JP4729889B2 - Molecular structure optimization system - Google Patents

Description

  The present invention relates to a molecular structure optimization system by parallel processing using a plurality of computers.

  Obtaining a stable molecular structure by simulation is important not only in the nanotechnology field but also in the biotechnology field. For example, there have been many reports on the actual three-dimensional structure of proteins, and pharmaceuticals have been developed based on this three-dimensional structure. In general, molecules have a high probability of adopting structures in the vicinity of energetically stable structures. For this reason, the properties of molecules in stable structures often reflect the properties of the whole molecule. In other words, elucidating the stable structure of a molecule is an effective means of elucidating the function of the molecule. Therefore, simulations for obtaining stable molecular structures are extremely important. However, much time is required to obtain a stable structure of a large molecule (with a large number of atoms) by quantum chemical calculation.

  In general, parallel processing is known as a method for increasing the processing capacity of a computer. In particular, recently, parallel processing by grid computing that enables large-scale computation by linking many personal computers via the Internet has been studied. Grid computing is an attempt to make effective use of personal computers under the circumstances where it can be said that computers around the world are now connected by a network due to the development of LAN environments and WAN environments such as ADSL and optical fiber communications. is there.

  However, there has been no research on parallel processing of molecular structure optimization in quantum chemical calculations. Calculations using shared memory or distributed memory on multi-CPU computers are becoming possible with quantum chemical calculations. However, these are parallel processes in the calculation to obtain molecular orbitals, and there is no example of performing parallel processes for structure optimization calculations.

  In addition, the use of grid computing in simulations in the nanotechnology and biotechnology fields is a developing stage. Examples of usage to date include a completely distributed processing method in which many separate calculations are executed on separate computers and the results are simply collected, and a process-distributed usage method for effectively using a sleeping computer, Most of them provide a simple usage environment for general users. In other words, there are few examples of highly efficient parallel processing of a single calculation. The main reasons are that although network communication is being accelerated, the communication speed is not high enough to be used for complex parallel computing, and the algorithm sufficient to utilize grid computing is immature.

On the other hand, conventional molecular structure optimization is based on an algorithm that is performed sequentially based on the quasi-Newton method, such as the Gaussian 03 program, and cannot be processed in parallel. In the quasi-Newton method, the vector g _k of the first derivative with the coordinates of the energy in the trial structure q _k (where the vector q _k represents the coordinates of the k th trial structure calculated immediately before) and the first derivative Q _{k + 1} = q _k -B _k ^-1 g _k using an approximate Hessian B _k that is updated based on changes (where Hessian means a matrix of second derivative in terms of energy coordinates). The operation of obtaining a new trial structure q _{k + 1} is repeated according to (Equation 1). For this reason, the new trial structure cannot be determined unless the calculation of the old trial structure is completed. That is, this algorithm is not suitable for parallelization.

  By the way, applications of grid computing related to quantum chemistry calculations include quantum chemistry calculation grid methods at the National Institute of Advanced Industrial Science and Technology (Non-patent Document 1 below), and methods for utilizing biomolecules in quantum chemistry calculations at NEC, etc. There exists patent document 2). The former method is intended to provide a wide range of scientists and engineers with an execution environment for large-scale quantum chemical calculations, and is not intended to speed up large-scale calculations. The latter method focuses on the use of QM / MM molecular dynamics. Therefore, there is no application example of grid computing in molecular structure optimization in quantum chemical calculation.

  On the other hand, a structure optimization method using grid computing based on the molecular force field method has been made by Nakashima et al. Of Tsukuba University (Non-patent Document 3 below). However, this method is intended to achieve high speed by optimizing the structure of each of the many conformations using separate computers. That is, this method is not related to structure optimization that seeks to find one most stable structure at high speed. In simulations in the nanotechnology field, it is often the case that only the most stable structure is desired at a high speed, rather than many conformations. This is because, from chemical experience, the most stable structure can often be predicted without calculation.

As described above, there is no precedent for an algorithm that optimizes a stable structure using grid computing.
T. Nishikawa, et al., "Design and implementation of Intelligent Scheduler for Gaussian Portal on Quantum Chemistry Grid", Lecture Notes in Computer Science (LNCS) 2003, 2659, 244. Toshikazu Takada et al., “Quantum chemical calculation of proteins using GRID computing”, Abstracts of the 2003 Annual Conference on Molecular Structures, 1Dp05. Yoshihiro Nakajima et al., “CONFLEX-G: Implementation and Performance Evaluation of Molecular Conformation Search Program on Grid Environment by OmniRPC”, IPSJ Transactions Computing System, 2004, 45, 254.

  An object of the present invention is to provide a molecular structure optimization system capable of elucidating an optimized structure of a target molecule at a higher speed than in the past.

  The present invention is basically based on the knowledge that, by collecting information on the first derivative based on energy coordinates in a large number of trial structures, the Hessian necessary for finding a new trial structure can be obtained accurately and at high speed. . In other words, multiple initial trial structures are generated, and the first derivative calculation is performed in parallel using different computers for each of them. Every time the calculation on one of the computers is completed, the cyan is updated from the calculation result. It is possible to optimize the structure at high speed by repeatedly generating a new trial structure and executing a first derivative calculation for the new trial structure. The conventional structure optimization calculates the first derivative of energy coordinates in a “one” trial structure, updates the cyan from the calculation result, generates a new trial structure, and creates a new trial structure. The calculation of the first derivative was repeated sequentially. Therefore, there is a limit even if parallel processing is performed, but in the system of the present invention, since a plurality of trial structures are obtained and quantum chemical calculations related to them are performed at the same time, a stable structure can be quickly obtained by taking advantage of parallel processing. Can do.

