Crystal structure prediction method

Abstract

A method for predicting a crystal structure that enables theoretical prediction of the crystal structure of an organic molecular crystal and reduces the time and cost required. [Solution] The method for predicting a crystal structure of the present invention is configured so that, in a planar view, groups G of a plurality of molecules 101 aligned in a first direction are aligned in a second direction perpendicular to the first direction, and the extension direction d of the molecules 101 for each group G is parallel to one another. The method includes: step A of simulating to determine, among a plurality of variables that give an expression for the crystal energy of the crystal structure, other second variables that satisfy the condition for minimizing the crystal energy when a predetermined numerical value is substituted for the first variable; and step B of substituting the determined second variables into the expression for the crystal energy to determine the first variables that satisfy the condition for minimizing the crystal energy, and step A is performed multiple times by changing the first variable.

Description

[Technical Field]

[0001] The present invention relates to a method for predicting a crystal structure. [Background technology]

[0002] Organic molecular crystals are known to be lightweight, flexible, inexpensive, and highly biocompatible materials. In addition, they have high carrier mobility, an important electrical property, and are therefore expected to be next-generation semiconductor materials.

[0003] Organic molecular crystals exist in crystalline polymorphism, and each organic molecule that makes up an organic molecular crystal is composed of many atoms and has a high degree of freedom. For this reason, it is difficult to theoretically predict the crystal structure from the structural formula of a single organic molecule. Predictions of the crystal structure of organic molecular crystals are based on the results of X-ray analysis of samples of organic molecular crystals that have actually been prepared (Patent Document 1, etc.). Furthermore, to understand the electrical properties of organic molecular crystals, it is necessary to actually operate devices prepared using the samples. The preparation of samples and devices requires enormous effort and cost, hindering the progress of research and development. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 7158683 Summary of the Invention [Problem to be solved by the invention]

[0005] The present invention has been made in view of the above circumstances, and aims to provide a method for predicting crystal structure that enables theoretical prediction of the crystal structure of organic molecular crystals while reducing the effort and cost involved. [Means for solving the problem]

[0006] In order to solve the above problems, the present invention employs the following means.

[0007] (1) A method for predicting a crystal structure according to one embodiment of the present invention is a method for predicting a crystal structure in which, in a planar view, groups of molecules aligned in a first direction are aligned in a second direction perpendicular to the first direction, and the extension directions of the molecules in each group are parallel to each other. The method includes: a step A of simulating a second variable that satisfies the condition for minimizing the crystal energy when a predetermined numerical value is substituted for a first variable among a plurality of variables that give an expression for the crystal energy of the crystal structure; and a step B of substituting the second variable thus determined into the expression for the crystal energy to determine the first variable that satisfies the condition for minimizing the crystal energy. Step A is performed multiple times by changing the first variable.

[0008] (2) In the method for predicting a crystal structure described in (1), the simulation of the second variable in step A from the second time onwards may be limited to a range that includes the second variable determined in step A in the previous time.

[0009] (3) In the method for predicting a crystal structure described in (1) or (2), the molecules may be arranged so that every other group overlaps in the second direction, and the angle between the extension directions of the molecules in adjacent groups may be set as the first variable, and the center-to-center distance between adjacent molecules in the first direction and the center-to-center distance between adjacent molecules in the second direction may be set as the second variable.

[0010] (4) Another aspect of the present invention provides a method for predicting a crystal structure, in which, in a planar view, a plurality of groups of molecules aligned in a first direction are aligned in a second direction perpendicular to the first direction, and the extension directions of the molecules in each group are parallel to each other. The method includes a step C of simulating and determining, among a plurality of variables that give an expression for the crystal energy of the crystal structure, the center-to-center distance between adjacent molecules in the first direction and the center-to-center distance between adjacent molecules in the second direction when the angle between the extension directions of the molecules in adjacent groups is fixed to 0, to determine the second variables that satisfy the condition for minimizing the crystal energy.

[0011] (5) In the method for predicting a crystal structure according to either (3) or (4), the second variable may be a displacement of a crystal plane in addition to the center-to-center distance between the molecules.

