An algorithm for generating cage-like cluster structures and predicting their properties

Abstract

The present invention proposes a cage-like cluster structure generation and property prediction algorithm, including a three-dimensional structure generation algorithm: using polyhedron generation software to generate all polyhedrons of a given size, calculating its topological distance matrix, calculating the coordinates embedded in the three-dimensional space from the distance matrix, and optimizing the coordinates by force field to obtain a preliminary reasonable structure; a property prediction algorithm: optimizing all the obtained preliminary reasonable structures with first principle software to obtain their property data respectively, using the property data as a data set to train a neural network, obtaining a method for extracting the initial features of the cage structure and a graph neural network including a connection order, and finally sending the initial features to the graph neural network to obtain a predicted value of the property. The present invention can quickly find a structure with a given property from a large number of isomers, and provides a good foundation for subsequent analysis and research on the cage-like cluster structure.

Description

Technical Field

[0001] The invention relates to the field of chemical technology, and in particular to an algorithm for generating cage-like cluster structures and predicting properties. Background Art

[0002] Cage clusters are an important type of cluster structure, which are polyhedral in shape. 60 It is a cage-like cluster, which is a polyhedron composed of pentagons and hexagons. Many cage-like clusters have strange properties and have attracted people's attention. 60 The discovery of the structure also won a Nobel Prize.

[0003] In addition to the cage clusters themselves, their derivatives have also attracted attention, such as atom replacement, functional group mounting, cage doping with other atoms, cage structure stacking, etc. The study of cage clusters requires the generation of their structures first.

[0004] There are algorithms that can generate the topological structure of cage clusters: Plantri software uses a size recursive method to generate topological connections of various cage structures. However, it is a difficult problem to obtain a three-dimensional structure from the topological connection. With a three-dimensional structure, various properties can be calculated using first-principles software. However, as the size increases, the number of isomers increases rapidly. Since first-principles software calculations are time-consuming, it is increasingly difficult to find a structure with a given property from a large number of isomers. How to quickly calculate the properties of cage structures is also a problem that needs to be solved. Summary of the invention

[0005] The present invention proposes a cage cluster structure generation and property prediction algorithm, which is used to solve the problem of how to quickly find a cage structure with given properties from a large number of isomers.

[0006] In order to solve the above problems, the present invention provides a cage cluster structure generation and property prediction algorithm, comprising the following steps:

[0007] S1. Algorithm for generating three-dimensional structure: Use polyhedron generation software to generate all polyhedrons of a given size, calculate their topological distance matrix, calculate the coordinates embedded in the three-dimensional space from the distance matrix, and optimize the force field of the coordinates to obtain a preliminary reasonable structure;

[0008] S2. Property prediction algorithm: All the preliminary reasonable structures obtained are optimized using first-principles software to obtain their property data respectively. The property data are used as data sets to train the neural network to obtain a method for extracting the initial features of the cage structure and a graph neural network including the connection order. Finally, the initial features are sent to the graph neural network to obtain the predicted values ​​of the properties.

[0009] First, generate all the topological connections of the dual graph of a cage cluster of a given size. The dual structure of a polyhedron is another polyhedron. It puts a point at the center of each face of the polyhedron. If two faces are adjacent, connect the two points to get a new polyhedron. The dual polyhedron is the original polyhedron with faces turned into points and points turned into faces. The dual of the dual polyhedron is the original structure. If the degree of each vertex of a polyhedron is 3, the dual polyhedron is a triangular polyhedron. Usually the dual polyhedron is easier to handle, so the research object here is the dual polyhedron.

[0010] In a preferred embodiment of the present invention, the specific steps of the algorithm for generating the three-dimensional structure in S1 are:

[0011] First, a rough three-dimensional structure is generated by topological connection. If two points are adjacent, their topological distance is recorded as 1, and the Floyd algorithm is used to calculate the pairwise distance. ,make:

[0012] ,

[0013] Where n is the number of vertices;

[0014] ,

[0015] I is the identity matrix, 1= (1,…,1) T ;

[0016] ,

[0017] right B Do singular value decomposition:

[0018] ,

[0019] Then the coordinate matrix embedded in the three-dimensional space is:

[0020] ,

[0021] in:

[0022] ;

[0023] The generated coordinates can be optimized using the force field to obtain reasonable three-dimensional coordinates. The force field is defined to be composed of spring elastic force and particle repulsion force. If two points are topologically adjacent, their distance is close to the bond length, and they are defined to be subject to an elastic force:

[0024] ,

[0025] in For point Click to The coordinate difference of the point, is the bond length. If two points are not adjacent, they are defined to be subject to a repulsive force:

[0026] ;

[0027] The potential energy corresponding to the elastic force and repulsive force is:

[0028] ,

[0029] in As mask, when , When the points are adjacent, the value is 1, and when they are not adjacent, the value is 0. Using the coordinate X generated above as the initial value, the BFGS algorithm is used to perform local optimization on the energy to obtain the optimized coordinates, which are the initial reasonable structure.

