\), the occupancy numbers are arranged in order from the orbitals with high energy. As shown in the following formula (2), in the occupied orbitals with low energy, the occupancy number does not fluctuate near 0, and in the unoccupied orbitals with high energy, the occupancy number does not fluctuate near 2. On the other hand, it is clear that the occupancy number fluctuates in the orbitals close to the HOMO / LUMO boundary.

[0038]

Number

Number

[0039] As each element of the matrix \(X\), assuming a molecular orbital that can store two electrons in one orbital, the occupancy number takes real values from 0 to 2. On the other hand, assuming a spin orbital in which a spin state is added to the molecular orbital, since only one electron can be stored, the occupancy number takes real values from 0 to 1.

[0040] Also, when regarding the above occupancy data as a random variable \(X\) i , \(i = 1, 2, \cdots, p\), then \(X\) i takes the value of \(x\) 1i , \(x\) 2i , \(\cdots\), \(x\) ni .

[0041] The variance of such a random variable \(X\) i is defined by the following formula (3), and the covariance of the random variable \(X\) i and the random variable \(X\) j is defined by the following formula (4). "E" in these formulas (3) and (4) refers to the expected value. Also, \(\mu(X\) i ) in formula (4) is \(X\) iThis refers to the average value, and in equation (4), μ(X j ) is X j This refers to the average value. Note that "i" and "j" refer to the orbital index.

[0042]

number

number

[0043] One aspect of the convergence process of occupation data is that while occupation numbers for low-energy occupied orbits and high-energy unoccupied orbits are unlikely to change from 2 or 0, orbits near HOMO / LUMO experience frequent changes in occupation numbers, resulting in a certain degree of variability.

[0044] By utilizing these statistical characteristics, this embodiment formulates a mathematical optimization model for determining the orbital to be selected for the active space.

[0045] Another aspect of occupation data is that its sum takes a theoretically invariant value as the total number of electrons in the molecule. Specifically, the total number of electrons N in the molecule e The relationship shown in equation (5) below satisfies the random variable X. i The condition that the sum remains constant means that the variance of the sum is statistically zero. Expressed in quadratic form, this is given by equation (6) below.

[0046]

number

number

[0047] Here, "1 p " is a p-dimensional column vector (1,1,···,1) where all elements are 1. "T" is the transpose symbol. "S" is the occupation number X.i This is the variance-covariance matrix for i=1, 2, ..., p, and is expressed by equation (7) below.

[0048]

number

[0049] Furthermore, the variance-covariance matrix S of the occupation number can be separated into a matrix V containing variance terms corresponding to the diagonal elements and a matrix C containing covariance terms corresponding to elements other than the diagonal elements, and there is a relationship S = V + C between them. When these matrices V and C are explicitly shown, we get equations (8) and (9) below.

[0050]

number

number

[0051] Here, the occupation number X in variational optimization, etc. i The properties of orbitals can be divided into low-energy occupied orbitals and high-energy unoccupied orbitals, which hardly change, and orbitals near HOMO / LUMO, which change rapidly.

[0052] Of these, the latter change occurs due to the inflow and outflow of electrons between orbitals, and the covariance σ corresponds to the two orbitals: the orbital in which electrons flow in and the orbital in which electrons flow out. ij Since it has a negative correlation, it takes a large negative value in absolute value. Therefore, this type of orbital pair is covariance σ ij It can be reasonably assumed that this is preferred over pairs of orbitals with positive correlation to be selected for the active space. In other words, covariance σ ij Pairs of orbitals with a large negative absolute value may be preferentially selected for the active space.

[0053] However, since electron exchange can occur in many-to-many relationships rather than one-to-one relationships, the selection of orbitals becomes a combinatorial optimization problem and can be treated as a type of integer programming problem. Specifically, the 0-1 integer programming problem when the number of orbitals to be selected is limited to k can be formulated as shown in equation (10) below.

[0054]

number

[0055] In equation (10) above, "C" represents the previously mentioned matrix of covariance terms. "b" is a p-dimensional 0-1 column vector, where an element value of 1 indicates that the orbital is included in the activation space, and an element value of 0 indicates that the orbital is not included in the activation space. For example, if b=(0,0,1,1,0), it indicates that the 3rd and 4th orbitals are selected for the activation space.