[0012] (6) In the method for predicting a crystal structure according to either (1) or (2), the angle between the extension directions of the molecules in adjacent groups may be set to 0°, the molecules may be arranged so that adjacent groups overlap in a direction different from the first direction and the second direction, and one of the following may be set as the first variable and the remaining as the second variable: the center-to-center distance between adjacent molecules in the first direction; the center-to-center distance between adjacent molecules in the second direction; the magnitude of the shift in the first direction between the centers of adjacent molecules in the second direction; and the magnitude of the shift in the second direction between the centers of adjacent molecules in the first direction. [Effects of the Invention]

[0013] According to the present invention, by focusing on a certain crystal structure and varying a limited number of specific variables, it is possible to predict the optimal crystal structure easily and quickly. This makes it possible to theoretically predict the crystal structure of an organic molecular crystal, and provides a method for predicting the crystal structure that reduces the effort and cost. [Brief explanation of the drawings]

[0014] [Figure 1] 1(a) to 1(c) are diagrams showing the organic molecular crystal according to each embodiment of the present invention, viewed from one direction in a plan view. [Figure 2] 1A and 1B are diagrams showing chain molecules constituting an organic molecular crystal according to a first embodiment, and a unit cell in which the chain molecules are arranged to form a herringbone structure. [Figure 3] 3(a) to 3(e) are diagrams showing examples of the crystal structure of the organic molecular crystal of the embodiment. [Figure 4] FIG. 2 is a diagram illustrating step A in the crystal structure prediction method according to the embodiment. [Figure 5] 1(a) to 1(d) are diagrams showing characteristic parts of the organic molecular crystals of Modifications 1 to 4. FIG. [Figure 6] FIG. 10 is a diagram showing a state in which chain molecules constituting an organic molecular crystal according to a third embodiment are arranged to form a π-stacked structure. [Figure 7] 1 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the crystallization energy of an organic molecular crystal, as predicted in Example 1. [Figure 8] 1 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the lattice constant of an organic molecular crystal, as predicted in Example 1. [Figure 9] 1 is a graph comparing the valence band structure predicted in Example 1 with the valence band structure obtained by actual measurement. [Figure 10] 1 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the effective mass of electrons propagating in an organic molecular crystal, as predicted in Example 1. [Figure 11] 10 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the crystallization energy of an organic molecular crystal, as predicted in Example 2. [Figure 12] 10 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the lattice constant of an organic molecular crystal, as predicted in Example 2. [Figure 13]10 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the crystallization energy of an organic molecular crystal, as predicted in Example 3. [Figure 14] 10 is a graph showing the relationship between the angle between the extending directions of adjacent chain molecules and the crystallization energy of an organic molecular crystal, as predicted in Example 4. [Figure 15] 1 is a graph showing the relationship between the amount of deformation of the lattice of an organic molecular crystal and the crystal energy, as predicted in Examples 5 to 8. DETAILED DESCRIPTION OF THE INVENTION

[0015] Hereinafter, a crystal structure prediction method according to an embodiment of the present invention will be described in detail with reference to the drawings. Note that the drawings used in the following description may show characteristic portions enlarged for the sake of clarity, and the dimensional ratios of each component element may not necessarily be the same as in reality. Furthermore, the materials, dimensions, etc. exemplified in the following description are merely examples, and the present invention is not limited thereto. Appropriate modifications can be made within the scope of the present invention.

[0016] 1(a) to 1(c) are diagrams showing organic molecular crystals 100 (100A, 100B, and 100C) according to embodiments of the present invention, as viewed in plan from a predetermined crystal axis b. The crystal structure prediction method according to each embodiment is a method for theoretically predicting the crystal structure of an organic molecular crystal from a single molecular structural formula without conducting experiments using a sample, etc.

[0017] The crystal structure of the organic molecular crystals 100A, 100B, and 100C of each embodiment is configured such that, in a planar view, groups G (here, G1, G2, and G3) of multiple molecules 101 aligned in the crystal axis a direction (first direction) are aligned in multiple directions along the crystal axis c direction (second direction) perpendicular to the crystal axis a direction, and the extension direction d (extension direction, longitudinal direction) of the molecules 101 in each group G is aligned parallel to one another.

