JP6911512B2 - Calculation method of bond dissociation potential between atoms and simulation method of polymer material - Google Patents

Description

The present invention relates to a method for calculating the bond dissociation potential between atoms and a method for simulating a polymer material.

In recent years, various simulation methods for evaluating the properties of polymer materials using a computer have been proposed for the development of polymer materials such as rubber (see, for example, Patent Document 1 below).

In this kind of simulation method, first, a polymer material model in which a molecular chain model including a plurality of particle models is arranged in a space (cell) defined on a computer is defined. This particle model corresponds to the atoms of the polymer chain. In addition, the potential, which is a function of the distance between the particle models, is defined between the particle models of the polymer material model. In such a polymer material model, relaxation calculation based on molecular dynamics is performed in the above space. After that, for example, deformation calculation using a polymer material model is performed, and the performance of the polymer material and the like are analyzed.

Japanese Unexamined Patent Publication No. 2013-195220

In an actual polymer material, for example, it is known that a molecular chain is cleaved when a large force is applied. However, in the above simulation method, a method for cleaving the molecular chain model has not yet been sufficiently established. In order to calculate the breakage of such a molecular chain model, it is important to define the potential between the particle models that can accurately express the bonds and dissociations between the atoms of the polymer chain.

The present invention has been devised in view of the above circumstances, and provides a method for calculating a bond dissociation potential and a method for simulating a polymer material, which can define a potential capable of accurately expressing a bond and dissociation between atoms. The main purpose is that.

The present invention is a method for calculating the bond dissociation potential between atoms constituting a molecule using a computer, and defines the computer as a molecular model in which particle models modeling the atoms are bonded to each other. The step includes a calculation step in which the computer calculates a wave function by quantum mechanics calculation using the molecular model, and an evaluation step in which the computer determines whether or not the wave function is stable. When it is determined that the wave function is stable, a step of obtaining the coupling dissociation potential between the particle models is carried out based on the wave function, and when it is determined that the wave function is not stable, the wave function is obtained. It is characterized in that the recalculation step of recalculating the wave function is carried out so that the energy of the wave function becomes low.

In the method for calculating the bond dissociation potential between atoms according to the present invention, it is desirable that the quantum mechanics calculation is performed based on the density functional theory.

In the method for calculating the bond dissociation potential between atoms according to the present invention, the calculation step includes a step of calculating the energy of the wave function, and the evaluation step is a quadratic variation of the energy by the wave function. When the eigenvalue does not include a negative eigenvalue, it is desirable to determine that the wavefunction is stable.

In the method for calculating the bond dissociation potential between atoms according to the present invention, it is desirable that the recalculation step recalculates the wave function so that the negative eigenvalue disappears.

The present invention is a simulation method for analyzing the breakage of a molecular chain of a polymer material by using the bond dissociation potential obtained by the calculation method according to any one of claims 1 to 4, wherein the molecule A step of defining a molecular chain model including a plurality of the particle models and a bond model that binds the particle models to the computer based on the chain, at least one of the molecules in the space defined by the computer. The step of defining the polymer material model in which the chain model is arranged and the step of cutting calculation in which the computer calculates the cutting of the molecular chain model based on predetermined conditions are included, and the cutting calculation step includes the step of calculating the cutting of the molecular chain model. It is characterized by including a step of defining a binding potential close to the binding dissociation potential between the particle models of the polymer material model.

In the method for simulating the polymer material according to the present invention, the bond potential is set to the bond dissociation potential in the range from the lower limit of the energy of the bond dissociation potential to 50% to 80% of the upper limit of the energy. It is desirable to be defined by an approximate function.

In the method for simulating a polymer material according to the present invention, in the cutting calculation step, the distance between the particle models adjacent to each other via the bond model is predetermined for the molecular chain model after the molecular mechanics calculation step. Further including a step of determining whether or not there is a detached particle model portion larger than the first distance, and when it is determined that the detached particle model portion exists, in the non-overall region including the detached particle model portion. When the distance between the particle models is larger than the predetermined second distance between the quantum mechanics calculation step of performing the quantum mechanics calculation for a certain first region and the first region after the quantum mechanics calculation step. It is desirable to include a step of cutting between them.

In the method for simulating a polymer material according to the present invention, it is desirable that the first distance is smaller than the second distance.

In the method of simulating the polymer material according to the present invention, the second distance is defined based on the distance between the particle models at the inflection point where the increment of energy of the bond dissociation potential becomes smaller. Is desirable.

The method for calculating the bond dissociation potential between atoms according to the first invention of the present application includes a calculation step in which a computer calculates a wave function by quantum mechanics calculation using a molecular model.

As a result of intensive research, the inventors may calculate an unstable wave function in the calculation process, and when the bond dissociation potential is obtained from the unstable wave function, the bond and dissociation between atoms are accurately expressed. I found that I couldn't do it. Furthermore, the inventors have found that a stable wave function can be obtained by relaxing the conditions used in quantum mechanics calculations.

Based on these findings, the first invention of the present application includes an evaluation step of determining whether or not the wave function is stable prior to the step of obtaining the bond dissociation potential. Then, when it is determined that the wave function is stable, a step of obtaining the coupling dissociation potential between the particle models is carried out based on the wave function, and when it is determined that the wave function is not stable, the said wave function A recalculation step is performed to recalculate the wavefunction so that the energy is low.

As described above, in the first invention of the present application, the bond dissociation potential is obtained based on the stable wave function. Moreover, when the wave function is not stable, the stable wave function can be obtained by recalculating the wave function so that the energy of the wave function becomes low. Therefore, in the first invention of the present application, it is possible to surely obtain the bond dissociation potential capable of accurately expressing the bond and dissociation between atoms.

The method for simulating a polymer material of the second invention of the present application includes a cutting calculation step in which a computer calculates the cutting of a molecular chain model based on predetermined conditions. The cutting calculation step includes a step of defining a bond potential that approximates the bond dissociation potential between the particle models of the polymer material model.

Since the bond dissociation potential is obtained by the calculation method of the first invention of the present application, the bond and dissociation between atoms can be accurately expressed. Therefore, in the second invention of the present application, the breakage between particle models can be approximated to the breakage of an actual molecular chain.

It is a perspective view which shows an example of the computer which executes the calculation method of the bond dissociation potential between atoms of this embodiment. It is a flowchart which shows an example of the processing procedure of the calculation method of the bond dissociation potential between atoms. It is a conceptual diagram which shows an example of a molecular model. It is a flowchart which shows an example of the processing procedure of a molecular model definition process. (A) to (c) are diagrams for explaining the potential. It is a side view of the molecular model of FIG. It is a graph which shows an example of a bond dissociation potential. It is a structural formula of polyisoprene. It is a flowchart which shows an example of the processing procedure of the simulation method of a polymer material. It is a conceptual diagram which shows an example of a molecular chain model. It is a flowchart which shows an example of the processing procedure of the molecular chain model setting process. It is a conceptual diagram which shows an example of a polymer material model. It is a flowchart which shows an example of the processing procedure of a cutting calculation process. It is a side view explaining an example of the elongation simulation of a polymer material model. It is a flowchart which shows an example of the processing procedure of the coupling potential definition process. It is a figure which shows an example of the molecular model used to obtain the bond dissociation potential. It is a graph which shows the bond dissociation potential and the bond potential. It is a flowchart which shows an example of the processing procedure of the quantum mechanics calculation process. It is a figure which shows the 1st region. It is a graph of the bond dissociation potential of Examples and Comparative Examples. It is a graph which showed the relationship between the number of cuts between the particle models of an Example, and the elongation rate of a polymer material model. It is a graph which showed the relationship between the stress of the polymer material of an Example, and the elongation rate of a polymer material model.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
The method for calculating the bond-dissociation potential between atoms of the present embodiment (hereinafter, may be simply referred to as "calculation method") is for obtaining the potential for expressing the bond and dissociation between atoms constituting the molecule by using a computer. belongs to.

FIG. 1 is a perspective view showing an example of a computer that executes the calculation method of the present embodiment. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Further, the storage device stores in advance the calculation method of the present embodiment and the processing procedure (program) for executing the simulation method described later.

