JP7401491B2 - Screening method - Google Patents

Description

The present invention relates to a method for screening alloys useful as solid catalysts.

Improving the performance of solid catalysts is becoming important not only for the development of the chemical industry but also for the realization of a sustainable society. In order to improve the performance of solid catalysts, many attempts have been made, for example, to alloy solid catalysts made of a single element by adding different elements. However, the performance of solid catalysts made of alloys varies greatly depending on structural elements such as constituent elements and atomic arrangement, and the number of combinations of these structural elements is virtually infinite. For this reason, it is almost impractical to find a solid catalyst that provides high performance only through experimental trial and error.

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

JP2020-006312A

However, in the technique described in Patent Document 1, only the adsorption energy when a base material element and a limited number of doping elements are combined is calculated, and the reaction rate of the catalytic reaction is not directly considered. Further, the technique described in Patent Document 1 does not have an index for selecting which element to select, and is not efficient when considering further combination variations when there are many candidate elements. Furthermore, the technology is not limited to a specific catalytic reaction consisting of a single elementary reaction like the technology described in Patent Document 1, but is also applicable to, for example, a reaction that promotes a reaction in a production process using multiple raw materials. There is a need for solid catalyst screening technology that can be applied to catalytic reactions that consist of multiple elementary reactions or that require consideration of other factors.

An object of the present invention is to efficiently screen alloys useful as solid catalysts.

A screening method according to one embodiment of the present invention screens for alloys that cause a desired catalytic reaction.
For each of the plurality of candidate elements that are candidates for the metal elements constituting the alloy, each reaction in a non-adsorbed state in the plurality of elementary reactions that constitute the catalytic reaction for a specific crystal plane formed by each candidate element. Basic information is created, including each state of the substrate, and the energy and frequency of each reaction substrate in the adsorbed state and each atom constituting it.
For each of the plurality of candidate elements, from the basic information, a plurality of activation energies corresponding to each of the plurality of elementary reactions, a plurality of differential energies obtained as relative values of the energies of each state, and the catalytic reaction. The reaction rate is required.
Evaluate linearity from the relationship between the plurality of candidate elements for each activation energy forming the plurality of activation energies and each differential energy forming the plurality of differential energies, and evaluate linearity from among the plurality of differential energies. , feature energies that provide high linearity for all of the plurality of activation energies are selected.
Using the feature energy and the reaction rate of the plurality of candidate elements, distribution information indicating a distribution of the reaction rate with respect to the feature energy is created.
Using the distribution information, a plurality of compositions that include at least two candidate elements among the plurality of candidate elements and that increase the reaction rate by forming the alloy are predicted.
A plurality of slab models are created corresponding to each of the plurality of compositions.
A stability index is calculated based on the energy calculated for each of the plurality of slab models.
An activity index is calculated based on the reaction rate determined from the distribution information using the feature amount energy calculated for each of the plurality of slab models.

An information processing device according to one embodiment of the present invention includes a processing unit capable of executing the following.
For each of the plurality of candidate elements that are candidates for the metal elements constituting the alloy, each reaction in a non-adsorbed state in the plurality of elementary reactions that constitute the catalytic reaction for a specific crystal plane formed by each candidate element. Basic information is created, including each state of the substrate, and the energy and frequency of each reaction substrate in the adsorbed state and each atom constituting it.
For each of the plurality of candidate elements, from the basic information, a plurality of activation energies corresponding to each of the plurality of elementary reactions, a plurality of differential energies obtained as relative values of the energies of each state, and the catalytic reaction. The reaction rate is required.
Evaluate linearity from the relationship between the plurality of candidate elements for each activation energy forming the plurality of activation energies and each differential energy forming the plurality of differential energies, and evaluate linearity from among the plurality of differential energies. , feature energies that provide high linearity for all of the plurality of activation energies are selected.
Using the feature energy and the reaction rate of the plurality of candidate elements, distribution information indicating a distribution of the reaction rate with respect to the feature energy is created.
Using the distribution information, a plurality of compositions that include at least two candidate elements among the plurality of candidate elements and that increase the reaction rate by forming the alloy are predicted.
A plurality of slab models are created corresponding to each of the plurality of compositions.
A stability index is calculated based on the energy calculated for each of the plurality of slab models.
An activity index is calculated based on the reaction rate determined from the distribution information using the feature amount energy calculated for each of the plurality of slab models.

A program according to one embodiment of the present invention causes the following to be executed as information processing.
For each of the plurality of candidate elements that are candidates for the metal elements constituting the alloy, each reaction in a non-adsorbed state in the plurality of elementary reactions that constitute the catalytic reaction for a specific crystal plane formed by each candidate element. Basic information is created, including each state of the substrate, and the energy and frequency of each reaction substrate in the adsorbed state and each atom constituting it.
For each of the plurality of candidate elements, from the basic information, a plurality of activation energies corresponding to each of the plurality of elementary reactions, a plurality of differential energies obtained as relative values of the energies of each state, and the catalytic reaction. The reaction rate is required.
Evaluate linearity from the relationship between the plurality of candidate elements for each activation energy forming the plurality of activation energies and each differential energy forming the plurality of differential energies, and evaluate linearity from among the plurality of differential energies. , feature energies that provide high linearity for all of the plurality of activation energies are selected.
Using the feature energy and the reaction rate of the plurality of candidate elements, distribution information indicating a distribution of the reaction rate with respect to the feature energy is created.
Using the distribution information, a plurality of compositions that include at least two candidate elements among the plurality of candidate elements and that increase the reaction rate by forming the alloy are predicted.
A plurality of slab models are created corresponding to each of the plurality of compositions.
A stability index is calculated based on the energy calculated for each of the plurality of slab models.
An activity index is calculated based on the reaction rate determined from the distribution information using the feature amount energy calculated for each of the plurality of slab models.