[0018] The method for predicting the crystal structure of the organic molecular crystal 100 mainly includes the following steps A and B. In step A, a predetermined value is substituted into a first variable among multiple variables that give an expression for the crystal energy of the crystal structure. In this case, other second variables that satisfy the conditions for minimizing the crystal energy E (stable state) are determined by simulation. This step A is performed multiple times (preferably three or more times) by changing the first variable to determine the optimal value of the second variable. In step B, the optimal value of the second variable determined in step A is substituted into the expression for the crystal energy E, and the first variable that satisfies the conditions for minimizing the crystal energy E is determined from the relational equation E(θ) between the first variable and the crystal energy. This relational equation E(θ) can be obtained using, for example, force field calculations such as density functional theory, Amber, or MMFF.

[0019] It is considered that the second variable obtained in steps A performed with slight changes in the first variable will have similar values. Therefore, the simulation of the second variable in the second or subsequent steps A may be limited to a range that includes the second variable obtained in the previous step A. By doing so, the simulation range can be reduced, and the time and effort required for the simulation can be reduced.

[0020] First Embodiment The organic molecular crystal 100A of the first embodiment shown in Fig. 1(a) is a crystal having a herringbone structure. In the herringbone structure, molecules 101 are arranged so that every other group G overlaps with another group G in the direction of the crystal axis c. Here, a molecule 101 of group G1 and a molecule 101 of group G3 overlap with each other in the direction of the crystal axis c.

[0021] The molecules 101 constituting the herringbone structure extend (are elongated) in a specific direction d for each group G in plan view. The extending direction d (extension direction) of the molecules 101 is aligned parallel to each other for each group G. In groups G adjacent to each other in the crystal axis c direction, the extending directions d of the molecules 101 are not aligned parallel to each other, and the angle θ between the extending directions d is greater than 0°.

[0022] Figure 2(a) is a diagram clarifying the arrangement of atoms 102 constituting molecule 101 in the herringbone structure shown in Figure 1(a). Molecule 101 is a chain molecule in which multiple atoms 102 are bonded together along the crystal axis direction b.

[0023] FIG. 2(b) is a plan view of the molecule 101 in FIG. 2(a) viewed from the crystal axis b direction. The molecule 101 viewed from the crystal axis b direction has a herringbone structure. In the crystal axis a direction, the center-to-center distance between adjacent molecules 101 is the lattice constant L a In the direction of the crystal axis c, the center-to-center distance between molecules 101 adjacent to every other group G is defined as the lattice constant L c It is preferable that the angle θ formed between the direction d1 and the direction d2 and the angle φ formed between the direction of the crystal axis a and the direction d1 satisfy the relationship θ=2φ.

[0024] Figure 3 shows an example of an organic molecular crystal with a herringbone structure. Figures 3(a) and (b) show DNT-W and DNT-V, respectively. Figures 3(c) and (d) show the stand and sleep phases of DNBDT, respectively. Figure 3(e) shows DNTT.

[0025] The above-described method for predicting a crystal structure can be applied to the herringbone structure of the organic molecular crystal 100A shown in FIG. 1(a). In this case, the angle θ between the extension directions D of the molecules 101 in adjacent groups G is set as the first variable. In addition, the distance between the centers of the molecules 101 in the direction of the crystal axis a (the lattice constant L a ), and the distance between the centers of the molecules 101 in the direction of the crystal axis c (lattice constant L c ) is the second variable.

[0026] FIG. 4 is a diagram illustrating the specific operation of step A in this case. The crystal energy expression E(θ, L a , L c ) among the variables that give the crystal energy E(0, L a , L c ) is the lattice constant L that satisfies the condition for minimizinga , L c is obtained by simulation. θ is set to 5,..., Similarly, when 50,... is substituted, the crystal energy E(θ, L a , L c ) is the lattice constant L that satisfies the condition for minimizing a , L c From the results of the simulation performed for angles at 5° intervals, the lattice constant L for each θ is calculated. a , L c The optimal value of is found. Note that here, the simulation is performed by selecting the angle substituted as the first variable at 5° intervals, but the intervals are not limited to this. The smaller the interval of θ and the more angles selected, the more accurate the results will be, and the larger the interval of θ and the fewer angles selected, the shorter the calculation time will be.

