A method for searching global structure of Zn-Zr-O cluster based on collaborative optimization of element machine learning potential function and genetic algorithm

Abstract

The present application relates to the field of computational materials science, theoretical catalysis and artificial intelligence assisted material design, in particular to a Zn-Zr-O cluster global structure search method based on element machine learning potential function and genetic algorithm collaborative optimization, which comprises the following steps: constructing a structure-energy-force dataset containing Zn, Zr, C, H and O elements, and training a machine learning potential function; randomly generating a plurality of Zn-Zr-O cluster structures for the target composition, constructing a genetic algorithm initial population through machine learning potential function optimization, molecular dynamics thermal disturbance sampling, structure deduplication and low energy screening; generating candidate structures through selection, crossover and mutation, and utilizing element machine learning potential function for structure optimization and energy evaluation, obtaining low-energy candidate structures through iterative search, and finally verifying and sorting by using first principle calculation. The present application can reduce the calculation cost of structure search and improve the efficiency of low-energy structure search of Zn-Zr-O cluster.

Description

Technical Field

[0001] This invention belongs to the fields of computational chemistry, theoretical catalysis, computational materials science, and artificial intelligence-aided materials design. Specifically, it relates to a global structure search method for Zn-Zr-O clusters based on the collaborative optimization of elemental machine learning potential functions and genetic algorithms. Background Technology

[0002] Zn-Zr-O multi-component oxide materials exhibit excellent catalytic performance and hold significant research and application value in catalytic reactions such as the hydrogenation of carbon dioxide to methanol. Existing theoretical studies typically employ periodic surface, interface, or crystal plane models to describe the local structure of catalytic materials and utilize density functional theory to investigate reactant adsorption, reaction pathways, and active sites.

[0003] However, real-world catalytic materials typically exhibit heterogeneous, non-planar, and multi-scale structural features, with their surfaces potentially containing clusters of varying sizes, undercoordinated atoms, and localized structural defects. Compared to ideal periodic surface models, oxide clusters can describe size effects, surface effects, and undercoordinated structures from an aperiodic structural perspective. Therefore, searching for stable structures of Zn-Zr-O clusters is crucial for establishing more rational catalyst structural models and investigating their potential active structures.

[0004] For cluster systems containing Zn, Zr, and O, the number of possible atomic configurations increases rapidly with the increase in cluster size and the spatial arrangement of elements. Using first-principles methods to perform geometry optimization and energy calculations on a large number of randomly generated cluster structures individually requires high computational costs and makes it difficult to conduct sufficient structure searches within a large configuration space.

[0005] Genetic algorithms can perform global searches in the structure space through operations such as selection, crossover, and mutation, and therefore can be used to search for stable cluster structures. However, directly using randomly generated cluster structures as the initial population of a genetic algorithm can easily lead to the generation of many high-energy structures and structures with unreasonable inter-atomic distances. At the same time, different random structures may converge to the same or similar local minima after local structure optimization, resulting in structural duplication and insufficient structural diversity in the initial population, which affects the efficiency of subsequent global searches.

[0006] Machine learning potential functions can establish a mapping relationship between atomic structure and system energy and atomic forces based on structure, energy, and atomic force data obtained from first-principles calculations, and perform large-scale structure optimization and energy evaluation at a lower cost than first-principles calculations. Therefore, using machine learning potential functions for cluster structure search can significantly reduce the computational cost of large-scale structure optimization and energy evaluation.

[0007] However, for oxide cluster systems such as Zn-Zr-O containing multiple elements and complex local structures, the predictive power of machine learning potential functions is closely related to the coverage of different element combinations, interatomic distances, local coordination environments, and structural configurations by the training data. When the training data mainly comes from a small number of pre-obtained stable or similar structures, insufficient coverage of local atomic environments can easily occur, limiting the predictive power of machine learning potential functions in structural regions not involved in the training. Therefore, it is necessary to increase the coverage of different element combinations and local atomic environments through methods such as random structure exploration, and to obtain representative training data through structure screening.