According to the present invention, alloys useful as solid catalysts can be efficiently screened.

1 is a flowchart showing a screening method according to an embodiment of the present invention. It is a figure which illustrates the distribution information created in step S05 of the said screening method. It is a figure for explaining step S06 of the above-mentioned screening method. It is a figure for explaining step S06 of the above-mentioned screening method. It is a figure which illustrates the alloy list which can be used in step S10 of the said screening method. FIG. 2 is a block diagram showing an information processing device that can implement the above screening method.

[Introduction]
A screening method according to an embodiment of the present invention is configured to be able to efficiently search for an alloy useful as a solid catalyst that causes a desired catalytic reaction by calculation using an information processing device. By feeding back the search results obtained by the screening method according to the present embodiment, it is possible to narrow down the alloys that have a huge number of combinations of structural elements to a small number that should be evaluated through experiments. This not only makes it possible to design a high-performance solid catalyst with less effort and cost, but also allows us to expect a solid catalyst with excellent performance and higher feasibility.

The screening method according to the present embodiment uses not only the catalytic reaction activity of the alloy but also the structural stability of the alloy as an index for searching for an alloy useful as a solid catalyst. This makes it possible to select an alloy that provides high performance as a solid catalyst from among configurations that can realize a stable structure. Therefore, in the screening method according to the present embodiment, configurations that are difficult to prepare in the first place or whose structure is likely to change over time can be excluded from the targets of experimental evaluation. This makes it possible to more efficiently search for alloys useful as solid catalysts that cause the desired catalytic reaction.

[Overall structure of screening method]
(Outline explanation)
The overall configuration of the screening method according to this embodiment will be described below. The screening method according to this embodiment includes steps S01 to S10 shown in FIG. Hereinafter, steps S01 to S10 of the screening method according to the present embodiment will be explained in detail along FIG. 1.

(Step S01: Selection of elementary reactions, candidate elements, and crystal planes)
In step S01, first, a target catalytic reaction is selected. A catalytic reaction refers to a series of chemical reactions that proceed or are promoted by the action of a catalyst. The desired catalytic reaction can be arbitrarily selected from those that can be realized using a solid catalyst and consist of sequential reactions on the same catalyst. Further, even if the substrate is desorbed during the reaction, the target catalytic reaction can be selected separately before and after desorption. Such catalytic reactions include, for example, the oxidation reaction of carbon monoxide, the transesterification reaction between esters and alcohols, the esterification reaction between fatty acids and alcohols, the hydrogenation of esters to produce alcohols, and the production of substituted amines between amines and alcohols. Reaction, hydrogenation reaction of fatty acids, hydrogenolysis reaction of alcohols, hydrodesulfurization reaction of sulfur, crossaldol reaction of aldehydes, hydrogenation reaction of aromatics, selective hydrogenation reaction of olefins, hydrogenation reaction of carbonyls, olefins Hydroisomerization reactions of dienes, ene cyclization reactions of dienes, oxygen oxidation reactions of alcohols, hydrogenation reactions of carbon monoxide and carbon dioxide (including hydrogenation reactions accompanied by carbon chain elongation reactions), and the like.

Next, a plurality of elementary reactions constituting the selected catalytic reaction are selected. An elementary reaction is a reaction at each stage when a catalytic reaction is broken down into multiple stages. That is, a plurality of elementary reactions can be selected depending on the desired catalytic reaction, and can be estimated from, for example, descriptions in literature.
Furthermore, a plurality of candidate elements are selected as candidates for the metal element that causes the selected catalytic reaction. As candidate elements, any two or more can be selected from all the metal elements, and for example, all the metal elements commonly used as solid catalysts can be selected in advance. The number of candidate elements is preferably 3 or more from the viewpoint of screening accuracy. Further, the number of candidate elements is preferably 30 or less from the viewpoint of screening efficiency.
In addition, a crystal structure is selected that will cause the selected catalytic reaction. The crystal structure can be arbitrarily selected from crystal structures constituting a body-centered cubic lattice, a face-centered cubic lattice, and a hexagonal close-packed structure; for example, a general crystal structure is selected as a crystal structure that causes a catalytic reaction. be able to. Further, for the crystal structure, any crystal plane expressed by Miller index, such as the general (111) plane, can be selected, and two or more crystal planes can also be selected. In addition, crystal planes can be determined by calculating the surface formation free energy using quantum chemical calculations, using the Wluff drawing method, or by referring to a database such as Crystalium, to determine which crystal planes are expected to exist on nanoparticles in an equilibrium state. You can select the face.

As an example, a case will be described in which a CO oxidation reaction (CO+0.5O ₂ →CO ₂ ) is selected as the target catalytic reaction. It is assumed that this catalytic reaction is composed of three elementary reactions by each reaction substrate, each represented by the following formula. Note that " ^* " in each formula indicates an adsorption site on the surface of the solid catalyst.
^* +CO→CO ^*
2 ^* +O ₂ ⇔O-O ^* + ^* →2O ^*
CO ^* +O ^* ⇔O-CO ^* + ^* →CO ₂ +2 ^*
Note that "⇔" in the above formula represents "a symbol that is a combination of an arrow → pointing to the right and an arrow ← pointing left."
In addition, the plurality of candidate elements that are candidates for the metal elements that cause this catalytic reaction may be selected from Ru, Ni, Rh, Cu, Pd, Pt, Ag, Au, etc., which are common elements constituting solid catalysts. I can do it. Further, as the crystal plane that causes this catalytic reaction, the (111) plane, which is generally used as a crystal plane that causes the catalytic reaction, can be selected, and two or more crystal planes can also be selected.