[1] That is, the molecular structure optimization system of the present invention is a molecular structure optimization system including a host computer and a plurality of client computers connected to the host computer. Means for a computer to input information relating to a computation whose structure is to be optimized; means for transmitting information relating to said computation to said plurality of client computers; and means for optimizing the structure in said host computer Means for inputting information relating to the structure of the molecule; means for obtaining a plurality of trial structures from the information relating to the structure of the inputted molecule; and information relating to the plurality of trial structures to the plurality of client computers. Means for sending and each of said clients Means for receiving information on the results of quantum chemistry calculations sent by the computer to the host computer, means for determining whether the structure of the molecules has been optimized from the information on the results of the quantum chemistry calculations, and the structure of the molecules If it is determined that the structure of the molecule has not been optimized, and if it is determined that the structure of the molecule has not been optimized, Means for obtaining a new trial structure from the information on the result of the method, and means for transmitting the information on the new trial structure to the client computer that has transmitted the result of the quantum chemical calculation, Each client computer connected to the host computer is the host computer. Means for inputting information relating to the calculation transmitted from the host computer, means for inputting information relating to the trial structure transmitted from the host computer, and information relating to the trial structure and calculation transmitted from the host computer. , Means for obtaining information on the first derivative of the energy in the trial structure by means of quantum chemical calculation, means for determining whether or not the quantum chemical calculation is completed, and determining that the quantum chemical calculation has been completed Means for transmitting information relating to the results of quantum chemical calculations to the host computer, and inputting information relating to calculations to optimize the structure to the host computer; A computer transmits information about the calculation to the plurality of client computers. Transmitting to the host computer, inputting to the host computer information regarding the structure of the molecule whose structure is to be optimized, and the host computer obtaining a plurality of trial structures from the input information regarding the structure of the molecule A step in which the host computer transmits information about the plurality of trial structures to the plurality of client computers, and a calculation in which each client computer connected to the host computer transmits from the host computer. A step of inputting information, a step of each client computer connected to the host computer inputting information on a trial structure transmitted from the host computer, and a client computer connected to the host computer. A computer using the information on the trial structure and calculation sent from the host computer to obtain information on the first derivative of the energy in the trial structure by coordinates using quantum chemical calculation, and each connected to the host computer The client computer determines whether or not the quantum chemical calculation has been completed, and each client computer connected to the host computer determines that the quantum chemical calculation has been completed. Transmitting information on the host computer, the host computer receiving information on the result of quantum chemical calculation transmitted from the client computer to the host computer, and the host computer calculating the quantum chemical calculation. From the information on the results, the step of judging whether the structure of the molecule has been optimized, and if the host computer judges that the structure of the molecule has been optimized, the quantum chemical calculation is stopped to each client computer. Issuing a command, and if the host computer determines that the structure of the molecule has not been optimized, obtaining a new trial structure from information relating to the result of the quantum chemical calculation, and the new trial structure A molecular structure optimizing system for obtaining a stable structure of a molecule, wherein a stable structure of the molecule is obtained by a process including a step of transmitting information relating to the client computer that has transmitted the result of the quantum chemical calculation.

[2] Further, in a preferred embodiment of the molecular structure optimization system of the present invention, the “host computer” includes all the means included in the client computer, and the host computer functions as one of the plurality of client computers. The molecular structure optimization system according to [1] above.

[3] Further, in a preferred embodiment of the molecular structure optimization system of the present invention, “calculation information” in the “means for the host computer to input information related to the calculation to optimize the structure” is a theoretical level. , Basis functions, and molecular structure optimization system according to any of the above, comprising information on whether to consider spin multiplicity.

[4] Also, a preferred embodiment of the molecular structure optimization system of the present invention is the “information about the structure of the molecule” in the “means for inputting information about the structure of the molecule whose structure is to be optimized to the host computer”. Is a molecular structure optimization system according to any one of the above, which is either information on constituent elements of molecules or information on constituent elements of molecules and their positional relationships.

[5] Further, in a preferred aspect of the molecular structure optimization system of the present invention, the “means for obtaining a plurality of trial structures” is configured based on numerical values set in advance from the inputted information on the structure of the molecule. The molecular structure optimization system according to any one of the above, wherein a plurality of molecular structure candidates in which an intermolecular distance of molecules and an angle between constituent molecules are changed are obtained.

[6] Further, in a preferred aspect of the molecular structure optimization system of the present invention, the “means for obtaining a plurality of trial structures” is the information regarding the inputted molecular structure is information regarding a partial structure of the molecule. In some cases, the initial structure related to the structure of the molecule is obtained from information on the stable structure of the molecule (partial molecule) constituting the molecule registered in advance, and the intermolecular distance between the constituent molecules of the initial structure and the angle formed by the constituent molecules are calculated. The molecular structure optimization system according to any one of the above, wherein a plurality of changed trial structures are obtained.

[7] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is the “quantum chemical calculation” in the “means for receiving information on the result of the quantum chemical calculation transmitted from each client computer to the host computer”. , Quantum chemical calculation, molecular force field calculation, density functional calculation, molecular orbital calculation, molecular calculation using parameters, or a combination of these, the molecular structure optimization according to any of the above System.

[8] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is the above-mentioned “means for judging whether or not the molecular structure is optimized from the information on the result of quantum chemical calculation” by quantum chemical calculation. The molecular structure optimization system according to any one of the above, wherein it is determined whether or not the absolute value of the obtained “first-order differential of energy in the trial structure by coordinates” vector is a certain value or less.

[9] Further, a preferred embodiment of the molecular structure optimization system of the present invention is the “quantum chemistry calculation system” in the “means for judging whether the molecular structure is optimized from the information on the result of the quantum chemistry calculation”. Molecular information optimization system according to any of the above, wherein “information about the result” includes “information about the energy value in the trial structure” and “information about the value of the first derivative of the energy in the trial structure by coordinates” It is.

[10] Also, a preferred embodiment of the molecular structure optimization system of the present invention is that “information about the result of quantum chemical calculation” in the “means for obtaining a new trial structure from information about the result of quantum chemical calculation” is , “Information on the value of the first derivative of the energy in the trial structure by coordinates”, and the “means for obtaining a new trial structure from the information on the result of the quantum chemical calculation” is the “energy in the trial structure” The molecular structure optimization system according to any one of the above, wherein the information on the hessian of the energy in the trial structure is updated based on the "information on the value of the first derivative by coordinates" to obtain a new trial structure It is.

[11] In addition, a preferable aspect of the molecular structure optimization system of the present invention is that “information about the result of quantum chemical calculation” in the “means for obtaining a new trial structure from information about the result of quantum chemical calculation” is , “Information on the value of the first derivative of the energy in the trial structure by coordinates”, and the “means for obtaining a new trial structure from the information on the result of the quantum chemical calculation” is “information on the trial structure” "," Information about the value of the first derivative by coordinates of energy in the structure with the lowest energy including those obtained by other computers "and" Information on the value of the first derivative by coordinates of energy in the trial structure " Based on, the information about the Hessian of the energy in the trial structure is updated, and a new trial structure is obtained. A molecular structure optimization system according to any one of the above.

[12] In addition, a preferable aspect of the molecular structure optimization system of the present invention is that “information about the result of quantum chemical calculation” in the “means for obtaining a new trial structure from information about the result of quantum chemical calculation” is , “Information on the value of the first derivative of the energy in the trial structure by coordinates”, and the “means for obtaining a new trial structure from the information on the result of the quantum chemical calculation” is the “energy in the trial structure” Information on the value of the first derivative by coordinates ”, information on the Hessian of the energy in the trial structure, information on the effective Hessian taking a positive value from the information on the Hessian, information on the trial structure, Information on the effective Hessian and “on the value of the first derivative by coordinates of the energy in the trial structure The molecular structure optimization system according to any one of the above, wherein a new trial structure is obtained from "information".

[13] In addition, a preferable aspect of the molecular structure optimization system of the present invention is that the “information about the result of quantum chemical calculation” in the “means for obtaining a new trial structure from the information about the result of quantum chemical calculation” is , “Information on the value of the first derivative of the energy in the trial structure by coordinates”, and the “means for obtaining a new trial structure from information on the result of quantum chemical calculation” includes the new trial structure, Any one of the above, wherein when the energy of the trial structure calculated immediately before is lowest, the energy is obtained by the equation (I), and when the energy of the trial structure calculated immediately before is not the lowest, the energy is obtained by the equation (II). This is a molecular structure optimization system.