[0056] Thus, the evaluation function of the mathematical optimization model shown in equation (10) above reduces to a minimization problem that gives a high evaluation to the selection of molecular orbital combinations in which the covariance between pairs of electron occupations is a large negative value.

[0057] In addition, it is also possible to formulate this as a maximization problem based on an idea similar to the mathematical optimization model shown in equation (10) above.

[0058] That is, from the above equation (6) and S=V+C, we get "1 p T C1 p = -1 p T V1 p It is clear that this is the case, but the evaluation function of equation (10) above is 1 on the left side p This is the form in which is replaced by the binary variable vector b. For this reason, the minimization problem shown in equation (10) above can be considered to be almost equivalent to the maximization problem shown in equation (11) below.

[0059]

number

[0060] Note that "1 p T C1 p = -1 p T V1 p The relationship " " is self-evident, but for any b it is not necessarily true that "b p T Cb p =-b p T Vb p The relationship '' is not necessarily satisfied. For this reason, the mathematical optimization model shown in equation (10) and the mathematical optimization model shown in equation (11) above do not necessarily give the same optimal solution.

[0061] Thus, the evaluation function of the mathematical optimization model shown in equation (11) above reduces to a minimization problem that gives a high evaluation to the selection of molecular orbitals with a large variance in electron occupation.

[0062] In addition, by combining equations (10) and (11) above, the 0-1 integer programming problem shown in equations (12) and (13) below can be further formulated.

[0063]

number

number

[0064] For example, the mathematical optimization model shown in equation (12) above is simply a combination of equations (10) and (11) above as a maximization problem, and the matrix V-matrix C corresponds to the covariance term of the variance-covariance matrix S with a negative sign.

[0065] On the other hand, the mathematical optimization model shown in equation (13) above has an occupation number X corresponding to the random variable. iThis is a problem of minimizing the variance of the sum of i=1,2,···,p, but due to the properties of the variance, the value of the evaluation function takes a non-negative value for any b, and in particular b=1 p In the sense that this is the most natural formulation, it is the optimal value when there are no equality constraints (the evaluation value is 0 from equation (6) above).

[0066] However, in cases where the equality constraint of equation (13) above exists, it is possible to satisfy the equality constraint by selecting only orbitals where the number of occupants hardly changes and both the variance and covariance are close to 0. For this reason, when using equation (13) above, it is also possible to set a specific threshold and exclude indices corresponding to such orbitals, such as low-energy occupied orbitals or high-energy empty orbitals, from the optimization target in advance.

[0067] Under the above formulation, the active space determination function according to this embodiment takes the above-mentioned occupancy data as input and calculates at least one solution from the mathematical optimization models shown in equations (10) to (13) above.

[0068] As a result, the active space determination function in this embodiment makes it possible to include molecular orbitals in the active space that experience frequent changes in occupancy numbers, in other words, molecular orbitals that have a significant impact on the accuracy of quantum chemical calculations.

[0069] One aspect of this is that selecting molecular orbitals that have a significant impact on the accuracy of quantum chemical calculations as active spaces will obviously improve calculation accuracy. Furthermore, even if the number of molecular orbitals designated as active spaces is reduced due to constraints such as computational resources and computation time, it is also obvious that selecting molecular orbitals that have a significant impact on the accuracy of quantum chemical calculations as active spaces will suppress the decrease in calculation accuracy.

[0070] Therefore, the active space determination function according to this embodiment enables the automation of active space determination, which contributes to quantum chemical calculations in various aspects such as calculation accuracy, computational resources, and calculation time. By providing information on the active space in this way, it is possible to achieve a good balance between the accuracy and time required for quantum chemical calculations in molecular orbital methods, even without advanced expertise in quantum chemical calculations or proficiency in quantum chemical calculation software. Thus, automation of active space determination is possible while eliminating reliance on individual expertise.

[0071] <Overall Structure> Figure 1 shows, as just one example of a use case, an example in which the server device 10 provides the above-mentioned active space determination function based on the occupation data obtained during the process of variational calculations and other quantum chemical calculations performed by the client terminal 30.