Note that in the screening method according to the present embodiment, at least a part of step S01 can be automatically performed by the information processing device. That is, in step S01, when 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 is automatically identified from the database. You can.
Further, in step S01, data prepared in advance may be used for at least one of the plurality of elementary reactions, the plurality of candidate elements, the plurality of adsorption structures, and the crystal planes, without specifying each time. For example, in an information processing device, past data specified regarding a catalytic reaction is stored in the storage unit, and if past data regarding the same catalytic reaction exists in the storage unit, the data is read out from the storage unit. You can.

(Step S02: Creation of basic information)
In step S02, basic information is created. The basic information is information that becomes the basis for calculating the activation energy, differential energy, and reaction rate in step S03.
The basic information created in step S02 includes each state of each reaction substrate in a non-adsorbed state, each reaction substrate in an adsorbed state, and each constituent component thereof in multiple elementary reactions calculated for each candidate element. Includes atomic energy and vibrational frequency. Each state of a plurality of elementary reactions indicates the initial state, final state, and transition state of each reaction substrate in each elementary reaction. The adsorption state of each constituent atom of the reaction substrate refers to the adsorption state when each atom making up the reaction substrate exists alone. The energy and vibration frequency of each state of a plurality of elementary reactions and constituent atoms of a reaction substrate can be calculated using a general quantum chemical calculation method or a calculation method having accuracy equivalent to quantum chemical calculation. Quantum chemical calculation methods that can be used to calculate the energy and frequency of each state of each reaction substrate in multiple elementary reactions include, for example, an electronic state calculation method based on density functional theory (DFT). Examples include. An example of a method for calculating the energy of a transition state is the NEB (Nudged Elastic Band) method. Furthermore, examples of calculation methods having accuracy equivalent to quantum chemical calculations include molecular dynamics calculation methods based on machine learning potentials.
Further, the basic information created in step S02 includes conditions for the catalytic reaction. Conditions for the catalytic reaction include, for example, temperature and gas partial pressure. Conditions for the catalytic reaction can be determined based on the environment in which the catalytic reaction actually occurs. In this way, by determining the conditions for the catalytic reaction based on the actual environment, it is possible to find an alloy that is more suitable for the intended solid catalyst application. In the catalytic reaction envisioned in this application, it is preferable to specify both temperature and gas partial pressure as basic information on the conditions of the catalytic reaction.

As an example, when the target catalytic reaction is the oxidation reaction of CO as in the above case, the adsorption states of each of the reaction substrates of the plurality of elementary reactions identified in step S01 and the constituent atoms of the reaction substrates are as follows. There are 10 states shown below.
CO (gas alone)
CO ₂ (gas alone)
O ₂ (gas alone)
CO ₂ ^* (adsorption state)
CO ^* (adsorption state)
O ₂ ^* (adsorption state)
O ^* (adsorption state)
C ^* (adsorption state)
O-O ^* (transition state)
O-CO ^* (transition state)
The energy and frequency of each of these 10 states are calculated using a quantum chemical calculation method. Furthermore, the conditions for the catalytic reaction can be calculated based on the environment that actually promotes the oxidation of CO, such as the location where CO is supplied.

(Step S03: Calculation of activation energy, differential energy, and reaction rate)
In step S03, activation energy, differential energy, and reaction rate are calculated for each candidate element from the basic information created in step S02. The activation energy, differential energy, and reaction rate are required for creating the distribution information in step S05.

The reaction rate is a physical quantity that is calculated for each candidate element and indicates the catalytic reaction activity of each candidate element. The reaction rate of the catalytic reaction of each candidate element is calculated based on the energy and frequency of each state of multiple elementary reactions for each candidate element, the temperature of the catalytic reaction, and the gas partial pressure, which are included in the basic information created in step S02. It can be calculated using the following conditions. The reaction rate of the catalytic reaction of each candidate element can be calculated using a general algorithm. Examples of algorithms that can calculate the reaction rate include Newton's method.
A plurality of activation energies are calculated for each candidate element corresponding to a plurality of elementary reactions. Each activation energy is a physical quantity indicating the energy required to cause each elementary reaction in each candidate element. The activation energy of each elementary reaction can be calculated using the energy of each state of a plurality of elementary reactions for each candidate element included in the basic information created in step S02.
The differential energy is obtained as a relative value of the energies of two states included in a plurality of elementary reactions for each candidate element. The differential energy is a physical quantity that is a candidate for the feature energy determined in step S04. The differential energy is calculated as the difference in energy between any two states included in a plurality of elementary reactions. As the differential energy, for example, adsorption energy or intermediate energy can be used. Note that the adsorption energy is a difference energy calculated as the difference in energy between the reaction substrate and each atom constituting the reaction substrate in a state where it is adsorbed to each candidate element and when it is in a gas state.

(Step S04: Selection of feature energy)
In step S04, a feature amount energy is selected from among the plurality of differential energies calculated in step S03 to be used as a key feature amount for promoting reaction by associating it with the reaction rate. Specifically, in step S04, linearity is evaluated for all combinations of a plurality of activation energies and a plurality of differential energies from the relationship between a plurality of candidate elements. Then, from among the plurality of differential energies, a differential energy that provides high linearity with respect to all of the plurality of activation energies is selected as the feature amount energy.
Here, the feature amount energy that provides high linearity with respect to all of the plurality of activation energies also provides high linearity with respect to the logarithm of the reaction rate. According to the Arrhenius equation, the activation energy of all elementary reactions that make up a catalytic reaction has a linear relationship with the logarithm of the reaction rate of each elementary reaction, so the overall reaction rate, which is a combination of elementary reactions, is also linear. Based on being in a relationship. Therefore, by associating the feature energy selected in step S04 with the reaction rate, it becomes possible to convert the feature energy into the reaction rate.