(In equations (I) and (II), the vector q _new represents the coordinates of the new trial structure. The vector q _k represents the coordinates of the trial structure calculated immediately before. The subscript k represents the quantum representing the order in which the chemical calculation has ended. matrices beta _k is .g _k that represent the Hessian at the k-th trial structure, .L ^proj representing a vector for "the energy in the k-th trial structure, first derivative by the coordinate" _{k, r} is one eigenvector randomly selected from a number of eigenvectors orthogonal to the vector −β _k ⁻¹ g _l , scalar C is a scale factor, and vector q _l is calculated immediately before If the energy of the trial structure is not the lowest among all trial structures up to the kth, it represents the coordinate of the trial structure with the lowest energy among all trial structures up to the kth, and the trial structure calculated immediately before Energy is kth Representing all of the cases the lowest among trial structural coordinates of trial structures most in the vicinity of the calculated attempted structure just before in all trials structures in.)

[14] Also, a preferred embodiment of the molecular structure optimization system of the present invention is that the initial value of the effective Hessian (β _k ), that is, β _{1 is used} as a unit matrix or a secondary differential matrix (calculated in advance at a low calculation level). The molecular structure optimization system according to any one of the above, which uses a second-order differential matrix based on the coordinates of the generated energy or a second-order differential matrix based on the energy coordinates calculated in any of the quantum chemical calculations described above. .

[15] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is a provisional hessian (B _k ) represented by any one of the following formulas (III) to (V) as the effective hessian (β _k ): ) Using any one of the above-described molecular structure optimization systems.

(In the formula (III), the bold letter 1 represents a unit matrix, Δq _kl = q _k −q _l , Δg _kl = g _k −g _l , and so on.)

[16] Further, a preferred embodiment of the molecular structure optimization system of the present invention is:
As the effective hessian (β _k ), when any of the provisional hessians (B _k ) described above is a positive value and satisfies the following formula (VI), the provisional hessian is used.
Otherwise, the molecular structure optimization system according to any one of the above, using the following formula (VII). If any two or more provisional hessians are positive and satisfy (VI), the provisional hessian can be selected arbitrarily.

In the above formulas (VI) and (VII), g _m is the first derivative in terms of energy coordinates in the trial structure with the lowest energy among all the trial structures up to the k-th (referred to as the m-th trial structure). Is a vector. The scalar R ^k _max is the search distance limit. ω _k is a scalar that is obtained so that effective Hessian has a positive value and satisfies the relational expression (VIII).

[17] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is any one of the above, wherein any value of 0.0 to 10.0 is used as the initial value of R ^k _max , ie, R ¹ _max . It is a molecular structure optimization system.

[18] Further, a preferred embodiment of the molecular structure optimization system of the present invention is:
As R ^k _max , the immediately preceding trial structure q _k is a structure found using the n th trial structure q _n and the first derivative vector g _n by the energy coordinates and the o th Hessian B _o. , If the energy of the immediately preceding structure q _k is the lowest among the trial structures up to _k , or if the n th trial structure q _n has the lowest energy, use the following formula (IX), otherwise The molecular structure optimization system according to any one of the above, using R ^k _max = R ^k-1 _max .

(In the above equation, E (q _i ) is the energy in the trial structure q _i obtained by quantum chemical calculation.)

[19] Further, a preferred embodiment of the molecular structure optimization system of the present invention is the molecular structure optimization system according to any one of the above, wherein L ^proj _{k, r} satisfies the following formula (X): .

（上記式においてNは，自由度の数を表す。）

(In the above formula, N represents the number of degrees of freedom.)

[20] Further, in a preferred embodiment of the molecular structure optimization system of the present invention, when λ ^proj _{k, r} defined in [17] is λ ^proj _{k, r} ² <0 as the scale factor C, When (λ) is used and λ ^proj _{k, r} ² ≧ 0, the molecular structure optimization system according to any one of the above, using the following formula (XII):

[21] A preferred embodiment of the molecular structure optimization system of the present invention is the molecular structure optimization system according to any one of the above, wherein C = 0 is used as the scale factor C.

[22] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is “primary by coordinates of energy in the trial structure by quantum chemical calculation using the information on the trial structure and calculation transmitted from the host computer. “Coordinates” in “Means for Deriving Information on Differentiation” indicate the relative positional relationship of atoms constituting the molecule, including interatomic distance, connection angle of 3 atoms, and dihedral diagonal of 4 atoms. The molecular structure optimization system according to any one of the above, which is a coordinate.

[23] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is “primary by coordinates of energy in the trial structure by quantum chemical calculation using the information on the trial structure and calculation transmitted from the host computer. In the “means for obtaining information relating to differentiation”, “coordinates” is the molecular structure optimization system according to any one of the above, which is Cartesian coordinates representing the positions of atoms constituting the molecule.

[24] In addition, a preferred embodiment of the molecular structure optimization system of the present invention relates to “first-order differentiation of energy in the trial structure by coordinates using quantum chemical calculation using information on the trial structure transmitted from the host computer. In the “means for obtaining information”, “information on the first derivative of the energy in the trial structure by coordinates” is “information on the value of the first derivative of the energy in the trial structure by coordinates” and “energy in the trial structure” The molecular structure optimization system according to any one of the above, comprising: Here, the first derivative of energy by coordinates represents the gradient of potential energy.

[25] In addition, a preferred embodiment of the molecular structure optimization system of the present invention is “primary by coordinate of energy in the trial structure by quantum chemical calculation using the information on the trial structure and calculation transmitted from the host computer. "Means for obtaining information relating to differentiation" is a quantum chemical calculation based on "information relating to calculation" in the above-mentioned "means for inputting information relating to calculation for which the host computer intends to optimize the structure". The molecular structure optimization system according to any one of the above.

[26] The molecular structure optimization method of the present invention comprises a molecular structure for obtaining a stable structure of a molecule using a molecular structure optimization system comprising a host computer and a plurality of client computers connected to the host computer. An optimization method, the step of inputting information relating to a calculation whose structure is to be optimized to the host computer, the step of the host computer sending information relating to the calculation to the plurality of client computers, A step of inputting information relating to a structure of a molecule whose structure is to be optimized to the host computer, a step of obtaining a plurality of trial structures from the inputted information relating to the structure of the molecule, and the host computer; Information about the plurality of trial structures Transmitting to the client computer, a step in which each client computer connected to the host computer inputs information relating to a calculation transmitted from the host computer, and a client computer connected to the host computer. , Inputting information on the trial structure transmitted from the host computer, and each client computer connected to the host computer uses the information on the trial structure and calculation transmitted from the host computer to Obtaining information on the first derivative of the energy in the trial structure by coordinates, by calculation, and each client computer connected to the host computer performs the quantum chemistry calculation. A step of determining whether or not each of the client computers connected to the host computer determines that the quantum chemical calculation has been completed, and a step of transmitting information relating to the result of the quantum chemical calculation to the host computer. The host computer receives information on the result of the quantum chemical calculation transmitted from the client computer to the host computer, and the host computer optimizes the molecular structure from the information on the result of the quantum chemical calculation. And if the host computer determines that the structure of the molecule has been optimized, the step of issuing a command to each client computer to stop the quantum chemical calculation, and the host computer The structure of is not optimized If it is determined, the step of obtaining a new trial structure from the information on the result of the quantum chemistry calculation and the information on the new trial structure are transmitted to the client computer that has transmitted the result of the quantum chemistry calculation. A molecular structure optimization method including a process.

