Molecular simulation methods

Abstract

This invention provides a molecular simulation method for quickly calculating the equilibrium density of a first molecular model, which is modeled as an all-atom model, and at least one of the terminal distance and radius of inertia. [Solution] The molecular simulation method includes an equilibrium state calculation step which includes a step S11 of inputting a plurality of first molecular models that model the first molecule as an all-atom model, a step S12 of inputting a second molecular model that model the second molecule as an all-atom model, a step S13 of inputting a mixed system model that includes a plurality of first molecular models and second molecular models, and a step S14 of calculating the equilibrium state of the mixed system model, and a density estimation step which calculates at least one of the terminal distance and radius of inertia of the first molecular models in the equilibrium state mixed system model, and estimates the equilibrium density of a system that includes only the first molecular model based on the equilibrium density of the second molecule, the mass of the first molecular model, the mass of the second molecular model, and the volume of the mixed system model in the equilibrium state.

Description

Technical Field

[0001] The present invention relates to a molecular simulation method.

Background Art

[0002] The following Patent Document 1 describes a simulation method for polymer materials. This method includes a step of calculating a relaxed structure of a first molecular chain model composed of an all-atom model or a united atom model of a polymer chain based on molecular dynamics calculation.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] In the all-atom model or united atom model as described above, since all atoms or all atoms except hydrogen atoms are modeled as they are, a relatively long calculation time is required during molecular dynamics calculation. Furthermore, these models tend to slow down in motion in proportion to approximately cube of the chain length. Therefore, there has been a problem that it takes a lot of time to calculate the equilibrium state of such a polymer chain model and to calculate the equilibrium density of the model, the end-to-end distance of the model, and the radius of inertia of the model.

[0005] The present invention has been devised in view of the above actual situation, and the main object is to provide a method capable of calculating at least one of the equilibrium density of a first molecular model modeled as an all-atom model or a united atom model, the end-to-end distance of the first molecular model, and the radius of inertia in a short time.

Means for Solving the Problems

[0006] The present invention is a molecular simulation method comprising the steps of: inputting into a computer a plurality of first molecular models, each modeling a first molecule formed by the bonding of a plurality of monomers, as a whole-atom model or a united-atom model; inputting into the computer at least one second molecular model, each modeling a second molecule having a smaller molecular weight than the first molecule, as a whole-atom model or the united-atom model; inputting into the computer a mixed system model including the plurality of first molecular models and the second molecular models; inputting into the computer the equilibrium density of the second molecule, wherein the computer performs the steps of: calculating structural relaxation based on molecular dynamics calculations for the mixed system model to calculate the equilibrium state of the mixed system model; calculating at least one of the terminal distance and radius of inertia of the first molecular model in the equilibrium state of the mixed system model; and estimating the equilibrium density of a system including only the first molecular model based on the equilibrium density of the second molecule, the mass of the first molecular model, the mass of the second molecular model, and the volume of the mixed system model in the equilibrium state. [Effects of the Invention]

[0007] The molecular simulation method of the present invention, by employing the above steps, makes it possible to quickly calculate the equilibrium density of a first molecular model, which is modeled as a whole-atom model or a united-atom model, and at least one of the terminal distance and radius of inertia of the first molecular model. [Brief explanation of the drawing]

[0008] [Figure 1] This is a perspective view showing an example of a computer used to perform molecular simulation methods. [Figure 2] This is the structural formula of the first molecule. [Figure 3] This flowchart shows an example of the processing procedure for a molecular simulation method. [Figure 4] This flowchart shows an example of the processing steps for the equilibrium state calculation process. [Figure 5] This is a conceptual diagram showing an example of a first molecular model. [Figure 6] This is a conceptual diagram showing an example of a second molecular model. [Figure 7] This figure shows an example of a mixed system model. [Figure 8] This is a flowchart illustrating an example of the processing steps for the density estimation process. [Figure 9] This figure shows an example of a second standalone model used to calculate the density of a second molecular model. [Figure 10] This flowchart shows an example of the processing procedure for the coarse-grained physical quantity identification process. [Figure 11] This is a conceptual diagram showing an example of the first standalone model. [Figure 12] This graph shows the relationship between the autocorrelation function and the time constant of the first molecular model. [Modes for carrying out the invention]

[0009] Embodiments of the present invention will be described below with reference to the drawings. It should be understood that the drawings contain exaggerations and representations that differ from the actual dimensional ratios of the structures in order to aid in understanding the content of the invention. Furthermore, the same or common elements are denoted by the same reference numerals throughout each embodiment, and redundant explanations are omitted. Moreover, the specific configurations shown in the embodiments and drawings are for the purpose of understanding the content of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0010] In the molecular simulation method of this embodiment, the first molecule to be analyzed and the second molecule, which has a smaller molecular weight than the first molecule, are input as a first molecule model and a second molecule modeled as a whole atom model or a unit atom model. Then, the equilibrium state of a mixed system model including the first molecule model and the second molecule model is calculated. Such an equilibrium state can be used for various purposes, such as calculating and analyzing the physical quantities of the first molecule to be analyzed. In this embodiment, the equilibrium state of the mixed system model is used to calculate an estimated value of the equilibrium density of the first molecule model (the density of a system consisting only of the first molecule model in the equilibrium state) and at least one of the end-to-end distance and radius of inertia of the first molecule model in the equilibrium state. Furthermore, the above-calculated physical quantities are used, for example, to convert the units of the first coarse-grained molecular model, which models the first molecule as a coarse-grained molecular model, to the units of the first molecule (i.e., real units) based on the procedure described in Patent Document 1.

[0011] In the molecular simulation method of this embodiment, a computer is used. Figure 1 is a perspective view showing an example of a computer 1 for performing the molecular simulation method.

[0012] The computer 1 of this embodiment is composed of a main unit 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main unit 1a is provided with, for example, a processing unit (CPU), ROM, working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Software for executing the molecular simulation method of this embodiment is pre-stored in the storage device. Therefore, the computer 1 is configured as a molecular simulation device.

[0013] The first molecule of this embodiment includes, for example, at least one of an oligomer and a polymer. The first molecule of this embodiment is composed of a polymer, and is exemplified as polyisoprene. However, the first molecule is not limited to polyisoprene; for example, it may be polybutadiene or a resin.

[0014] Figure 2 shows the structural formula of the first molecule N1. Multiple monomers 3 are bonded to the first molecule N1. In this embodiment, when the first molecule N1 is polyisoprene, the monomer 3 of the first molecule N1 contains a methine group (-CH-), a methylene group (-CH2-), and a methyl group (-CH3-). The first molecule N1 is formed by the bonding of such monomers 3 at a degree of polymerization. Note that at the end of the first molecule (polyisoprene) N1, a methyl group (-CH3) is bonded instead of a methylene group (-CH2).

[0015] In this embodiment, multiple first molecule models are set up, either as whole-atom models or united-atom models, that model the first molecule N1. The whole-atom model models all atoms based on the actual structure of the first molecule N1. On the other hand, the united-atom model treats the carbon atom and the hydrogen atom bonded to the carbon atom as a single particle in the first molecule N1. Such first molecule models can handle finer structures and motions compared to, for example, coarse-grained molecular models in which monomer 3 is modeled as a single bead, thus improving the accuracy of the simulation.