In the calculation method of the present embodiment, an embodiment in which the bond dissociation potential between the carbon atom and the sulfur atom of _{methanethiol (CH 3 SH) is calculated is exemplified.} It should be noted that the bond dissociation potential between the atoms constituting various molecules can be calculated without being limited to methanethiol. FIG. 2 is a flowchart showing an example of the processing procedure of the calculation method of the present embodiment.

In the calculation method of the present embodiment, the molecular model is first defined in the computer 1 (molecular model definition step S1). FIG. 3 is a conceptual diagram showing an example of a molecular model.

The molecular model 2 is configured as an all-atomic model. The molecular model 2 includes a plurality of particle models 3, and these particle models 3 are bound to each other. The molecular model 2 of the present embodiment includes a bond model 4 that bonds between the particle models 3. FIG. 4 is a flowchart showing an example of the processing procedure of the molecular model definition step S1.

In the molecular model definition step S1 of the present embodiment, first, as shown in FIG. 3, the particle model 3 is set in the computer 1 (step S11). The particle model 3 is treated as a mass point of the equation of motion in a simulation based on quantum mechanics calculation described later. That is, in the particle model 3, parameters such as mass, diameter, charge, or initial coordinates are defined.

The particle model 3 of this embodiment models a carbon particle model 3C that models a carbon atom, a hydrogen particle model 3H that models a hydrogen atom, and a sulfur atom for a molecule (methanethiol in this embodiment). Includes the sulfur particle model 3S.

Next, in the molecular model definition step S1 of the present embodiment, the bond model 4 is set in the computer 1 (step S12). The bond model 4 constrains between the particle models 3 and 3. The bond model 4 of the present embodiment is between the carbon particle model 3C and the sulfur particle model 3S, between the carbon particle model 3C and the hydrogen particle model 3H, and between the sulfur particle model 3S and the hydrogen particle model 3H. Each is provided.

Next, in the molecular model definition step S1 of the present embodiment, the potential for interaction (including repulsive force and attractive force) to occur between the adjacent particle models 3 and 3 is defined (step S13). 5 (a) to 5 (c) are diagrams for explaining the potential.

As shown in FIGS. 5 (a) to 5 (b), the molecular model 2 is provided with a bond distance (bond length) r, which is a bond length between the particle models 3 and 3, and a bond model 4. A bond angle θ, which is an angle formed by three consecutive particle models 3, is defined. Further, as shown in FIG. 5 (c), in the molecular model 2, one plane 5A and the other plane 5A formed by the three adjacent particle models 3 in the four continuous particle models 3 via the bond model 4 are shown. An angled dihedral angle φ with the plane 5B is defined. The bond distance r, the bond angle θ, and the dihedral angle φ change depending on the external force or the internal force acting on the molecular model 2.

ここで、各定数及び変数は、次のとおりである。
ｒ：結合距離
ｒ₀：平衡距離（平衡長）
ｋ₁、ｋ₂：ばね定数
θ：結合角
θ₀：平衡角度
ｋ₃：二面角ポテンシャルの強度
Ｎ−1：二面角ポテンシャル多項式の次数
φ：二面角
Ａ_n：二面角定数
なお、結合距離ｒ及び平衡距離ｒ₀は、各粒子モデル３の中心３ｃ（図６に示す）間の距離として定義される。 The bond distance r, the bond angle θ, and the dihedral angle φ are the bond potential U _{bond (r) defined by the following equation (1), the bond angle potential U angle} (θ) defined by the following equation (2), and the bond angle potential U angle (θ). , It is set by the _{bond angle potential U torsion} (φ) defined by the following equation (3).

Here, each constant and variable is as follows.
r: Bond distance r ₀ : Equilibrium distance (equilibrium length)
k ₁ , k ₂ : Spring constant θ: Bond angle θ ₀ : Equilibrium angle k ₃ : Dihedral angle potential strength N-1: Dihedral angle potential Polygon order φ: Dihedral angle _An : Dihedral angle constant Note that , Bond angle r and equilibrium distance r ₀ are defined as the distance between the centers 3c (shown in FIG. 6) of each particle model 3.

The constants of each bond potential U _bond (r), bond angle potential U _angle (θ), and bond dihedral angle potential U _torsion (φ) can be appropriately set. It is desirable that these potentials are set according to the structure of the molecular chain Mc based on the paper (J. Phys. Chem. 94, 8897 (1990)).

By defining these potentials between the adjacent particle models 3 and 3, the molecular model 2 shown in FIG. 3 is defined. The molecular model 2 is stored in the computer.

Next, in the calculation method of the present embodiment, the theory and basis functions used in the quantum mechanics calculation described later are defined between the particle models 3 and 3 (step S2). As a theory defined in this embodiment, for example, a density functional theory (functional: B3LYP) is defined. Further, as the basis function, for example, a basis function (6-31G (d)) is defined. The theory and basis functions used for these quantum mechanics calculations can be defined by using the quantum chemistry calculation program Gaussian03 or Gaussian09 manufactured by Gaussian. These theories and basis functions are stored in computer 1.

Next, in the calculation method of the present embodiment, the conditions (constraints) used in the quantum mechanics calculation are defined (step S3). The conditions relate to molecular orbitals. Examples of conditions include charges, spin multiplicity, spatial orbits, symmetry restrictions, and the like. These conditions are parameters used in the quantum mechanics calculation and are stored in the computer 1.

Next, in the calculation method of the present embodiment, the computer 1 calculates the wave function by quantum mechanics calculation using the molecular model 2 (calculation step S4). In the calculation step S4, the quantum mechanics calculation is performed based on the conditions (constraints) predetermined in the above step S3.

In quantum mechanics calculations, the electronic state of the particle model 3 is tracked at each unit-time step of the simulation, assuming that the molecular model 2 follows an interaction based on nuclei and electrons. Therefore, the quantum mechanics calculation has higher calculation accuracy than the molecular mechanics calculation. Such quantum mechanics calculations can be processed using the quantum chemistry calculation program described above.

FIG. 6 is a side view of the molecular model of FIG. _{As shown in FIG. 6, in the molecular model 2, the equilibrium distance r 0} of the particle models 3 and 3 is determined by the balance of the interaction based on the nucleus and the electron according to the above theory and the basis function. In the calculation step S4 of the present embodiment, for example, from the state where the particle models 3 and 3 are _{in contact with each other until the distance r between the particle models 3 and 3 becomes larger than the equilibrium distance r 0} (for example, 4.5 Å). During that time, a quantum mechanics calculation is performed to separate the particle models 3 and 3 by 0.1 Å per unit time step, and the energy of the wave function is calculated.

In the calculation step S4 of the present embodiment, the spin multiplicity is set to a singlet. As a result, in the calculation step S4, the energy of the wave function having no unpaired electrons is calculated. The energy of the wave function is input to the computer 1.

Next, as shown in FIG. 2, in the calculation method of the present embodiment, the computer 1 determines whether or not the wave function is stable (evaluation step S5). The wave function becomes more stable as its energy decreases. In general, if the eigenvalue of the current wavefunction energy is quadratically varied by the wavefunction and contains a negative eigenvalue, it means that there is a stable wavefunction with lower energy. In such a case, the current wave function can be determined to be unstable. Such instability of the wave function is likely to occur when calculating molecules with very long interatomic distances, especially in the density functional theory, which considers only a single electron configuration. In the evaluation step S5 of the present embodiment, the wave function is stable when the eigenvalues obtained by subdividing the energy of the wave function by the wave function do not include negative eigenvalues (that is, they are all positive eigenvalues). It is judged that it is. As a result, in the evaluation step S5 of the present embodiment, a stable wave function can be reliably determined.

When the computer 1 determines in the evaluation step S5 that the wave function is stable (“Y” in the evaluation step S5), the particle models 3 and 3 (shown in FIG. 6) are based on the stable wave function. The bond dissociation potential between them is obtained (step S6). On the other hand, when the computer 1 determines that the wave function is not stable (“N” in the evaluation step S5), the recalculation step S7 recalculates the wave function so that the energy of the current wave function becomes low. Is carried out.

