Screening method

Abstract

The purpose of the present invention is to efficiently screen alloys useful as solid catalysts. In one aspect of the present invention, screening of alloys that cause a target catalytic reaction is performed. For each of the plurality of candidate elements, basic information is created that includes the energy and vibration frequency of each of the reaction matrices in a non-adsorbed state, each of the reaction matrices in an adsorbed state, and each of the atoms constituting the reaction matrices, and a plurality of activation energies, a plurality of differential energies, and a reaction rate are obtained. The linearity is evaluated with respect to each activation energy and each of the plurality of differential energies, and a characteristic quantity energy is selected from the plurality of differential energies, said characteristic quantity energy being capable of obtaining a high linearity with respect to all of the plurality of activation energies. Distribution information indicating the distribution of the reaction speed with respect to the characteristic quantity energy is created. A plurality of compositions, the reaction rates of which increase as a result of constituting the alloy, are predicted. A stability index and an activity index are calculated for each of a plurality of slab models created with respect to a plurality of compositions.

Description

Technical Field

[0001] The present invention relates to a method for screening alloys useful as solid catalysts. Background Art

[0002] The high performance of solid catalysts is important not only for the development of the chemical industry, but also for the realization of a sustainable society. As a method of improving the high performance of solid catalysts, many attempts have been made to achieve alloying by adding heterogeneous elements to solid catalysts containing a single element. However, in solid catalysts containing alloys, the performance varies greatly depending on the structural elements such as the elements and atomic arrangement, and it can be said that the number of combinations of these structural elements is essentially infinite. Therefore, it is generally unrealistic to find a solid catalyst that can achieve high performance only through experimental trial and error.

[0003] In view of this, attempts have been made to efficiently search for high-performance solid catalysts by utilizing computational chemistry such as quantum chemical calculations. For example, Patent Document 1 discloses a technique for finding a solid catalyst with high activity for a catalytic reaction that promotes the reaction of a second gas in the presence of a first gas. In this technique, the base material element and the doping element constituting the solid catalyst are determined based on the amount of change in the adsorption energy of the first gas and the second gas caused by the presence or absence of the doping element.

[0004] Prior Art Literature

[0005] Patent Literature

[0006] Patent Document 1: Japanese Patent Application Publication No. 2020-006312 Summary of the invention

[0007] Problems to be solved by the invention

[0008] However, in the technology described in Patent Document 1, only the adsorption energy when the parent material element and the preferred doping element are combined is calculated, and the reaction rate of the catalytic reaction is not directly considered. In addition, in the technology described in Patent Document 1, when there is no index for selecting which element and there are many candidate elements, it is inefficient to further study the variation of the combination. Furthermore, the following solid catalyst screening technology is sought: it is not limited to a specific catalytic reaction consisting of a single elementary reaction as in the technology described in Patent Document 1, for example, it can be applied to a catalytic reaction consisting of multiple elementary reactions such as a reaction that promotes a reaction in a production process that utilizes multiple raw materials, and a catalytic reaction that needs to consider other factors.

[0009] An object of the present invention is to efficiently select an alloy useful as a solid catalyst.

[0010] Components for solving problems

[0011] A screening method according to one aspect of the present invention screens an alloy that causes a target catalytic reaction.

[0012] For each of a plurality of candidate elements that are candidates for the metal element constituting the alloy, basic information is prepared about a specific crystal plane formed by each candidate element, the basic information including each state of each reaction substrate in a non-adsorbed state and each reaction substrate in an adsorbed state among a plurality of elementary reactions constituting the catalytic reaction, and the energy and vibration frequency of each atom constituting the same,

[0013] For each of the plurality of candidate elements, a plurality of activation energies corresponding to the plurality of elementary reactions, a plurality of differential energies obtained as relative values ​​of the energies of the respective states, and a reaction rate of the catalytic reaction are obtained based on the basic information.

[0014] Regarding each activation energy constituting the plurality of activation energies and each differential energy constituting the plurality of differential energies, linearity is evaluated based on the relationship between the plurality of candidate elements, and a characteristic quantity energy that can obtain high linearity for all of the plurality of activation energies is selected from the plurality of differential energies,

[0015] using the characteristic energy and the reaction rate in the plurality of candidate elements, to create distribution information indicating the distribution of the reaction rate with respect to the characteristic energy,

[0016] using the distribution information, predicting a plurality of compositions in which the reaction rate increases by constituting the alloy including at least two candidate elements among the plurality of candidate elements,

[0017] creating a plurality of slab models corresponding to the plurality of components,

[0018] calculating a stability index based on the energy calculated for each of the plurality of slab models,

[0019] An activity index is calculated based on the reaction rate obtained from the distribution information using the characteristic energy calculated for each of the plurality of slab models.

[0020] An information processing device according to one aspect of the present invention includes a processing unit that executes the following processing.

[0021] For each of a plurality of candidate elements that are candidates for the metal element constituting the alloy, basic information is prepared about a specific crystal plane formed by each candidate element, the basic information including each state of each reaction substrate in a non-adsorbed state and each reaction substrate in an adsorbed state among a plurality of elementary reactions constituting the catalytic reaction, and the energy and vibration frequency of each atom constituting the same,

[0022] For each of the plurality of candidate elements, a plurality of activation energies corresponding to the plurality of elementary reactions, a plurality of differential energies obtained as relative values ​​of the energies of the respective states, and a reaction rate of the catalytic reaction are obtained based on the basic information.

[0023] Regarding each activation energy constituting the plurality of activation energies and each differential energy constituting the plurality of differential energies, linearity is evaluated based on the relationship between the plurality of candidate elements, and a characteristic quantity energy that can obtain high linearity for all of the plurality of activation energies is selected from the plurality of differential energies,

[0024] using the characteristic energy and the reaction rate in the plurality of candidate elements, to create distribution information indicating the distribution of the reaction rate with respect to the characteristic energy,

[0025] using the distribution information, predicting a plurality of compositions in which the reaction rate increases by constituting the alloy including at least two candidate elements among the plurality of candidate elements,

[0026] creating a plurality of slab models corresponding to the plurality of components,

[0027] calculating a stability index based on the energy calculated for each of the plurality of slab models,

[0028] An activity index is calculated based on the reaction rate obtained from the distribution information using the characteristic energy calculated for each of the plurality of slab models.

[0029] A program according to one aspect of the present invention causes the following processing to be executed as information processing.