[0008] Furthermore, using only machine learning potential functions for structure optimization of random clusters can still be affected by the initial structure distribution, and some structures may converge to the same or similar local minima, making it difficult to fully cover the configuration space of complex clusters. Therefore, how to combine the low-cost structure optimization and energy evaluation capabilities of machine learning potential functions, the ability of molecular dynamics thermal perturbations to generate structure rearrangements, and the global search capabilities of genetic algorithms to construct an efficient structure search method suitable for Zn-Zr-O multi-component oxide clusters remains a problem to be solved. Summary of the Invention

[0009] The purpose of this invention is to provide a global structure search method for Zn-Zr-O clusters based on the co-optimization of element-wise machine learning potential functions and genetic algorithms. This method addresses the problems in existing technologies, such as the high computational cost caused by performing structural optimization and energy evaluation on a large number of cluster candidate structures one by one using first-principles calculations, and the low efficiency of complex Zn-Zr-O cluster configuration space search caused by directly using random structures to construct the initial population of genetic algorithms, which easily leads to high-energy structures, repetitive structures, and insufficient structural diversity.

[0010] This invention further constructs elemental machine learning potential functions based on the local atomic environment and interaction relationships among Zn, Zr, C, H and O elements, and expands the candidate cluster configuration space by using machine learning molecular dynamics thermal perturbation sampling. On this basis, an initial population of genetic algorithms with low average energy and high structural diversity is constructed. Thus, the low-energy structure search of Zn-Zr-O clusters is completed by the collaboration of machine learning potential functions and genetic algorithms, and the final candidate structure is verified with high precision through first-principles calculations.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] This invention provides a global structure search method for Zn-Zr-O clusters based on the co-optimization of element-wise machine learning potential functions and genetic algorithms, comprising the following steps:

[0013] S1. Construct a Zn-Zr-CHO structure dataset. For the five elements Zn, Zr, C, H, and O, the Random Exploration of Imaginary Chemical Optimization (REICO) method is used to generate structural configurations with different elemental compositions, atomic numbers, spatial arrangements, and local coordination environments. The random structures are then optimized to obtain candidate structures with different local atomic environments and inter-elemental interactions.

[0014] The sampled structures are screened and deduplicated to obtain representative structural data. The energy and atomic forces of the structures are then calculated using first-principles calculations to form a structure-energy-force dataset.

[0015] S2. Training Element-based Machine Learning Potential Function. The structure-energy-force dataset is divided into training data and validation data. A machine learning model is used to fit the local atomic environment, energy, and atomic forces of Zn, Zr, C, H, and O elements to obtain the element-based machine learning potential function (EMLP).

[0016] In a preferred embodiment, an E(3) equivariant graph neural network is used as the fitting model for the element-wise machine learning potential function; further, the fitting model is a MACE model.

[0017] The predictive ability of the elemental machine learning potential function for the system's energy and atomic forces was evaluated using test data, and its structural optimization and energy prediction capabilities were verified using an untrained Zn-Zr-CHO structure.

[0018] S3. Based on the target cluster composition and size, multiple initial Zn-Zr-O cluster structures are randomly generated, and the element machine learning potential function is used to perform geometric optimization on the initial structures to obtain optimized candidate cluster structures.

[0019] S4. Thermal perturbation sampling is performed using machine learning molecular dynamics. The optimized cluster structure obtained in step S3 is used as the initial configuration for machine learning molecular dynamics, and molecular dynamics simulations are performed under preset temperature, simulation time, and integration time step conditions.

[0020] During the thermal perturbation sampling process, the interatomic interactions are calculated using the element machine learning potential function, and the motion trajectory of cluster atoms is obtained through molecular dynamics integration. This causes changes in the spatial positions, interatomic distances, and local coordination relationships of Zn, Zr, and O atoms, thereby obtaining candidate cluster configurations with different spatial arrangements and local atomic environments.

[0021] Multiple candidate configurations are extracted from molecular dynamics trajectories at preset time intervals or in a random manner, and the structure is optimized using elemental machine learning potential functions.