  According to the present invention, by performing quantum chemical calculation using an algorithm different from the quasi-Newton method, it is possible to perform parallel calculation by a plurality of computers, thereby elucidating the optimized structure of the target molecule faster than before. A molecular structure optimization system can be provided.

1. Molecular structure optimization system The molecular structure optimization system of the present invention is a molecular structure optimization system comprising a host computer and a plurality of client computers connected to the host computer, wherein (A) the host computer is , (A-1) means for inputting information related to the calculation to be optimized by the host computer, and (A-2) means for transmitting the information related to the calculation to the plurality of client computers. (A-3) means for inputting information on the structure of the molecule whose structure is to be optimized to the host computer, and (A-4) a plurality of trials based on the inputted information on the structure of the molecule. Means for determining a structure; and (A-5) information about the plurality of trial structures to the plurality of client computers. Means for transmitting, (A-6) means for receiving information on the result of quantum chemistry calculation transmitted from each client computer to the host computer, and (A-7) information on the result of quantum chemistry calculation , Means to determine whether the molecular structure has been optimized, and (A-8) if it is determined that the molecular structure has been optimized, it instructs each client computer to stop the quantum chemical calculation. And (A-9) means for obtaining a new trial structure from the information on the result of the quantum chemical calculation, and (A-9) 10) means for transmitting information on the new trial structure to the client computer that has transmitted the result of the quantum chemical calculation, and (B) the host computer. Each of the connected client computers has (B-1) means for inputting information related to the calculation transmitted from the host computer, and (B-2) inputs information regarding the trial structure transmitted from the host computer. And (B-3) means for obtaining information relating to the first derivative of the energy of the trial structure by means of quantum chemical calculation using coordinates, using information on the trial structure and calculation transmitted from the host computer. (B-4) means for determining whether or not the quantum chemistry calculation is completed; and (B-5) information regarding the result of the quantum chemistry calculation when it is determined that the quantum chemistry calculation is completed. Means for transmitting to the host computer.

Then, a step (step 1) of inputting information related to the calculation to optimize the structure to the host computer, and a step of transmitting the information related to the calculation to the plurality of client computers (step 2). And a step (step 3) of inputting information on the structure of the molecule whose structure is to be optimized to the host computer, and the host computer obtains a plurality of trial structures from the inputted information on the structure of the molecule. A step of obtaining (step 4), a step in which the host computer transmits information on the plurality of trial structures to the plurality of client computers (step 5), and each client computer connected to the host computer, Total transmitted from the host computer A step of inputting information on the host computer (step 6), a step of each client computer connected to the host computer inputting information on a trial structure transmitted from the host computer (step 7), and a step of Each linked client computer uses the information on the trial structure and calculation transmitted from the host computer to obtain information on the first derivative of the energy in the trial structure by coordinates by quantum chemical calculation (step 8) Each client computer connected to the host computer determines whether the quantum chemical calculation is completed (step 9), and each client computer connected to the host computer includes: When it is determined that the quantum chemistry calculation has been completed, a step (step 10) of transmitting information related to the result of the quantum chemistry calculation to the host computer; and the quantum chemistry transmitted from the host computer to the host computer by the host computer. A step of receiving information on the result of the calculation (step 11), a step of determining whether or not the structure of the molecule is optimized from the information on the result of the quantum chemical calculation (step 12), and the host computer However, if it is determined that the molecular structure has been optimized, a step (step 13) for instructing each client computer to stop the quantum chemical calculation and the host computer optimize the molecular structure. If it is determined that the A step of obtaining a new trial structure from the information obtained (step 14), and a step of sending information on the new trial structure to the client computer that has transmitted the result of the quantum chemical calculation (step 15). The stable structure of the molecule is determined by the process.
(A-1) Means for the host computer to input information related to the calculation whose structure is to be optimized "Information related to the calculation" in "Means for the host computer to input information related to the calculation whose structure is to be optimized""Is information related to the calculation level of quantum chemistry calculations, such as information about whether to consider the theoretical level, basis functions, and spin multiplicity. As this information, what is usually used may be appropriately used when performing quantum chemical calculations. The theoretical levels include HF, UHF, ROHF, MP2, and CCSD (T). The basis functions are STO-3G, 3-21G, 6-31G, 6-31 + G, 6-31 + G ^* , 6-311 + G ^* , cc-pVDZ, aug-cc-pVDZ, etc. It is done. “+” In the basis function is a function added to the whole molecule (diffuse function), and “ ^* ” in the basis function is a function added to the polarization function. These are also known in quantum chemical calculations.
(A-2) The means for transmitting the information related to the calculation to the plurality of client computers is not particularly limited as long as the information related to the calculation can be transmitted to the plurality of client computers. The host computer and each client computer are preferably connected via the Internet or an intranet.
(A-3) “Means for inputting information on the structure of molecules to be optimized into the host computer”
“Information about the structure of a molecule” in “Means for inputting information about the structure of a molecule whose structure is to be optimized to the host computer” is information about the constituent elements of the molecule, or the constituent elements of the molecule and their positional relationships. Any of the information about. When the molecule for which a stable structure is sought is carbon disulfide (CS ₂ ), “information on the constituent elements of the molecule” includes C, S, S, and the like. Also, as “information about the constituent elements of molecules and their positional relations”, information about constituent molecules C, S, S and positional relations S = C = S (the distance between C = S is 1.56 angstroms and S = C = The angle formed by S is 0 degree). In addition, the three-dimensional structure of a molecule such as a protein may be obtained from information obtained by X-ray structural analysis or information obtained by NMR, and the information on the constituent molecule and the three-dimensional structure may be used as “information on the structure of the molecule”. .
(A-4) Means for obtaining a plurality of trial structures from input molecular structure information “Means for obtaining a plurality of trial structures” are based on the input “information about molecular structures” and are used for each client. This is a means for obtaining a trial structure in which a computer (or each client computer and host computer) performs quantum chemical calculations. As a “means for obtaining multiple trial structures”, multiple molecular structures in which the intermolecular distances of the constituent molecules and the angles formed by the constituent molecules are changed from information on the structure of the input molecules based on preset numerical values. That seeks candidates. For example, if the intermolecular distance is shifted by 0.1 angstrom and the intermolecular angle is shifted by 1 degree, S = C = S (the distance between C = S is 1.56 angstrom, and 1.66 angstrom and S = C = S S = C = S (Distance between C = S is 1.56 angstrom and 1.66 angstrom and S = C = S is 1 degree), S = C = S (C = S The distance between them is 1.66 angstroms and the angle formed by S = C = S is 0 degree), S = C = S (the distance between C = S is 1.66 angstroms and the angle formed by S = C = S is 1 degree) , And S = C = S (the distance between C = S is 1.56 angstroms and 1.76 angstroms and the angle formed by S = C = S is 1 degree).

  In the conventional structure optimization, quantum chemical calculations were repeated for one trial structure to optimize the structure. Based on such an algorithm, the processing speed does not improve much even if parallel computation using a plurality of computers is performed. Furthermore, even if the number of computers is increased, the calculation speed does not increase. However, according to the present invention, since different quantum chemical calculations are performed by the respective computers, the structure optimization can be quickly performed by making the best use of the processing speed of the respective computers.