[0016] On the other hand, when constructing a first molecular model (whole-atom model or united-atom model), the atoms are artificially arranged, which tends to result in unnatural spread and density of the first molecular model N1. Therefore, it is important to perform molecular dynamics calculations until such artificial initial arrangements are sufficiently eliminated to calculate the equilibrium state of the first molecular model. However, during molecular dynamics calculations, the relaxation time of the molecular model increases in proportion to approximately the cube of the chain length. Therefore, if a first molecular model that reproduces the chain length of an actual polymer material is used, it may become impossible to complete the structural relaxation calculation in a realistic time. Thus, while it is possible to shorten the time required for relaxation calculations by using a first molecular model with a shorter chain length, if the chain length is too short, the proportion of molecular ends in the first molecular model across the entire system increases, changing the physical properties and making it impossible to predict the physical properties of the polymer material with high accuracy. Therefore, there was a problem that there was a limit to the time reduction for structural relaxation calculations of the first molecular model.

[0017] As a result of diligent research, the inventors discovered that by performing molecular dynamics calculations on a mixed system model that includes multiple first molecular models and at least one second molecular model that models a second molecule (not shown) with a smaller molecular weight than the first molecule N1, the structural relaxation of the mixed system model including the first molecular model can be completed in a short time. The equilibrium state of such a mixed system model can be used to calculate the equilibrium density of the first molecular model, calculate at least one of the end-to-end distance and radius of inertia in the equilibrium state of the first molecular model, and convert from the units of the first coarse-grained molecular model to the units of the first molecule (i.e., real-world units).

[0018] [Molecular Simulation Method (First Embodiment)] In the molecular simulation method of this embodiment, based on the above findings, it is possible to calculate the equilibrium density of the first molecular model and at least one of the terminal distance and radius of inertia of the first molecular model in a short time. Figure 3 is a flowchart showing an example of the processing procedure of the molecular simulation method.

[0019] [Calculating the equilibrium state of the mixed system model (equilibrium state calculation process)] In the molecular simulation method of this embodiment, first, computer 1 (shown in Figure 1) calculates the equilibrium state of the mixed system model (equilibrium state calculation step S1). Figure 4 is a flowchart showing an example of the processing procedure for equilibrium state calculation step S1.

[0020] [Enter multiple first-molecule models] In the equilibrium state calculation step S1 of this embodiment, first, multiple first molecular models, which model the first molecule N1 shown in Figure 2 as an all-atom model or a united atom model, are input to the computer 1 (shown in Figure 1) (step S11). In this embodiment, the multiple first molecular models are modeled as all-atom models, but they may also be modeled as united atom models.

[0021] Figure 5 is a conceptual diagram showing an example of the first molecular model M1. The first molecular model M1 in this embodiment is composed of a plurality of particle models 5 and bonds 6 that connect the particle models 5, 5.

[0022] In step S11 of this embodiment, first, particle model 5 and bond 6 are linked based on the unit structure representing monomer 3 of the first molecule N1 shown in Figure 2. This sets up monomer model 7. Next, multiple monomer models 7 are linked together based on a predetermined number of monomers (i.e., degree of polymerization) to set up the first molecule model M1.

[0023] Particle model 5 is treated as a point mass in the equations of motion in the simulation based on molecular dynamics calculations described later. That is, parameters such as mass, diameter, charge, or initial coordinates are defined for particle model 5. Particle model 5 in this embodiment includes a carbon particle model 5c that models the carbon atoms of the first molecule N1, and a hydrogen particle model 5h that models the hydrogen atoms of the first molecule N1.

[0024] Bond 6 constrains the particle models 5, 5. Bond 6 in this embodiment includes a main chain 6a connecting the carbon particle models 5c, 5c and a side chain 6b connecting the carbon particle model 5c and the hydrogen particle model 5h. These main chain 6a and side chain 6b are treated, for example, as springs with defined equilibrium length and spring constant.

[0025] The first molecular model M1 has defined bond length, bond angle, and dihedral angle. The bond length is the bond length between each particle model 5, 5. The bond angle is the angle formed by three consecutive particle model 5 connected via bond 6. The dihedral angle is the angle formed by three adjacent particle model 5 in four consecutive particle model 5 connected via bond 6. Thus, the first molecular model M1 has a three-dimensional structure. As is customary, the bond length, bond angle, and dihedral angle of the first molecular model M1 change when subjected to external or internal forces. This allows the first molecular model M1 to change its three-dimensional structure.

[0026] Bond length, bond angle, and dihedral angle can be defined by a potential (GAFF) set based, for example, on paper 1 (J. Comput. Chem. 25, 1157-1174 (2004)). The potential is preferably set according to the structure of the first molecule N1 (shown in Figure 2). Such a first molecule model M1 can be created using material property simulation software (e.g., J-OCTA from JSOL Corporation).

[0027] The number of monomers can be appropriately set based on, for example, the structure of the first molecule N1 (shown in Figure 2) or the performance of computer 1 (shown in Figure 1) which performs the molecular dynamics calculations described later. If the first molecule N1 in this embodiment is a polymer, the number of monomers can be selected from, for example, 5 to 60. However, the number of monomers is not limited to this embodiment.

[0028] In step S11, multiple first molecular models M1 are set. In this embodiment, multiple first molecular models M1 with the same number of monomers are set, but the embodiment is not limited to this configuration. For example, multiple first molecular models M1 with different numbers of monomers may be set. The multiple first molecular models M1 are numerical data that can be handled by the computer 1 shown in Figure 1. The multiple first molecular models M1 are input into the computer 1.

[0029] [Enter the second molecular model] Next, in the equilibrium state calculation step S1 of this embodiment, at least one second molecule model, which models the second molecule (not shown) as a whole atom model or a united atom model, is input to computer 1 (shown in Figure 1) (step S12). The molecular weight of the second molecule is smaller than the molecular weight of the first molecule N1 shown in Figure 2.

[0030] The second molecule (not shown) is not particularly limited as long as its molecular weight is smaller than that of the first molecule N1 shown in Figure 2. In this embodiment, the second molecule is composed of a polymer (oligomer) with a smaller monomer number (i.e., degree of polymerization) than that of the first molecule N1. Examples of the second molecule composed of an oligomer include monomer 3, a dimer (not shown) in which two monomer 3s are bonded, or a trimer (not shown) in which three monomer 3s are bonded. In this embodiment, the second molecule is composed of a dimer in which two monomer 3s of the first molecule N1 are bonded.

[0031] Figure 6 is a conceptual diagram showing an example of the second molecular model M2. Similar to the first molecular model M1 shown in Figure 5, the second molecular model M2 in this embodiment is composed of multiple particle models 5 and bonds 6 connecting the particle models 5. Details of the particle models 5 and bonds 6 are as described above. Furthermore, similar to the first molecular model M1, the second molecular model M2 has defined bond lengths, bond angles, dihedral angles, and so on.