[0030] In a preferred embodiment of the present invention, the specific steps of the property prediction algorithm in S2 are:

[0031] Using the preliminary reasonable structure obtained in S1, the properties of interest are calculated using first principles to generate a data set. Then, a graph neural network is used to predict the properties, with the topological connection of the dual graph as input, without considering the characteristics of the edges, and different initial point features are selected according to different research systems.

[0032] For C fullerene, it is a polyhedron composed of pentagons and hexagons. Non-classical fullerenes may also contain quadrilaterals and heptagons. Its dual graph is a triangular polyhedron, with the degree of the vertex as the initial point feature. For the system where C fullerene replaces the C atom, there are 8 possible rings, and the number of each type is the initial feature.

[0033] The graph neural network layer aggregates the information of neighboring points to the central node i. Unlike the general graph neural network, the neighboring points here are in order. To this end, an improved graph convolution operation that contains the order information of neighboring points is proposed. Consider the three consecutive neighboring points j-1, j, j+1 of the central node i, and add the feature h of node j to the convolution operation. j Its left and right neighboring point features h j-1 and h j+1 Splice to get h j ||(h j-1 +h j+1 ), followed by a fully connected layer and an activation layer to map it into a new vector g j , and then use the general graph convolution operation to converge the neighboring point features to the central node i:

[0034] ;

[0035] in Gl It is composed of all the point features g obtained above, W l For the l The weight matrix of the layer graph convolution layer is the activation function, is the matrix obtained by adjacency matrix A;

[0036] ;

[0037] If the initial point feature is an integer, the network uses an embedding layer to convert it into a vector, followed by two graph convolutional layers, and then a fully connected layer to convert the point feature vector into 1 dimension. Finally, the features of n points are added together and a number is output as the predicted value of the property.

[0038] The implementation of the present invention has the following beneficial effects:

[0039] Starting from the topological connection of cage clusters, the present invention designs a graph neural network algorithm, which can also predict its properties; different initial feature generation methods are designed for different cage cluster force systems; the graph neural network can quickly predict the properties of cage clusters, so that it can quickly find structures with given properties from massive isomers, providing a good foundation for subsequent analysis and research on cage cluster structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0041] Figure 1 A schematic diagram of the flow of the cage cluster structure generation and property prediction algorithm provided by the present invention;

[0042] Figure 2 is the initial three-dimensional structure generated by the topological structure;

[0043] Figure 3 It is the three-dimensional structure after the initial three-dimensional structure is optimized by the force field;

[0044] Figure 4 Replace all possible rings of the N atom system for C fullerene;

[0045] Figure 5 is the feature generation method;

[0046] Figure 6 This is a comparison chart of energy structures. DETAILED DESCRIPTION

[0047] The following will be combined with the accompanying drawings in the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] See also Figure 1 , Figure 1 A schematic diagram of the flow of the cage-like cluster structure generation and property prediction algorithm provided by the present invention; the present invention provides a cage-like cluster structure generation and property prediction algorithm, comprising the following steps:

[0049] S1. Algorithm for generating three-dimensional structure: Use polyhedron generation software to generate all polyhedrons of a given size, calculate their topological distance matrix, calculate the coordinates embedded in the three-dimensional space from the distance matrix, and optimize the coordinates by force field to obtain a preliminary reasonable structure.

[0050] That is to say: first generate all the topological connections of the dual graph of a cage cluster of a given size. The dual structure of a polyhedron is another polyhedron. It puts a point at the center of each face of the polyhedron. If two faces are adjacent, connect the two points to get a new polyhedron. The dual polyhedron is the original polyhedron with faces turned into points and points turned into faces. The dual of the dual polyhedron is the original structure. If the degree of each vertex of a polyhedron is 3, the dual polyhedron is a triangular polyhedron. Usually the dual polyhedron is easier to handle, so the research object here is the dual polyhedron.