[0030] For each of a plurality of candidate elements that are candidates for the metal element constituting the alloy, basic information is prepared about a specific crystal plane formed by each candidate element, the basic information including each state of each reaction substrate in a non-adsorbed state and each reaction substrate in an adsorbed state among a plurality of elementary reactions constituting the catalytic reaction, and the energy and vibration frequency of each atom constituting the same,

[0031] For each of the plurality of candidate elements, a plurality of activation energies corresponding to the plurality of elementary reactions, a plurality of differential energies obtained as relative values ​​of the energies of the respective states, and a reaction rate of the catalytic reaction are obtained based on the basic information.

[0032] Regarding each activation energy constituting the plurality of activation energies and each differential energy constituting the plurality of differential energies, linearity is evaluated based on the relationship between the plurality of candidate elements, and a characteristic quantity energy that can obtain high linearity for all of the plurality of activation energies is selected from the plurality of differential energies,

[0033] using the characteristic energy and the reaction rate in the plurality of candidate elements, to create distribution information indicating the distribution of the reaction rate with respect to the characteristic energy,

[0034] using the distribution information, predicting a plurality of compositions in which the reaction rate increases by constituting the alloy including at least two candidate elements among the plurality of candidate elements,

[0035] creating a plurality of slab models corresponding to the plurality of components,

[0036] calculating a stability index based on the energy calculated for each of the plurality of slab models,

[0037] An activity index is calculated based on the reaction rate obtained from the distribution information using the characteristic energy calculated for each of the plurality of slab models.

[0038] Effects of the Invention

[0039] According to the present invention, alloys useful as solid catalysts can be efficiently screened. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flowchart showing a screening method according to one embodiment of the present invention.

[0041] Figure 2 This is a diagram illustrating the distribution information created in step S05 of the above-mentioned screening method.

[0042] Figure 3 It is a diagram for explaining step S06 of the above-mentioned screening method.

[0043] Figure 4 It is a diagram for explaining step S06 of the above-mentioned screening method.

[0044] Figure 5 This is a diagram illustrating a list of alloys that can be used in step S10 of the above-mentioned screening method.

[0045] Figure 6 It is a block diagram showing an information processing device capable of implementing the above-mentioned screening method. DETAILED DESCRIPTION

[0046] [Preface]

[0047] The screening method involved in one embodiment of the present invention is configured to efficiently search for alloys useful as solid catalysts that cause target catalytic reactions by using calculations of an information processing device. By feeding back the search results of the screening method involved in this embodiment, the alloys that should be evaluated by experiments can be narrowed down to a small number of alloys with a large number of combinations of structural elements. Thus, not only can a high-performance solid catalyst be designed with less labor and cost, but it also has excellent performance, and thus a solid catalyst with high feasibility can be expected.

[0048] In the screening method involved in the present embodiment, as an index for searching for alloys useful as solid catalysts, not only the activity of the catalytic reaction in the alloy is used, but also the stability of the structure of the alloy is used. Thus, an alloy that can obtain high performance can be selected from a structure that can achieve a stable structure as a solid catalyst. Therefore, in the screening method involved in the present embodiment, a structure that is originally difficult to modulate or is prone to structural changes over time can be excluded from the object of experimental evaluation. Thus, an alloy useful as a solid catalyst that causes a target catalytic reaction can be searched more efficiently.

[0049] [Overall structure of the screening method]

[0050] (Brief description)

[0051] The overall structure of the screening method according to the present embodiment is described below. Figure 1 The steps S01 to S10 shown in the figure are as follows. Figure 1 Steps S01 to S10 of the screening method according to the present embodiment will be described in detail.

[0052] (Step S01: Selection of elementary reactions, candidate elements, and crystal planes)

[0053] In step S01, the target catalytic reaction is first selected. The so-called catalytic reaction refers to a series of chemical reactions that progress or are promoted by the action of a catalyst. The target catalytic reaction can be achieved by a solid catalyst, and can be arbitrarily selected from the reactions consisting of a series of reactions on the same catalyst. In addition, with respect to the target catalytic reaction, even in the case of substrate desorption in the middle of the reaction, it can be selected separately before and after desorption. Furthermore, the target catalytic reaction can be any one of a liquid phase reaction and a gas phase reaction. In addition, as the energy given for the target catalytic reaction, thermal energy or mechanical energy is preferred, and in addition to these, for example, electrical energy, light energy, etc. can also be cited. As a method for giving thermal energy, in addition to heating by a heater, for example, microwave heating, etc. can also be cited. As a method for giving mechanical energy, for example, the application of pressure, etc. can be cited. In addition, as a target catalytic reaction, for example, an exchange reaction of a part of the molecule or base of the exchange compound, an additional reaction of a part of the molecule or base of the additional compound, a decomposition reaction, etc. can be cited. As an exchange reaction and an additional reaction, for example, an oxidation reaction, a hydrogenation reaction, an isomerization reaction, a cyclization reaction, etc. can be cited. As decomposition reactions, for example, desulfurization reactions, deacidification elementary reactions, dehydration elementary reactions, etc. Specific examples of the target catalytic reaction selected in step S01 include oxidation reactions of carbon monoxide, transesterification reactions based on esters and alcohols, esterification reactions based on fatty acids and alcohols, alcohol formation reactions based on hydrogenation of esters, substituted amine formation reactions based on amines and alcohols, hydrogenation reactions of fatty acids, hydrogenation decomposition reactions of alcohols, hydrodesulfurization reactions of sulfur, cross-aldol condensation reactions of aldehydes, hydrogenation reactions of aromatics, selective hydrogenation reactions of olefins, hydrogenation reactions of carbonyls, hydroisomerization reactions of olefins, cyclocyclization reactions of dienes, oxygen oxidation reactions of alcohols, hydrogenation reactions of carbon monoxide and carbon dioxide (including hydrogenation reactions accompanied by carbon chain extension reactions), etc.

[0054] Next, multiple elementary reactions constituting the selected catalytic reaction are selected. The so-called elementary reaction is each reaction in each stage when the catalytic reaction is decomposed into multiple stages. That is, multiple elementary reactions can be selected according to the target catalytic reaction, for example, they can be inferred according to records such as documents. In addition, the multiple elementary reactions can include reactions with a possibility of existence as candidates in addition to the inferred reactions.

[0055] Furthermore, multiple candidate elements that are candidates for the metal element that causes the selected catalytic reaction are selected. As candidate elements, any two or more can be selected from all metal elements, for example, a metal element generally used as a solid catalyst can be selected. From the perspective of screening accuracy, the number of candidate elements is preferably 3 or more. In addition, from the perspective of screening efficiency, the number of candidate elements is preferably 30 or less.