[0022] The machine learning molecular dynamics thermal perturbation sampling is used to expand the sampling range of the cluster configuration space and to provide candidate structures for the genetic algorithm (GA), rather than to evaluate the thermal stability of the cluster.

[0023] S5. Perform structural deduplication and low-energy screening on the candidate cluster structures obtained in S4 to obtain the initial population for the genetic algorithm.

[0024] S6. Use a genetic algorithm to perform a global structure search. Each cluster structure obtained in step S5 is used as an individual in the genetic algorithm. The structure energy calculated by the element machine learning potential function is used as the fitness evaluation criterion. For cluster structures with the same elemental composition and number of atoms, the lower the structure energy, the higher its retention priority.

[0025] Select a predetermined number of low-energy clusters from the current population as parent structures, and perform crossover and mutation operations on the parent structures.

[0026] The crossover operation involves combining partial spatial regions, local structural units, or atomic arrangements from two parent clusters to generate new candidate cluster structures.

[0027] The mutation operations include changing the spatial positions, atomic coordinates, spatial arrangement, or local coordination relationships of Zn, Zr, and O atoms to generate candidate cluster structures that are different from the parent structure.

[0028] The new candidate structures generated by crossover and mutation are checked for interatomic distance and structural legitimacy, and the element machine learning potential function is used for structural optimization and energy evaluation.

[0029] Candidate structures are sorted according to their structural energy, and low-energy structures are retained to enter the next generation population. The selection, crossover, mutation, structural optimization and energy evaluation processes are repeated until the preset convergence condition is met or the preset maximum number of iterations is reached.

[0030] S7. First-principles high-precision verification. A predetermined number of candidate structures are selected from the low-energy candidate cluster structures obtained by the genetic algorithm iteration, and high-precision calculations are performed using the first-principles method.

[0031] In one implementation, firstly, the candidate structures are subjected to first-principles single-point energy calculations, and preliminary screening is performed based on the single-point energies; then, the screened low-energy candidate structures are subjected to first-principles geometric optimization, and the candidate structures are reordered based on the system energy after geometric optimization.

[0032] The low-energy structure obtained from first-principles calculations is used as a stable candidate structure for the target composition and size Zn-Zr-O cluster.

[0033] Through the above steps, the potential function of element-based machine learning is used to undertake large-scale structure optimization and energy evaluation, the genetic algorithm is used to expand and search the cluster configuration space, and first-principles calculations are used to perform high-precision verification of the final low-energy candidate structure, thereby reducing the amount of first-principles calculations in the overall structure search process.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] (1) The present invention uses the element machine learning potential function to replace the first-principles structure optimization and energy evaluation of a large number of candidate structures in the genetic algorithm search process. While ensuring the description of the Zn-Zr-O cluster structure and local atomic environment, it improves the computational efficiency of large-scale candidate structure screening and optimization.

[0036] (2) This invention obtains structural data of different element combinations, interatomic distances and local coordination relationships through random structure exploration and local atomic environment sampling, and calculates the system energy and atomic forces in combination with first principles, which are used to train the element machine learning potential function, thereby improving the coverage of different Zn-Zr-O local structures by the machine learning potential function.

[0037] (3) This invention introduces machine learning molecular dynamics thermal perturbation sampling before the genetic algorithm search. It uses thermal motion to induce spatial rearrangement and local coordination changes of Zn, Zr and O atoms to obtain candidate configurations that are different from the initial structure, providing richer structural candidates for the genetic algorithm.

[0038] (4) The present invention constructs the initial population of the genetic algorithm through the process of “random structure generation - machine learning potential function optimization - machine learning molecular dynamics thermal perturbation - configuration extraction - structure optimization - similarity deduplication - low energy screening”, which reduces the proportion of high energy and repetitive structures while preserving structural diversity, which is conducive to improving the global search capability of the genetic algorithm.