In step S6 for obtaining the bond dissociation potential, the bond dissociation potential in a unit time step is obtained based on the wave function. That is, the bond dissociation potential is obtained based on the relationship between the distance r between the particle models 3 and 3 (shown in FIG. 6) and the energy of the wave function. The bond dissociation potential is input to computer 1.

In the recalculation step S7 of the present embodiment, the electrons are arranged so that the eigenvalues obtained by quadratic variation of the energy of the current wavefunction by the wavefunction have no negative eigenvalues (that is, all have positive eigenvalues). Alternatively, the order of the orbits is changed. Such rearrangement of electron arrangement and orbital order can be calculated by adding the option "Stable = Opt" in the above-mentioned quantum chemistry calculation program. As a result, in the recalculation step S7, a wave function having a lower energy can be calculated.

Next, as shown in FIG. 2, in the calculation method of the present embodiment, the computer 1 separates the particle models 3 and 3 (shown in FIG. 6) by a predetermined distance (for example, 4.5 Å). It is determined whether or not this has been done (step S8). When it is determined in step S8 that the particle models 3 and 3 are separated by a predetermined distance (“Y” in step S8), a series of processes of the calculation method of the present embodiment is completed.

On the other hand, in step S8, when it is determined that the particle models 3 and 3 (shown in FIG. 6) are not separated by a predetermined distance (“N” in step S6), one unit time step is advanced. (Step S9), the calculation steps S4 to S8 are carried out again. As a result, it is possible to obtain the bond dissociation potential from the state in which the particle models 3 and 3 are in contact until the distance r between the particle models 3 and 3 _{becomes larger than the equilibrium distance r 0 (for example, 4.5 Å).} can. In the calculation step S4, the wave function is calculated after redefining the conditions relaxed in the recalculation step S7 to the original conditions.

FIG. 7 is a graph showing an example of the bond dissociation potential Pu. In the graph of FIG. 7, the bond dissociation potential Pu is the potential of the wave function as the distance r between the particle models 3 and 3 shown in FIG. 6 _{becomes smaller than the equilibrium distance r 0 (2.1 in this embodiment).} The energy (repulsive force between particle models 3 and 3) increases. Further, the bond dissociation potential Pu has the minimum potential energy when the distance r becomes 2.1, and no repulsive force or attractive force acts between the particle models 3 and 3. Further, in the bond dissociation potential Pu, as the distance r becomes _{larger than the equilibrium distance r 0} , the potential energy of the wave function (the attractive force between the particle models 3 and 3) becomes larger. In this way, the bond dissociation potential Pu can define the repulsive force and the attractive force according to the distance r.

The bond dissociation potential Pu has an inflection point 8 in which the increment of the energy of the wave function becomes small in the region where the distance r between the particle models 3 and 3 (shown in FIG. 6) _{is larger than the equilibrium distance r 0.} .. The inflection point 8 is a pair that approximates the coupling dissociation potential Pu in the region where the distance r is expected to be larger than the inflection point 8 and the region where the distance r is expected to be smaller than the inflection point 8. It can be specified at the intersection of the straight lines 9a and 9b.

In the region Tb where the distance r is smaller than the inflection point 8, the increase in the energy of the wave function is larger than in the region Ta where the distance r between the particle models 3 and 3 (shown in FIG. 6) is larger than the inflection point 8. big. This indicates that the bond between the particle models 3 and 3 is firmly maintained in the region Tb smaller than the inflection point 8. Further, in the region Ta where the distance r is larger than the inflection point 8, cutting or bond order is reduced between the particle models 3 and 3, and the increment of the energy of the wave function is small. Therefore, the inflection point 8 can be considered as the boundary between the bond and the dissociation between the particle models 3 and 3. Therefore, the bond dissociation potential Pu of the present embodiment can accurately represent the bond and dissociation between atoms.

As described above, in the calculation method of the present embodiment, the bond dissociation potential Pu can be obtained by using only the stable wave function. Moreover, if the wavefunction is not stable, it is recalculated until the wavefunction is stable. Therefore, the calculation method of the present embodiment can surely obtain the bond dissociation potential Pu capable of accurately expressing the bond and dissociation between atoms.

Further, in the present embodiment, since the quantum mechanics calculation is performed based on the density functional theory (DFT), the calculation time is shortened as compared with other theories (for example, MP2, CCSDT, CASSCF, MRCI, etc.). can do. Therefore, in the calculation method of the present embodiment, the bond dissociation potential Pu capable of accurately expressing the bond and dissociation between atoms can be obtained in a short time.

Next, a polymer material simulation method for analyzing the breakage of molecular chains of the polymer material using the bond dissociation potential obtained by the calculation method of the present embodiment (hereinafter, simply referred to as “simulation method”). Yes) will be explained.

The simulation method of this embodiment is a method for analyzing the breakage of a molecular chain of a polymer material by using a computer 1 (shown in FIG. 1). In order to calculate the breakage of a molecular chain, it is important to define the potential that can accurately express the bond and dissociation between atoms of the polymer chain. In this embodiment, since the bond dissociation potential Pu obtained by the above calculation method is used, it is useful for accurately analyzing the breakage of the molecular chain.

Examples of the polymer material include rubber, resin, elastomer and the like. The polymer material of the present embodiment is cis-1,4 polyisoprene (hereinafter, may be simply referred to as "polyisoprene"). FIG. 8 is a structural formula of polyisoprene.

The molecular chain 11A constituting the polyisoprene is an isoprene monomer composed of a methine group or the like (for example, -CH =,> C =), a methylene group (-CH _2- ), and a methyl group (-CH _3). (Isoprene molecule) 12 is linked at a degree of polymerization n. A polymer material other than polyisoprene may be used as the polymer material 11.

FIG. 9 is a flowchart showing an example of the processing procedure of the simulation method of the present embodiment. In the simulation method of the present embodiment, first, a molecular chain model is defined in the computer 1 based on the molecular chain 11A shown in FIG. 8 (molecular chain model setting step S21). FIG. 10 is a conceptual diagram showing an example of the molecular chain model 13.

The molecular chain model 13 is configured as an all-atomic model. The molecular chain model 13 of this embodiment is set as a polyisoprene in which one sulfur atom is crosslinked. The molecular chain model 13 includes a plurality of particle models 3 and a bond model 4 that connects the particle models 3 and 3.

The particle model 3 and the bond model 4 are linked based on the unit structure forming the monomer 12 of the molecular chain 11A shown in FIG. As a result, the monomer model 14 is set. The monomer model 14 is linked based on the molecular weight (degree of polymerization) Mn. As a result, the molecular chain model 13 is set. FIG. 11 is a flowchart showing an example of the processing procedure of the molecular chain model setting step S21.

In the molecular chain model setting step S21 of the present embodiment, the particle model 3 is first set as shown in FIG. 10 (step S211). The particle model 3 is treated as a mass point of the equation of motion in a simulation based on molecular dynamics calculation, molecular mechanics calculation, and quantum mechanics calculation, which will be described later. That is, in the particle model 3, parameters such as mass, diameter, charge, or initial coordinates are defined.

The particle model 3 of the present embodiment includes a carbon particle model 3C, a hydrogen particle model 3H, and a sulfur particle model 3S. These particle models 3 are stored in the computer 1.

Next, in the molecular chain model setting step S21, the bond model 4 is set (step S212). The bond model 4 constrains between the particle models 3 and 3. The bond model 4 of the present embodiment includes a main chain 4a and a side chain 4b. The main chain 4a connects the carbon particle models 3C and 3C. The side chain 4b connects between the carbon particle model 3C and the hydrogen particle model 3H, and between the carbon particle model 3C and the sulfur particle model 3S. These bond models 4 are stored in the computer 1.