[0072] The server device 10 is an example of an information processing device that provides the above-described active space determination function. For example, the server device 10 can be implemented as a SaaS (Software as a Service) type application. In this case, the above-described active space determination function may be provided as a cloud service. In addition, the server device 10 does not prevent the above-described active space determination function from being provided on-premises.

[0073] Client terminal 30 is an example of a computer that receives the above-described active space determination function. Users of such an active space determination function may be anyone involved in performing quantum chemical calculations using molecular orbital methods. For example, this may include employees of manufacturers of chemical products or pharmaceuticals, or experts such as developers.

[0074] <Configuration of client terminal 30> Next, an example of the functional configuration of the client terminal 30 according to this embodiment will be described. Figure 1 schematically shows the blocks related to the functions related to the function of generating the number of occupied devices that the client terminal 30 has.

[0075] As shown in Figure 1, the client terminal 30 includes a reception unit 31, a quantum chemistry calculation unit 33, and an output unit 35. Note that Figure 1 only shows a selection of functional units related to the function corresponding to the occupation number data generation function described above, and the client terminal 30 may also be equipped with functional units other than those shown.

[0076] The reception unit 31 is a processing unit that receives various requests. For example, the reception unit 31 can receive a request to perform a quantum chemical calculation via a user interface (not shown).

[0077] When receiving such a request, the reception unit 31 can accept input of "compound data" that represents the three-dimensional structure of the molecule targeted for quantum chemical calculation. For example, the compound data may include the types of atoms that make up the compound and the XYZ coordinates of the atoms. Furthermore, it may accept input of "specified conditions" to be used when executing the quantum chemical calculation, such as the number of iterations and the active space.

[0078] The quantum chemistry calculation unit 33 is a processing unit that performs quantum chemistry calculations. In one embodiment, the quantum chemistry calculation unit 33 can generate the above-mentioned occupancy data by executing software that realizes quantum chemistry calculations according to the above-mentioned compound data and the above-mentioned specified conditions. Such quantum chemistry calculation software may be open source or any existing software regardless of the vendor.

[0079] Here, the quantum chemical calculation performed by the quantum chemical calculation unit 33 may be distinguished from the quantum chemical calculation performed after the determination of the active space according to the specification of the active space, for the following reasons, and the algorithms and parameters used in the two may be different.

[0080] One aspect of this is that the quantum chemical calculations performed by the quantum chemical calculation unit 33 do not need to be iterated until the optimization, such as variational calculations in molecular orbital methods, converges. For this reason, as one of the specified conditions above, the number of iterations for variational calculations can be set to any number greater than or equal to 1 iteration.

[0081] Another aspect is that the quantum chemical calculations performed by the quantum chemical calculation unit 33 only need to have a calculation accuracy sufficient to calculate orbital energies. From this perspective, one of the specified conditions above may be an algorithm that is faster than the quantum chemical calculations performed after the determination of the active space. For example, the active space to be applied to the VQE (Variational Quantum Eigensolver) method can be obtained from the calculation process of a post-HF model such as a faster CCSD method.

[0082] Furthermore, in use cases where the computational load for all molecular orbitals is large due to the size of the compound or other factors, it may not be possible to perform even one iteration of variational calculations, etc., as this would be a balance with the available computational resources. In this case, one of the specified conditions mentioned above is that the active space can be specified as HOMO-m / LUMO+n type. In addition, by accepting the specification of domain partitioning, such as DMET (Density Matrix Embedding Theory), it is also possible to obtain the results of one iteration of variational calculations, etc.

[0083] The output unit 35 is a functional unit that outputs various types of information. One aspect of this is that the output unit 35 can output the occupied data obtained as a result of the quantum chemical calculation performed by the quantum chemical calculation unit 33 to the acquisition unit 11 of the server device 10.

[0084] <Configuration of Server Device 10> Next, an example of the functional configuration of the server device 10 according to this embodiment will be described. Figure 1 schematically shows the blocks related to the functions related to the active space determination function of the server device 10.