[0032] In step S12 of this embodiment, the monomer model 7 is linked based on a predetermined number of monomers (i.e., degree of polymerization) to set up the second molecule model M2. The number of monomers in the second molecule model M2 is set appropriately, for example, according to the magnitude of the number of monomers in the first molecule N1. In this embodiment, the number of monomers is set to "2". Therefore, the second molecule model M2 in this embodiment is defined as a dimer model that models a dimer.

[0033] In step S12 of this embodiment, multiple second molecular models M2 are set. In this embodiment, multiple second molecular models M2 with the same number of monomers are set, but the embodiment is not limited to this configuration, and for example, multiple second molecular models M2 with different numbers of monomers may be set. The multiple second molecular models M2 are numerical data that can be handled by the computer 1 shown in Figure 1 and are input to the computer 1.

[0034] [Enter a mixed system model] Next, in the equilibrium state calculation step S1 of this embodiment, a mixed system model including multiple first molecular models M1 and second molecular models M2 is input to the computer 1 (shown in Figure 1) (step S13). Figure 7 shows an example of the mixed system model 10. In Figure 7, a portion of the first molecular model M1 and a portion of the second molecular model M2 are shown representatively.

[0035] In step S13 of this embodiment, first, a cell 11, which is the virtual space to be analyzed, is defined. This cell 11 is the computational domain for structural relaxation based on molecular dynamics calculations, which will be described later.

[0036] In this embodiment, cell 11 is defined as a cube having three pairs of planes 12, 12 facing each other. Periodic boundary conditions are defined for each plane 12. This allows, for example, that a portion of the first molecular model M1 that exits from one plane 12 enters from the opposite plane 12 in cell 11. Therefore, one plane 12 and the opposite plane 12 can be treated as continuous (connected). Furthermore, the length La of one side of cell 11 can be appropriately set, for example, based on the description in Patent Document 1 mentioned above.

[0037] Next, multiple first molecular models M1 and second molecular models M2 are placed inside cell 11. This allows for the creation of a mixed system model 10. The placement of the first molecular models M1 and second molecular models M2 inside cell 11 can be carried out, for example, based on the Monte Carlo method.

[0038] The number of first molecular models M1 and second molecular models M2 can be appropriately set based on, for example, the computing power of computer 1 (shown in Figure 1), the size of cell 11, the size (degree of polymerization) of first molecular model M1, and the size (degree of polymerization) of second molecular model M2. The number of first molecular models M1 can be set to, for example, 10 to 60. The number of second molecular models M2 can be set to, for example, 400 to 1200.

[0039] Next, an interaction potential P1 is defined between adjacent first molecular models M1, M1, between adjacent second molecular models M2, M2, and between adjacent first molecular model M1 and second molecular model M2, between adjacent particle models 5, 5 that are not connected by bond 6. In this embodiment, the interaction potential P1 is defined as the LJ potential U LJ (r ij ) can be adopted. This will reduce the distance r between particle models 5 and 5. ij Depending on the situation, repulsive and attractive forces can be defined. Note that the LJ potential U LJ (r ij Details of the above are as described in Patent Document 1. The mixed system model 10 is stored in the computer 1 shown in Figure 1.

[0040] [Calculate the equilibrium state of a mixed-system model] Next, in the equilibrium state calculation step S1 of this embodiment, computer 1 (shown in Figure 1) calculates structural relaxation based on molecular dynamics calculations for the mixed system model 10 shown in Figure 7, and calculates the equilibrium state of the mixed system model 10 (step S14).

[0041] In molecular dynamics calculations, for example, Newton's equations of motion are applied to a mixed system model 10 (cell 11), assuming that all first molecular models M1 and second molecular models M2 follow classical mechanics for a predetermined time. The movement of all particle models 5 at each time (unit time) is then tracked and stored in computer 1 (shown in Figure 1). Furthermore, the conditions for molecular dynamics calculations are kept constant, for example, the number, volume, and temperature of particle models 5 in the system. For such molecular dynamics calculations, a molecular dynamics calculation program such as LAMMPS can be used.

[0042] In this embodiment, molecular dynamics calculations are performed on the particle model 5 of the first molecular model M1, which has a larger molecular weight than the second molecular model M2, until artificial initial configurations are sufficiently eliminated. This allows the equilibrium state (relaxed state) of the mixed system model 10, which includes the first molecular model M1 and the second molecular model M2, to be calculated.

[0043] In this embodiment, the mixed system model 10 includes a second molecular model M2, which has a smaller molecular weight than the first molecular model M1. This second molecular model M2 moves (diffuses) faster than the first molecular model M1 during molecular dynamics calculations. As the second molecular model M2 moves rapidly around the first molecular model M1, the motion of the first molecular model M1 is promoted, and the equilibrium state of the mixed system model 10 including the first molecular model M1 can be calculated in a short time.

[0044] In order to quickly calculate the equilibrium state of the mixed system model 10 including the first molecular model M1, it is preferable that the molecular weight of the second molecule modeled as the second molecular model M2 be set to 0.5 times or less the molecular weight of the first molecule N1 modeled as the first molecular model M1. This speeds up the motion (diffusion) of the second molecular model M2 during molecular dynamics calculations, effectively promoting the motion of the first molecular model M1, so that the equilibrium state of the mixed system model 10 including the first molecular model M1 can be calculated in a short time. From this viewpoint, the molecular weight of the second molecule is preferably 0.3 times or less the molecular weight of the first molecule N1, and more preferably 0.2 times or less.

[0045] Furthermore, it is preferable that the volume fraction of the second molecular model M2 relative to the mixed system model 10 be set to 0.5 or higher. As a result, since the second molecular model M2 is positioned in greater proportion than the first molecular model M1, the movement of the first molecular model M1 can be effectively promoted. This allows the equilibrium state of the mixed system model 10, including the first molecular model M1, to be calculated in a short time. From this viewpoint, the volume fraction of the second molecular model M2 is preferably 0.6 or higher, and more preferably 0.7 or higher.

[0046] The mixed system model 10 after structural relaxation (the first molecular model M1 in equilibrium) is stored in computer 1 shown in Figure 1.

[0047] As described above, in this embodiment, the estimated equilibrium density of the first molecular model M1 and at least one of the terminal distance and radius of inertia of the first molecular model M1 are calculated from the equilibrium state of the mixed system model 10. Furthermore, these physical quantities calculated from the equilibrium state of the mixed system model 10 are used to convert the units of the first coarse-grained molecular model to the units of the first molecular N1 shown in Figure 2 (i.e., real-world units), as described in Patent Document 1 above. To perform such a conversion accurately, the equilibrium density ρ of the system containing only the first molecular model M1 in the mixed system model 10 in the equilibrium state shown in Figure 7 is calculated. l It is important to estimate this with high accuracy.

[0048] In the mixed system model 10 shown in FIG. 7, since not only the first molecular model M1 but also the second molecular model M2 is included, a method for accurately obtaining the equilibrium density ρ1 of the first molecular model M1 from the calculation results of the mixed system model 10 after structural relaxation is not obvious. This is because in the mixed system model 10, there are multiple methods for defining the interface that divides the regions occupied by the first molecular model M1 and the second molecular model M2, and the results may differ for each definition. Also, in order to calculate the equilibrium density ρ1, for example, a method of performing Voronoi division based on the positions of each particle model 5 can be considered, but it has the drawback of requiring a lot of calculation time.