Specifically, the linearity between the activation energy Ea1 included in the plurality of activation energies and the differential energy Eb1 included in the plurality of differential energies is expressed as a two-dimensional graph with the activation energy Ea1 and each differential energy Eb1 as two axes. This can be evaluated from the linearity of the plot in a scatter diagram obtained by plotting the activation energy Ea1 and the differential energy Eb1 of all candidate elements.
The linearity of a plot for selecting a feature energy that provides high linearity can be evaluated using, for example, the coefficient of determination r ² in the least squares method as an index. In an evaluation using the coefficient of determination r ² as an index, for example, the coefficient of determination r ² is listed in descending order (or in descending order of numerical value), and multiple differential energies are divided into groups with high and low coefficients of determination r ² . The difference energy belonging to the high group can be selected as the feature amount energy. At this time, in grouping a plurality of differential energies, for example, differential energies whose coefficient of determination ^r2 is greater than or equal to a predetermined threshold value can be grouped into a high group, preferably 0.7 or greater, more preferably 0.8 or greater. A group with high differential energy can be formed. Further, among a plurality of differential energies listed in descending order of determination coefficient ^r2 , differential energies having a predetermined rank or higher can be selected as feature energy. Note that the method for selecting feature energy from a plurality of differential energies is not limited to the above method, and any known method can be used.

The number of mutually different feature energies to be selected from the plurality of differential energies in step S04 can be arbitrarily calculated depending on the number of dimensions of the distribution information created in step S05. That is, when creating N-dimensional distribution information in step S05, N mutually different feature amounts energies are selected in step S04.
As an example, when the target catalytic reaction is the oxidation reaction of CO, and two-dimensional distribution information that is easy to visually understand is created in step S05, from among a plurality of differential energies, for example, , the adsorption energy of CO and the adsorption energy of O can be selected as two mutually different feature energy amounts.

(Step S05: Creation of distribution information)
In step S05, distribution information is created which is a graph showing the distribution of reaction speeds with respect to the feature energy selected in step S04. The distribution information indicates the feature energy and the reaction rate in a continuous relationship, that is, it is information that associates an arbitrary feature energy with the reaction rate. In step S05, in addition to plots of a plurality of candidate elements obtained from the reaction rate calculated in step S03 and the feature energy selected in step S04, areas where no plots exist are plotted using the reaction rate from the feature energy at an arbitrary resolution. By calculating , it is possible to interpolate and create distribution information.
That is, according to the distribution information, it is possible to obtain the reaction rate from the feature amount energy, which can be easily calculated as a relative value of energy, without using complicated calculations. With distribution information, the reaction rate can be determined from the feature energy for any metal, and the reaction rate can also be determined from the feature energy not only for a single metal but also for an alloy of any composition. Therefore, according to the distribution information, the reaction rate of any alloy can be easily determined.

As an example, FIG. 2 shows two-dimensional distribution information when the target catalytic reaction is the oxidation reaction of CO and the feature energy is the adsorption energy of CO and the adsorption energy of O, as described above. The distribution information shown in Figure 2 is shown as a two-dimensional heat map in which the reaction rate (common logarithm) is displayed as different colors in a graph where the vertical and horizontal axes are the adsorption energy of CO and the adsorption energy of O, respectively. . By creating the distribution information as a heat map in this way, it becomes easier to visually recognize areas where a large reaction rate is obtained.

(Step S06: Prediction of composition)
In step S06, based on the distribution information created in step S05, compositions of multiple alloys containing at least two of the multiple candidate elements and having a high possibility of obtaining a higher reaction rate (candidate elements constituting the alloy and the composition ratio of each candidate element in the combination. Specifically, in step S06, the composition of the alloy that is likely to have a high reaction rate is predicted from the positional relationship between the target plot P corresponding to the target value of the reaction rate in the distribution information and the plot of each candidate element. The target plot P is usually set at a position where the reaction rate is the highest. For example, in the heat map shown in FIG. 2, the target plot P can be set within the region with the darkest color. The composition of an alloy that will yield a reaction rate close to the target plot P can be predicted using, for example, the plots of a plurality of candidate elements in the distribution information and the coordinate information of the target plot P. By using the coordinate information in this way, it becomes possible to predict mechanically and with high accuracy the composition of an alloy that increases the reaction rate.

このとき、β＋γ＜１、β＞０、γ＞０の条件をすべて満たす場合、３つの候補元素Ａ，Ｂ，Ｃの組成比Ａ：Ｂ：Ｃは「１－（β＋γ）：β：γ」と算出することができる。なお、上記の条件を満たすことは、図３に示すプロットＡ，Ｂ，Ｃを頂点とする三角形の内側に目標プロットＰが位置していることを意味する。本実施形態では、候補元素のプロットを結んだ線で囲まれた領域内に目標プロットＰが存在する組成を、大きい反応速度が得られる可能性がある合金の組成の候補とすることができる。つまり、候補元素のプロットを結んだ線で囲まれた領域内に目標プロットＰが存在しない組成については、大きい反応速度が得られる可能性がある合金の組成の候補から除外することができる。
更に、上記で得られた係数β，γから、下記の式に基づいて指標ｍを算出する。