[0056] In addition, a crystal structure that causes the selected catalytic reaction is selected. As a crystal structure, it can be arbitrarily selected from the crystal structures constituting a body-centered cubic lattice, a face-centered cubic lattice, and a hexagonal closest structure. For example, as a crystal structure that causes a catalytic reaction, a general crystal structure can be selected. Furthermore, for the crystal structure, any crystal face characterized by the Miller index, such as a general (111) face, etc., can be selected, and more than two crystal faces can also be selected. In addition, the crystal face, for example, is calculated by quantum chemical calculation to calculate the surface formation free energy, and the Wulff mapping method can be used, or a database such as Crystalium can be referenced to select a crystal face that is expected to exist on the nanoparticles in equilibrium.

[0057] As an example, the case where the oxidation reaction of CO (CO+0.5O2→CO2) is selected as the target catalytic reaction is described. It is assumed that the catalytic reaction is composed of three elementary reactions based on the reaction substrates shown in the following formulas. Here, the so-called "reaction substrate" refers to a compound that is determined by the type of catalytic reaction and whose reaction progresses or is promoted by the action of the catalyst. In addition, the " * ” represents the adsorption sites on the surface of solid catalyst.

[0058] * +CO→CO *

[0059] 2 * +O2 OO * + * →2O *

[0060] CO * +O * O-CO * + * →CO2+2 *

[0061] In addition, in the above formula, “ "Represents" a symbol that combines an arrow pointing right → and an arrow pointing left ←.

[0062] In addition, as a plurality of candidate elements that can be candidates for the metal element causing the catalytic reaction, it is possible to select from Ru, Ni, Rh, Cu, Pd, Pt, Ag, Au, etc., which are generally elements constituting solid catalysts. Furthermore, as the crystal plane causing the catalytic reaction, it is possible to select the (111) plane, which is generally a crystal plane causing the catalytic reaction, or it is possible to select two or more crystal planes.

[0063] In addition, in the screening method according to the present embodiment, at least a part of step S01 can be automatically performed by an information processing device. That is, in step S01, if a target catalytic reaction is input, at least one of a plurality of elementary reactions, a plurality of candidate elements, a plurality of adsorption structures, and a crystal plane can be automatically determined from a database.

[0064] Furthermore, in step S01, at least one of the plurality of elementary reactions, the plurality of candidate elements, the plurality of adsorption structures, and the crystal plane may be determined not every time but using pre-prepared data. For example, in an information processing device, a storage unit may store past data determined regarding a catalytic reaction, and when past data regarding the same catalytic reaction exists in the storage unit, the data may be read from the storage unit.

[0065] (Step S02: Creation of basic information)

[0066] In step S02, basic information is prepared. The basic information is information that serves as a basis for calculating the activation energy, differential energy, and reaction rate in step S03.

[0067] The basic information prepared in step S02 includes the energy and vibration frequency of each state of each reaction matrix in a non-adsorbed state and each reaction matrix in an adsorbed state and each atom constituting the same in a plurality of elementary reactions calculated for each candidate element. The so-called states of the plurality of elementary reactions respectively show the initial state, final state and transition state of each reaction matrix in each elementary reaction. The so-called adsorption state of each constituent atom of the reaction matrix represents the adsorption state of the atoms constituting the reaction matrix when they exist separately. The energy and vibration frequency of each state / constituent atom of the reaction matrix of the plurality of elementary reactions can be calculated using a general quantum chemical calculation method or a calculation method with an accuracy equivalent to that of quantum chemical calculation. As a quantum chemical calculation method that can be used to calculate the energy and vibration frequency of each state of each reaction matrix in the plurality of elementary reactions, for example, an electronic state calculation method based on density functional theory (DFT: Density Functional Theory) can be cited. As a calculation method for the energy of the transition state, for example, the NEB (Nudged Elastic Band) method can be cited. Furthermore, as a calculation method having an accuracy comparable to that of quantum chemical calculation, for example, a molecular dynamics calculation method based on machine learning potential can be cited.

[0068] In addition, the basic information made in step S02 includes the conditions of catalytic reaction. As the conditions of catalytic reaction, for example, temperature, gas partial pressure, etc. can be cited. The conditions of catalytic reaction can be determined based on the environment that actually causes the catalytic reaction. In this way, by determining the conditions of catalytic reaction based on the actual environment, an alloy that is more suitable for the intended purpose of the solid catalyst can be found. In the catalytic reaction envisioned in the present application, as the basic information of the conditions of catalytic reaction, it is preferred to determine both temperature and gas partial pressure.

[0069] As an example, when the target catalytic reaction is set to the oxidation reaction of CO as described above, there are 10 states shown below in the adsorption states of each reaction substrate of the plurality of elementary reactions and the constituent atoms of the reaction substrate determined in step S01.

[0070] CO (gas monomer)

[0071] CO2 (gas monomer)

[0072] O2 (gas monomer)

[0073] CO2 * (Adsorption state)

[0074] CO * (Adsorption state)

[0075] O2 * (Adsorption state)

[0076] O * (Adsorption state)

[0077] C * (Adsorption state)

[0078] OO * (Transition state)

[0079] O-CO * (Transition state)

[0080] The energy and vibration frequency of each of these 10 states are calculated using a quantum chemical calculation method. In addition, the conditions of the catalytic reaction can be calculated based on the environment that actually promotes the oxidation of CO, such as the place where CO is supplied.

[0081] (Step S03: Calculation of activation energy, differential energy, and reaction rate)

[0082] In step S03, activation energy, differential energy, and reaction rate are calculated for each candidate element based on the basic information prepared in step S02. The activation energy, differential energy, and reaction rate are necessary for preparing the distribution information in step S05.

[0083] The reaction rate is calculated for each candidate element and is a physical quantity representing the activity of the catalytic reaction of each candidate element. The reaction rate of the catalytic reaction of each candidate element can be calculated using the energy and vibration frequency of each state of multiple elementary reactions of each candidate element contained in the basic information prepared in step S02 and the temperature of the catalytic reaction and the gas partial pressure conditions. The reaction rate of the catalytic reaction of each candidate element can be calculated using a general algorithm. As an algorithm that can calculate the reaction rate, for example, Newton's method can be cited.

[0084] A plurality of activation energies are calculated corresponding to a plurality of elementary reactions for each candidate element. Each activation energy is a physical quantity representing the energy required to generate each elementary reaction in each candidate element. The activation energy of each elementary reaction can be calculated using the energy of each state of the plurality of elementary reactions of each candidate element contained in the basic information prepared in step S02.