[0049] Therefore, in the molecular simulation method of the present embodiment, under the assumption that the volumes of the first molecular model M1 and the second molecular model M2 do not change before and after mixing, based on the following procedure, the equilibrium density of the second molecule (second molecular model M2), the mass of the first molecular model M1, the mass of the second molecular model M2, and the equilibrium state volume of the mixed system model 10, the equilibrium density ρ of the system containing only the first molecular model M1 l can be calculated in a short time. In the molecular simulation method of the present embodiment, without separately performing a molecular dynamics calculation targeting only the first molecular model M1 that requires a lot of calculation time, by using part of the calculation results of the mixed system model 10 after structural relaxation, the equilibrium density ρ of the system containing only the first molecular model M1 l is estimated, so an increase in calculation time can be suppressed.

[0050] [Estimate the equilibrium density ρ of the system containing only the first molecular model l [Density estimation step S2] Next, in the molecular simulation method of the present embodiment, the computer 1 (shown in FIG. 1) estimates the equilibrium density ρ of the system (not shown) containing only the first molecular model M1. The system containing only the first molecular model M1 is a system in which the second molecular model M2 is not mixed in the mixed system model 10 shown in FIG. 7. l The equilibrium density ρ of the system containing only the first molecular model M1

[0051] The equilibrium density ρ of the system containing only the first molecular model M1l This can be calculated as appropriate. In this embodiment, for example, assuming that the volume occupied by the first molecular model M1 and the second molecular model M2 does not change due to mixing, the mass m of the first molecular model M1 contained in the mixed system model 10 is calculated as shown in equation (1) below. l The volume V occupied by the first molecular model M1 contained in the mixed system model 10 l By dividing by this, the equilibrium density ρ of the system containing only the first molecular model M1 is obtained. l However, it can be calculated approximately. Calculations based on such assumptions are performed when the physical properties of the first molecular model M1 and the second molecular model M2 are similar, thereby determining the equilibrium density ρ l This makes it possible to calculate with high accuracy. ρ l =m l / V l … (1) Here, ρ l : Equilibrium density of a system containing only the first molecular model m l : Mass of the first molecular model M1 in the mixed system model V l : The volume occupied by the first molecular model M1 in the mixed system model.

[0052] The mass m in equation (1) above l This is obtained by summing the masses of the particle model 5 for all first molecular models M1 included in the mixed system model 10 shown in Figure 7. Note that the volume V in equation (1) above l Since this is obtained by subtracting the volume Vs occupied by the second molecular model M2 contained in the mixed system model 10 from the equilibrium volume V of the mixed system model 10, the equilibrium density ρ of the system containing only the first molecular model M1 can be obtained based on the following equation (2), which is a transformation of the above equation (1). l It is possible to calculate this. ρ l =m l / (VV s ) … (2) Here, ρ l : Equilibrium density of a system containing only the first molecular model ml : Mass of the first molecule model in the mixed system model V: Volume of the equilibrium state in the mixed system model. V s : The volume occupied by the second molecule model in the mixed system model.

[0053] In equation (2) above, the equilibrium volume V of the mixed system model 10 can be identified as the volume occupied by all the first molecular model M1 and all the second molecular model M2 in the mixed system model 10 after structural relaxation shown in Figure 7. Furthermore, the volume V occupied by the second molecular model M2 contained in the mixed system model 10 is also defined as V. s The mass m of the second molecular model contained in the mixed system model 10. s This is obtained by dividing by the equilibrium density ρs of the second molecule (second molecule model M2). Therefore, based on the following equation (3), which is a transformation of the above equation (2), the equilibrium density ρ of the system containing only the first molecule model M1 is obtained. l It is possible to calculate this. ρ l =m l / (Vm s / ρ s ) … (3) Here, ρ l : Equilibrium density of a system containing only the first standalone model m l : Mass of the first molecule model in the mixed system model V: Volume of the equilibrium state in the mixed system model. m s : Mass of the second molecule model in the mixed system model ρ s : Equilibrium density of the second molecule (second molecule model)

[0054] The mass m of the second molecule model M2 contained in the mixed system model 10 s This is obtained by summing the masses of particle model 5 for all second molecule models M2 included in the mixed system model 10 shown in Figure 7. Furthermore, the equilibrium density ρ of the second molecule is obtained. s This is the equilibrium density ρ of the second molecular model M2. sThis can be calculated as follows, but it can also be obtained without necessarily using molecular dynamics calculations. This equilibrium density ρ s For example, experimental values ​​obtained in experiments may be used, or values ​​described in the literature may be used. Also, the equilibrium density ρ of the second molecular model M2 s This can be obtained by separately calculating structural relaxation based on molecular dynamics calculations targeting only the second molecular model M2 shown in Figure 6 (the system containing only the second molecular model M2 (hereinafter sometimes referred to as the "second standalone model")). Since this second molecular model M2 has a smaller molecular weight than the first molecular model M1 shown in Figure 5, the equilibrium state of the second standalone model can be calculated in a short time. Therefore, the equilibrium density ρ of the second molecular model M2 s It can be easily obtained.

[0055] In the density estimation step S2 of this embodiment, first, the equilibrium density of the second molecule is input. In this embodiment, instead of using experimental values ​​of the equilibrium density of the second molecule, the structural relaxation based on molecular dynamics calculations for the second molecule model M2 shown in Figure 6 is calculated to determine the equilibrium density ρ of the second molecule model M2. s The following is calculated: Then, the equilibrium density ρ of the second molecule (second molecule model M2) s And the calculation results of the mixed system model 10 after structural relaxation shown in Figure 7 (in this example, the mass m of the first molecular model M1 included in the mixed system model 10) l The mass m of the second molecule model M2 contained in the mixed system model 10 s Based on the volume V) of the equilibrium state of the mixed system model 10, the equilibrium density ρ of the system containing only the first molecular model M1 is determined. l This is estimated. Figure 8 is a flowchart showing an example of the processing procedure for the density estimation step S2.

[0056] [Enter the equilibrium density of the second molecule] Next, in the density estimation step S2 of this embodiment, first, the equilibrium density ρ of the second molecule is determined. s However, this is input to computer 1 shown in Figure 1 (step S21). As described above, in this embodiment, the equilibrium density ρ of the second molecule sWithout using experimental values, etc., we calculate the structural relaxation based on molecular dynamics calculations for the second molecular model M2, and determine the equilibrium density ρ of the second molecular model M2. s The following is calculated. Figure 9 shows the equilibrium density ρ of the second molecular model M2. s This figure shows an example of the second standalone model 13 used in the calculation. In Figure 9, a portion of the second molecular model M2 is shown as representative.

[0057] In step S21 of this embodiment, first, a cell 11, which is a virtual space to be analyzed, is defined separately from the mixed system model 10 shown in Figure 7. Next, multiple second molecular models M2 are placed inside the cell 11. This sets up a system containing only the second molecular models M2 (i.e., the second standalone model 13). The placement of the second molecular models M2 inside the cell 11 is preferably carried out based on the Monte Carlo method, for example. The number of second molecular models M2 (total number of monomers) is set to, for example, 100 to 100,000 monomers.