Next, in the molecular chain model setting step S21, the potential for interaction (including repulsive force and attractive force) is defined between the adjacent particle models 3 and 3 via the bond model 4 (potential definition step S213). ). As shown in FIG. 10, the potential includes the first potential P1 defined between the adjacent particle models 3 and 3 via the bond model 4 and the adjacent particle models 3 and 3 without passing through the bond model 4. The second potential P2 defined between them is defined. The first potential P1 is set based on the above formulas (1) to (3), similarly to the molecular model 2 shown in FIGS. 3 and 5.

The second potential P2 is the LJ potential _ULJ (r _ij ) defined by the following equation (4).

ここで、各定数及び変数は、Lennard-Jones ポテンシャルのパラメータであり、次のとおりである。
ｒ_ij：粒子モデル間の距離
ε：粒子モデル間に定義されるＬＪポテンシャルの強度
σ：粒子モデルの直径に相当
なお、距離ｒ_ijは、各粒子モデル３、３の中心（図示省略）間の距離として定義される。

Here, each constant and variable is a parameter of the Lennard-Jones potential and is as follows.
r _ij : Distance between particle models ε: Strength of LJ potential defined between particle models σ: Corresponds to the diameter of the particle model Note that the distance r _ij is between the centers of the particle models 3 and 3 (not shown). Defined as a distance.

The second potential P2 is as the distance r _ij between particles model 3 and 3 is smaller than _{r c,} increases the repulsive force acting between the particles model 3,3. The second potential P2 becomes a minimum when the distance r _ij between particles model becomes r _c, does not work repulsion or attraction between particles model 3,3. Further, the second potential P2, when the distance r _ij between particles model is larger than r _c, it acts attractive force acting between the particles model 3,3. In this way, the second potential P2 can define the repulsive force and the attractive force according to _{the distance r ij between the particle models.}

In this embodiment, between sulfur particle models 3S and 3S, between carbon particle models 3C and 3C, between carbon particle model 3C and hydrogen particle model 3H, between sulfur particle model 3S and carbon particle model 3C, and sulfur. Different second potentials P2 are set between the particle model 3S and the hydrogen particle model 3H. Each second potential P2 has a different constant in the above equation (4). Each constant can be appropriately set based on, for example, a paper (J. Phys. Chem. 94, 8897 (1990)).

Next, in the simulation method of the present embodiment, the polymer material model is defined in the computer 1 (step S22). FIG. 12 is a conceptual diagram showing an example of a polymer material model. The polymer material model 15 is defined by arranging at least one molecular chain model 13 in the space 16 defined on the computer 1.

The space 16 of this embodiment is defined as a rectangular parallelepiped having three pairs of planes 16a and 16b facing each other. Periodic boundary conditions are defined on the planes 16a and 16b. Thereby, in the space 16, for example, it is possible to calculate so that a part of the molecular chain model 13 that has exited from one plane 16a enters from the opposite plane 16b. Therefore, it can be treated as if one plane 16a and the other plane 16b are continuous (connected).

The lengths L1, L2, and L3 of one side of the space 16 can be appropriately set. It is desirable that the length L1 of this embodiment is at least twice the inertial radius (not shown) of the molecular chain model 13. The radius of inertia is a quantity indicating the spread of the molecular chain model 13. In such a space 16, collision with the self-image due to the periodic boundary condition is less likely to occur in the molecular dynamics calculation, and the spatial extent of the molecular chain model 13 can be appropriately calculated. Further, the size of the space 16 is set to a stable volume at, for example, 1 atm. Such a space 16 can define the volume of at least a part of the polymer material. Further, the number of molecular chain models 13 arranged in the space 16 can be appropriately set. The number of molecular chain models 13 of the present embodiment is preferably set to, for example, one or more, preferably 30 or more.

In this embodiment, relaxation calculation by molecular dynamics (MD) calculation is performed using the space 16 in which the molecular chain model 13 is arranged. As a result, the polymer material model 15 is set.

In the molecular dynamics calculation of the present embodiment, for example, Newton's equation of motion is applied assuming that the molecular chain model 13 follows classical mechanics for a predetermined time in space 16. Then, the movement of the particle model 3 at each time is tracked for each unit time step. Such structural relaxation calculations can be processed using, for example, COGNAC included in the Soft Material Comprehensive Simulator (OCTA).

In the molecular dynamics calculation, the pressure and temperature are kept constant, or the volume and temperature are kept constant in the space 16. Further, in the molecular dynamics calculation, the artificial initial arrangement of the molecular chain model 13 is performed until it can be considered that the artificial initial arrangement is sufficiently excluded. As a result, in step S22, the initial arrangement of the molecular chain model 13 can be accurately relaxed by approximating the molecular motion of the actual polymer material. The polymer material model 15 is defined through such relaxation calculations. The polymer material model 15 is stored in the computer 1.

Next, in the simulation method of the present embodiment, the computer 1 calculates the cleavage of the molecular chain model 13 based on predetermined conditions (cutting calculation step S23). In the cutting calculation step S23 of the present embodiment, an elongation simulation is performed in which the polymer material model 15 shown in FIG. 12 is elongated in the uniaxial direction (for example, the Z-axis direction).

In the elongation simulation of the present embodiment, the elongation of the polymer material model 15 is calculated for each unit time step by using the molecular mechanics calculation (Molecular Mechanics: MM) and the quantum mechanics calculation (Quantum Mechanics: QM). Then, by advancing the unit time step, the polymer material model 15 extended to a predetermined length (upper limit value) is calculated. Due to the extension of the polymer material model 15, the molecular chain model 13 is separated from the particle models 3 and 3. The state in which the molecular chain model 13 is cut is calculated as the particle models 3 and 3 are separated from each other. The molecular mechanics calculation can be calculated by the above software similar to the molecular dynamics calculation.

In the quantum mechanics calculation, the electronic state and movement of the particle model 3 are tracked at each unit time step of the simulation, assuming that the molecular chain model 13 follows the interaction based on the nucleus and the electron. Therefore, the quantum mechanics calculation has higher calculation accuracy than the molecular mechanics calculation. Such quantum mechanics calculations can be processed using the quantum chemistry calculation program described above.

In the present embodiment, the elongation simulation is carried out by using the molecular mechanics calculation for the entire region of the polymer material model 15. Then, the cutting of the molecular chain model 13 is calculated in detail by using the quantum mechanics calculation only for the portion of the molecular chain model 13 that is likely to be cut between the particle models 3 and 3. Therefore, in the cutting calculation step S23 of the present embodiment, the calculation time can be significantly shortened as compared with the case where the quantum mechanics calculation is performed for the entire region of the polymer material model 15, for example. FIG. 13 is a flowchart showing an example of the processing procedure of the cutting calculation step S23 of the present embodiment.

In the cutting calculation step S23 of the present embodiment, first, the initial conditions for carrying out the elongation simulation of the polymer material model 15 are set (step S31). FIG. 14 is a side view illustrating an example of an elongation simulation of the polymer material model 15. As an initial condition, the lengths L1, L2, and L3 of the polymer material model 15 at each unit time step are defined based on the Poisson's ratio of the polymer material model 15. As a result, in the cutting calculation step S23, it is possible to carry out a simulation of extending the polymer material model in the uniaxial direction (for example, the Z-axis direction) based on the Poisson's ratio of the polymer material model 15.

The elongation rate Va in the uniaxial direction of the polymer material model 15 can be appropriately set according to the polymer material to be analyzed and the simulation conditions. The extension speed Va of this embodiment is set to, for example, 50 to 200 m / sec. As a result, in the cutting calculation step S23 of the present embodiment, it is possible to calculate the state in which the polymer material is stretched at high speed. These initial conditions are stored in the computer 1.

Next, in the cutting calculation step S23 of the present embodiment, the bond potential Pn used in the molecular mechanics calculation is defined (bond potential definition step S32). The binding potential Pn is defined in the molecular chain model 13 between the adjacent particle models 3 and 3 via the bond model 4. As the bond potential Pn of the present embodiment, a potential close to the bond dissociation potential Pu (shown in FIG. 7) obtained by the above calculation method is defined. Since such a coupling potential Pn approximates the potential in the quantum mechanics calculation, the difference between the result of the molecular mechanics calculation and the result of the quantum mechanics calculation can be minimized.