  “Means for obtaining a plurality of trial structures” means that when the information on the structure of the inputted molecule is information on the partial structure of the molecule, the stability of the molecule (partial molecule) constituting the molecule registered in advance. It is preferable to obtain an initial structure relating to the structure of a molecule from information relating to the structure, and to obtain a plurality of trial structures in which the intermolecular distances of the constituent molecules of the initial structure and the angles formed by the constituent molecules are changed. For example, when obtaining the structure of carbon disulfide dimer (dimer), the structure of carbon disulfide monomer registered in advance may be combined to obtain the initial structure of carbon disulfide dimer.

(A-5) Means for transmitting information on a plurality of trial structures to the plurality of client computers “Means for transmitting information on a plurality of trial structures to the plurality of client computers” includes a plurality of trials. There is no particular limitation as long as information on the structure can be transmitted to the plurality of client computers. The host computer and each client computer are preferably connected via the Internet or an intranet.
(A-6) Means for receiving information on the results of quantum chemistry calculations sent by each client computer to the host computer “Means for receiving information on the results of quantum chemistry calculations sent by each client computer to the host computer” The client computer is not particularly limited as long as it can receive information on the result of the quantum chemical calculation transmitted to the host computer. Ordinary computers and servers have such means.
(A-7) Means for judging whether the structure of a molecule has been optimized from information on the results of quantum chemistry calculations “To judge whether the structure of molecules has been optimized from information on the results of quantum chemistry calculations” The means of “determines whether or not the molecular structure has been optimized from the information on the result of the quantum chemical calculation. Specifically, this means determines whether or not the absolute value of the “first-order differential of energy in the trial structure by coordinates” vector obtained by quantum chemical calculation is less than a certain value. One that is judged to have been optimized. Here, “optimized structure” means that a molecule is located at least at the energy position of the local minimum on its potential energy surface (preferably, located at the structure with the lowest energy). Means).

“Information about the results of quantum chemistry calculations” in “Means for determining whether the structure of a molecule has been optimized from the information about the results of quantum chemistry calculations” includes “information about the value of energy in the trial structure” and “ "Information on the value of the first derivative of the energy in the trial structure by coordinates". “Information about energy values in a trial structure” is usually used when finding a new trial structure. In the structure optimization calculation, information on the energy value in the trial structure (optimized structure) is important for comparing the thermodynamic stability of the molecules. In addition, “information on the value of the first derivative of the energy in the trial structure by coordinates” is newly used when obtaining the trial structure.
(A-8) Means for instructing each client computer to stop quantum chemistry calculations “Means for issuing instructions to each client computer to stop quantum chemistry calculations” This is a means for instructing each client computer to stop the quantum chemistry calculation when it is determined that the structure is optimized, and to stop the subsequent calculations.
(A-9) Means for obtaining a new trial structure from information on the results of quantum chemistry calculations The means for obtaining a new trial structure from information on the results of quantum chemistry calculations is as follows. This is a means for finding a new trial structure from information on the results of quantum chemical calculations when it is determined that the optimization has not been achieved.

  “Information on the result of quantum chemistry calculations from information on the results of quantum chemistry calculations” as “Information on the results of quantum chemistry calculations”, Include. Or “information about the result of quantum chemical calculation” includes “information about the value of energy in the trial structure” and “information about the value of the first derivative of the energy in the trial structure by coordinates”.

  “Means for obtaining a new trial structure from information on the results of quantum chemistry calculations”, “Information on the value of the first derivative by coordinates of energy in the trial structure” One that updates information and seeks a new trial structure.

  In addition, as “means for obtaining a new trial structure from information on the results of quantum chemistry calculations”, “information on the trial structure”, “energy in the structure with the lowest energy including those obtained by other computers” Based on the information on the value of the first derivative by coordinates and the information on the value of the first derivative by coordinates in the trial structure, the information on the Hessian of the energy in the trial structure is updated to give a new trial. One that seeks the structure.

  In addition, as "means for obtaining a new trial structure from information on the results of quantum chemistry calculations", the information on the energy in the trial structure is based on "information on the value of the first derivative of the energy in the trial structure by coordinates". Obtain information about the Hessian, obtain information about the effective Hessian that takes a positive value from the information about the Hessian, information about the trial structure, information about the effective Hessian, and “value of the first derivative of the energy in the trial structure by coordinates. Information ”is a new trial structure.

  In the conventional quasi-Newton method, the positive value of the Hessian is maintained when the Hessian is updated. Therefore, even if hessian was used as it was, it did not become a big problem. However, when structural stabilization is performed by the method of the present invention, there are often cases where the positive value of Hessian is not maintained. That the Hessian is not positive means that the approximate energy surface becomes a convex surface. For this reason, when obtaining a new trial structure, it is preferable to use effective helium that maintains a positive value instead of the updated Hessian as described above. The effective hessian includes hessians represented by the following formulas (III) and (IV).

As a “means for obtaining a new trial structure from information on the results of quantum chemistry calculations”, the energy of the new trial structure, which is the last trial structure (its coordinate vector is q _k ), is the lowest. It is another preferred embodiment of the present invention that is obtained by the formula (I) and is obtained by the formula (II) when the energy of the trial structure calculated immediately before is not the lowest.

(In equations (I) and (II), the vector q _new represents the coordinates of the new trial structure. The vector q _k represents the coordinates of the trial structure calculated immediately before. The subscript k represents the quantum representing the order in which the chemical calculation has ended. matrices beta _k is .g _k that represent the Hessian at the k-th trial structure, .L ^proj representing a vector for "the energy in the k-th trial structure, first derivative by the coordinate" _{k, r} is one eigenvector randomly selected from a number of eigenvectors orthogonal to the vector −β _k ⁻¹ g _l , scalar C is a scale factor, and vector q _l is calculated immediately before If the energy of the trial structure is not the lowest among all trial structures up to the kth, it represents the coordinate of the trial structure with the lowest energy among all trial structures up to the kth, and the trial structure calculated immediately before Energy is kth Representing all of the cases the lowest among trial structural coordinates of trial structures most in the vicinity of the calculated attempted structure just before in all trials structures in.)
As an initial value of the effective Hessian (β _k ), that is, β ₁ , a unit matrix or a second-order differential matrix with energy coordinates (according to energy coordinates calculated at a calculation (theoretical) level lower than the quantum chemical calculation) It is another preferred embodiment of the present invention to use either a secondary differential matrix or a secondary differential matrix based on energy coordinates calculated at the same theoretical level as the quantum chemical calculation.

In addition, it is another preferable embodiment of the present invention to use temporary helium (B _k ) represented by any one of the following formulas (III) to (V) as the effective helium (β _k ).

（式（II）中，太文字の１は単位行列を表し，Δｑ_k-l＝ｑ_k−ｑ_lであり，Δｇ_k-l＝ｇ_k−ｇ_lである。）

(In the formula (II), the bold letter 1 represents a unit matrix, and Δq _kl = q _k −q _l and Δg _kl = g _k −g _l .)