[0058] The aforementioned interaction potential P1 is defined between adjacent second molecular models M2, M2. Then, structural relaxation is calculated based on molecular dynamics calculations targeting only the second molecular model M2. In this embodiment, molecular dynamics calculations are performed on the particle model 5 of the second molecular model M2 until artificial initial configurations are sufficiently eliminated. This allows the equilibrium state (relaxed state) of the second molecular model M2 to be calculated.

[0059] As mentioned above, the second molecular model M2 has a smaller molecular weight than the first molecular model M1 (shown in Figure 7). Therefore, the equilibrium state of the second molecular model M2 can be calculated in a short time by performing structural relaxation calculations that target only the second molecular model M2.

[0060] Next, in step S21 of this embodiment, in the second standalone model 13 in which the equilibrium state of the second molecular model M2 has been calculated, the volume occupied by all the second molecular models M2 and the total mass obtained by summing the masses of the particle models 5 contained in all the second molecular models M2 are obtained. Then, by dividing the total mass by the volume, the equilibrium density ρ of the second molecular model M2 is obtained.s The equilibrium density ρ of the second molecular model M2 is calculated. s This is stored in computer 1 (shown in Figure 1). Note that the equilibrium density ρ of the second molecular model M2 is also stored. s Instead, the equilibrium density ρ of the second molecule s If obtained, the equilibrium density ρ of the obtained second molecule s However, this is stored in computer 1 (shown in Figure 1).

[0061] [Equilibrium density ρ of a system containing only the first molecular model] l [estimated] Next, in the density estimation step S2 of this embodiment, the computer 1 (shown in Figure 1) calculates the equilibrium density ρ of the second molecule (second molecule model M2). s Based on the calculation results of the mixed system model 10 after structural relaxation (shown in Figure 7), the equilibrium density ρ of the system containing only the first molecular model M1 is calculated. l (Step S22) is used to estimate the mass of the first molecular model M1 contained in the mixed system model 10. l And the mass m of the second molecule model M2 contained in the mixed system model 10 s Then, the volume V of the equilibrium state of the mixed system model 10 is determined. These can be determined based on the procedure described above.

[0062] In this embodiment, the equilibrium density ρ of the second molecule (second molecule model M2) input in step S21 s This is substituted into equation (3) above. Furthermore, the mass m of the first molecular model contained in the mixed system model 10, which was identified from the calculation results of the mixed system model 10 after structural relaxation l And the mass m of the second molecule model included in the mixed system model 10 s Then, the volume V of the equilibrium state of the mixed system model 10 is substituted into equation (3) above. This gives the equilibrium density ρ of the system containing only the first molecular model M1. l This can be estimated. This estimated equilibrium density ρ l This is stored in computer 1, as shown in Figure 1.

[0063] In the molecular simulation method of this embodiment, the equilibrium state of the first molecular model M1 in the mixed system model 10 is calculated in a short time, while the equilibrium density ρ of the system containing only the first molecular model, which tends to have reduced accuracy due to the influence of the second molecular model M2 included in the mixed system model 10, is calculated. l However, it can be estimated with good accuracy.

[0064] [Calculate at least one of the end-to-end distance and radius of inertia of the first molecular model] Next, in the molecular simulation method of this embodiment, computer 1 (shown in Figure 1) calculates at least one of the terminal distance and radius of inertia of the first molecular model M1 in the equilibrium mixed system model 10 (step S3). These terminal distances and radii of inertia are used to convert the units of the first coarse-grained molecular model to the units of the first molecule N1 shown in Figure 2 (i.e., real-world units).

[0065] At least one of the end-to-end distance and radius of inertia of the first molecular model M1 is used in step S5, described later, to convert the units of the first coarse-grained molecular model to the units of the first molecule N1 shown in Figure 2. In this embodiment, for example, as described in Patent Document 2 (Japanese Patent No. 6050903) and Patent Document 3 (Japanese Patent No. 7347148), the ratio of the number of beads (spatial units) of the first coarse-grained molecular model to the number of monomers (spatial units) of the first molecule N1 is calculated.

[0066] In this embodiment, the terminal distance is calculated as the Euclidean distance between the two ends of the first molecular model M1 included in the equilibrium mixed system model 10. If the mixed system model 10 includes multiple first molecular models M1, as in this embodiment, the average value of the terminal distances of these first molecular models M1 may be calculated, for example.

[0067] The radius of inertia can be appropriately calculated from the first molecular model M1 included in the equilibrium mixed system model 10, for example, based on the procedure described in Patent Document 1 above. If the mixed system model 10 includes multiple first molecular models M1, as in this embodiment, the average value of the radii of inertia of these first molecular models M1 may be calculated, for example.

[0068] The total length can be appropriately calculated from the first molecular model M1 included in the equilibrium mixed system model 10, for example, based on the procedure described in Patent Document 1 above.

[0069] Thus, in this embodiment, physical quantities such as the end-to-end distance and radius of inertia of the first molecular model M1 in equilibrium are calculated in a short time based on the equilibrium mixed system model 10. This allows the units of the first coarse-grained molecular model to be converted in a short time to the units of the first molecular N1 shown in Figure 2 (i.e., real-world units). In this embodiment, the end-to-end distance of the first molecular model M1 is calculated. The end-to-end distance is stored in the computer 1 shown in Figure 1.

[0070] [Calculate at least one of the end-to-end distance and radius of inertia of the first coarse-grained molecular model (coarse-grained model physical quantity identification step)] Next, in the molecular simulation method of this embodiment, computer 1 (shown in Figure 1) calculates at least one of the terminal distance and the radius of inertia of the first coarse-grained molecular model (coarse-grained physical quantity identification step S4). Figure 10 is a flowchart showing an example of the processing procedure for the coarse-grained physical quantity identification step S4.

[0071] [Input the first coarse-grained molecular model] Next, in the coarse-grained physical quantity identification step S4 of this embodiment, a first coarse-grained molecular model, which models the first molecule N1 shown in Figure 2, is input to the computer 1 (shown in Figure 1) as a coarse-grained molecular model (step S41). Figure 11 is a conceptual diagram showing an example of the first standalone model 17. In Figure 11, a part of the first coarse-grained molecular model M3 is shown representatively.

[0072] The first coarse-grained molecular model M3 of this embodiment is composed of a plurality of beads 15 and a binding chain 16 that connects the beads 15, 15.

[0073] Bead 15 corresponds to monomer 3 of the first molecule N1 shown in Figure 2. Each bead 15 is represented as a sphere with a diameter. In molecular dynamics calculations, bead 15 is treated as a point mass in the equation of motion. That is, parameters such as mass, diameter, charge, or initial coordinates are defined for bead 15.

[0074] The number of beads can be appropriately set based on, for example, the structure of the first molecule N1 shown in Figure 2, or the performance of computer 1 (shown in Figure 1) which performs the molecular dynamics calculations described later. In this embodiment, for example, the number of beads can be selected from 5 to 1000.