[0085] The differential energy is obtained as a relative value of the energy of two states contained in a plurality of elementary reactions for each of the candidate elements. The differential energy is a physical quantity determined in step S04 as a candidate for the characteristic energy. The differential energy is calculated as the difference between the energy of any two states contained in a plurality of elementary reactions. As the differential energy, for example, adsorption energy, energy of an intermediate, etc. can be used. In addition, the so-called adsorption energy is a differential energy calculated as the difference between the energy of the state in which the reaction matrix and each atom constituting the reaction matrix are adsorbed on each candidate element and the energy of the state in which the reaction matrix is ​​in a gas state.

[0086] (Step S04: Selection of characteristic energy)

[0087] In step S04, a characteristic energy is selected from the plurality of differential energies calculated in step S03 as a characteristic energy that is a key to promoting the reaction by establishing a correlation with the reaction rate. Specifically, in step S04, the linearity of all combinations of the plurality of activation energies and the plurality of differential energies is evaluated based on the relationship between the plurality of candidate elements. Then, the differential energy that can obtain high linearity for all the plurality of activation energies is selected from the plurality of differential energies as the characteristic energy.

[0088] Here, the characteristic energy that can obtain high linearity for all the activation energies can also obtain high linearity for the logarithm of the reaction rate. This is based on the following situation: because the activation energy of all elementary reactions constituting the catalytic reaction is linearly related to the logarithm of the reaction rate of each elementary reaction through the Arrhenius formula, the combination of elementary reactions, that is, the overall reaction rate, is also linearly related. Therefore, by associating the characteristic energy selected in step S04 with the reaction rate, the characteristic energy can be converted into the reaction rate.

[0089] Specifically, the activation energy E contained in the plurality of activation energies a1 The differential energy E contained in the multiple differential energies b1 The linearity can be determined by converting the activation energy E a1 And the differential energy E b1 The activation energy E of all candidate elements is plotted as a two-dimensional graph with two axes. a1 and the differential energy E b1 The linearity of the plotted points in the obtained scatter plot was evaluated.

[0090] For example, the coefficient of determination r in the least squares method can be used as an indicator 2 The linearity of the selected plot points for obtaining the characteristic energy with high linearity is evaluated by using the determination coefficient r 2 For example, the coefficient of determination r 2 The differential energies are tabulated in descending order (or in descending order of values), and multiple differential energies are divided into determination coefficients r 2 The energy of the high value of the group and the low value of the group are selected as the characteristic energy. In this case, in the grouping of multiple differential energies, for example, the determination coefficient r 2 The differential energy above a given threshold is set as a high group, preferably 0.7 or more, more preferably 0.8 or more, can be set as a high group. 2 The plurality of differential energies listed in descending order can also select differential energies above a given order as feature energy. In addition, the method of selecting feature energy from a plurality of differential energies is not limited to the above, and any known method can be used.

[0091] The number of mutually different feature energies selected from the plurality of differential energies in step S04 can be arbitrarily calculated according to the dimension of the distribution information generated in step S05. That is, when N-dimensional distribution information is generated in step S05, N mutually different feature energies are selected in step S04.

[0092] As an example, when the target catalytic reaction is set to the oxidation reaction of CO as described above and two-dimensional distribution information that is easy to understand visually is created in step S05, for example, the adsorption energy of CO and the adsorption energy of O can be selected from multiple differential energies as two different characteristic energies.

[0093] (Step S05: Creation of distribution information)

[0094] In step S05, a graph showing the distribution of the reaction speed with respect to the characteristic energy selected in step S04, i.e., distribution information is prepared. The distribution information shows the characteristic energy and the reaction speed in a continuous relationship, that is, it is information that associates an arbitrary characteristic energy with the reaction speed. In step S05, for an area where no plot points exist except for the plot points of a plurality of candidate elements obtained from the reaction speed calculated in step S03 and the characteristic energy selected in step S04, the reaction speed can be calculated from the characteristic energy at an arbitrary resolution for interpolation, thereby preparing the distribution information.

[0095] That is, according to the distribution information, the reaction rate can be obtained without complicated calculations based on the characteristic energy that can be easily calculated as a relative value of energy. In the distribution information, the reaction rate can be obtained for any metal based on the characteristic energy, and further, the reaction rate can be obtained not only for a single metal but also for an alloy of any composition based on the characteristic energy. Therefore, the reaction rate of any alloy can be easily obtained based on the distribution information.

[0096] As an example, Figure 2 Similar to the above, two-dimensional distribution information is shown when the target catalytic reaction is set to the oxidation reaction of CO and the characteristic energy is set to the adsorption energy of CO and the adsorption energy of O. Figure 2 The distribution information shown is shown as a two-dimensional heat map in which the reaction rate (common logarithm) is displayed as a color difference in a graph with the adsorption energy of CO and the adsorption energy of O as the vertical axis and the horizontal axis, respectively. In this way, by making the distribution information into a heat map, it is easy to visually identify the area where a large reaction rate can be obtained.

[0097] (Step S06: Prediction of composition)

[0098] In step S06, the composition of multiple alloys (combinations of candidate elements constituting the alloys and composition ratios of the candidate elements in the combinations) that are likely to have a higher reaction rate and contain at least two of the multiple candidate elements are predicted based on the distribution information generated in step S05. Specifically, in step S06, the composition of the alloy that will have a higher reaction rate is predicted based on the positional relationship between the target plot point P corresponding to the target value of the reaction rate in the distribution information and the plot points of the candidate elements. The target plot point P is usually set at the position where the reaction rate is the highest. For example, Figure 2 In the heat map shown, the target plot point P can be set in the darkest region. For example, the composition of the alloy that will give a reaction rate close to the target plot point P can be predicted using the plot points of a plurality of candidate elements in the distribution information and the coordinate information of the target plot point P. By using the coordinate information in this way, the composition of the alloy that has a higher reaction rate can be mechanically predicted with higher accuracy.

[0099] As an example, a case will be described where the composition of the alloy is a ternary system consisting of a combination of candidate elements A, B, and C. In this case, for example, two-dimensional distribution information created using two characteristic amount energies can be used.

[0100] Figure 3 Indicates that the plot point A (A) of candidate elements A, B, and C is displayed on the distribution information. x , A y )、B(B x , B y )、C(C x , C y ) and the target plot point P (P x , P y That is, the two characteristic energy quantities of candidate element A are A x , A y , the two characteristic energies of candidate element B are B x , B y , the two characteristic energies of candidate element C are C x , C y In addition, the two characteristic energy of the target plot point P is P x , P y .