なお，式（III）は，BFGS法（C. G. Broyden, J. Inst. Math. Appl. 1970, 6, 76; R. Flether, Comput. J. 1970, 13, 317; D. Goldfarb, Math. Comput. 1970, 24, 23; D. F. Shanno, Math. Comput. 1970, 24, 647）に類似したヘシアン更新の式である。式（V）はDFP法（W. C. Davidon, AEC Res. and Dev. Report 1959, ANL-5990; R. Fletcher and M. J. D. Powell，Comput. J. 1963, 6, 163.）に類似したヘシアン更新の式である。

Equation (III) can be expressed by the BFGS method (CG Broyden, J. Inst. Math. Appl. 1970, 6, 76; R. Flether, Comput. J. 1970, 13, 317; D. Goldfarb, Math. Comput. 1970, 24, 23; DF Shanno, Math. Comput. 1970, 24, 647). Equation (V) is a Hessian update equation similar to the DFP method (WC Davidon, AEC Res. And Dev. Report 1959, ANL-5990; R. Fletcher and MJD Powell, Comput. J. 1963, 6, 163.). is there.

As the effective Hessian (β _k ), if the provisional Hessian (B _k ) is positive and satisfies the following formula (VI), the provisional Hessian is used; otherwise, the following formula (VII) is used: , Another preferred embodiment of the present invention.

In the above formulas (VI) and (VII), g _m is the first derivative in terms of energy coordinates in the trial structure with the lowest energy among all the trial structures up to the k-th (referred to as the m-th trial structure). Is a vector. The scalar R ^k _max is the search distance limit. ω _k is a scalar that is obtained so that effective Hessian has a positive value and satisfies the relational expression (VIII). Note that ω _k can be obtained by making it self-careless.

It is another preferred embodiment of the present invention to use any value from 0.0 to 10.0 as the initial value of R ^k _max , that is, R ¹ _max .

R ^k _max is determined empirically, and as R ^k _max , the immediately preceding trial structure q _k is changed to the nth trial structure q _n and the first derivative vector g _n and the o th A structure found using cyan _Bo , where the previous structure q _k has the lowest energy or the nth trial structure q _n has the lowest energy among the trial structures up to the k th If this is the case, then using the following formula (IX), otherwise using R ^k _max = R ^k-1 _max is another preferred embodiment of the present invention.

(In the above equation, E (q _i ) is the energy in the trial structure q _i obtained by quantum chemical calculation.)

The use of an eigenvector L ^proj _{k, r} that satisfies the following formula (X) is another preferred embodiment of the present invention.

(In the above formula, N represents the number of degrees of freedom.)
Further, as a scale factor, it is preferable to use the following formula (XI) when λ ^proj _{k, r} ² <0, and use the following formula (XII) when λ ^proj _{k, r} ² ≧ 0. It is another embodiment.

Alternatively, using C = 0 as the scale factor C is another preferred embodiment of the present invention.

In this specification, “coordinates” refers to internal coordinates including the interatomic distance, the connection angle of 3 atoms, and the two-surface diagonal of 4 atoms, representing the relative positional relationship of the atoms constituting the molecule, or the molecule. There are Cartesian coordinates that represent the positions of the constituent atoms.
(A-10) Means for sending information about new trial structure to client computer that sent the result of quantum chemistry calculation “Information about new trial structure has been sent result of quantum chemistry calculation The “means for transmitting to the client computer” is not particularly limited as long as the information on the new trial structure can be transmitted to the client computer that has transmitted the result of the quantum chemical calculation.
(B-1) Means for inputting information relating to the computation transmitted from the host computer The means for inputting information relating to the computation transmitted from the host computer includes information relating to the computation transmitted from the host computer. There is no particular limitation as long as it can be input to the client computer for quantum chemical calculation.
(B-2) Means for inputting information on trial structure transmitted from host computer Means for inputting information on trial structure transmitted from host computer include information on trial structure transmitted from host computer. There is no particular limitation as long as it can be input to the client computer for quantum chemical calculation.
(B-3) Means for obtaining information relating to the first derivative of the energy in the trial structure by means of quantum chemical calculation using the information on the trial structure sent from the host computer “Trial structure sent from the host computer And means for obtaining information on the first derivative of the coordinates of the energy in the trial structure by means of quantum chemical calculation using the information on the calculation, as in a known quantum chemical calculation program such as the GAUSSIAN program. Information (constituent molecules and their position information) is used to perform quantum chemical calculations to obtain information about the first derivative of energy in the trial structure by coordinates. “Information about the first derivative of energy in the trial structure by coordinates” includes information on the value of energy in the trial structure and the value of the first derivative by coordinates of energy in the trial structure.
“The means for the host computer to optimize the structure by using the information on the trial structure transmitted from the host computer as a means for obtaining information on the first derivative of the energy in the trial structure by coordinates by quantum chemical calculation”. It is preferable to perform quantum chemical calculation based on “information about calculation” in “means for inputting information about calculation to be performed”. For example, a stable structure is obtained by adjusting a predetermined calculation level such as MP2 / 6-31 + G ^* or a function to be considered. For example, in the initial calculation, after obtaining a stable structure at a low calculation level, the calculation level is gradually increased while considering the physical properties of the molecule.
(B-4) Means for judging whether or not quantum chemistry calculations have been completed “Means for judging whether or not quantum chemistry calculations have been completed” are those that can determine whether or not quantum chemistry calculations have been completed. There is no particular limitation. “Means for determining whether or not quantum chemistry calculation has been completed” can be performed by determining whether or not the absolute value of the primary differential vector is within a predetermined range.
(B-5) Means for sending information about the results of quantum chemistry calculations to the host computer when it is determined that quantum chemistry calculations are completed “Quantum chemistry calculations when it is determined that quantum chemistry calculations are completed” The means for transmitting information related to the result of the above to the host computer ”is particularly suitable if it is capable of transmitting information related to the result of the quantum chemical calculation to the host computer when it is determined that the quantum chemical calculation is completed. It is not limited. “Information on the results of quantum chemical calculations” includes information on the structure of the trial structure, information on the energy in the trial structure, information on the first derivative in the trial structure, and the like.
2. How to find a stable structure In the following, we explain the structure optimization method using the above system. In this method, a stable structure of a molecule is obtained by the following steps.

  Input information about the calculation to optimize the structure to the host computer (Step 1).

  The host computer transmits information related to the calculation to the plurality of client computers (step 2).

  Information on the structure of the molecule whose structure is to be optimized is input to the host computer (step 3).

  The host computer obtains a plurality of trial structures from the inputted information on the molecular structure (step 4).

  The host computer transmits information on the plurality of trial structures to the plurality of client computers (step 5).

  Each client computer connected to the host computer inputs information relating to the calculation transmitted from the host computer (step 6).

  Each client computer connected to the host computer inputs information regarding the trial structure transmitted from the host computer (step 7).

  Each client computer connected to the host computer uses the information on the trial structure and calculation transmitted from the host computer to obtain information on the first derivative of the energy in the trial structure by coordinates using quantum chemical calculation (step) 8).

  Each client computer connected to the host computer determines whether the quantum chemical calculation has been completed (step 9).