[0075] The binding chain 16 is constructed as a binding potential that defines an equilibrium length between beads 15, 15. Here, "equilibrium length" is the binding distance between beads 15, 15. If this binding distance changes, the binding chain 16 maintains the original equilibrium length. This allows the first coarse-grained molecular model M3 to maintain a linear three-dimensional structure. The equilibrium length is defined as the distance between the centers of adjacent beads 15, 15. The binding potential of the binding chain 16 can be set, for example, based on the description in the above-mentioned Patent Document 2. Such a first coarse-grained molecular model M3 is numerical data that can be handled by the computer 1 shown in Figure 1.

[0076] As described above, when calculating the ratio of the number of beads to the number of monomers, it is preferable to fit at least one of the end-to-end distance and radius of inertia of multiple first coarse-grained molecular models with different numbers of beads to at least one of the end-to-end distance and radius of inertia of multiple first molecular models M1 (shown in Figure 6) with different numbers of monomers. Therefore, in this embodiment, multiple first coarse-grained molecular models M3 with different numbers of beads (chain lengths) are set up.

[0077] In this embodiment, similar to the above-mentioned Patent Document 2, the beads 15 are linked together based on a plurality of different numbers of beads. This sets up a plurality of first coarse-grained molecular models M3 with different numbers of beads. The plurality of first coarse-grained molecular models M3 are input into computer 1 (shown in Figure 1).

[0078] [Calculate the equilibrium state of the first coarse-grained molecular model] Next, in the coarse-graining physical quantity identification step S4 of this embodiment, computer 1 (shown in Figure 1) calculates the structural relaxation of the first coarse-grained molecular model M3 using molecular dynamics calculations to calculate the equilibrium state of the first coarse-grained molecular model M3 (step S42). As in this embodiment, when multiple first coarse-grained molecular models M3 with different numbers of beads are set, the equilibrium state is calculated for each of these multiple first coarse-grained molecular models M3.

[0079] In step S42 of this embodiment, similar to the above-mentioned Patent Document 2, each first coarse-grained molecular model M3 with a different number of beads is placed in an independently provided cell 11. This sets up multiple first individual models 17, each with its own determined initial arrangement of first coarse-grained molecular models M3. Each first individual model 17 contains multiple first coarse-grained molecular models M3 with the same number of beads. The first coarse-grained molecular models M3 can be arranged in the cell 11, for example, based on the Monte Carlo method. The number of first coarse-grained molecular models M3 placed in each cell 11 is determined based on the above-mentioned Patent Document 2.

[0080] An interaction potential P2 is defined between adjacent first coarse-grained molecular models M3 and M3 beads 15, 15, respectively. The interaction potential P2 can be appropriately set, for example, based on the description in Patent Document 2 mentioned above.

[0081] Next, in step S42 of this embodiment, structural relaxation based on molecular dynamics calculations is performed for each of the multiple first individual models 17, which are set for each first coarse-grained molecular model M3 with a different number of beads.

[0082] In molecular dynamics calculations, for example, Newton's equations of motion are applied to each first individual model 17 (cell 11), assuming that all first coarse-grained molecular models M3 follow classical mechanics for a predetermined time. The movement of all beads 15 at each time (unit time) is then tracked and stored in computer 1 (shown in Figure 1). Furthermore, the conditions for molecular dynamics calculations are kept constant, for example, the number, volume, and temperature of the beads 15 in the system. For such molecular dynamics calculations, a molecular dynamics calculation program such as LAMMPS can be used.

[0083] In this embodiment, molecular dynamics calculations are performed on the beads 15 of the first coarse-grained molecular model M3 until artificial initial arrangements are sufficiently eliminated. This allows the equilibrium state (relaxed state) of the first coarse-grained molecular model M3 to be calculated. Since the monomer 3 shown in Figure 2 is modeled as a single bead 15 in this first coarse-grained molecular model M3, the equilibrium state of the first coarse-grained molecular model M3 can be calculated in a shorter time compared to the first molecular model M1 shown in Figure 7. Multiple structurally relaxed first individual models 17 (first coarse-grained molecular model M3 in equilibrium state) are input into computer 1 (shown in Figure 1).

[0084] [Calculate the equilibrium density of the first coarse-grained molecular model in equilibrium state] Next, in the coarse-graining physical quantity identification step S4 of this embodiment, the equilibrium density of the first coarse-grained molecular model M3 in equilibrium state is calculated (step S43). In this embodiment, the equilibrium density of the first coarse-grained molecular model M3 is calculated for each first coarse-grained molecular model M3 with a different number of beads.

[0085] The equilibrium density of the first coarse-grained molecular model M3 in equilibrium is calculated by dividing the mass of the first coarse-grained molecular model M3 by its volume, similar to equation (1) above.

[0086] The mass of the first coarse-grained molecular model M3 is obtained by summing the masses of the beads 15 for all the first coarse-grained molecular models M3 included in the first standalone model 17 shown in Figure 11. The volume of the first coarse-grained molecular model M3 can be determined as the volume occupied by all the first coarse-grained molecular models M3 in the first standalone model 17. From these masses and volumes, the equilibrium density of the first coarse-grained molecular model M3 in equilibrium state can be calculated.

[0087] Thus, since the first standalone model 17 does not include any models other than the first coarse-grained molecular model M3, the equilibrium density ρ of the system containing only the first molecular model M1 is... l Unlike the previous method, the equilibrium density of the first coarse-grained molecular model M3 can be obtained easily and quickly. The equilibrium densities calculated for each first coarse-grained molecular model M3 with a different number of beads are stored in computer 1 shown in Figure 1.

[0088] [Calculate at least one of the end-to-end distance and radius of inertia of the first coarse-grained molecular model] Next, in the coarse-grained physical quantity identification step S4 of this embodiment, computer 1 (shown in Figure 1) calculates at least one of the end-to-end distance and the radius of inertia of the first coarse-grained molecular model M3 after structural relaxation (step S44).

[0089] At least one of the end-to-end distance and radius of inertia of the first coarse-grained molecular model M3 is used in step S5, described later, to convert the units of the first coarse-grained molecular model M3 to the units of the first molecule N1 shown in Figure 2.

[0090] The terminal distance of the first coarse-grained molecular model M3 is calculated as the Euclidean distance between the beads 15, 15 located at both ends of the first coarse-grained molecular model M3 in an equilibrium state. In this embodiment, when multiple first coarse-grained molecular models M3 with different numbers of beads (chain lengths) are set up, it is preferable to determine the terminal distance for each first coarse-grained molecular model M3 with each number of beads.

[0091] The radius of inertia of the first coarse-grained molecular model M3 is calculated from the coordinate values ​​of the beads 15 of the first coarse-grained molecular model M3 in equilibrium, for example, similar to the above-mentioned Patent Document 2. In this embodiment, when multiple first coarse-grained molecular models M3 with different numbers of beads (chain lengths) are set, it is preferable to determine the radius of inertia for each first coarse-grained molecular model M3 with each number of beads.

[0092] The total length of the first coarse-grained molecular model M3 can be determined, for example, by multiplying the equilibrium internuclear distance between adjacent beads in the first coarse-grained molecular model M3 by the number of beads, similar to the above-mentioned Patent Document 2. In this embodiment, when multiple first coarse-grained molecular models M3 with different numbers of beads (chain lengths) are set, it is preferable to determine the total length for each first coarse-grained molecular model M3 with each number of beads.