[0085] As shown in Figure 1, the server device 10 includes an acquisition unit 11, a calculation unit 13, and an output unit 15. Note that Figure 1 only shows a selection of functional units related to the function corresponding to the active space determination function described above, and the server device 10 may also be equipped with functional units other than those shown.

[0086] The acquisition unit 11 is a processing unit that acquires the above-mentioned occupancy data. In one embodiment, the acquisition unit 11 can acquire the above-mentioned occupancy data from the execution results of quantum chemical calculations performed by the quantum chemical calculation unit 33 of the client terminal 30. The acquisition of such occupancy data may be performed on demand, or it may be performed automatically in cooperation with the quantum chemical calculation unit 33 of the client terminal 30.

[0087] The calculation unit 13 is a processing unit that calculates the solution of a mathematical optimization model. In one embodiment, the calculation unit 13 takes occupation data as input and calculates the solution of at least one of the mathematical optimization models shown in equations (10) to (13) above. The optimization problems formulated in these mathematical optimization models can be solved by executing software called a mathematical programming solver. The solver used for solving here is not limited to a specific type, and any solver can be applied, from general-purpose solvers to high-performance solvers, such as high-speed or high-precision solvers. Furthermore, among equations (10) to (13) above, equation (11) is a special case in that the selection of orbits corresponds one-to-one with the selection of the variance term, and does not need to be solved as a combinatorial optimization problem. That is, the problem can be solved by selecting the indices of a specified number of orbits in descending order of variance value, without having to solve it as an integer quadratic program. Furthermore, transforming a 0-1 integer quadratic programming problem into a form where the constraints are included in the evaluation function results in a problem known as QUBO (Quadratic Unconstrained Binary Optimization), which can be solved using quantum annealing techniques.

[0088] Note that equations (10) to (13) above impose equality constraints, but inequality constraints as shown in equation (14) below may also be used. Also, let b be a binary variable vector b = (b1, b2, ...b p ) T ∈[0,1] p It is also possible to approximate the activation space by relaxing the solution to a continuous variable vector like (where [] is a closed interval) and selecting the indices of the k orbitals in descending order of their values ​​from the result.

[0089]

number

[0090] The output unit 15 is a processing unit that performs output control to the client terminal 30. As an example, the output unit 15 can output to the client terminal 30 as active space information a list of indexes of k molecular orbitals obtained as a result of calculations by the calculation unit 13, for example, as a solution to a mathematical optimization model. In this case, if multiple mathematical optimization models from the mathematical optimization models shown in equations (10) to (13) above are used in the calculation, various ensemble methods, such as majority voting, can be applied to the solutions of the multiple mathematical optimization models.

[0091] When such active space information is output from the server device 10 to the client terminal 30, the client terminal 30 can set the active space information as one of the specified conditions for the actual quantum chemistry calculation performed by the quantum chemistry calculation unit 33, and cause the quantum chemistry calculation unit 33 to perform the actual quantum chemistry calculation, such as variational optimization based on the VQE method.

[0092] <Processing flow> Next, the processing flow performed by each device in this embodiment will be described. Here, we will first describe the (1) occupancy count data generation process performed by the client terminal 30, and then the (2) active space determination process performed by the server device 10.

[0093] (1) Generation process of occupancy count data Figure 4 is a flowchart showing the process for generating occupancy data. This process can be started, as an example, when a request to perform a quantum chemical calculation is received by the reception unit 31.

[0094] As shown in Figure 4, the quantum chemistry calculation unit 33 reads the compound data entered when the above request is received, and also reads the specified conditions that specify the number of iterations for variational calculations, etc., and the active space (steps S101 and S102). Subsequently, the quantum chemistry calculation unit 33 sets the initial state of the quantum chemistry calculation (step S103).

[0095] Subsequently, the quantum chemistry calculation unit 33 executes loop processing 1, repeating step S104 below a number of times corresponding to the number of iterations N included in the specified conditions read in step S102. That is, the quantum chemistry calculation unit 33 performs the nth variational optimization, etc. (step S104).

[0096] As this loop process 1 is repeated, a data matrix X is obtained as the occupation data, which consists of a time series of n points in an occupation vector whose elements include the occupation numbers of p molecular orbitals.