[0101] Here, if Figure 4 As shown in the figure, if the plot point A is taken as the origin, then the vector b ((b x , b y ) = (B x -A x , B y -A y )) represents the plotted point B, which can be represented by the vector c((c x , c y ) = (C x -A x , C y -A y )) represents the plotted point C, which can be represented by the vector p((p x , p y ) = (P x -A x , P y -A y )) represents the target plot point P. In addition, the plot point A can be represented by the zero vector a(0,0). In this case, the vector p can be represented by the following formula using the vectors b, c, and the coefficients β, γ.

[0102] p = βb + γc

[0103] This equation can be transformed into the following equation using the coefficient matrix D.

[0104] [Mathematical formula 1]

[0105]

[0106] At this time, if all the conditions of β+γ<1, β>0, and γ>0 are satisfied, the composition ratio A:B:C of the three candidate elements A, B, and C can be calculated as "1-(β+γ):β:γ". In addition, satisfying the above conditions means that the target plot point P is located at Figure 3 The plot points A, B, and C shown are the inside of a triangle as vertices. In the present embodiment, the composition in which the target plot point P exists in the region surrounded by the line connecting the plot points of the candidate elements can be set as a candidate for the composition of the alloy that is likely to obtain a high reaction rate. That is, the composition in which the target plot point P does not exist in the region surrounded by the line connecting the plot points of the candidate elements can be excluded from the candidate for the composition of the alloy that is likely to obtain a high reaction rate.

[0107] Furthermore, the index m is calculated based on the following formula from the coefficients β and γ obtained above.

[0108] [Mathematical formula 2]

[0109]

[0110] The index m represents the square of the distance between the centroid of the triangle with the plot points A, B, and C as vertices and the target plot point P. Therefore, the composition with a smaller index m means that the ratios of the candidate elements are closer, and the composition of the alloy that can obtain a high reaction rate, which is difficult to predict based on the characteristic energy of a single element, can be predicted. Therefore, as the prediction result of the composition of the alloy with similar ratios of the candidate elements, a given number of compositions can be listed in the order of the index m from small to large. In this way, in the present embodiment, for an alloy containing a plurality of candidate elements, a given number of compositions can be listed in the order of the distances from the plot points estimated on the distribution information to the target plot point P from near to far.

[0111] Next, the composition of the alloy is described as consisting of four or more candidate elements A1, A2, ..., A （n-1） , A n In this case, for example, (n-1)-dimensional distribution information created by (n-1) feature energy can be used.

[0112] The distribution information shows the candidate elements A1, A2, ..., A （n-1） , A n The plot point A1 (A 11 , A 12 ,···,A 1（n-2） , A 1（n-1） )、A2(A 21 , A 22 ,···,A2（n-2） , A 2（n-1） )、···、A （n-1） (A （n-1）1 , A （n-1）2 ,···,A （n-1）（n-2） , A （n-1）（n-1） )、A n (A n1 , A n2 ,···,A n（n-2） , A n（n-1） ), and the target plot point P (P1, P2, ···, P （n-2） , P （n-1） ).

[0113] Here, the plot point A1 can be used as the origin, and the plot points A2, ..., A （n-1） , A n are shown as vectors a2, ···, a （n-1） 、a n (a 21 , a 22 ,···,a 2（n-2） , a 2（n-1） )、···、(a （n-1）1 , a （n-1）2 ,···,a （n-1）（n-2） , a （n-1）（n-1） )、(a n1 , a n2 ,···,a n（n-2） , a n（n-1） ) = (A 21 -A 11 , A 22 -A 12 ,···,A 2（n-2） -A 1（n-2） , A 2（n-1） -A 1（n-1） )、···、(A （n-1）1 -A 11 , A （n-1）2 -A 12 ,···,A （n-1）（n-2） -A 1（n-2） , A （n-1）（n-1） -A 1（n-1 )、(A n1 -A 11 , A n2 -A 12 ,···,A n（n-2） -A 1（n-2） , A n（n-1） -A 1（n-1 )), the target plot point P can be shown as a vector p((p1, p2, ···, p （n-2） , p （n-1）) = (P1-A 11 , P2-A 12 ,···,P （n-2） -A 1（n-2） , P （n-1） -A 1（n-1） )). In addition, the plot point A1 can be represented by the zero vector a1 (0, 0, . . . , 0, 0). In this case, the vector p can be represented by the vectors a2, . . . , a （n-1） 、a n and coefficients β1, ···, β （n-2） , β （n-1） , which is represented by the following formula.

[0114] p=β1a2+···+β （n-2） a （n-1） +β （n-1） a n

[0115] This equation can be transformed into the following equation using the coefficient matrix D.

[0116] [Mathematical formula 3]

[0117]

[0118] At this time, if all of the following conditions are satisfied, the candidate elements A1, A2, ..., A （n-1） , A n The composition ratio of A1: A2: ···: A （n-1） : A n It can be calculated as "1-(β1+β2+···+β （n-2）、 β （n-1） ):β1:···:β （n-2） :β （n-1） ”.

[0119] [Formula 4]

[0120]

[0121] Furthermore, according to the coefficients β1, ···, β （n-2） , β （n-1） The index m is calculated based on the following formula.

[0122] [Formula 5]

[0123]

[0124] The smaller the index m, the closer the ratio of each candidate element is, and the composition of the alloy that can obtain a high reaction rate, which is difficult to predict based on the characteristic energy of a single element, can be predicted. Therefore, as the prediction result of the composition of the alloy with a similar ratio of each candidate element, the composition of a given number can be listed in the order of the index m from small to large.

[0125] (Step S07: Creation of slab model)

[0126] In step S07, in order to calculate the reaction rate and stability index for multiple compositions predicted in step S06 as compositions with high probability of obtaining a large reaction rate, multiple slab models corresponding thereto are made. In the making of the slab model, from the viewpoint of efficiency, it is preferred to use an existing database. As such a database, it is preferred to use a DFT calculation database such as CatApp that stores structural data of a slab model that is easy to use in quantum chemical calculations. In addition, as a database, in addition to the DFT calculation database, for example, a crystal structure database such as Materials Project can also be used. In addition, in step S07, a unit cell can be obtained from an existing database with respect to the composition predicted in step S06, and a slab model can be made based on the unit cell obtained.