[0051] The specific steps of the three-dimensional structure generation algorithm are:

[0052] First, a rough three-dimensional structure is generated by topological connections, see Figure 2 , Figure 2 is the initial three-dimensional structure generated by the topological structure. If two points are adjacent, their topological distance is recorded as 1. The Floyd algorithm is used to calculate the pairwise distance ,make:

[0053] ,

[0054] Where n is the number of vertices;

[0055] ,

[0056] I is the identity matrix, 1= (1,…,1) T ;

[0057] ,

[0058] right B Do singular value decomposition:

[0059] ,

[0060] Then the coordinate matrix embedded in the three-dimensional space is:

[0061] ,

[0062] in:

[0063] ;

[0064] By optimizing the generated coordinates using the force field, we can get the preliminary reasonable three-dimensional coordinates. The force field is defined to be composed of spring elastic force and particle repulsion force. If two points are topologically adjacent, their distance is close to the bond length, and they are defined to be subject to an elastic force:

[0065] ,

[0066] in For point Click to The coordinate difference of the point, is the bond length. If two points are not adjacent, they are defined to be subject to a repulsive force:

[0067] ;

[0068] The potential energy corresponding to the elastic force and repulsive force is:

[0069] ,

[0070] in As mask, when , When the points are adjacent, the value is 1, and when they are not adjacent, the value is 0. Using the coordinate X generated above as the initial value, the BFGS algorithm is used to optimize the energy locally to obtain the optimized coordinates. This coordinate is the initial reasonable structure. Figure 3 , Figure 3 It is the three-dimensional structure after the initial three-dimensional structure is optimized by force field.

[0071] S2. Property prediction algorithm: All the preliminary reasonable structures obtained are optimized using first-principles software to obtain their property data respectively. The property data are used as data sets to train the neural network to obtain a method for extracting the initial features of the cage structure and a graph neural network including the connection order. Finally, the initial features are sent to the graph neural network to obtain the predicted values ​​of the properties.

[0072] The specific steps of the property prediction algorithm are as follows: using the preliminary reasonable structure obtained in S1, the properties of interest are calculated by first principles to generate a data set; then a graph neural network is used to predict the properties, with the topological connection of the dual graph as input, without considering the characteristics of the edges, and different initial point features are selected according to the different research systems. For C fullerene, it is a polyhedron composed of pentagons and hexagons. Non-classical fullerenes may also contain quadrilaterals and heptagons. Its dual graph is a triangular polyhedron, with the degree of the vertex as the initial point feature. For the system where C fullerene replaces the C atom, there are 8 possible rings, please refer to Figure 4 , Figure 4 Replace all possible rings of the N atom system for C fullerene, using the number of each as the initial feature.

[0073] The graph neural network layer aggregates the information of neighboring points to the central node i. Unlike the general graph neural network, the neighboring points here are in order. To this end, we propose an improved graph convolution operation that includes the order information of neighboring points. Consider the three consecutive neighboring points j-1, j, j+1 of the central node i, and add the feature h of node j to the convolution operation. j Its left and right neighboring point features h j-1 and h j+1 Splice to get h j ||(h j-1 +h j+1 ), followed by a fully connected layer and an activation layer to map it into a new vector g j , and then use the general graph convolution operation to converge the neighboring point features to the central node i:

[0074] ;

[0075] in G l It is composed of all the point features g obtained above, W l For the l The weight matrix of the layer graph convolution layer is the activation function, is the matrix obtained by adjacency matrix A;

[0076] ;

[0077] If the initial point feature is an integer, the network uses an embedding layer to convert it into a vector, followed by two graph convolutional layers, and then a fully connected layer to convert the point feature vector into 1D. Finally, the features of n points are added together and a number is output as the predicted value of the property. See Figure 5 , Figure 5 The feature generation method.

[0078] N replaces C 60The number of cluster isomers increases rapidly with the number of substituted N atoms, and the number of isomers is shown in Table 1 below.

[0079] Table 1 Number of C60 cluster isomers

[0080]

[0081] It is impossible to perform first-principles calculations on a large number of isomers to find the lowest energy structure. Therefore, graph neural networks can be used to quickly predict the energy of all isomers and thus find the lowest energy structure.

[0082] Select C 56 N4、C 51 N9, C 48 N 12 3019, 3175, and 1152 isomers were used to calculate their energies using first-principles calculations to form the training set. 49 N 11 A graph neural network was trained with 1000 isomers as the test set. 60 The dual topology with N atoms replaced is used as input. Each point is represented by a number from 0 to 7, which is the ring type of the original structure. The average binding energy of the predicted structure. The test error of the network is 2.283 meV. The binding energies of all isomers with N atoms from 2 to 12 are then predicted, with 6700 structures predicted per second. For each size, the first 500 structures with the lowest predicted energy are selected, and finally the lowest energy structure is determined by first-principles calculations. At multiple sizes of N=7-12, lower energy structures than those reported in the literature are found. See Figure 6 , Figure 6 This is an energy structure comparison chart, which shows the structure we found and compares it with the structure in the literature.