[0097] Subsequently, the output unit 35 outputs the occupied data obtained in loop processing 1 to the server device 10 (step S105), and the process ends.

[0098] (2) Active space determination process Figure 5 is a flowchart showing the procedure for determining the active space. This process can be started, as an example, when the above-mentioned occupancy data is obtained from the client terminal 30.

[0099] As shown in Figure 5, the calculation unit 13 reads the data matrix X of the total number of occupancies acquired by the acquisition unit 11 (step S301). Subsequently, the calculation unit 13 calculates the variance-covariance matrix S of the occupancies from the data matrix X (step S302).

[0100] Then, the acquisition unit 11 accepts the specification of the number of orbitals k to be selected from all molecular orbitals as a subset corresponding to the active space (step S303).

[0101] Then, the calculation unit 13 takes the occupancy-covariance matrix S calculated in step S302 and the number of orbitals k specified in step S303 as input and calculates one or more solutions from the above equations (10) to (13) (step S304).

[0102] Subsequently, the output unit 15 outputs a list of indexes of k molecular orbitals obtained as a result of the calculation in step S304, for example as a solution to a mathematical optimization model, to the client terminal 30 as active space information (step S305), and terminates the process.

[0103] <One aspect of the effect> As described above, the server device 10 in this embodiment takes time-series data of the number of occupancies of each orbital in the optimization process as input, keeps the sum of the occupancies constant, and calculates a solution to a mathematical model that highly values ​​orbital selection where the change in the number of occupancies has a negative correlation when selecting an active space from all orbitals.

[0104] Therefore, the server device 10 according to this embodiment enables the automation of the determination of the active space, which contributes to quantum chemical calculations in various aspects such as calculation accuracy, computational resources, and calculation time. By providing information on the active space in this way, it is possible to balance the accuracy and time required for quantum chemical calculations in molecular orbital methods, even without advanced expertise in quantum chemical calculations or proficiency in quantum chemical calculation software. Thus, it is possible to automate the determination of the active space while eliminating reliance on individual expertise.

[0105] <Example 2> Now, although we have described Example 1 of this disclosure, various applications are possible, and furthermore, it may be implemented in various different forms other than Example 1 described above.

[0106] <Exhibiting creative abilities> The details described in Example 1 above, such as the types and parameters of the algorithms used for quantum chemical calculations or mathematical programming solvers, are merely examples and can be modified. Furthermore, the flowchart described in Example 1 can also be modified in terms of processing order, provided it is consistent with the original design.

[0107] <System> The processing procedures, control procedures, specific names, and various data and parameters shown in the above documents and drawings may be changed at will unless otherwise specified. For example, one or more of the acquisition unit 11, calculation unit 13, and output unit 15 of the server device 10 may be configured as separate devices.

[0108] Furthermore, the components of each illustrated device are functionally conceptual and do not necessarily need to be physically configured as shown. In other words, the specific forms of distribution and integration of each device are not limited to those shown. That is, all or part of them can be functionally or physically distributed and integrated in any units according to various loads and usage conditions. Note that each configuration may also be a physical configuration.

[0109] For example, in the above embodiment 1, the generation of the occupied data is shown to be performed on the client terminal 30, but the server device 10 can also perform the generation of the occupied data. Furthermore, in the above embodiment 1, the server device 10 outputs the active space information to the client terminal 30, but the server device 10 may also perform quantum chemical calculations based on the active space information.

[0110] Furthermore, each processing function performed by each device may be implemented, in whole or in part, by a CPU (Central Processing Unit) and a program executed by that CPU, or by wired logic hardware.

[0111] <Hardware> Next, we will describe the hardware configuration examples of the computers listed in Example 1 and Example 2. Figure 6 is a diagram showing the hardware configuration example. As shown in Figure 6, the server device 10 has a communication device 10a, a storage device 10b, memory 10c, and a processor 10d. Note that the parts shown in Figure 6 may be interconnected by a bus or the like.

[0112] The communication device 10a is a network interface card, etc. The storage device 10b is a storage device such as an HDD (Hard Disk Drive) or SSD (Solid State Drive). For example, the storage device 10b stores programs and databases that operate the functions shown in Figure 1.