[0093] In step S44 of this embodiment, the end-to-end distance of the first coarse-grained molecular model M3 is calculated, similar to the first molecular model M1. The end-to-end distance is stored in the computer 1 shown in Figure 1.

[0094] [Convert the units of the first coarse-grained molecular model to the units of the first molecule] Next, in the molecular simulation method of this embodiment, the computer 1 shown in Figure 1 converts the units of the first coarse-grained molecular model M3 shown in Figure 11 to the units of the first molecule N1 shown in Figure 2 (step S5). Such a conversion is performed based on at least one of the terminal distance and radius of inertia of the first coarse-grained molecular model M3 and at least one of the terminal distance and radius of inertia of the first molecular model M1 shown in Figure 7.

[0095] As described above, in this embodiment, the ratio of the number of beads (spatial units) of the first coarse-grained molecular model M3 shown in Figure 11 to the number of monomers (spatial units) of the first molecule N1 shown in Figure 2 is calculated. In this case, for example, similar to the above-mentioned Patent Document 3, the ratio of the Kuhn length to the Packing length (effective density) of the first molecular model M1 shown in Figure 7 is calculated. k / p and the ratio of Kuhn length to Packing length (effective density) of the first coarse-grained molecular model M3 shown in Figure 11.k / p is required.

[0096] Furthermore, it is preferable that the Kuhn length and Packing length be calculated based on the following equations (4) and (5). l k =6 <R g 2 > / L … (4) Here l k : Kuhn length of the first molecular model or the first coarse-grained molecular model L: Total length of the first molecular model or the first coarse-grained molecular model R g : Radius of inertia of the first molecular model or the first coarse-grained molecular model p = M / (6 <R g 2 >ρN A ) … (5) Here p: Packing length of the first molecular model or the first coarse-grained molecular model M: Mass of the first molecular model or the first coarse-grained molecular model R g : Radius of inertia of the first molecular model or the first coarse-grained molecular model ρ: Density of the first molecular model or the first coarse-grained molecular model N A Avogadro's number

[0097] And the effective density of the first molecular model M1 k / p and monomer number N FA The relationship and the effective density of the first coarse-grained molecular model M3 k / p and the number of beads (particles) N CG Based on this relationship, the number of monomers of the first molecule N1 per bead 15 of the first coarse-grained molecular model M3 can be determined. This makes it possible to convert the units (spatial units) of the first coarse-grained molecular model M3 to the units (spatial units) of the first molecule N1. The ratio of the number of beads of the first coarse-grained molecular model M3 to the number of monomers (spatial units) of the first molecule N1 is stored in the computer 1 shown in Figure 1.

[0098] In the molecular simulation method of the present embodiment, the equilibrium state of the mixed system model 10 including the first molecular model M1 shown in FIG. 7 is calculated in a short time. Further, in the molecular simulation method of the present embodiment, the equilibrium density ρ of the system including only the first molecular model M1 l and at least one of the end-to-end distance and the radius of gyration are calculated in a short time. Therefore, in the molecular simulation method of the present embodiment, compared with Patent Documents 2 and 3 described above, the unit of the first coarse-grained molecular model M3 shown in FIG. 11 can be converted into the unit of the first molecule N1 shown in FIG. 2 in a short time. Further, in the present embodiment, the equilibrium density ρ of the system including only the first molecular model l and at least one of the end-to-end distance and the radius of gyration are accurately estimated, so that the unit of the first coarse-grained molecular model M3 can be accurately converted into the unit of the first molecule N1.

[0099] [Perform simulation using the first coarse-grained molecular model] Next, in the molecular simulation method of the present embodiment, the computer 1 (shown in FIG. 1) performs simulations under various conditions using the first coarse-grained molecular model M3 shown in FIG. 11 (step S6). In the present embodiment, for example, the first single model 17 including the first coarse-grained molecular model M3 is used as a polymer material model that models the polymer material including the first molecule N1 shown in FIG. 2, and deformation and the like of the first single model 17 are calculated.

[0100] In step S6 of the present embodiment, the first coarse-grained molecular model M3 is newly set based on the ratio of the number of beads of the first coarse-grained molecular model M3 (shown in FIG. 11) to the number of monomers of the first molecule N1 (shown in FIG. 2). By using such a newly set first coarse-grained molecular model M3, it becomes possible to obtain a result approximated to the first molecule N1.

[0101] [Determine whether the simulation results are good] Next, in the simulation method of this embodiment, computer 1 (shown in Figure 1) determines whether the simulation results are good (i.e., whether they have the desired performance) or not (step S7). In step S7, similar to the above-mentioned Patent Document 2, the time unit of the first coarse-grained molecular model M3 (shown in Figure 11) may be converted to the time unit of the first molecule N1 based on the correspondence between the time unit of the first coarse-grained molecular model M3 and the time unit of the first molecule N1 (shown in Figure 2). This makes it possible to treat the calculation results of molecular dynamics calculations under various conditions using the first coarse-grained molecular model M3 as the actual motion of the first molecule N1, thereby enabling accurate evaluation of the simulation results.

[0102] If the simulation results are deemed favorable ("Yes" in step S7), a material containing the first molecule N1 shown in Figure 2 is manufactured (step S8). On the other hand, if the simulation results are deemed unfavorable ("No" in step S7), the structure and conditions of the first molecule N1 are changed (step S9), and the equilibrium state calculation steps S1 to S7 are performed again. This makes it possible to develop an unknown first molecule N1 with the desired performance.

[0103] In this embodiment, the molecular simulation method allows for the calculation of the equilibrium state of the first molecular model M1 in the mixed system model 10 shown in Figure 7 in a short time. Therefore, the units of the first coarse-grained molecular model M3 can be converted to the units of the first molecular model N1 in a short time. As a result, simulation results can be obtained in a short time, which reduces the development cost of the first molecular model N1.

[0104] [Molecular Simulation Method (Second Embodiment)] In the previous embodiments, the second molecule was configured as a dimer in which two monomer 3s of the first molecule N1 shown in Figure 2 were bonded together, but the embodiment is not limited to this configuration. For example, the second molecule may include a molecule that acts as a solvent for the first molecule N1. By including a second molecule model M2, which models such a second molecule, in the mixed system model 10 shown in Figure 7, the motion of the first molecule model M1 is more effectively promoted, and the equilibrium state of the first molecule model M1 can be calculated in an even shorter time. In order to reduce the influence of the second molecule model M2 on the radius of inertia and end-to-end distance of the first molecule model M1, it is preferable that the second molecule model M2 be the theta solvent for the first molecule model M1.

[0105] Although particularly preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be implemented in various modified forms. [Examples]

[0106] Molecular simulations were performed, including an equilibrium state calculation step to calculate the equilibrium state of the mixed system model (Examples and Comparative Examples).

[0107] In the examples, several first and second molecular models were defined based on the processing procedure shown in Figure 4. The first molecular model is a whole-atom model of a first molecule composed of multiple monomers bonded together. The second molecular model is a whole-atom model of a second molecule with a smaller molecular weight than the first molecule.