  When each client computer connected to the host computer determines that the quantum chemical calculation has been completed, the client computer transmits information about the result of the quantum chemical calculation to the host computer (step 10).

  The host computer receives information on the result of the quantum chemical calculation transmitted from the client computer to the host computer (step 11).

  The host computer determines whether or not the molecular structure has been optimized from the information on the result of the quantum chemical calculation (step 12).

  If the host computer determines that the molecular structure has been optimized, it issues a command to each client computer to stop the quantum chemical calculation (step 13).

  If the host computer determines that the molecular structure has not been optimized, a new trial structure is obtained from the information on the result of the quantum chemical calculation (step 14).

  Information on the new trial structure is transmitted to the client computer that has transmitted the result of the quantum chemical calculation (step 15). And it returns to said step 7 and repeats until it judges that the structure of the molecule | numerator was optimized.

  Hereinafter, the present invention will be described with reference to calculation examples of specific stable structure optimization of molecules. In the following examples, experiments were performed using a system as shown in FIG. As the host computer (and one of the client computers) of the present invention, Dell PowerEdge 2600 (PowerEdge 2600) was used. As client computers, Origin 2000 (SGI), Tezro (SGI), and SX-6 (NEC) were used. The molecular structure was optimized using a system based on the algorithm as described above. The target molecules were water dimer, water trimer, azobenzene, tetraphenylporphyrin, and cytosidine-guanosine cluster. Figure 2 shows the structure optimization of a water dimer. FIG. 2A shows the initial trial structure. FIG. 2B shows the structure obtained as a result of structural stabilization. Fig. 3 is a diagram showing the structure optimization of a water trimer. FIG. 3A shows the initial trial structure. FIG. 3B shows the structure obtained as a result of the structural stabilization. Figure 4 shows the structure optimization of azobenzene. FIG. 4A shows the initial trial structure. FIG. 4B shows the structure obtained as a result of structural stabilization. FIG. 5 is a diagram showing the structure optimization of tetraphenylporphyrin. FIG. 5A shows the initial trial structure. FIG. 5B shows the structure obtained as a result of the structural stabilization. FIG. 6 shows the structural optimization of the cytosidine-guanosine cluster. FIG. 6A shows the initial trial structure. FIG. 6B shows the structure obtained as a result of the structural stabilization.

  Table 1 shows the calculation time. As shown in Table 1, when the molecular structure is optimized by using the molecular structure optimization system of the present invention consisting of four computers, the calculation can be performed faster than the calculation by one computer. As a result, high parallelization efficiency was obtained. From this, it was found that the molecular structure optimization system of the present invention can obtain the optimization calculation of the molecular structure at high speed. Further, it has been found that according to the molecular structure optimization method of the present invention, calculations related to a stable structure can be performed at a higher speed than the conventional molecular structure optimization method.

  The present invention relates to molecular structure analysis by a computer, and in particular, enables high-speed computation by utilizing parallel processing, and is used for material development in the nanotechnology field and biological function elucidation in the medical field. It can be used for molecular simulation.

FIG. 1 is a diagram illustrating a basic configuration example of a system used in the first embodiment. Figure 2 shows the structure optimization of a water dimer. FIG. 2A shows the initial trial structure. FIG. 2B shows the structure obtained as a result of structural stabilization. Fig. 3 is a diagram showing the structure optimization of a water trimer. FIG. 3A shows the initial trial structure. FIG. 3B shows the structure obtained as a result of the structural stabilization. Figure 4 shows the structure optimization of azobenzene. FIG. 4A shows the initial trial structure. FIG. 4B shows the structure obtained as a result of structural stabilization. FIG. 5 is a diagram showing the structure optimization of tetraphenylporphyrin. FIG. 5A shows the initial trial structure. FIG. 5B shows the structure obtained as a result of the structural stabilization. FIG. 6 shows the structural optimization of the cytosidine-guanosine cluster. FIG. 6A shows the initial trial structure. FIG. 6B shows the structure obtained as a result of the structural stabilization.

Claims (7)

A molecular structure optimization system comprising a host computer (A) and a plurality of client computers (B) connected to the host computer (A),

The host computer (A)

The host computer (A) is a first input means (A-1) for inputting information relating to a calculation for which the structure is to be optimized. The information relating to the calculation includes a theoretical level, a basis function, and a spin. Including information on whether to consider multiplicity,

First transmission means (A-2) for transmitting the information related to the calculation input by the first input means (A-1) to the plurality of client computers;

Second input means (A-3) for inputting information on the structure of the molecule to be optimized to the host computer (A), wherein the information on the structure of the molecule is:
Information on the constituent elements of the molecule, and information on the positional relationship of the constituent elements of the molecule ;

Trial structure acquisition means (A-4) for obtaining a plurality of trial structures from information on the structure of the molecule inputted by the second input means (A-3), and reading preset numerical values A plurality of molecular structure candidates in which the intermolecular distance and the angle formed by the constituent molecules in the structure of the input molecule are changed by the numerical value as the plurality of trial structures;

Second transmission means (A-5) for transmitting each of the information on the plurality of trial structures obtained by the trial structure acquisition means (A-4) to any of the plurality of client computers; Including

Each of the client computers (B) connected to the host computer (A)
Third input means (B-1) for inputting information relating to the calculation transmitted from the first transmission means (A-2) of the host computer;
Fourth input means (B-2) for inputting information on the trial structure transmitted from the second transmission means (A-5) of the host computer;
Using the information about the calculation input by the third input means (B-1) and the information about the trial structure input by the fourth input means (B-2) , the energy coordinates in the trial structure Quantum chemical calculation means (B-3) for performing a quantum chemical calculation for obtaining a vector relating to the first derivative according to
Computation end judging means (B-4) for judging whether or not the quantum chemistry calculation is finished, information on a certain range for the end of the calculation is read out, and the quantum chemistry computation means (B-3) When the absolute value of the vector of the first derivative based on the energy coordinates in the trial structure obtained by (1) is within the certain range, it is determined that the quantum chemical calculation is completed,
When the calculation end judging means (B-4) judges that the quantum chemical calculation is finished, the third sending means (B-5) for sending information related to the result of the quantum chemical calculation to the host computer. And the result of the quantum chemistry calculation is an absolute value of a first-order differential vector by energy coordinates for the trial structure obtained by the quantum chemistry calculation,
Comprising

The host computer (A) further includes receiving means (A-6) for receiving information on the result of the quantum chemical calculation transmitted from the third transmitting means (B-5) of each client computer to the host computer. When,

Structure optimization judgment means (A-7) for judging whether or not the structure of the molecule is optimized from the information on the result of the quantum chemistry calculation received by the reception means (A-6), A constant value for determination is read out, and the absolute value of the first-order differential vector based on energy coordinates for the trial structure is compared with the constant value to determine whether the absolute value is equal to or less than the constant value. things and,

If the structure optimization judging means (A-7) judges that the structure of the molecule has been optimized, a command for issuing a command to the client computer (B) to stop quantum chemical calculation Means (A-8);

If the structure optimization judging means (A-7) judges that the structure of the molecule has not been optimized, a new trial structure for obtaining the coordinates of a new trial structure is obtained from information on the result of the quantum chemical calculation. Trial structure acquisition means ( A-9 ),