The bond dissociation potential Pu (not shown) differs depending on the type of particle model 3 to be bonded. In this embodiment, between sulfur particle models 3S and 3S, between carbon particle models 3C and 3C, between carbon particle model 3C and hydrogen particle model 3H, between sulfur particle model 3S and carbon particle model 3C, and sulfur. Different bond dissociation potentials Pu are required between the particle model 3S and the hydrogen particle model 3H. FIG. 15 is a flowchart showing an example of the processing procedure of the coupling potential definition step of the present embodiment. FIG. 16 is a diagram showing an example of the molecular model 2 used to obtain the bond dissociation potential Pu.

In the binding potential definition step S32 of the present embodiment, the molecular model 2 is first set (step S321). In the molecular model 2, all combinations of the pair of particle models 3 and 3 are set in the molecular chain model 13. In the present embodiment, a molecular model 2A in which sulfur particle models 3S and 3S are bonded, a molecular model in which carbon particle models 3C and 3C are bonded (not shown), and a molecular model in which carbon particle model 3C and hydrogen particle model 3H are bonded (not shown). A molecular model (not shown) in which the sulfur particle model 3S and the carbon particle model 3C are connected (not shown), and a molecular model (not shown) in which the sulfur particle model 3S and the hydrogen particle model 3H are connected are set. In FIG. 16, the molecular model 2A in which the sulfur particle models 3S and 3S are bound is represented as a representative.

The molecular model 2 of the present embodiment includes a pair of particle models 3 and 3 (in this embodiment, sulfur particle models 3S and 3S) and a bond model 4. In each particle model 3, the number of hydrogens obtained by subtracting the number of bonds (for example, 1) of the particle model 3 from the valence of the atom modeled in the particle model 3 (for example, in the case of sulfur atom: 2) The particle model 3H (for example, one) is connected via the bond model 4. As a result, the molecular model 2 can maintain a stable structure in the quantum mechanics calculation. Based on such a method, each of the above-mentioned molecular models 2 is set. These molecular models 2 are stored in the computer 1.

Next, in the binding potential definition step S32 of the present embodiment, the theory and basis functions used for quantum mechanics calculation are defined between the particle models 3 and 3 of each molecular model 2 (step S322). The theory and basis functions similar to the above-mentioned calculation method are defined and stored in the computer 1.

Next, in the bond potential definition step S32 of the present embodiment, the bond dissociation potential Pu (shown in FIG. 7) between the particle models 3 and 3 of the molecular model 2 is obtained based on the above calculation method (step S323). ). In step S323, quantum mechanics calculations are performed for all of the above-mentioned molecular models 2. As a result, the bond dissociation potential Pu between the sulfur particle models 3S and 3S, the bond dissociation potential Pu between the carbon particle models 3C and 3C, the bond dissociation potential Pu between the carbon particle model 3C and the hydrogen particle model 3H, and the sulfur particle model The bond dissociation potential Pu between the 3S and the carbon particle model 3C and the bond dissociation potential Pu between the sulfur particle model 3S and the hydrogen particle model 3H are obtained, respectively. Each bond dissociation potential Pu is stored in computer 1.

Next, in the bond potential definition step S32 of the present embodiment, a potential (bond potential) Pn that approximates the bond dissociation potential Pu is obtained (step S324). FIG. 17 is a graph showing the bond dissociation potential Pu and the bond potential Pn. In step S324 of the present embodiment, the harmonic oscillator type function based on Hooke's law is approximated to the bond dissociation potential Pu. As a result, the coupling potential Pn is obtained. The harmonic oscillator type function is defined by the following equation (5).

ここで、
Ｖ：分子モデルのエネルギー
ｋ：バネ定数
ｒ：粒子モデル間の距離
ｒ₀：粒子モデル間の平衡距離

here,
V: Energy of the molecular model k: Spring constant r: Distance between particle models r ₀ : Equilibrium distance between particle models

The harmonic oscillator type function of the above equation (5) is a quadratic function showing the relationship between the distance r between the particle models 3 and 3 and the energy of the molecular model (energy of the wave function). In the present embodiment, the bond potential Pn is obtained by approximating the harmonic oscillator type function to the bond dissociation potential Pu in the region Tb where the distance r is smaller than the inflection point 8 shown in FIG. Therefore, the bond potential Pn of the present embodiment is close to the bond dissociation potential Pu before cutting or a decrease in bond order occurs between the particle models 3 and 3.

As a method of approximating the harmonic oscillator type function to the bond dissociation potential Pu, for example, the least squares method can be used. In such a bond potential Pn, a complex bond dissociation potential Pu can be represented by a simple harmonic oscillator type function.

In step S324, the harmonic oscillator type is used in the range from the lower limit of the energy of the bond dissociation potential Pu (the energy of the molecular model 2) (that is, the equilibrium distance r ₀ ) to 50% to 80% of the upper limit of the energy. It is desirable to approximate the function to the bond dissociation potential Pu. As a result, the bond potential Pn can be accurately approximated to the bond dissociation potential Pu in the region Tb where the _{distance r 0 is smaller than the inflection point 8 shown in FIG.}

In the range approximated to the harmonic oscillator type function, when 80% of the upper limit of the energy of the bond dissociation potential Pu is exceeded, the region Ta having a distance larger than the inflection point 8 shown in FIG. 7 is included. There is a risk of approximating the harmonic oscillator type function. On the contrary, if it is less than 50% of the upper limit of the energy of the bond dissociation potential Pu, the range to be approximated to the bond dissociation potential Pu becomes small, and there is a possibility that the bond dissociation potential Pu cannot be approximated accurately. From such a viewpoint, it is more preferably 70% or less, more preferably 60% or more of the upper limit value of the energy of the bond dissociation potential Pu in the range approximated to the harmonic oscillator type function.

In step S324, the bond dissociation potential Pu between the sulfur particle models 3S and 3S, the bond dissociation potential Pu between the carbon particle models 3C and 3C, and the bond dissociation between the carbon particle model 3C and the hydrogen particle model 3H shown in FIG. The bond potential Pn is obtained for the potential Pu, the bond dissociation potential Pu between the sulfur particle model 3S and the carbon particle model 3C, and the bond dissociation potential Pu between the sulfur particle model 3S and the hydrogen particle model 3H, respectively.

In step S324, in the molecular chain model 13 shown in FIG. 10, a binding potential Pn is defined in place of the first potential P1 between the adjacent particle models 3 and 3 via the bond model 4, respectively. The second potential P2 defined between the adjacent particle models 3 and 3 without going through the bond model 4 is maintained.

Next, in the cutting calculation step S23 of the present embodiment, a deformation calculation for stretching the polymer material model 15 (shown in FIG. 12) is performed (stretching step S33). In this embodiment, the deformation of the polymer material model 15 is calculated based on the Poisson's ratio set as the initial condition.

In the stretching step S33, the polymer material model 15 (shown in FIG. 14) stretched in the uniaxial direction is calculated in the current unit time step. Due to the elongation of the polymer material model 15, the molecular chain model 13 shown in FIG. 12 is also elongated in the uniaxial direction, and the distance r (shown in FIG. 10) between the adjacent particle models 3 and 3 via the bond model 4 is determined. At least part of it gets bigger.

Next, in the cutting calculation step S23 of the present embodiment, molecular mechanics calculation (MM) is performed on the polymer material model 15 deformed in the elongation step S33 (first molecular mechanics calculation step S34). .. In the first molecular mechanics calculation step S34, a physical quantity including the energy Ea of the polymer material model 15 and the force Fa acting on the polymer material model 15 is calculated. A physical quantity including such energy Ea and force Fa is stored in the computer 1.

Next, in the cutting calculation step S23 of the present embodiment, with respect to the molecular chain model 13 after the first molecular mechanics calculation step S34, the distance r between the adjacent particle models 3 and 3 via the bond model 4 (shown in FIG. 10). ) Is determined whether or not there is a detached particle model unit 21 larger than the predetermined first distance La (step S35).