[0113] The processor 10d runs a process that performs the functions described in Figure 1 by reading a program that performs the same processing as the processing unit shown in Figure 1 from the storage device 10b or the like and loading it into memory 10c.

[0114] Such a process implements functions similar to those of the processing unit in the server device 10. For example, the processor 10d reads a program having functions similar to those of the acquisition unit 11, the calculation unit 13, and the output unit 15 from the storage device 10b, etc. Then, the processor 10d executes a process that performs the same processing as the acquisition unit 11, the calculation unit 13, and the output unit 15, etc.

[0115] Thus, the server device 10 operates as an information processing device that executes the active space determination method by reading and executing a program. Furthermore, the server device 10 can also achieve the same functionality as in Embodiment 1 by reading the program from a recording medium using a media reader and executing the read program. Note that the program in Embodiment 2 is not limited to being executed by the server device 10. For example, the functionality of this disclosure can be similarly applied when another computer or server executes the program, or when they collaborate to execute the program.

[0116] The above program can be distributed via a network such as the Internet. Furthermore, the program can be recorded on any storage medium and executed by reading it from the medium by a computer. For example, the storage medium can be a hard disk, flexible disk (FD), CD-ROM, MO (Magneto-Optical disk), DVD (Digital Versatile Disc), etc.

[0117] With respect to embodiments including those described above, the following additional information is disclosed.

[0118] (Note 1) Obtain occupation data that includes data showing the time-series change in the number of electrons occupied by each of multiple molecular orbitals. Using the aforementioned occupancy data as input, the solution to a mathematical optimization model is calculated, which is formulated with the constraint that the sum of electron occupancy in the multiple molecular orbitals remains constant, and an objective function that, when selecting a subset from the multiple molecular orbitals to be used in quantum chemical calculations, gives a relatively higher evaluation to the selection of molecular orbital combinations in which the time-series change of electron occupancy has a negative correlation, compared to molecular orbital combinations in which the time-series change of electron occupancy has a positive correlation. Output the result of the above calculation. An active space determination program characterized by having a computer perform the processing.

[0119] (Note 2) The active space determination program described in Note 1, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of molecular orbital combinations in which the covariance between pairs of electron occupations is a large negative value.

[0120] (Note 3) The mathematical optimization model is characterized in that an objective function is formulated that gives a high evaluation to the selection of molecular orbitals with a large variance in the number of electrons occupied, as described in Note 1.

[0121] (Note 4) The active space determination program described in Note 1, characterized in that the occupation data is obtained by iterative optimization calculations in molecular orbital method.

[0122] (Note 5) The active space determination program according to Note 4, characterized in that the occupation data is pre-convergence data obtained during the iterative calculation process.

[0123] (Note 6) Obtain occupation data that includes data showing the time-series change in the number of electrons occupied by each of the multiple molecular orbitals, Using the aforementioned occupancy data as input, the solution to a mathematical optimization model is calculated, which is formulated with the constraint that the sum of electron occupancy in the multiple molecular orbitals remains constant, and an objective function that, when selecting a subset from the multiple molecular orbitals to be used in quantum chemical calculations, gives a relatively higher evaluation to the selection of molecular orbital combinations in which the time-series change of electron occupancy has a negative correlation, compared to molecular orbital combinations in which the time-series change of electron occupancy has a positive correlation. Output the result of the above calculation. A method for determining the active space, characterized in that the processing is performed by a computer.

[0124] (Note 7) The method for determining the active space described in Note 6, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of combinations of molecular orbitals in which the covariance between pairs of electron occupations is a large negative value.

[0125] (Note 8) The method for determining the active space described in Note 6, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of molecular orbitals with a large variance in the number of electrons occupied.

[0126] (Note 9) The method for determining the active space according to Note 6, characterized in that the occupation data is obtained by iterative optimization calculations in the molecular orbital method.

[0127] (Note 10) The method for determining the active space according to Note 9, characterized in that the occupation data is pre-convergence data obtained in the process of the iterative calculation.