指標ｍは、プロットＡ，Ｂ，Ｃを頂点とする三角形の重心と目標プロットＰとの距離の２乗を表している。このため、指標ｍが小さい組成ほど、各候補元素の割合が近くなり、単一元素の特徴量エネルギからは予測が困難な、大きい反応速度が得られる合金の組成を予測できる。したがって、各候補元素の割合が近い合金の組成の予測結果として、指標ｍが小さい順に所定数の組成をリストアップすることができる。このように、本実施形態では、複数の候補元素で構成される合金について、分布情報上において推定されるプロットと目標プロットＰとの距離が近い順に所定数の組成をリストアップすることができる。 As an example, a case where the composition of the alloy is a ternary system consisting of a combination of candidate elements A, B, and C will be described. In this case, for example, two-dimensional distribution information created using two feature amounts of energy can be used.
FIG. 3 shows the plots A (A _x , A _y ), B (B _x , B _y ), C (C _x , C _y ) of candidate elements A, B, and C, and the target plot P (P _x , P _y ) is displayed on the distribution information. In other words, the two feature energies of candidate element A are A _x and A _y , the two feature energies of candidate element B are B _x and B _y , and the two feature energies of candidate element C are C _x , _Cy . Furthermore, the two feature energies of the target plot P are P _x and P _y .
Here, as shown in Figure 4, if plot A is the origin, plot B can be represented by vector b ((b _x , b _y ) = (B _x - A _x , B _y - A _y )). , the plot C can be represented by the vector c ((c _x , c _y ) = (C _x - A _x , C _y - A _y )), and the target plot P can be represented by the vector p ((p _x , p _y ) = (P _x −A _x , P _y −A _y )). Note that plot A can be represented by a zero vector a(0,0). At this time, vector p can be expressed by the following equation using vectors b and c and coefficients β and γ.
p=βb+γc
This equation can be converted into the following equation using the coefficient matrix D.

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 is "1-(β+γ):β:γ" It can be calculated as follows. Note that satisfying the above condition means that the target plot P is located inside a triangle whose vertices are plots A, B, and C shown in FIG. In the present embodiment, a composition in which the target plot P exists within a region surrounded by a line connecting the plots of candidate elements can be set as a candidate for the composition of the alloy that has the possibility of obtaining a high reaction rate. That is, compositions in which the target plot P does not exist within the region surrounded by the line connecting the plots of the candidate elements can be excluded from the candidates for alloy compositions that have the possibility of obtaining a high reaction rate.
Furthermore, an index m is calculated from the coefficients β and γ obtained above based on the following formula.

The index m represents the square of the distance between the center of gravity of a triangle having plots A, B, and C as vertices and the target plot P. Therefore, the smaller the index m is in a composition, the closer the proportions of each candidate element are, and it is possible to predict the composition of an alloy that provides a high reaction rate, which is difficult to predict from the feature energy of a single element. Therefore, a predetermined number of compositions can be listed in descending order of index m as a prediction result of compositions of alloys having similar proportions of each candidate element. In this manner, in this embodiment, for alloys composed of a plurality of candidate elements, a predetermined number of compositions can be listed in descending order of the distance between the plot estimated on the distribution information and the target plot P.

このとき、以下の条件をすべて満たす場合、候補元素Ａ_１，Ａ_２，・・・，Ａ_{（ｎ－１）}，Ａ_ｎの組成比Ａ_１：Ａ_２：・・・：Ａ_{（ｎ－１）}：Ａ_ｎは、「１－（β_１＋β_２＋・・・＋β_{（ｎ－２）}，β_{（ｎ－１）}）：β_１：・・・：β_{（ｎ－２）}：β_{（ｎ－１）}」と算出することができる。

更に、上記で得られた係数β_１，・・・，β_{（ｎ－２）}，β_{（ｎ－１）}から、下記の式に基づいて指標ｍを算出する。

指標ｍが小さい組成ほど、各候補元素の割合が近くなり、単一元素の特徴量エネルギからは予測が困難な、大きい反応速度が得られる合金の組成を予測できる。したがって、各候補元素の割合が近い合金の組成の予測結果として、指標ｍが小さい順に所定数の組成をリストアップすることができる。 Next, a case where the composition of the alloy is an n-element system consisting of a combination of four or more candidate elements A ₁ , A ₂ , . . . , A _(n-1) , A _n will be described. In this case, for example, (n-1) dimensional distribution information created by (n-1) feature amounts of energy can be used.
On the distribution information, plots A ₁ (A ₁₁ , A ₁₂ , ..., A 1 _(n-2)) of each candidate element A ₁ , A ₂ , ..., A _(n-1) , A _n are shown. , A _1(n-1) ), A ₂ (A ₂₁ , A ₂₂ ,..., A _2(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 P(P ₁ , P ₂ ,..., P _(n-2) , P _{( n-1)} ) is shown.
Here, if plot A ₁ is the origin, plots A ₂ ,..., A _(n-1) , A _n are vectors a ₂ ,..., 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 )), and the target plot P can be expressed as a vector p((p ₁ , p ₂ ,..., p _{( n-2)} ,p _(n-1) )=(P ₁ -A ₁₁ ,P ₂ -A ₁₂ ,...,P _(n-2) -A _1(n-2) ,P _{(n-1 )} -A _1(n-1) )) The plot A ₁ can be represented by the zero vector a ₁ (0,0,...,0,0).In this case, Vector p can be calculated as follows using vectors a ₂ ,..., a _(n-1) , a _n and coefficients β ₁ ,..., β _(n-2) , β _(n-1). It can be expressed by the formula.
p=β ₁ a ₂ +...+β _(n-2) a _(n-1) +β _(n-1) a _n
This equation can be converted into the following equation using the coefficient matrix D.

At this time, if all of the following conditions are satisfied, the composition ratio of candidate elements A ₁ , A ₂ ,..., A _(n-1) , A _n is A ₁ :A ₂ :...:A _{(n-1 )} :A _n is "1-(β ₁ +β ₂ +...+β _(n-2) ,β _(n-1) ):β ₁ :...:β _(n-2) :β _{(n -1)} " can be calculated.