In step S35, the distance r between the adjacent particle models 3 and 3 is calculated via the bond model 4 for all the molecular chain models 13 arranged in the space 16. In step S35, the distance between the particle models 3 and 3 not constrained by the bond model 4 is not calculated. Then, the pair of particle models 3 and 3 and the bond model 4 in which the distance r between the particle models 3 and 3 is larger than the first distance La is determined as the separation particle model unit 21.

The first distance La of the present embodiment is set to be smaller than the distance r (Ln) between the particle models 3 and 3 at the inflection point 8 of the bond dissociation potential Pu shown in FIG. As described above, the inflection point 8 can be considered as the boundary point between the bond and the dissociation between the particle models 3 and 3. Therefore, in the separated particle model unit 21 in which the distance r is larger than the first distance La, it can be considered that there is a high possibility of cutting between the particle models 3 and 3. Therefore, in step S35, it is possible to determine the presence or absence of the detached particle model portion 21 (shown in FIG. 19) that is likely to be cut between the particle models 3 and 3.

Further, the first distance La can be appropriately set as long as it is smaller than the distance r at the inflection point 8. In the present embodiment, as shown in FIG. 17, the distance r at the intersection point 22 between the bond dissociation potential Pu and the bond potential Pn is determined as the first distance La. As a result, the presence or absence of the detached particle model unit 21 can be accurately determined based on the molecular mechanics calculation that can shorten the calculation time as compared with the quantum mechanics calculation.

When it is determined in step S35 that the detached particle model unit 21 exists (“Y” in step S35), the next quantum mechanics calculation step S36 is carried out for the detached particle model unit 21. On the other hand, when it is determined that the detached particle model unit 21 does not exist (“N” in step S35), step S40 described later is carried out.

Next, in the cutting calculation step S23 of the present embodiment, the quantum mechanics calculation is performed for the first region 23 including the detached particle model unit 21 (quantum mechanics calculation step S36). FIG. 18 is a flowchart showing an example of the processing procedure of the quantum mechanics calculation step S36.

In the quantum mechanics calculation step S36 of the present embodiment, first, the first region 23 including the detached particle model unit 21 is set (step S361). FIG. 19 is a diagram showing the first region 23. The first region 23 is a non-overall region obtained by extracting only the detached particle model portion 21 from the molecular chain model 13 of the polymer material model 15. When a plurality of separated particle model parts 21 are present in the polymer material model 15, all the separated particle model parts 21 are included in the first region 23.

Further, in each particle model 3 of the detached particle model unit 21, the number of bonds of the particle model 3 (for example, 1) is obtained from the valence of the atom modeled by the particle model 3 (for example, in the case of a carbon atom: 4). The number of hydrogen particle models 3H (for example, 3) obtained by subtracting the above is connected via the bond model 4. This makes it possible to set the detached particle model unit 21 having a stable structure in the quantum mechanics calculation.

Next, in the quantum mechanics calculation step S36 of the present embodiment, the theory and basis functions used for the quantum mechanics calculation are defined in the particle model 3 of the detached particle model unit 21 (step S362). In step S362, the theory and basis functions used in the quantum mechanics calculation are defined by disabling the coupling potential Pn set between the particle models 3 and 3 of the separated particle model unit 21. The theory and basis functions used in the quantum mechanics calculation are as described above.

Next, in the quantum mechanics calculation step S36 of the present embodiment, the quantum mechanics calculation is carried out in the first region 23 based on the Poisson's ratio set as the initial condition (step S363). As described above, in the quantum mechanics calculation, the electronic state and motion of the particle model 3 are tracked for each unit time step of the simulation, as follows the interaction based on the nucleus and the electron. Therefore, in step S363, the elongation of the first region 23 and the detached particle model unit 21 can be calculated with higher accuracy than the molecular mechanics calculation. Further, in step S363, the quantum mechanics calculation is performed only for the first region 23 extracted from the polymer material model 15. Therefore, the calculation time can be significantly shortened as compared with the case where the quantum mechanics calculation is performed for the entire region of the polymer material model 15 shown in FIG.

In step S363, a physical quantity including the energy Ec of the first region 23 and the force Fc acting on the first region 23 is calculated. The physical quantity including such energy Ec and force Fc is stored in the computer 1.

Next, in the cutting calculation step S23 of the present embodiment, the molecular mechanics calculation is performed for the first region 23 (second molecular mechanics calculation step S37). As shown in FIG. 19, the first region 23 is a non-overall region obtained by extracting only the detached particle model portion 21 from the molecular chain model 13 of the polymer material model 15 deformed in the stretching step S33. Therefore, in the second molecular mechanics calculation step S37, a physical quantity including the energy Eb of the first region 23 and the force Fb acting on the first region 23 is calculated. Such a physical quantity including the energy Eb and the force Fb is used to obtain the energy Et of the polymer material model 15 and the force Ft acting on the polymer material model 15 according to the ONIOM method described later. The physical quantity including the energy Eb and the force Fb is stored in the computer 1. Further, in the second molecular mechanics calculation step S37, the coupling potential Pn is set between the particle models 3 and 3 of the separated particle model unit 21.

Next, in the cutting calculation step S23 of the present embodiment, the energy Et of the polymer material model 15 is calculated (step S38). The energy Et of the present embodiment is calculated based on the following equation (6) according to the ONIOM (Our own N-layered Integrated molecular Orbital and molecular Mechanics) method.
Et = Ea-Eb + Ec ... (6)
here,
Ea: Energy of the polymer material model obtained in the first molecular mechanics calculation process Eb: Energy of the first region obtained in the second molecular mechanics calculation process Ec: Energy of the first region obtained in the quantum mechanics calculation process

In the above formula (6), the energy Ea obtained in the first molecular mechanics calculation step S34 is the energy in the entire region of the polymer material model 15. Further, the energy Eb obtained in the second molecular mechanics calculation step S37 is the energy in the first region 23. Since these energies Ea and Eb are obtained by molecular mechanics calculation, the calculation accuracy is lower than that of quantum mechanics calculation. The energy Ec obtained in the quantum mechanics calculation step S36 is the energy of the first region 23. Since this energy Ec is obtained by quantum mechanics calculation, the calculation accuracy is higher than that of molecular mechanics calculation.

The ONIOM method is a method of obtaining an optimum solution by combining hierarchical structures having different calculation accuracy. In the present embodiment, among the energies Ea of the polymer material model having relatively low calculation accuracy, the energy Eb in the first region is replaced with the energy Ec in the first region having relatively high calculation accuracy. We are looking for 15 energy Ets. Since such energy Et can consider the influence of the cleavage of the molecular chain model 13 in detail, the calculation accuracy can be improved. Further, in the present embodiment, for example, the energy Et of the polymer material model 15 can be obtained without obtaining the energy of the entire region of the polymer material model 15 based on the quantum mechanics calculation, so that the calculation time is shortened. be able to. The energy Et is stored in the computer 1.

Next, in the cutting calculation step S23 of the present embodiment, the force Ft acting on the polymer material model 15 is calculated (step S39). The force Ft of this embodiment is calculated based on the following equation (7) according to the ONIOM method, similarly to the energy Et of the polymer material model.
Ft = Fa-Fb + Fc ... (7)
here,
Fa: Force acting on the polymer material model obtained in the first molecular mechanics calculation process Fb: Force acting on the first region obtained in the second molecular mechanics calculation process Fc: Force obtained in the quantum mechanics calculation process Force acting on one area

In the present embodiment, among the forces Fa of the polymer material model 15 having relatively low calculation accuracy, the force Fb in the first region 23 is replaced with the force Fc in the first region 23 having relatively high calculation accuracy. The force Ft of the molecular material model 15 is obtained. Since such a force Ft can consider the influence of the cleavage of the molecular chain model 13 in detail, the calculation accuracy can be improved. Further, in the present embodiment, it is not necessary to calculate the force acting on the entire region of the polymer material model 15 based on the quantum mechanics calculation, so that the calculation time can be shortened. This force Ft is stored in the computer 1.