[0108] Next, in the example, a mixed system model was defined that included multiple first molecular models and second molecular models. The volume fraction of the second molecular models was set to 0.75. Then, in the example, structural relaxation based on molecular dynamics calculations was performed on the mixed system model, and the equilibrium state of the mixed system model was calculated.

[0109] Furthermore, in the embodiment, a density estimation step was performed to estimate the equilibrium density of a system containing only the first molecular model, based on the processing procedure shown in Figure 8. In the density estimation step of the embodiment, first, the equilibrium density of the second molecule was input. In this step, structural relaxation based on molecular dynamics calculations for the second molecular model was calculated to determine the equilibrium density of the second molecular model. Then, based on the equilibrium density of the second molecular model, the mass of the first molecular model contained in the mixed system model, the mass of the second molecular model contained in the mixed system model, and the volume of the mixed system model in equilibrium, a step was performed to estimate the equilibrium density of a system containing only the first molecular model. Furthermore, the terminal distance of the first molecular model was calculated in the mixed system model in equilibrium.

[0110] On the other hand, in the comparative example, a single model containing only multiple first-molecule models was defined, as in the conventional method. In the comparative example, structural relaxation based on molecular dynamics calculations was performed for the single model, and the equilibrium state of the first-molecule model was calculated. The equilibrium density and end-to-end distance of the first-molecule model were then calculated. The common specifications are as follows: Molecular 1: Polyisoprene (number of monomers: 40) Molecular 2: Polyisoprene (number of monomers: 3)

[0111] Figure 12 is a graph showing the relationship between the autocorrelation function and the time constant of the first molecular model. In Figure 12, six times the time constant τ when the autocorrelation function of the terminal vectors of the first molecular model is 1 / e is identified as the time at which the equilibrium state of the first molecular model is calculated.

[0112] The time constant τ when the autocorrelation function of the example was 1 / e was 4.8% of the time constant τ when the autocorrelation function of the comparative example was 1 / e. Therefore, the example was able to calculate the equilibrium state, equilibrium density, and terminal distance of the first molecular model in a shorter time compared to the comparative example.

[0113] Furthermore, the equilibrium density of the system containing only the first molecular model estimated in the example approximated the equilibrium density of the first molecular model in the comparative example. Therefore, in the example, the equilibrium density of the first molecular model, which tends to have reduced accuracy due to the influence of the second molecular model included in the mixed system model, was estimated with good accuracy. As a result, in the example, the units of the first coarse-grained molecular model could be converted to the units of the first molecule in a shorter time compared to the comparative example. Moreover, the mean absolute percentage error, obtained by dividing the absolute value of the difference between the monomer count / bead count of the comparative example and the monomer count / bead count of the example by the monomer count / bead count of the comparative example, was 0.9%. Therefore, the example was able to convert with good accuracy, similar to the comparative example. Consequently, in the example, simulations under various conditions using the first coarse-grained molecular model could be calculated in a shorter time and with higher accuracy compared to the comparative example, and the development cost of the first molecule was reduced.

[0114] [Note] The present invention includes the following embodiments.

[0115] [Invention 1] A molecular simulation method, The process involves inputting multiple first-molecule models, each modeling a first molecule composed of multiple monomers bonded together, into a computer, as either a whole-atom model or a united-atom model. The steps include inputting into the computer at least one second molecule model, which is a model of a second molecule having a smaller molecular weight than the first molecule, as the whole atom model or the united atom model, A step of inputting a mixed system model, which includes a plurality of the first molecular models and the second molecular models, into the computer, The process includes the step of inputting the equilibrium density of the second molecule into the computer, The aforementioned computer, The process involves calculating structural relaxation based on molecular dynamics calculations for the aforementioned mixed system model, and then calculating the equilibrium state of the mixed system model. In the equilibrium mixed system model, the steps include calculating at least one of the terminal distance and radius of inertia of the first molecular model, The process involves estimating the equilibrium density of a system containing only the first molecular model, based on the equilibrium density of the second molecule, the mass of the first molecular model, the mass of the second molecular model, and the volume of the mixed system model in equilibrium. Molecular simulation methods. [2nd Invention] The molecular simulation method according to Invention 1, wherein the first molecule comprises at least one of an oligomer and a polymer. [Invention 3] The second molecule is a molecular simulation method according to the present invention, comprising a theta solvent. [4th Invention] The molecular simulation method according to any one of claims 1 to 3 of the present invention, wherein the molecular weight of the second molecule is 0.5 times or less the molecular weight of the first molecule. [5th ​​Invention] A molecular simulation method according to any one of claims 1 to 4 of the present invention, wherein the volume fraction of the second molecular model with respect to the mixed system model is 0.5 or more. [Invention 6] The process further includes inputting a coarse-grained molecular model, which is a model of the first molecule described above, into the computer. A molecular simulation method according to any one of inventions 1 to 5, wherein the computer further performs a step of converting the units of the coarse-grained molecular model to the units of the first molecule based on at least one of the terminal distance and radius of inertia of the coarse-grained molecular model, the equilibrium density of the first molecular model, and at least one of the terminal distance and radius of inertia of the first molecular model. [Explanation of symbols]

[0116] 10 Mixed System Models M1 First Molecular Model M2 Second Molecular Model

Claims

1. A molecular simulation method, The process involves inputting multiple first-molecule models, each modeling a first molecule composed of multiple monomers bonded together, into a computer, as either a whole-atom model or a united-atom model. The steps include inputting into the computer at least one second molecule model, which is a model of a second molecule having a smaller molecular weight than the first molecule, as the whole atom model or the United Atom model, A step of inputting a mixed system model, which includes a plurality of the first molecular models and the second molecular models, into the computer, The process includes the step of inputting the equilibrium density of the second molecule into the computer, The aforementioned computer, The process involves calculating structural relaxation based on molecular dynamics calculations for the aforementioned mixed system model, and then calculating the equilibrium state of the mixed system model. In the equilibrium mixed system model, the steps include calculating at least one of the terminal distance and radius of inertia of the first molecular model, The process involves estimating the equilibrium density of a system containing only the first molecular model, based on the equilibrium density of the second molecule, the mass of the first molecular model, the mass of the second molecular model, and the volume of the mixed system model in equilibrium. Molecular simulation methods.

2. The molecular simulation method according to claim 1, wherein the first molecule comprises at least one of an oligomer and a polymer.

3. The molecular simulation method according to claim 2, wherein the second molecule comprises a theta solvent.

4. The molecular simulation method according to claim 1, wherein the molecular weight of the second molecule is 0.5 times or less the molecular weight of the first molecule.

5. The molecular simulation method according to claim 1, wherein the volume fraction of the second molecular model with respect to the mixed system model is 0.5 or more.

6. The process further includes inputting the coarse-grained molecular model obtained by modeling the first molecule into the computer, The molecular simulation method according to claim 1, wherein the computer further performs the step of converting the units of the coarse-grained molecular model to the units of the first molecule based on at least one of the terminal distance and radius of inertia of the coarse-grained molecular model, the equilibrium density of the first molecular model, and at least one of the terminal distance and radius of inertia of the first molecular model.

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