[0027] Here, the simulation is performed when the angle θ is set at 5° intervals, using the lattice constant L obtained in the previous step when the angle θ was set at an angle 5° smaller. a , L c By narrowing down the area to include the above, the effort and time required for the simulation can be reduced.

[0028] In step B, the determined lattice constant L a , L c The crystal energy expression E(θ, L a , L c ) to find the angle θ that satisfies the condition for minimizing the crystal energy E. In this way, the angle θ and the lattice constant L a , L c By finding the optimal value of , the herringbone structure can be predicted with high accuracy.

[0029] 5(a) to 5(c) are diagrams showing characteristic portions of organic molecular crystals according to Modifications 1 to 3 of the first embodiment. The organic molecular crystals described above are rectangular crystals in which the angle γ between the crystal axis a direction and the crystal axis b direction and the angle α between the crystal axis b direction and the crystal axis c direction are all 90°. In contrast, in the organic molecular crystal of Modification 1, the angle γ between the crystal axis a direction and the crystal axis b direction is greater than 90°. Furthermore, in the organic molecular crystal of Modification 2, the angle α between the crystal axis b direction and the crystal axis c direction is smaller than 90°. Furthermore, in the organic molecular crystal of Modification 3, the angle γ between the crystal axis a direction and the crystal axis b direction is greater than 90°, and the angle α between the crystal axis b direction and the crystal axis c direction is smaller than 90°. The organic molecular crystals of Modifications 1 to 3 are triclinic crystals in which the crystal plane containing the crystal axes a and c (ac plane) is tilted compared to when α is 90° and γ is 90°.

[0030] 5(d) is a diagram showing a characteristic portion of an organic molecular crystal according to Modification 4 of the first embodiment. In the organic molecular crystal described above, the ends of the chain molecules 101 are aligned. In contrast, in the organic molecular crystal of Modification 4, the positions of some of the chain molecules 101 are shifted in the direction of the crystal axis b. In the organic molecular crystal of Modification 4, compared to when the ends of the chain molecules 101 are aligned, the ac plane has an uneven structure.

[0031] The crystal structure of such organic molecular crystals can be predicted by adding the displacement x of the ac plane as a second variable to the above-mentioned crystal structure prediction method. In Modifications 1 to 3, the displacement x is the displacement of the center of a parallelogram with two sides in the crystal axis a direction and the crystal axis c direction. In Modification 4, the displacement x is the depth of the recesses or the height of the protrusions in the uneven structure of the ac plane.

[0032] As described above, the crystal structure prediction method of this embodiment focuses on a specific crystal structure (a structure in which multiple groups of molecules aligned in a first direction are aligned in a second direction perpendicular to the first direction, and the extension directions of the molecules in each group are parallel to each other) and uses only a procedure of varying specific, limited variables, thereby enabling simple and rapid prediction of an optimal crystal structure. Furthermore, crystal structures specific to organic molecular crystals, such as those shown in Figures 1(a) to 1(c), can be theoretically predicted using a crystal energy expression derived from a single-molecule structural formula. Specifically, each component of the crystal structure when the crystal energy is stable can be calculated. Furthermore, information such as band structure and effective mass can be obtained from the calculated crystal structure, and the electrical properties of the organic molecular crystal can be predicted from this information. The crystal structure prediction method of this embodiment does not require the preparation of organic molecular crystal samples or structural analysis using X-rays or the like, thereby enabling crystal structure prediction with reduced effort and cost.

[0033] Second Embodiment The organic molecular crystal 100B of the second embodiment shown in FIG. 1(b) is a crystal having a brickwork structure. In the brickwork structure, in groups G adjacent to each other in the direction of the crystal axis c, the extension directions d of the molecules 101 are aligned parallel to each other, and the angle θ between the extension directions d is 0°. The other configuration of the brickwork structure is the same as that of the herringbone structure of the first embodiment. In the brickwork structure, among the multiple variables that give the expression of the crystal energy of the crystal structure, the angle θ corresponding to the first variable of the first embodiment is fixed to 0, and the lattice constant L is fixed as the second variable. a , L c Therefore, the crystal structure can be predicted only in step C, in which the second variable that satisfies the condition for minimizing the crystal energy is determined by simulation.