Furthermore, an index m is calculated from the coefficients β ₁ , . . . , β _(n-2) , β _(n-1) obtained above based on the following formula.

The smaller the index m is, the closer the proportions of each candidate element are, and it is possible to predict the composition of an alloy that will yield a high reaction rate, which is difficult to predict from the feature energy of a single element. Therefore, a predetermined number of compositions can be listed in descending order of index m as a prediction result of compositions of alloys having similar proportions of each candidate element.

(Step S07: Creation of slab model)
In step S07, in order to calculate the reaction rate and stability index for the plurality of compositions predicted to have a high possibility of obtaining a high reaction rate in step S06, a plurality of slab models corresponding to each composition are created. From the viewpoint of efficiency, it is preferable to use an existing database to create the slab model. As such a database, it is preferable to use a DFT calculation database such as CatApp, which stores structural data of slab models that are easy to use for quantum chemical calculations. In addition to the DFT calculation database, for example, a crystal structure database such as Materials Project can also be used as the database. Further, in step S07, a unit cell may be obtained from an existing database for the composition predicted in step S06, and a slab model may be created based on the obtained unit cell.

Additionally, for alloys for which no database exists, you can create your own slab model. Although the method for creating the slab model is not limited to a specific method, the following method can be used as an example. In the method of creating a slab model according to an example, first, when a predetermined element constituting the candidate element contained in each composition exists alone, it has a stable crystal structure (face-centered cubic lattice, body-centered cubic lattice, hexagonal close-packed structure, etc.). ), a first unit cell model is created. Next, a second unit cell model is created in which some atoms constituting the first unit cell model are replaced with atoms of a candidate element other than the predetermined element. The slab model is obtained by creating a second unit cell model with stable crystal planes ((111) plane, (211) plane, etc.) when the candidate element constituting the first unit cell model exists alone. Note that the crystal structure and crystal plane that are stable when a metal element exists alone can be obtained from, for example, a crystal structure database such as Materials Project.

(Step S08: Calculation of stability index)
In step S08, a stability index indicating structural stability is calculated for each slab model created in step S07. The structural stability of each slab model is evaluated based on the energy possessed by the slab model. The energy used to evaluate the structural stability of the slab model may be any energy that can be calculated from the slab model, such as the total energy of the slab model and the surface energy of the slab model. Specifically, general physicochemical calculation methods can be used to evaluate the stability of the slab model. Examples of physical and chemical calculation methods that can be used to evaluate the stability of slab models include the Monte Carlo method.

The stability index only needs to be able to compare the structural stability between slab models, and a common index is used for all slab models. Specifically, as the stability index, for example, the energy calculated from the slab model can be used as is. In this case, it can be seen that the slab model with smaller energy as a stability index has higher structural stability. In addition to this, other values calculated based on the energy calculated from the slab model can also be used as the stability index.

(Step S09: Calculation of activity index)
In step S09, an activity index indicating 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, feature energy is calculated for each slab model using the same method as in step S02. Then, for each slab model, the reaction rate corresponding to the feature energy is obtained using the distribution information created in step S04.

As the activity index, it is sufficient that the activity can be compared between slab models, and a common index is used for all slab models. Specifically, as the activity index, for example, the reaction rate calculated from the slab model can be used as is. In this case, it can be seen that the slab model with a higher reaction rate as an activity index has a higher actual reaction rate (activity). In addition to this, other values calculated based on the reaction rate calculated from the slab model can also be used as the activity index.

(Step S10: Identification of alloy)
In step S10, high structural stability and high catalytic reaction activity are combined 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. Identify alloys with expected results. In step S10, various techniques can be used to identify the alloy from the stability index and activity index of each slab model.

As an example, an alloy list as illustrated in FIG. 5 can be used to specify the alloy. The alloy list shown in FIG. 5 lists data in which the stability index (energy) and activity index (reaction rate) are shown side by side for each type of alloy specified by the slab model. For example, in the alloy list, a plurality of alloys can be listed in descending order of activity index. In this case, for example, a threshold value of the stability index is determined in advance, alloys with a stability index larger than the threshold value are excluded from the plurality of alloys, and a predetermined number of alloys are selected in order from the top of the alloy list. be able to. The threshold value of the stability index is preferably set to a sufficiently small value so as to obtain high structural stability. Further, in the alloy list, a plurality of alloys can be displayed in descending order of stability index. In this case, for example, a threshold value of the activity index may be determined in advance, alloys with activity indexes smaller than the threshold value may be excluded from the plurality of alloys, and a predetermined number of alloys may be selected in order from the top of the alloy list. can. The threshold value of the activity index is preferably set to a sufficiently large value to allow the catalytic reaction to proceed smoothly.

(Other forms)
In the screening method according to this embodiment, various changes can be made to the above configuration within a range where the above effects can be appropriately obtained.
For example, in step S09, the activity index may be calculated only for the slab model whose stability index was good in step S08. This reduces the calculation load in step S09 and narrows down the slab model candidates for identifying the alloy in step S10. Alternatively, the order of steps S08 and 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 may be calculated in step S08. In this case, in step S08, the stability index may be calculated only for the slab model whose activity index was good in step S09.

[Additional configuration of screening method]
(Outline explanation)
The screening method according to this embodiment is not limited to the configuration described above, and may include additional configurations to further improve the accuracy of alloy screening. An example of an additional configuration effective for the screening method according to the present embodiment will be described below.