[0127] In addition, for alloys that do not exist in the database, a slab model can be made independently. The method for making a slab model is not limited to a specific method. As an example, the method shown below can be used. In the method for making a slab model involved in one example, first, a model of a unit cell of a stable crystal structure (face-centered cubic lattice, body-centered cubic lattice, hexagonal closest structure, etc.) is made for a given element constituting the candidate elements contained in each composition when it exists alone, that is, a first unit cell model. Next, a second unit cell model is made in which a part of the atoms constituting the first unit cell model is replaced with atoms of a candidate element other than the given element. The slab model can be obtained by making a second unit cell model with a crystal plane ((111) plane, (211) plane, etc.) that is stable when the candidate element constituting the first unit cell model exists alone. In addition, the stable crystal structure and crystal plane when the metal element exists alone can be obtained from a crystal structure database such as Materials Project.

[0128] (Step S08: Calculation of stability index)

[0129] In step S08, a stability index representing the stability of the structure is calculated for each slab model created in step S07. The stability of the structure in each slab model is evaluated based on the energy possessed by the slab model. The energy used to evaluate the stability of the structure of the slab model can be any energy that can be calculated based on the slab model, for example, the total energy of the slab model, the surface energy of the slab model, etc. Specifically, in the evaluation of the stability of the slab model, general physicochemical calculation methods can be used. As a physicochemical calculation method that can be used in the evaluation of the stability of the slab model, for example, the Monte Carlo method can be cited.

[0130] As a stability index, as long as the stability of the structure between each slab model can be compared, a common index can be used for all slab models. Specifically, as a stability index, for example, the energy calculated from the slab model can be used as it is. In this case, it can be known that the slab model with a smaller energy as a stability index has a higher structural stability. In addition, as a stability index, other values ​​calculated based on the energy calculated from the slab model can also be used.

[0131] (Step S09: Calculation of Activity Index)

[0132] In step S09, an activity index representing the activity of the catalytic reaction is calculated for each slab model created in step S07. The activity of the catalytic reaction in each slab model is evaluated based on the reaction rate. Specifically, in step S09, first, for each slab model, the characteristic energy is calculated by the same method as step S02. Then, for each slab model, the distribution information created in step S04 is used to obtain the reaction rate corresponding to the characteristic energy.

[0133] As an activity index, as long as the activity between the slab models can be compared, a common index can be used for all slab models. Specifically, as an activity index, for example, the reaction speed calculated according to the slab model can be used as it is. In this case, it can be known that the greater the reaction speed of the slab model as an activity index, the greater the actual reaction speed (activity). In addition, as an activity index, other values ​​calculated based on the reaction speed calculated according to the slab model can also be used.

[0134] (Step S10: Determination of alloy)

[0135] In step S10, an alloy expected to have both high structural stability and high catalytic reaction activity is determined based on the stability index of each slab model calculated in step S08 and the activity index of each slab model calculated in step S09. In step S10, various methods can be used to determine the alloy from the stability index and activity index of each slab model.

[0136] As an example, in determining the alloy, one can use Figure 5 Such alloys are listed as examples. Figure 5 In the alloy list shown, data of stability index (energy) and activity index (reaction speed) are listed side by side for each type of alloy determined by the slab model. For example, in the alloy list, multiple alloys can be shown side by side from the top in the order of activity index from large to small. In this case, for example, the threshold value of the stability index can be predetermined, and a given number of alloys are selected in order from the top of the alloy list on the basis of excluding alloys with stability index greater than the threshold from multiple alloys. The threshold value of the stability index is preferably set to a sufficiently small value so that a high structural stability can be obtained. In addition, in the alloy list, multiple alloys can also be shown side by side from the top in the order of stability index from large to small. In this case, for example, the threshold value of the activity index can be predetermined, and a given number of alloys are selected in order from the top of the alloy list on the basis of excluding alloys with activity index less than the threshold from multiple alloys. The threshold value of the activity index is preferably set to a sufficiently large value in order to make the catalytic reaction progress smoothly.

[0137] (Other forms)

[0138] In the screening method according to the present embodiment, various modifications can be added to the above-mentioned structure within the range in which the above-mentioned effects can be appropriately obtained.

[0139] For example, in step S09, the activity index may be calculated only for the slab model with a good stability index in step S08. Thus, the calculation burden in step S09 can be reduced, and the candidate slab model when determining the alloy in step S10 can be narrowed down. In addition, the order of step S08 and step S09 may be reversed, that is, after calculating the activity index of each slab model in step S09, the stability index of each slab model is calculated in step S08. In this case, in step S08, the stability index is calculated only for the slab model with a good activity index in step S09.

[0140] [Additional structure of screening method]

[0141] (Brief description)

[0142] The screening method according to the present embodiment is not limited to the above-described configuration, and may include an additional configuration for further improving the accuracy of alloy screening. An example of an effective additional configuration will be described below with respect to the screening method according to the present embodiment.

[0143] (Search for alloy composition using selectivity as an indicator)

[0144] In the above embodiment, the activity index is output, but in the case of a catalytic reaction with two or more reaction paths and the same characteristic energy, the selectivity distribution information (heat map) can be described in the same way as the above activity index. In this case, in addition to the main reaction activity, the selectivity of the main reaction product can also be added to the output. For example, when the products are i and j and the reaction rates are r i 、r j When , the selectivity S can be defined as follows.

[0145] S=r i / (r i +r j )

[0146] (Search for further alloy compositions)

[0147] In the above-mentioned embodiment, in order to determine an alloy containing multiple metals, distribution information made about a crystal structure containing only a single metal is used. That is, in order to determine the alloy, the interaction between the metals produced in the actual alloy is not considered. Therefore, in the alloy determined in the above-mentioned embodiment, there is a possibility of some deviations from the composition that can actually obtain the maximum reaction rate. Therefore, there is a possibility that the alloy with high activity of catalytic reaction can be further found by further searching for the composition near the composition of the alloy determined in the above-mentioned embodiment. For example, the search for such a composition can be implemented by making a slab model of a plurality of alloys that only deviate from the composition relative to the alloy determined in the above-mentioned embodiment and evaluating the stability index.