[0034] In this embodiment, too, when the ac plane is inclined or has irregularities as in Modifications 1 to 4 of the first embodiment, the displacement amount x of the ac plane can be added as a second variable in step A.

[0035] Third Embodiment The organic molecular crystal 100C of the third embodiment shown in Fig. 1(c) is a crystal having a π-stacked structure. In the π-stacked structure, the angle between the extension directions d of the molecules 101 of adjacent groups G is set to 0°, and the molecules 101 of adjacent groups G are arranged so that they overlap in a direction (diagonal direction) different from the crystal axis a direction and the crystal axis c direction. The π-stacked structure differs from the herringbone structure and brickwork structure in that the molecules 101 of adjacent groups G do not overlap in the crystal axis a direction and the crystal axis c direction.

[0036] FIG. 6 is a diagram clarifying the arrangement of atoms 102 constituting molecules 101 in the π-stacked structure shown in FIG. 1(c). The molecules 101 in each group have the same extension direction d, which is parallel to the crystal axis a direction (first direction). In the π-stacked structure, variables that define the crystal structure include the center-to-center distance e1 between adjacent molecules 101 in the crystal axis a direction, the center-to-center distance e2 between adjacent molecules in the crystal axis c direction (second direction), the offset e3 between the centers of adjacent molecules in the crystal axis a direction, and the offset e4 between the centers of adjacent molecules in the crystal axis c direction.

[0037] In the method for predicting the crystal structure of a π-stacked structure, one of these four variables is designated as the first variable and the remaining variables as the second variables. For example, if the magnitude of misalignment e4 is designated as the first variable and the center-to-center distances e1, e2, and the magnitude of misalignment e3 are designated as the second variables, the crystal structure can be predicted using the following procedure.

[0038] Among the variables that give the crystal energy expression E(e1, e2, e3, e4) of the π-stack structure, when predetermined numerical values ​​m3 and m4 are substituted for the magnitudes of deviation e3 and e4, the center-to-center distances e1 and e2 that satisfy the condition for minimizing the crystal energy E(e1, e2, m3, m4) are determined by simulation.

[0039] Next, in the crystal energy expression E(e1, e2, e3, e4), when the previously determined values ​​m1, m3, and m4 are substituted for the center-to-center distance e1 and the magnitude of deviation e3 and e4, respectively, a simulation is performed to determine the center-to-center distance e2 that satisfies the condition for minimizing the crystal energy E(m1, m2, e3, e4).

[0040] Next, in the crystal energy expression E(e1, e2, e3, e4), the previously determined values ​​m1, m2, and m3 are substituted for the center-to-center distance e1 and e2 and the deviation e3. In this case, the deviation e4 that satisfies the condition for minimizing the crystal energy E(m1, m2, m3, e4) is determined using density functional theory or the like. [Example]

[0041] The effects of the present invention will be more clearly understood from the following examples. Note that the present invention is not limited to the following examples and can be practiced with appropriate modifications within the scope of the present invention.

[0042] Example 1 DNBDT was selected as an organic molecular crystal having a herringbone structure, and its crystal structure was predicted using the crystal structure prediction method of the first embodiment.

[0043] Figure 7 is a graph showing the relationship between the angle θ between the extension directions of adjacent chain molecules predicted by the crystal structure prediction method and the crystal energy E of the organic molecular crystal. The crystal energy E here is normalized so that its minimum value is 0 [eV]. The horizontal axis of the graph shows the angle θ [°] between the extension directions of molecules in adjacent groups in the DNBDT. The vertical axis of the graph shows the crystal energy E [eV] of the DNBDT.

[0044] In this graph, the angle θ that gives the minimum value of the crystallization energy E corresponds to the angle θ between the molecular extension directions of adjacent groups of DNBDT. There are two angles θ that give the minimum value of the crystallization energy E, the higher energy angle θ1 corresponds to the stand phase DNBDT, and the lower energy angle θ2 corresponds to the sleep phase DNBDT. Angle θ1 is 50°, and angle θ2 is 120°.