(Search for alloy composition using selectivity as an index)
In the above embodiment, the activity index is output, but if the feature amount energy is the same for a catalytic reaction with two or more reaction paths, selectivity distribution information can be used in the same manner as the activity index described above. (heat map) can be described. In this case, in addition to the main reaction activity, the percentage selectivity of the main reaction product can be added to the output. For example, when the products are i and j and the reaction rates are ri and rj, the selectivity S can be defined as follows.
S=ri/(ri+rj)

(Search for further alloy compositions)
In the embodiment described above, distribution information created for a crystal structure composed of only a single metal is used to identify an alloy composed of a plurality of metals. In other words, the interactions between metals that occur in actual alloys are not considered in order to specify alloys. For this reason, the alloy specified in the above embodiment may deviate slightly from the composition that actually provides the highest reaction rate. Therefore, by further searching for compositions near the composition of the alloy specified in the above embodiment, it is possible that an alloy with even higher catalytic reaction activity can be discovered. Such a composition search can be carried out, for example, by creating slab models and evaluating stability indicators for multiple alloys with only the compositions shifted from the alloys specified in the above embodiment. .

As an example, a plurality of alloys in which the composition ratio of each candidate metal is increased or decreased by 1 relative to the composition of the alloy specified in the above embodiment can be searched. For example, if the composition of the alloy specified in the above embodiment is a ternary system containing candidate elements A, B, and C in a composition ratio of A:B:C, 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, A-1:B:C+1 alloys with six different composition ratios will be searched. . For a plurality of alloys to be searched, slab models are created as in step S07, reaction rates are determined as in step S09, and the alloy with the highest reaction rate is identified. Furthermore, by repeating the same search for the alloys specified in this way, it is thought that the composition of the alloy that provides the highest reaction rate will be approached. Such a search for a composition can be repeated, for example, until the rate of increase in the reaction rate for the previously identified alloy becomes less than or equal to a predetermined value, that is, it is determined that the reaction rate has converged. Further, the composition search may be repeated a predetermined number of times.

(Evaluation using nanoparticle model)
In the embodiment described above, the stability of the alloy structure is evaluated using a slab model, but the stability of the alloy structure may not be accurately evaluated with a slab model that focuses only on a single crystal plane. In this regard, by using a nanoparticle model that expresses the three-dimensional structure of alloy nanoparticles, it becomes possible to more accurately evaluate the stability of the alloy structure. Therefore, the screening method according to the present embodiment can incorporate evaluation using a nanoparticle model of the alloy in order to more reliably evaluate the stability of the alloy. A known modeling method can be used to create the nanoparticle model of the alloy.
Examples of methods for modeling catalyst nanoparticles according to the composition of the alloy slab model include a genetic algorithm method.

The structural stability of each nanoparticle model is evaluated based on the energy of the nanoparticle model. The energy used to evaluate the structural stability of the nanoparticle model may be any energy that can be calculated from the nanoparticle model, such as the energy of the nanoparticle model. For calculating the energy of the nanoparticle model, the same physicochemical calculation method as used for evaluating the stability of the slab model in step S08 can be used. The results obtained using the nanoparticle model can be used as a stability index that indicates the structural stability of the alloy. This stability index can be used in place of the stability index calculated in step S08, and can be used in conjunction with the stability index calculated in step S08 as a second stability index.

As an example, for each slab model created in step S07, a nanoparticle model is created in which a plurality of candidate elements constituting the slab model are common. Then, nanoparticle information in which energy, composition ratio, and all atomic coordinates are associated is created for each nanoparticle model. The degree of similarity can be calculated by comparing the surrounding information of a specific atom obtained from the all-atomic coordinates of the nanoparticle with the surrounding information of the specific atom obtained from the all-atomic coordinates forming the slab model. The peripheral information of a specific atom includes, for example, the coordination number and the radial distribution function, and the degree of similarity includes the difference in the coordination number and the integral value of the difference in the radial distribution function. By identifying the nanoparticle model with the highest degree of similarity for each slab model, it is adopted as the energy for the nanoparticle model corresponding to each slab model. It can be seen that alloys with lower energy obtained from nanoparticle information have higher structural stability.

[Information processing device]
The screening method according to the embodiment described above can be realized using, for example, the information processing apparatus 100 shown in FIG. 6. The information processing apparatus 100 according to the present embodiment can be composed of various computers, and may be composed of a single computer or a combination of two or more computers. The information processing device 100 includes an input section 101, an output section 102, a processing section 103, and a storage section 104.

The input unit 101 is configured as a user interface and is used, for example, to input a target catalytic reaction, a plurality of elementary reactions, a plurality of candidate elements, a crystal plane, etc. in step S01. The output unit 102 is configured to be able to output information to a display device such as various displays, and can display, for example, the distribution information created in step S04, the alloy index used in step S10, and the like. The processing unit 103 is configured to be able to execute all or part of the processing included in the screening method according to the above embodiment according to a program. The storage unit 104 is configured to be able to store various data, and stores, for example, programs for causing the processing unit 103 to execute various processes, various data necessary for each process by the processing unit 103, and the like. Furthermore, the information processing device 100 may include a configuration other than the above, and may include a communication unit for acquiring data from a database on the cloud through communication, for example.

[Other embodiments]
Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and it goes without saying that various changes can be made without departing from the gist of the present invention.