[0148] As an example, multiple alloys obtained by increasing or decreasing the composition ratio of each candidate metal by 1 relative to the composition of the alloy determined in the above embodiment can be used as the object of search. For example, in the case where the composition of the alloy determined in the above embodiment is a ternary system containing candidate elements A, B, and C in the composition ratio A: B: C, alloys with 6 composition ratios of A+1: B-1: C, A+1: B: C-1, A: B+1: C-1, A: B-1: C+1, A-1: ​​B+1: C, and A-1: ​​B: C+1 are set as the object of search. For multiple alloys set as the object of search, a slab model is made in the same way as step S07, and the reaction rate is obtained in the same way as step S09 to determine the alloy with the highest reaction rate. Furthermore, it is believed that by repeating the same search for the alloy determined in this way, the composition of the alloy that can obtain the maximum reaction rate will be continuously approached. Such a composition search can be repeated, for example, until the rate of increase of the reaction rate of the alloy determined last time becomes below a given value, that is, until the reaction rate is judged to converge. Furthermore, the constituent searches may be repeated a predetermined number of times.

[0149] (Evaluation using nanoparticle model)

[0150] In the above-mentioned embodiment, the stability of the structure of the alloy is evaluated by the slab model, and sometimes the stability of the structure of the alloy cannot be correctly evaluated by the slab model that only focuses on a single crystal face. In this regard, by using the nanoparticle model of the three-dimensional structure of the performance alloy nanoparticle, the stability of the structure of the alloy can be more correctly evaluated. Therefore, the screening method involved in the present embodiment can introduce the evaluation of the nanoparticle model that utilizes the alloy in order to more surely evaluate the stability of the alloy. In the making of the nanoparticle model of the alloy, known modeling methods can be used.

[0151] As a method of modeling catalyst nanoparticles like the composition of an alloy slab model, for example, a genetic algorithm can be used.

[0152] The energy based on nanoparticle model is used to evaluate the stability of the structure in each nanoparticle model. As the energy used for evaluating the stability of the structure of the nanoparticle model, it is the energy that can be calculated according to the nanoparticle model, for example, the energy of the nanoparticle model can be cited. The same physicochemical calculation technique as the evaluation of the stability of the slab model in step S08 can be used in the calculation of the energy of the nanoparticle model. The result obtained by the nanoparticle model can be utilized as a stability index representing the stability of the structure of the alloy. This stability index can replace the stability index calculated in step S08 and utilize, in addition, it can be utilized as the second stability index together with the stability index calculated in step S08.

[0153] As an example, make a nanoparticle model common to a plurality of candidate elements constituting the slab model by each of the slab models made in step S07.Then, make the nanoparticle information that energy, composition ratio and full atomic coordinates are established in association by each of the nanoparticle models.The peripheral information of the specific atom obtained from the full atomic coordinates of the nanoparticle and the peripheral information of the specific atom obtained from the full atomic coordinates constituting the slab model can be compared to calculate similarity. In the peripheral information of the specific atom, for example, coordination number, radial distribution function, etc. are arranged. About similarity, the integral value of the difference of coordination number, radial distribution function, etc. can be cited.By determining the nanoparticle model with the highest similarity by each of the slab models, the energy of the nanoparticle model corresponding to each slab model is adopted.And it can be known that the alloy with smaller energy obtained from the nanoparticle information has higher stability of structure.

[0154] [Information processing device]

[0155] The screening method according to the above embodiment can be used, for example, Figure 6 The information processing device 100 shown in FIG.

[0156] The information processing device 100 according to the present embodiment can be constituted by various computers, and may be constituted by a single computer or by combining two or more computers.

[0157] The functions implemented by the components described in this specification can be installed in a general-purpose processor, a special-purpose processor, an integrated circuit, ASICs (Application Specific Integrated Circuits), a CPU (a Central Processing Unit), a conventional circuit, and / or a combination of these, a circuit or a processing circuit that is programmed to implement the functions described. The processor includes transistors and other circuits, which are considered as circuits or processing circuits. The processor can also be a programmable processor that executes a program stored in a memory.

[0158] In this specification, circuits, components, and subassemblies are hardware programmed to implement the described functions, or hardware that performs the described functions. The hardware may be all the hardware disclosed in this specification, or hardware programmed to implement the described functions, or all the hardware known as hardware that performs the described functions.

[0159] When the hardware is a processor of a type regarded as a circuit, the circuit, unit or component is a combination of hardware and software used to constitute the hardware and / or processor.

[0160] The input unit 101 is configured as a user interface, for example, to input the target catalytic reaction, multiple elementary reactions, multiple candidate elements, and crystal planes in step S01. The output unit 102 can be configured to output information to various display devices such as displays, for example, it can be configured to display at least one of the distribution information prepared in step S04 and the alloy index (stability index and activity index) used in step S10. The processing unit 103 is configured to perform all or part of the processing contained in the screening method involved in the above-mentioned embodiment according to the program. The storage unit 104 is configured to store various data, for example, to store programs for the processing unit 103 to perform various processing, various data required for the processing of the processing unit 103, etc. Furthermore, the information processing device 100 may also have a structure other than the above, for example, it may have a communication unit in order to obtain data from a database on the cloud through communication.

[0161] [Other embodiments]

[0162] As mentioned above, although embodiment of this invention is described, this invention is not limited to only the said embodiment, It is a matter of course that various changes can be added within the range which does not deviate from the summary of this invention.

[0163] Explanation of symbols

[0164] 100…Information processing device

[0165] 101…Input section

[0166] 102…Output section

[0167] 103…Processing Department

[0168] 104 ...storage unit.

Claims

1. A screening method for an alloy that causes a target catalytic reaction, wherein: For each of a plurality of candidate elements that are candidates for the metal element constituting the alloy, basic information is prepared about a specific crystal plane formed by each candidate element, the basic information including each state of each reaction substrate in a non-adsorbed state and each reaction substrate in an adsorbed state among a plurality of elementary reactions constituting the catalytic reaction, and the energy and vibration frequency of each atom constituting the same, For each of the plurality of candidate elements, a plurality of activation energies corresponding to the plurality of elementary reactions, a plurality of differential energies obtained as relative values ​​of the energies of the respective states, and a reaction rate of the catalytic reaction are obtained based on the basic information. Regarding each activation energy constituting the plurality of activation energies and each differential energy constituting the plurality of differential energies, linearity is evaluated based on the relationship between the plurality of candidate elements, and a characteristic quantity energy that can obtain high linearity for all of the plurality of activation energies is selected from the plurality of differential energies, using the characteristic energy and the reaction speed in the plurality of candidate elements, to create distribution information indicating the distribution of the reaction speed with respect to the characteristic energy, using the distribution information, predicting a plurality of compositions in which the reaction rate increases by constituting the alloy including at least two candidate elements among the plurality of candidate elements, creating a plurality of slab models corresponding to the plurality of components, calculating a stability index based on the energy calculated for each of the plurality of slab models, An activity index is calculated based on the reaction rate obtained from the distribution information using the characteristic energy calculated for each of the plurality of slab models.