Next, in the cutting calculation step S23 of the present embodiment, the coordinate values and velocities of each particle model 3 of the molecular chain model 13 are updated in the current unit time step (step S40). In this embodiment, the acceleration is obtained from the energy Et and the force Ft calculated by the ONIOM method. Then, based on the acceleration from the energy Et and the force Ft, from the coordinate values of each particle model 3 of the molecular chain model 13 before the first molecular mechanics calculation step S34 is executed, new coordinate values of each particle model 3 ( That is, the coordinate value used in the next unit time step) is calculated.

Since the coordinate values of each particle model 3 include the coordinate values calculated by quantum mechanics of the first region 23 that is likely to be cut, it is possible to accurately analyze the cut of the molecular chain model 13. can. Further, since the molecular mechanics calculation with relatively low accuracy is performed for the portion having a low possibility of being cut, the calculation time can be shortened.

In the present embodiment, the bond potential Pn that approximates the bond dissociation potential Pu is defined in the first molecular mechanics calculation step S34 and the second molecular mechanics calculation step S37. Therefore, it is possible to minimize the difference between the force acting on each particle model 3 after the second molecular mechanics calculation step S37 and the force acting on each particle model 3 after the quantum mechanics calculation step S36. can. Therefore, the calculation accuracy of the coordinate values based on the ONIOM method can be improved. The velocity of each particle model 3 is calculated based on the coordinate values of each particle model 3 of the molecular chain model 13, the energy Et of the polymer material model 15, and the force Ft acting on the polymer material model 15. ..

When it is determined in the above-mentioned step S35 that the separated particle model unit 21 does not exist (“N” in the step S35), the quantum mechanics calculation (step S36) and the molecular mechanics for the first region 23 are performed. The calculation (step S37) has not been performed. In this case, in step S40, the coordinate values of the particle model 3 obtained by the molecular mechanics calculation for the polymer material model 15, the energy Ea obtained in the first molecular mechanics calculation step, and the first molecular mechanics calculation. The coordinate values and speeds are updated from the force Fa obtained in the process.

Next, in the cutting calculation step S23 of the present embodiment, the particle models 3, 3 are obtained for the first region 23 after the quantum mechanics calculation step S36, and in the present embodiment, after the quantum mechanics calculation step S36 and the second molecular mechanics calculation step S37. It is determined whether or not there is a detached particle model unit 21 in which the distance r between them is larger than the predetermined second distance Lb (step S51). In step S51, based on the coordinate values of each particle model 3 of the molecular chain model 13 updated in step S40, all the separated particle model portions 21 arranged in the first region 23 are between the particle models 3 and 3. Distance r is calculated.

The second distance Lb of the present embodiment is defined based on the distance Ln between the particle models 3 and 3 at the inflection point 8 of the bond dissociation potential Pu shown in FIG. The second distance Lb of the present embodiment is set to be larger than the first distance La. Further, the second distance Lb is set to be equal to or greater than the distance Ln between the particle models at the inflection point 8.

As described above, the inflection point 8 can be considered as the boundary point between the bond and the dissociation between the particle models 3 and 3. Therefore, when the distance r between the particle models 3 and 3 is larger than the second distance Lb, it can be determined that the particles are cut between the particle models 3 and 3. Therefore, in step S51, the presence or absence of the detached particle model unit 21 that is cut between the particle models 3 and 3 by determining whether or not the distance r between the particle models 3 and 3 is larger than the second distance Lb. Can be judged. The second distance Lb is larger than the distance Ln between the particle models 3 and 3 at the inflection point 8 in order to accurately determine the separated particle model portion 21 cut between the particle models 3 and 3. It is desirable that the distance Ln at the inflection point 8 is greater than 100%, and 130% or less is desirable.

In step S51, when it is determined that the separated particle model portion 21 having a distance r between the particle models 3 and 3 is equal to or greater than the second distance Lb (“Y” in step S51) exists, the next cutting step S52 is performed. NS. On the other hand, when it is determined in all the separated particle model units 21 that the distance between the particle models 3 and 3 is less than the second distance Lb (“N” in step S51), the polymer material model 15 is predetermined. Step S53, which will be described later, is carried out to determine whether or not the particles have been extended to the specified conditions.

Next, in the cutting calculation step S23 of the present embodiment, the particle models 3 and 3 are cut (cutting step S52). In the cutting step S52, the definition of the bond model 4 between the particle models 3 and 3 is invalidated for the particle models 3 and 3 determined that the distance r is equal to or greater than the second distance Lb. This defines the break between the particle models 3 and 3. It should be noted that the break between the particle models 3 and 3 is defined not by the particle model 3 of the first region 23 shown in FIG. 19 but by the molecular chain model 13 corresponding to the particle model 3 of the first region 23 (FIG. Cleavage is defined between the particle models 3 and 3 (shown in 10).

As described above, in the simulation method of the present embodiment, the particle models 3 and 3 are targeted at the first region 23 including the separated particle model unit 21 based on the result of the quantum mechanics calculation having higher calculation accuracy than the molecular mechanics calculation. There is a gap. Therefore, in the present embodiment, the cutting of the molecular chain model 13 can be approximated to the actual cutting of the molecular chain, which is useful for accurately analyzing the polymer material.

Further, since the bond dissociation potential Pu is obtained based on the calculation method of the present embodiment, the bond and dissociation between atoms can be accurately expressed. Therefore, in the simulation method of the present embodiment, the cleavage between the particle models 3 and 3 can be approximated by the actual cleavage of the molecular chain.

Further, the presence or absence of the detached particle model unit 21 on which the quantum mechanics calculation is performed is determined in step S35 based on the result of the molecular mechanics calculation whose calculation time is shorter than that of the quantum mechanics calculation. Therefore, it is not necessary to carry out the quantum mechanics calculation for the entire region of the polymer material model 15. Therefore, in the simulation method of the present embodiment, the calculation time can be shortened.

The definition of cutting can be set by invalidating the bond model 4 that constrains the particle models 3 and 3. Further, the binding potential Pn defined between the cut particle models 3 and 3 is invalidated, and the second potential P2 defined between the adjacent particle models 3 and 3 is defined without going through the bond model 4. NS.

For the cleaved particle models 3 and 3, for example, the number of bonds of the particle model 3 (for example, 1) is subtracted from the valence of the atom modeled in the particle model 3 (for example, in the case of a sulfur atom: 2). A number of hydrogen particle models 3H (eg, one) are linked via a bond model 4. As a result, the molecular chain model 13 can maintain a stable structure.

Next, in the cutting calculation step S23 of the present embodiment, it is determined whether or not the polymer material model 15 is stretched to a predetermined condition (step S53). In step S53, when it is determined that the polymer material model 15 has extended to the upper limit value (“Y” in step S53), the next step S24 is carried out. On the other hand, when it is determined that the polymer material model 15 has not extended to the upper limit value (“N” in step S53), one unit time step is advanced (step S54), and steps S33 to S53 Will be implemented again. As a result, in the cutting calculation step S23, the polymer material model can be extended to the upper limit value and the cutting of the molecular chain model 13 can be analyzed.

Next, in the simulation method of the present embodiment, it is determined whether or not the physical quantity of the polymer material model 15 is within the permissible range (step S24). The permissible range of the physical quantity can be appropriately set based on, for example, the performance required for the polymer material. When it is determined in step S24 that the physical quantity of the polymer material model 15 is within the permissible range (“Y” in step S24), the polymer material is manufactured based on the polymer material model 15 (step S24). S25). On the other hand, when the physical quantity of the polymer material model 15 is determined to be out of the permissible range (“N” in step S24), the conditions of the molecular chain model 13 are changed (step S26), and steps S21 to 1 to step 2 S24 is carried out again. As described above, in the present embodiment, since the conditions of the molecular chain model 13 are changed until the physical quantity of the polymer material model 15 is within the permissible range, the polymer material having desired performance is efficiently designed. can do.

Although the particularly preferable embodiments of the present invention have been described in detail above, the present invention is not limited to the illustrated embodiments and can be modified into various embodiments.

[Example A]
The bond dissociation potential between the atoms constituting the molecule was calculated according to the processing procedure shown in FIGS. 2 and 4 (Example 1). In Example 1, quantum mechanics calculations were performed based on the theory of density functional theory (DFT), and bond dissociation potentials were calculated only from stable wavefunctions.