[0045] FIG. 8 shows the relationship between the angle θ between the extension directions of adjacent chain molecules and the lattice constant L of the organic molecular crystal, as predicted in Example 1. a , L c The graph shows the relationship between the angle θ [°] and the lattice constant L a , L c The lattice constants corresponding to the angles θ1 and θ2 of the DNBDT predicted in Figure 7 are almost consistent with the experimental values. From this result, it can be seen that by using the above-mentioned method for predicting the crystal structure, it is possible to obtain the three parameters that define the herringbone structure, the lattice constant L a , L c , and the angle θ can be correctly predicted.

[0046] FIG. 9 is a graph showing the valence band structure of DNBDT predicted in Example 1 and the valence band structure of DNBDT obtained experimentally. The horizontal axis of the graph represents the wave vector, and the vertical axis represents the energy band structure [eV] of DNBDT. FIG. 10 is a graph showing the relationship between the angle θ of DNBDT and the effective mass m0 of electrons propagating through DNBDT in the crystal axis a direction and the crystal axis c direction, and comparing it with the experimental value. The predicted value of the effective mass m0 was calculated from the shape of the valence band structure in FIG. 9 obtained from the predicted crystal structure.

[0047] In Figures 9 and 10, the predicted valence band structure and effective mass of the electrons are almost in agreement with the experimental results. The angle θ and lattice constant L obtained in the same way for organic molecular crystals other than DNBDT are a , L c , and effective mass m a , mc These are shown in Table 1 along with the experimental values ​​for comparison. For DNT-W, DNT-V, and DNTT, the predicted values ​​and experimental values ​​are also in close agreement. These results demonstrate that the crystal structure prediction method of the present invention can accurately predict not only the crystal structure of an organic molecular crystal, but also the electrical properties that vary depending on the crystal structure. Furthermore, by using the crystal structure prediction method of the present invention, the crystal structure and electrical properties of an organic molecular crystal can be known without conducting experiments that require time and money.

[0048] [Table 1]

[0049] Example 2 DNTT was selected as an organic molecular crystal having a herringbone structure, and its crystal structure was predicted using the crystal structure prediction method of the first embodiment.

[0050] Figure 11 is a graph showing the relationship between the angle θ between the extension directions of adjacent chain molecules predicted by the crystal structure prediction method and the crystal energy E of the organic molecular crystal. The crystal energy E here is normalized so that its minimum value is 0 [eV]. The horizontal axis of the graph shows the angle θ [°] between the extension directions of molecules in adjacent groups in DNTT. The vertical axis of the graph shows the crystal energy E [eV] of DNTT.

[0051] In this graph, the angle θ that gives the minimum value of the crystallization energy corresponds to the angle θ between the molecular extension directions of adjacent groups of DNTT. There are two angles θ that give the minimum value of the crystallization energy, both of which correspond to DNTT. Here, one of the angles is designated as θ3.

[0052] FIG. 12 shows the relationship between the angle θ and the lattice constant L of the DNBDT predicted in Example 2. a , L c The graph shows the relationship between the angle θ [°] and the lattice constant La , L c The lattice constants corresponding to the angle θ3 of DNTT predicted in Figure 11 are almost consistent with the experimental values. From this result, it can be seen that by using the above-mentioned method for predicting the crystal structure, it is possible to obtain the three parameters that define the herringbone structure, the lattice constant L a , L c , and the angle θ can be correctly predicted.

[0053] Example 3 In step B, the force field calculation method by Amber was used to determine the relational expression E(θ) between the angle θ of DNTT and the crystal energy E. The other procedures were the same as in Example 1.

[0054] Example 4 In step B, a force field calculation method using MMFF was used to determine the relational expression E(θ) between the angle θ of DNTT and the crystal energy E. The other procedures were the same as in Example 1.

[0055] 13 and 14 are graphs showing the relationship between the angle θ and the crystal energy E of DNTT obtained in Examples 3 and 4, respectively. In both graphs, as in Example 2, curves are obtained where the crystal energy is minimized at two angles, and it can be seen that the crystal structure can be predicted from these curves. When density functional theory is used, it takes several days to calculate the relationship E(θ). In contrast, when force field calculations are used, the calculation time for the relationship E(θ) can be reduced to within one hour.