100... Information processing device 101... Input section 102... Output section 103... Processing section 104... Storage section

Claims (8)

A method for screening alloys that cause a desired catalytic reaction, the method comprising:
For each of the plurality of candidate elements that are candidates for the metal elements constituting the alloy, each reaction in a non-adsorbed state in the plurality of elementary reactions that constitute the catalytic reaction for a specific crystal plane formed by each candidate element. Including the initial state, final state, and transition state of the substrate, the energy and vibration frequency of each reaction substrate in the adsorption state and each atom constituting it, and the temperature and gas partial pressure of the catalytic reaction. Create basic information,
For each of the plurality of candidate elements, from the basic information, a plurality of activation energies corresponding to each of the plurality of elementary reactions, a plurality of differential energies obtained as relative values of the energies of each state, and the catalytic reaction. Find the reaction rate and,
Evaluate linearity from the relationship between the plurality of candidate elements for each activation energy forming the plurality of activation energies and each differential energy forming the plurality of differential energies, and evaluate linearity from among the plurality of differential energies. , select a feature energy that provides relatively high linearity for all of the plurality of activation energies;
Using the feature energy and the reaction rate of the plurality of candidate elements, create distribution information indicating a distribution of the reaction rate with respect to the feature energy,
Using the distribution information, predicting a plurality of compositions that include at least two candidate elements among the plurality of candidate elements and that increase the reaction rate by forming the alloy,
Creating a plurality of slab models corresponding to each of the plurality of compositions,
Calculating a stability index based on the energy calculated for each of the plurality of slab models,
calculating an activity index based on the reaction rate determined from the distribution information using the feature amount energy calculated for each of the plurality of slab models ;
Identifying an alloy based on the stability index and the activity index
Screening method. The screening method according to claim 1, wherein the feature amount energy includes adsorption energy. The feature energy is composed of two mutually different feature energies,
The screening method according to claim 1 or 2, wherein the distribution information is created as a two-dimensional heat map. In order to predict the plurality of compositions, a target plot is set on the distribution information, a plot of the at least two candidate elements is selected, and coordinate information between the target plot and the candidate element plot is used, The screening method according to any one of claims 1 to 3, further comprising predicting the at least two candidate elements and their composition ratios that will give the reaction rate close to the target plot. obtaining unit cells containing the at least two candidate elements from a database, and creating the plurality of slab models based on the obtained unit cells, or
A first unit cell model is created for a crystal structure that is stable when existing alone for a predetermined element constituting the at least two candidate elements, and some atoms constituting the first unit cell model are A second unit cell model is created in which atoms of candidate elements other than the predetermined element are substituted, and the plurality of slab models are created based on the second unit cell model. Screening method described in. In order to calculate the stability index, nanoparticle models corresponding to the at least two candidate elements are created, the composition ratio and the energy according to the peripheral information of a specific atom are calculated for the nanoparticle model, and the 6. The method according to claim 1, wherein the energy of the nanoparticle model corresponding to each of the plurality of slab models is obtained based on the composition ratio of the plurality of slab models and peripheral information of a specific atom. Screening method. An information processing device that screens alloys that cause a desired catalytic reaction,
For each of the plurality of candidate elements that are candidates for the metal elements constituting the alloy, each reaction in a non-adsorbed state in the plurality of elementary reactions that constitute the catalytic reaction for a specific crystal plane formed by each candidate element. Including the initial state, final state, and transition state of the substrate, the energy and vibration frequency of each reaction substrate in the adsorption state and each atom constituting it, and the temperature and gas partial pressure of the catalytic reaction. Create basic information,
For each of the plurality of candidate elements, from the basic information, a plurality of activation energies corresponding to each of the plurality of elementary reactions, a plurality of differential energies obtained as relative values of the energies of each state, and the catalytic reaction. Find the reaction rate and,
Evaluate linearity from the relationship between the plurality of candidate elements for each activation energy forming the plurality of activation energies and each differential energy forming the plurality of differential energies, and evaluate linearity from among the plurality of differential energies. , select a feature energy that provides relatively high linearity for all of the plurality of activation energies;
Using the feature energy and the reaction rate of the plurality of candidate elements, create distribution information indicating a distribution of the reaction rate with respect to the feature energy,
Using the distribution information, predicting a plurality of compositions that include at least two candidate elements among the plurality of candidate elements and that increase the reaction rate by forming the alloy,
Creating a plurality of slab models corresponding to each of the plurality of compositions,
Calculating a stability index based on the energy calculated for each of the plurality of slab models,
calculating an activity index based on the reaction rate determined from the distribution information using the feature amount energy calculated for each of the plurality of slab models ;
Identifying an alloy based on the stability index and the activity index
An information processing device including a processing unit that performs the following operations. A program for screening alloys that cause a desired catalytic reaction,
For each of the plurality of candidate elements that are candidates for the metal elements constituting the alloy, each reaction in a non-adsorbed state in the plurality of elementary reactions that constitute the catalytic reaction for a specific crystal plane formed by each candidate element. Including the initial state, final state, and transition state of the substrate, the energy and vibration frequency of each reaction substrate in the adsorption state and each atom constituting it, and the temperature and gas partial pressure of the catalytic reaction. Create basic information,
For each of the plurality of candidate elements, from the basic information, a plurality of activation energies corresponding to each of the plurality of elementary reactions, a plurality of differential energies obtained as relative values of the energies of each state, and the catalytic reaction. Find the reaction rate and,
Evaluate linearity from the relationship between the plurality of candidate elements for each activation energy forming the plurality of activation energies and each differential energy forming the plurality of differential energies, and evaluate linearity from among the plurality of differential energies. , select a feature energy that provides relatively high linearity for all of the plurality of activation energies;
Using the feature energy and the reaction rate of the plurality of candidate elements, create distribution information indicating a distribution of the reaction rate with respect to the feature energy,
Using the distribution information, predicting a plurality of compositions that include at least two candidate elements among the plurality of candidate elements and that increase the reaction rate by forming the alloy,
Creating a plurality of slab models corresponding to each of the plurality of compositions,
Calculating a stability index based on the energy calculated for each of the plurality of slab models,
calculating an activity index based on the reaction rate determined from the distribution information using the feature amount energy calculated for each of the plurality of slab models ;
Identifying an alloy based on the stability index and the activity index
A program that causes an information processing device to perform a certain task.