[0128] (Note 11) Obtain occupation data that includes data showing the time-series change in the number of electrons occupied by each of the multiple molecular orbitals. Using the aforementioned occupancy data as input, the solution to a mathematical optimization model is calculated, which is formulated with the constraint that the sum of electron occupancy in the multiple molecular orbitals remains constant, and an objective function that, when selecting a subset from the multiple molecular orbitals to be used in quantum chemical calculations, gives a relatively higher evaluation to the selection of molecular orbital combinations in which the time-series change of electron occupancy has a negative correlation, compared to molecular orbital combinations in which the time-series change of electron occupancy has a positive correlation. Output the result of the above calculation. An information processing apparatus characterized by having a control unit that performs processing.

[0129] (Note 12) The information processing apparatus according to Note 11, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of molecular orbital combinations in which the covariance between pairs of electron occupations is a large negative value.

[0130] (Note 13) The information processing apparatus according to Note 11, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of molecular orbitals with a large variance in the number of electrons occupied.

[0131] (Note 14) The information processing device according to Note 11, characterized in that the occupation data is obtained by iterative optimization calculations in molecular orbital method.

[0132] (Note 15) The information processing device according to Note 11, characterized in that the occupation data is pre-convergence data obtained in the process of the iterative calculation. [Explanation of symbols]

[0133] 10 Server devices 11 Acquisition Department 13 Arithmetic section 15 Output section 30 client terminals 31 Reception Department 33 Quantum Chemistry Computation Department 35 Output section

Claims

1. We obtain occupancy data that includes data showing the time-series changes in the number of electrons occupied by each of multiple molecular orbitals. Using the aforementioned occupancy data as input, the solution to a mathematical optimization model is calculated, which is formulated with the constraint that the sum of electron occupancy in the multiple molecular orbitals remains constant, and an objective function that, when selecting a subset from the multiple molecular orbitals to be used in quantum chemical calculations, gives a relatively higher evaluation to the selection of molecular orbital combinations in which the time-series change of electron occupancy has a negative correlation, compared to molecular orbital combinations in which the time-series change of electron occupancy has a positive correlation. Output the result of the above calculation. An active space determination program characterized by having a computer perform the processing.

2. The active space determination program according to claim 1, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of molecular orbital combinations in which the covariance between pairs of electron occupations is a large negative value.

3. The active space determination program according to claim 1 or 2, characterized in that the mathematical optimization model formulates an objective function that gives a high evaluation to the selection of molecular orbitals with a large variance in the number of electrons occupied.

4. The active space determination program according to claim 1, characterized in that the aforementioned occupancy data is obtained by iterative optimization calculations in molecular orbital method.

5. The active space determination program according to claim 4, characterized in that the occupation data is pre-convergence data obtained during the iterative calculation process.

6. We obtain occupancy data that includes data showing the time-series changes in the number of electrons occupied by each of multiple molecular orbitals. Using the aforementioned occupancy data as input, the solution to a mathematical optimization model is calculated, which is formulated with the constraint that the sum of electron occupancy in the multiple molecular orbitals remains constant, and an objective function that, when selecting a subset from the multiple molecular orbitals to be used in quantum chemical calculations, gives a relatively higher evaluation to the selection of molecular orbital combinations in which the time-series change of electron occupancy has a negative correlation, compared to molecular orbital combinations in which the time-series change of electron occupancy has a positive correlation. Output the result of the above calculation. A method for determining the active space, characterized in that the processing is performed by a computer.

7. We obtain occupancy data that includes data showing the time-series changes in the number of electrons occupied by each of multiple molecular orbitals. Using the aforementioned occupancy data as input, the solution to a mathematical optimization model is calculated, which is formulated with the constraint that the sum of electron occupancy in the multiple molecular orbitals remains constant, and an objective function that, when selecting a subset from the multiple molecular orbitals to be used in quantum chemical calculations, gives a relatively higher evaluation to the selection of molecular orbital combinations in which the time-series change of electron occupancy has a negative correlation, compared to molecular orbital combinations in which the time-series change of electron occupancy has a positive correlation. Output the result of the above calculation. An information processing apparatus characterized by having a control unit that performs processing.

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