2. The screening method according to claim 1, wherein The characteristic energy includes adsorption energy.

3. The screening method according to claim 1 or 2, wherein: The characteristic quantity energy is composed of two characteristic quantity energies that are different from each other. The distribution information is made into a two-dimensional heat map.

4. The screening method according to any one of claims 1 to 3, wherein In order to predict the plurality of compositions, a target plot point is set on the distribution information, plot points of the at least two candidate elements are selected, and coordinate information of the target plot point and the plot points of the candidate elements is used to predict the at least two candidate elements and their composition ratios that can obtain the reaction rate close to the target plot point.

5. The screening method according to any one of claims 1 to 4, wherein Acquire a unit cell including the at least two candidate elements from a database, and create the plurality of slab models based on the acquired unit cell, or, A first unit cell model is created for a crystal structure that is stable when a given element constituting the at least two candidate elements exists alone, a second unit cell model is created by replacing a portion of atoms constituting the first unit cell model with atoms other than the given element among the at least two candidate elements, and the multiple slab models are created based on the second unit cell model.

6. The screening method according to any one of claims 1 to 5, wherein In order to calculate the stability index, a nanoparticle model corresponding to the at least two candidate elements is created, the composition ratio of the nanoparticle model and the energy corresponding to the surrounding information of a specific atom are calculated, and the energy of the nanoparticle model corresponding to the multiple slab models is obtained based on the composition ratio of the multiple slab models and the surrounding information of the specific atom.

7. An information processing device for screening an alloy that causes a target catalytic reaction, the information processing device comprising a processing unit, the processing unit performing the following processing: For each of a plurality of candidate elements that are candidates for the metal element constituting the alloy, basic information is prepared about a specific crystal plane formed by each candidate element, the basic information including each state of each reaction substrate in a non-adsorbed state and each reaction substrate in an adsorbed state among a plurality of elementary reactions constituting the catalytic reaction, and the energy and vibration frequency of each atom constituting the same, For each of the plurality of candidate elements, a plurality of activation energies corresponding to the plurality of elementary reactions, a plurality of differential energies obtained as relative values ​​of the energies of the respective states, and a reaction rate of the catalytic reaction are obtained based on the basic information. Regarding each activation energy constituting the plurality of activation energies and each differential energy constituting the plurality of differential energies, linearity is evaluated based on the relationship between the plurality of candidate elements, and a characteristic quantity energy that can obtain high linearity for all of the plurality of activation energies is selected from the plurality of differential energies, using the characteristic energy and the reaction rate in the plurality of candidate elements, to create distribution information indicating the distribution of the reaction rate with respect to the characteristic energy, using the distribution information, predicting a plurality of compositions in which the reaction rate increases by constituting the alloy including at least two candidate elements among the plurality of candidate elements, creating a plurality of slab models corresponding to the plurality of components, calculating a stability index based on the energy calculated for each of the plurality of slab models, An activity index is calculated based on the reaction rate obtained from the distribution information using the characteristic energy calculated for each of the plurality of slab models.

8. The information processing device according to claim 7, wherein: The characteristic energy selected by the processing unit includes adsorption energy.

9. The information processing device according to claim 7 or 8, wherein: In the processing unit, the feature quantity energy is composed of two feature quantity energies different from each other, and the distribution information is created as a two-dimensional heat map.

10. The information processing device according to any one of claims 7 to 9, wherein: In the processing unit, in order to predict the plurality of compositions, a target plot point is set on the distribution information, plot points of the at least two candidate elements are selected, and coordinate information of the target plot point and the plot points of the candidate elements is used to predict the at least two candidate elements and their composition ratios that can obtain the reaction rate close to the target plot point.

11. The information processing device according to any one of claims 7 to 10, wherein: In the processing unit, Acquire a unit cell including the at least two candidate elements from a database, and create the plurality of slab models based on the acquired unit cell, or, A first unit cell model is created for a crystal structure that is stable when a given element constituting the at least two candidate elements exists alone, a second unit cell model is created by replacing a portion of atoms constituting the first unit cell model with atoms other than the given element among the at least two candidate elements, and the multiple slab models are created based on the second unit cell model.

12. The information processing device according to any one of claims 7 to 11, wherein: In the processing unit, in order to calculate the stability index, a nanoparticle model corresponding to the at least two candidate elements is created, the composition ratio of the nanoparticle model and the energy corresponding to the surrounding information of a specific atom are calculated, and the energy of the nanoparticle model corresponding to the multiple slab models is obtained based on the composition ratio of the multiple slab models and the surrounding information of the specific atom.

13. The information processing device according to any one of claims 7 to 12, wherein: In the processing unit, the characteristic amount energy is composed of two characteristic amount energies different from each other, The information processing device includes an output unit that outputs the distribution information in the form of a two-dimensional heat map.

14. The information processing device according to any one of claims 7 to 13, wherein: The information processing device further comprises: An output unit capable of displaying the distribution information created by the processing unit and at least one of the stability index and the activity index calculated by the processing unit.

15. A program for screening an alloy that causes a target catalytic reaction, the program causing an information processing device to execute the following processing: For each of a plurality of candidate elements that are candidates for the metal element constituting the alloy, basic information is prepared about a specific crystal plane formed by each candidate element, the basic information including each state of each reaction substrate in a non-adsorbed state and each reaction substrate in an adsorbed state among a plurality of elementary reactions constituting the catalytic reaction, and the energy and vibration frequency of each atom constituting the same, For each of the plurality of candidate elements, a plurality of activation energies corresponding to the plurality of elementary reactions, a plurality of differential energies obtained as relative values ​​of the energies of the respective states, and a reaction rate of the catalytic reaction are obtained based on the basic information. Regarding each activation energy constituting the plurality of activation energies and each differential energy constituting the plurality of differential energies, linearity is evaluated based on the relationship between the plurality of candidate elements, and a characteristic quantity energy that can obtain high linearity for all of the plurality of activation energies is selected from the plurality of differential energies, using the characteristic energy and the reaction speed in the plurality of candidate elements, to create distribution information indicating the distribution of the reaction speed with respect to the characteristic energy, using the distribution information, predicting a plurality of compositions in which the reaction rate increases by constituting the alloy including at least two candidate elements among the plurality of candidate elements, creating a plurality of slab models corresponding to the plurality of components, calculating a stability index based on the energy calculated for each of the plurality of slab models, An activity index is calculated based on the reaction rate obtained from the distribution information using the characteristic energy calculated for each of the plurality of slab models.

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