[0056] (Examples 5 to 8) As in Modifications 1 to 4 of the first embodiment, for organic crystals (triclinic crystals) in which the ac plane was displaced, the change in crystal energy E when the displacement amount x was changed was calculated as Examples 5 to 8, respectively. Figure 15 is a graph showing the calculation results. The horizontal axis of the graph represents the displacement amount x [Å], and the vertical axis of the graph represents the crystal energy E [eV].

[0057] In the graph of FIG. 15, the crystal energy E is at a minimum when the displacement x is 0. A displacement x of 0 corresponds to the case where the ac plane is not tilted (α and γ are 90°), as in Example 1. The displacement x is also at a minimum when the displacement x is near -10 and 10. This corresponds to a state where the organic molecular crystal structure can be formed despite the tilted displacement of the ac plane. When the displacement x in Example 6 is -7.5, the crystal energy E is at a minimum, nearly matching the experimental value. These results demonstrate that, for triclinic crystals with tilted ac planes, the crystal structure can be predicted in the same way as for orthorhombic crystals by adjusting the displacement x under conditions where the crystal energy E is at a minimum. [Explanation of symbols]

[0058] 100...Organic molecular crystal 100A···Organic molecular crystal with herringbone structure 100B: Organic molecular crystal with brickwork structure 100C···π-stacked organic molecular crystals 101...molecule 102...atom a, b, c...crystal axis d, d1, d2, d3, d4... Extension direction of molecules e1, e2: Center-to-center distance between molecules e3, e4: The magnitude of the offset between the centers of the molecules G, G1, G2, G3... groups L a , L c Lattice constant x: Displacement

Claims

1. A method for predicting a crystal structure, in which, in a plan view, a plurality of groups of molecules aligned in a first direction are aligned in a second direction perpendicular to the first direction, and the extension directions of the molecules in each group are aligned in parallel, A step A of simulating a second variable that satisfies a condition for minimizing the crystal energy when a predetermined value is substituted for a first variable among a plurality of variables that give an expression for the crystal energy of the crystal structure; and a step B of substituting the second variable thus determined into the crystallization energy expression to determine the first variable that satisfies the condition for minimizing the crystallization energy, A method for predicting a crystal structure, characterized in that step A is performed multiple times while changing the first variable.

2. The method for predicting a crystal structure according to claim 1, characterized in that the simulation of the second variable in step A from the second time onwards is performed by narrowing the range to include the second variable determined in step A in the previous time.

3. arranging the molecules so that every other group overlaps in the second direction; The angle between the extending directions of the molecules in the adjacent groups is defined as the first variable, 3. The method for predicting a crystal structure according to claim 1, wherein the second variables are the center-to-center distance between adjacent molecules in the first direction and the center-to-center distance between adjacent molecules in the second direction.

4. A method for predicting a crystal structure, in which, in a plan view, a plurality of groups of molecules aligned in a first direction are aligned in a second direction perpendicular to the first direction, and the extension directions of the molecules in each group are aligned in parallel, Among a plurality of variables that give an expression for the crystal energy of the crystal structure, when an angle formed between the extension directions of the molecules between adjacent groups is fixed to 0, a center-to-center distance between adjacent molecules in the first direction and a center-to-center distance between adjacent molecules in the second direction are set as second variables; A method for predicting a crystal structure, comprising a step C of simulating and determining the second variable that satisfies the condition for minimizing the crystal energy.

5. 5. The method for predicting a crystal structure according to claim 3, wherein the second variable is a displacement of a crystal plane in addition to the center-to-center distance between the molecules.

6. The angle between the extending directions of the molecules in the adjacent groups is set to 0°, arranging the molecules so that adjacent groups overlap with each other in a direction different from the first direction and the second direction; 3. The method for predicting a crystal structure according to claim 1, wherein one of the following is the first variable and the remaining is the second variable: the center-to-center distance between the molecules adjacent in the first direction; the center-to-center distance between the molecules adjacent in the second direction; the magnitude of the shift in the first direction between the centers of the molecules adjacent in the second direction; and the magnitude of the shift in the second direction between the centers of the molecules adjacent in the first direction.

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