[0083] Figure 6 The top middle row shows the lowest energy structure found by the graph neural network, and the bottom row shows the structure reported in previous literature. The numbers show how much higher the energy of the structure in the literature is than the structure we found.

[0084] The present invention proposes an algorithm for generating a three-dimensional structure of a cage cluster from a topological structure, and a graph neural network algorithm for predicting properties based only on the topological structure. The three-dimensional structure generation algorithm can also be used for the display of polyhedrons, and provide structural coordinates for the analysis of the physical and chemical properties of cage clusters. The topological link of the cluster structure is known, the topological distance between the atoms in the cluster structure is calculated, the distance matrix is ​​embedded in the three-dimensional coordinate space to obtain the initial coordinates, and then a force field consisting of a spring elastic force and a particle repulsive force is given to the atoms. The structure is locally optimized with the minimum cluster energy as the objective function to obtain reasonable three-dimensional coordinates. Starting from the topological connection of the cage cluster, we designed a graph neural network algorithm that can also predict its properties. Different initial feature generation methods are designed for different cage cluster force systems. The graph neural network can quickly predict the properties of the cage cluster, so that a structure with given properties can be found from a large number of isomers.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A cage cluster structure generation and property prediction algorithm, characterized in that: The following steps are involved: S1. Algorithm for generating three-dimensional structure: Use polyhedron generation software to generate all polyhedrons of a given size, calculate their topological distance matrix, calculate the coordinates embedded in the three-dimensional space from the distance matrix, and optimize the force field of the coordinates to obtain a preliminary reasonable structure; The specific steps are: First, a rough three-dimensional structure is generated by topological connection. If two points are adjacent, their topological distance is recorded as 1, and the Floyd algorithm is used to calculate the pairwise distance. ,make: ， Where n is the number of vertices; ， I is the identity matrix, 1= (1,…,1) T ; ， right B Do singular value decomposition: ， Then the coordinate matrix embedded in the three-dimensional space is: ， in: ； By optimizing the generated coordinates using the force field, we can get the preliminary reasonable three-dimensional coordinates. The force field is defined to be composed of spring elastic force and particle repulsion force. If two points are topologically adjacent, their distance is close to the bond length, and they are defined to be subject to an elastic force: ， in For point Click to The coordinate difference of the point, is the bond length. If two points are not adjacent, they are defined to be subject to a repulsive force: ； The potential energy corresponding to the elastic force and repulsive force is: ， in As mask, when , When the points are adjacent, the value is 1, and when they are not adjacent, the value is 0. Using the coordinate X generated above as the initial value, the BFGS algorithm is used to optimize the energy locally to obtain the optimized coordinates, which are the initial reasonable structure. S2. Property prediction algorithm: All the preliminary reasonable structures obtained are optimized using first-principles software to obtain their property data respectively. The property data are used as data sets to train the neural network to obtain a method for extracting the initial features of the cage structure and a graph neural network including the connection order. Finally, the initial features are sent to the graph neural network to obtain the predicted values ​​of the properties.

2. The cage cluster structure generation and property prediction algorithm according to claim 1, characterized in that: The specific steps of the property prediction algorithm in S2 are: Using the preliminary reasonable structure obtained in S1, the properties of interest are calculated using first principles to generate a data set. Then, a graph neural network is used to predict the properties, with the topological connection of the dual graph as input, without considering the characteristics of the edges, and different initial point features are selected according to different research systems. The graph neural network layer aggregates the information of neighboring points to the central node i, considers the three consecutive neighboring points j-1, j, j+1 of the central node i, and transforms the feature h of node j into j Its left and right neighboring point features h j-1 and h j+1 Splice to get h j ||(h j-1 +h j+1 ), followed by a fully connected layer and an activation layer to map it into a new vector g j , and then use the general graph convolution operation to converge the neighboring point features to the central node i: ； in G l It is composed of all the point features g obtained above, W l For the l The weight matrix of the layer graph convolution layer is the activation function, is the matrix obtained by adjacency matrix A; ； If the initial point feature is an integer, the network uses an embedding layer to convert it into a vector, followed by two graph convolutional layers, and then a fully connected layer to convert the point feature vector into 1 dimension. Finally, the features of n points are added together and a number is output as the predicted value of the property.

Images