The primary differential vector based on the energy coordinates of the trial structure received by the receiving means (A-6) is read, and the primary differential vector based on the energy coordinates of the trial structure received by the receiving means (A-6) In the lowest case of the primary differential vector by coordinates, the coordinate (q _new ) of the _new trial structure is obtained by the formula (I), and the primary differential by the coordinate of the energy of the trial structure received by the receiving means (A-6). When the vector is not the lowest, the coordinates (q _new ) of the _new trial structure are obtained by the formula (II),

(In the formulas (I) and (II), the vector q _new represents the coordinates of the new trial structure. The vector q _k represents the coordinates of the trial structure calculated immediately before. The subscript k represents the quantum. Represents the order in which chemical calculations are completed, the matrix β _k represents the effective Hessian in the k th trial structure, and g _k represents a vector relating to the “first derivative by the energy coordinates in the k th trial structure.” L ^proj _{k , R} is an eigenvector randomly selected from a number of eigenvectors orthogonal to the vector −β _k ⁻¹ g _l , scalar C is a scale factor, and vector q _l is calculated immediately before If the energy of the trial structure is not the lowest among all the trial structures up to the kth, it represents the coordinate of the trial structure with the lowest energy among all the trial structures up to the kth, Energy trial structures represent all cases the lowest among trial structural coordinates of trial structures most in the vicinity of the calculated attempted structure just before in all trials structure to k-th.)
When the new trial structure is obtained by the formula (I), a vector (q _k ) indicating the coordinates of the trial structure received by the receiving means (A-6) and an inverse matrix (β of the effective Hessian in the trial structure _k ⁻¹ ) and a vector (g _k ) related to the first derivative by the energy coordinate in the trial structure, and the first order by the effective Hessian inverse matrix (β _k ⁻¹ ) and the energy coordinate in the trial structure. It obtains a vector _{(g k)} and the product (β _k ^-1 g _k) relating to differentiation, a vector indicating the coordinates of the trial structures _{(q k),} obtaining the difference between the product (β _k ^-1 g _k) To obtain the coordinates (q _new ) of the _new trial structure,
When the new trial structure is obtained by the formula (II), the coordinates (q _l ) of the trial structure having the lowest energy among all the trial structures are read and received by the receiving means (A-6) The product (β _k ⁻ ) of the inverse matrix (β _k ⁻¹ ) of the effective Hessian in the trial structure and the vector (g _l ) related to the first derivative by the energy coordinates in the trial structure having the lowest energy among all the trial structures. ¹ g _l ), one eigenvector L ^proj _{k, r} is obtained from a number of eigenvectors orthogonal to the vector −β _k ⁻¹ g _l , the scale factor C is read, and the eigenvector L ^proj _{k, r} and the scale The product (CL ^proj _{k, r} ) with the factor C is obtained, the coordinates (q _l ) of the trial structure having the lowest energy among all the trial structures, and the product (β _k ⁻¹ g _l ) and the product (CL ^proj _{k, r} ) to obtain q _l −β _k ⁻¹ g _l −CL ^proj _{k, r} ,

The client computer (B) that has transmitted the result of the quantum chemistry calculation by the third transmission means (B-5), the information about the coordinates of the new trial structure acquired by the new trial structure acquisition means ( A-9 ). 4th transmission means ( A-10 ) for transmitting to),
Equipped with,

To the host computer, a step of inputting information about the calculation to be optimizing the structure,
The host computer sending information about the calculation to the plurality of client computers;
Inputting into the host computer information about the structure of the molecule whose structure is to be optimized;
The host computer obtaining a plurality of trial structures from the inputted information on the structure of the molecule;
The host computer sending information about any of the plurality of trial structures to any of the plurality of client computers;
Each client computer connected to the host computer inputting information relating to the calculation transmitted from the host computer;
Each client computer connected to the host computer inputs information regarding the trial structure transmitted from the host computer;
Each client computer connected to the host computer uses the information on the trial structure and calculation transmitted from the host computer to obtain a vector relating to the first derivative based on energy coordinates in the trial structure by quantum chemical calculation; ,
Each client computer connected to the host computer determines whether the quantum chemical calculation is completed;
Each client computer connected to the host computer, when it is determined that the quantum chemical calculation has been completed, sending information on the result of the quantum chemical calculation to the host computer;
The host computer receiving information on the results of quantum chemical calculations sent by the client computer to the host computer;
The host computer determining from the information about the result of the quantum chemical calculation whether the molecular structure has been optimized;
If the host computer determines that the structure of the molecule has been optimized, issuing instructions to each client computer to stop quantum chemistry calculations;
If the host computer determines that the molecular structure has not been optimized,
Obtaining a new trial structure coordinate (q _new ) from information on the result of the quantum chemistry calculation;
Transmitting information about the coordinates (q _new ) of the _new trial structure to a client computer that has transmitted the result of the quantum chemical calculation;
To obtain a stable structure of molecules by a process including
Molecular structure optimization system for obtaining stable molecular structure.
2. The molecular structure optimization system according to claim 1, wherein an initial value (that is, β ₁ ) of the effective Hessian (β _k ) is either a unit matrix or a secondary differential matrix based on energy coordinates.
2. The molecular structure optimization system according to claim 1, wherein temporary helium (B _k ) represented by any one of the following formulas (III) to (V) is used as the effective helium (β _k ).

(In the formula (III), 1 of bold represents the identity matrix, a _{Δq k-l = q k -q} l, a _{Δg k-l = g k -g} l. Hereinafter, the same.)

The molecular structure optimization system according to claim 3,
As the effective Hessian (β _k ),
If any of the provisional hessian (B _k ) is positive and satisfies the following formula (VI), the provisional hessian is used,
Otherwise, a system using the following formula (VII).

(In the above formulas (VI) and (VII), g _m is the primary in terms of energy coordinates in the trial structure having the lowest energy among all the trial structures up to the k th (referred to as the m th trial structure). (The scalar R ^k _max is the limit value of the search distance. Ω _k is a scalar that is obtained so that effective Hessian becomes positive and satisfies the relational expression (VIII).)

The molecular structure optimization system according to claim 4, wherein any one of 0.0 to 10.0 is used as an initial value of R ^k _max (ie, R ^l _max ).
As R ^k _max , the immediately preceding trial structure q _k is a structure found using the n th trial structure q _n and the first derivative vector g _n by the energy coordinates and the o th Hessian Bo, among the attempts the structure of k to th, the case when the energy of the structure q _k immediately before the minimum or the n-th trial structure q _n has the lowest energy, using the following equation (IX), if not, R The molecular structure optimization system according to claim 4, wherein ^k _max = R ^k−1 _max is used.

(In the above equation, E (q _i ) is the energy in the trial structure q _i obtained by quantum chemical calculation.)
The molecular structure optimization system according to claim 1, wherein the L ^proj _{k, r} satisfies the following formula (X).

(In the above formula, B _k represents one of the above formulas (III) to (V). Λ ^proj _{k, r} ² represents an eigenvalue obtained so as to satisfy the above formula (X). Represents the number of degrees.)

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