For comparison, the bond dissociation potential was calculated based on the same procedure as the conventional method without performing an evaluation step for determining whether or not the wave function is stable (Comparative Examples 1 to 5). That is, the bond dissociation potential of Comparative Examples 1 to 5 is calculated from both a stable wave function and an unstable wave function. In Comparative Examples 1 to 5, quantum mechanics calculations were performed based on the theory shown in Table 1. The common specifications are as follows.
Computer: SGI workstation
Number of CPU cores: 12 cores
On-board memory: 64GB
Molecules: Methanethiol FIG. 20 is a graph of bond dissociation potentials of Examples 1 and Comparative Examples 1-5. The calculation time is shown in Table 1.

As a result of the test, the bond dissociation potential of Example 1 was calculated based on the theory (MRCI) with the highest calculation accuracy as compared with Comparative Example 1 calculated based on the same theory (DFT) as in Example 1. It was possible to approximate the bond dissociation potential of Comparative Example 2. Therefore, the examples could define the potential to accurately represent the bonds and dissociations between atoms. As shown in Table 1, Example 1 was able to significantly reduce the calculation time as compared with Comparative Examples 2 to 5. Therefore, in Example 1, the bond dissociation potential could be obtained accurately while shortening the calculation time.

[Example B]
A molecular chain model and a polymer model were defined according to the processing procedure shown in FIGS. 9 and 11, and a cutting step of cutting the molecular chain model was carried out (Example 2, Comparative Example 6).

In the cutting step of Example 2, the step of performing molecular mechanics calculation based on the polymer material model according to the processing procedure shown in FIGS. 13, 15 and 18, and the distance between the particle models is larger than the first distance La. A step of performing quantum mechanics calculation for the first region including the separated particle model part and a step of performing molecular mechanics calculation for the first region are carried out, based on the above equations (6) and (7). , The energy Et of the polymer material model and the force Ft acting on the polymer material model were calculated.

In the process of performing molecular mechanics calculation, an approximate potential close to the bond dissociation potential was defined between the particle models of the molecular chain model. The bond dissociation potential was obtained only from the stable wave function according to the processing procedure shown in FIGS. 2 and 4. In the cutting step of Example 2, when the distance between the particle models was larger than the second distance Lb, a step of cutting between them was carried out.

In the cutting step of Comparative Example 6, quantum mechanics calculation was performed for the entire region of the polymer material model, and cutting of the molecular chain model was calculated according to the distance between the particle models. The potentials set between the particle models are as described in the specification. The common specifications are as follows, and the computer used is the same as in Example A.
Polymer model:
Length of one side L1: 2.3 nm
Number of molecular chain models: 1 Molecular chain model:
Crosslink sulfur (1 atom) to polyisoprene (isoprene molecule: 100 polymerization)
Number of particle models (atoms): 1301 Distance at inflection point Ln: 3.09 Å
First distance La: 2.69 Å
Second distance Lb: 3.35 Å
Stretch simulation:
Extension direction: Uniaxial direction (Z-axis direction)
Elongation speed Va: 250 m / sec

FIG. 21 is a graph showing the relationship between the number of cuts between the particle models of Example 2 and the elongation rate of the polymer material model. As shown in FIG. 21, in Example 2, it was possible to show a state in which the number of cuts between the particle models increases as the polymer material model grows. Further, in Example 2, the cleavage of the CS bond was calculated when the elongation rate was about 300%, and the cleavage of the CC bond was calculated when the elongation rate was about 560%. As described above, in Example 2, it was possible to calculate the elongation rate at which cutting starts for each particle model.

FIG. 22 is a graph showing the relationship between the stress of the polymer material of Example 2 and the elongation rate of the polymer material model. As shown in FIG. 15, the stress sharply increases from the elongation rate of about 500%, but the stress sharply decreases from the elongation rate of about 600%. This is because the stress was reduced by breaking the CC bond.

As described above, in Example 2, the elongation simulation using the polymer material model was able to calculate the cutting of the molecular chain model with high accuracy, so that the polymer material could be analyzed with high accuracy. Further, in Example 2, since the bond dissociation potential is calculated only from the stable wave function based on the calculation method of the present invention, it can be approximated to the actual breakage of the molecular chain. Further, in Example 2, since the quantum mechanics calculation is performed only for the first region including the separated particle model portion which is likely to be cut between the particle models, the calculation time can be shortened.

On the other hand, in Comparative Example 6, since the quantum mechanical calculation is performed for the entire region of the polymer material model, it is practically impossible to carry out the same deformation simulation as in Example 2 due to the processing power of the computer. Is considered to be. Therefore, in Comparative Example 6, the cleavage of the molecular chain model could not be calculated.

S1 Step to define molecular model S4 Calculation step S5 Evaluation step S6 Find bond dissociation potential S7 Recalculation step

Claims (8)

A method for calculating the bond dissociation potential between the atoms that make up a molecule using a computer.
The process of defining a molecular model in which the particle models that model the atoms are bonded to each other in the computer, and
A calculation process in which the computer calculates the wave function by quantum mechanics calculation using the molecular model.
The computer includes an evaluation step of determining whether or not the wave function is stable.
When it is determined that the wave function is stable, a step of obtaining the bond dissociation potential between the particle models is carried out based on the wave function.
When it is determined that the wave function is not stable, a recalculation step of recalculating the wave function is carried out so that the energy of the wave function becomes low .
The calculation step includes a step of calculating the energy of the wave function.
The evaluation step determines that the wave function is stable when the eigenvalue obtained by quadratic variation of the energy by the wave function does not include a negative eigenvalue.
The recalculation step is a method for calculating a bond dissociation potential between atoms , which comprises recalculating the wave function so that the negative eigenvalue disappears. The method for calculating the bond dissociation potential between atoms according to claim 1, wherein the quantum mechanics calculation is performed based on the density functional theory. The recalculation step arranges the electrons in the molecular model so that the negative eigenvalues disappear.
Alternatively, the method for calculating a bond dissociation potential between atoms according to claim 1 or 2 , wherein the order of the orbitals is changed. A simulation method for analyzing the breakage of a molecular chain of a polymer material by using the bond dissociation potential obtained by the calculation method according to any one of claims 1 to 3.
A step of defining in the computer a molecular chain model including a plurality of the particle models and a bond model that binds the particle models based on the molecular chains.
A step of defining a polymer material model in which at least one of the molecular chain models is arranged in a space defined by the computer, and a process of defining the polymer material model.
The computer comprises a cleavage calculation step of calculating the cleavage of the molecular chain model based on predetermined conditions.
The cutting calculation step is a method for simulating a polymer material, which comprises a step of defining a bond potential close to the bond dissociation potential between the particle models of the polymer material model . The high value according to claim 4, wherein the bond potential is defined by a function that approximates the bond dissociation potential in the range from the lower limit of the energy of the bond dissociation potential to 50% to 80% of the upper limit of the energy. Simulation method for molecular materials. The cutting calculation step is
An extension step for performing deformation calculation for extending the polymer material model, and
The first molecular mechanics calculation step of performing the molecular mechanics calculation on the polymer material model deformed in the elongation step, and
Regarding the molecular chain model after the first molecular mechanics calculation step, whether or not there is a detached particle model portion in which the distance between the adjacent particle models via the bond model is larger than the predetermined first distance. Including the process of determining whether
When it is determined that the detached particle model portion exists, the quantum mechanics calculation step of performing the quantum mechanics calculation for the first region, which is a non-whole region including the detached particle model portion, and
4. The fourth or fifth aspect of the first region after the quantum mechanics calculation step, which includes a step of cutting between the particle models when the distance between the particle models is larger than a predetermined second distance. Method of simulating polymer materials. The method for simulating a polymer material according to claim 6, wherein the first distance is smaller than the second distance. The method for simulating a polymer material according to claim 6 or 7, wherein the second distance is defined based on the distance between the particle models at an inflection point where the increment of energy of the bond dissociation potential becomes smaller.

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