[0039] (5) This invention utilizes the potential function of element machine learning to complete the rapid optimization and energy evaluation of large-scale candidate structures, uses the genetic algorithm to search the structure space, and uses first-principles calculation to perform high-precision verification and ranking of the final low-energy candidate structures, thereby achieving a balance between computational efficiency and structural reliability.

[0040] (6) While maintaining the basic principle of the above technical solution, the present invention can be further used for the structural search of other multi-component oxide clusters. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the global structure search method for Zn-Zr-O clusters based on the collaborative optimization of elemental machine learning potential function and genetic algorithm according to the present invention.

[0042] Figure 2 This is an energy and force correlation diagram of the training and validation sets of the element-based machine learning potential function in this invention;

[0043] Figure 3 This is a comparison of potential function energy and DFT single-point energy during the EMLP geometric optimization process of the random cluster structure in this invention; the black curve represents the EMLP optimization trajectory, and the red curve represents the DFT single-point energy of the corresponding structure. The energy is referenced to the EMLP convergence value as the zero point.

[0044] Figure 4 The Zn4Zr cluster in this invention 27 O 58 Machine learning molecular dynamics thermal perturbation sampling energy variation graph;

[0045] Figure 5 The Zn4Zr cluster in this invention 27 O 58 Genetic algorithm population energy evolution graph;

[0046] Figure 6 This is a schematic diagram of low-energy stable candidate structures of Zn-Zr-O clusters of different sizes with a Zn / (Zn+Zr) ratio of approximately 13% in this invention. Detailed Implementation

[0047] The present invention will now be described in further detail with reference to the accompanying drawings. It should be noted that the following specific embodiments are for illustrative purposes only and should not be construed as limiting the scope of protection of the present invention. Those skilled in the art can adjust the specific parameters and implementation steps without departing from the technical concept of the present invention.

[0048] Example 1: Zn-Zr-CHO Machine Learning Potential Function Training

[0049] Training data for elemental machine learning potential functions were constructed for five elements: Zn, Zr, C, H, and O. First, structural configurations with different elemental combinations, atomic numbers, and spatial arrangements were randomly generated to ensure that the sampled data covered interactions in different chemical environments.

[0050] In this embodiment, the REICO strategy is used to explore randomly generated structures, and candidate structures with different local atomic environments are obtained from the structure exploration and optimization process. The candidate structures are then screened and deduplicated to remove obviously unreasonable or highly repetitive structures.

[0051] The selected structures are used to calculate the system energy and atomic forces using first-principles methods, forming a structure-energy-force dataset. This dataset is then divided into a training set and a validation set according to a predetermined ratio.

[0052] The data is fitted using an E(3) equivariant graph neural network to obtain an element-based machine learning potential function EMLP. In this embodiment, MACE is used as the fitting model for the E(3) equivariant graph neural network.

[0053] Evaluate the prediction error of EMLP for system energy and atomic forces using test data. Figure 2 The generalization ability of the machine learning potential function of the elements is evaluated. The application verification of EMLP in practical Zn-Zr-O cluster structure optimization is as follows: Figure 3 As shown.

[0054] The Zn-Zr-CHO elemental machine learning potential function constructed in this embodiment is not limited to describing only specific structures containing five elements, but is used to establish a unified potential energy description of the interactions between Zn, Zr, C, H, and O elements. In the subsequent Zn-Zr-O cluster structure search process of this invention, the aforementioned elemental machine learning potential function is invoked based on the elemental composition of the target cluster for structure optimization, molecular dynamics sampling, and energy evaluation.

[0055] Example 2: Zn4Zr 27 O 58 Cluster machine learning molecular dynamics thermal perturbation sampling

[0056] A Zn-Zr-O cluster system with a Zn / (Zn+Zr) ratio of approximately 13% was selected as the specific implementation object. Zn4Zr... 27 O 58 As one specific example of elemental composition, it has a total of 89 atoms, and the Zn / (Zn+Zr) ratio is approximately 12.9%. Zn₄Zr 27 O 58 This refers to the elemental composition and number of atoms in a cluster, not its unique spatial structure. For the same elemental composition and number of atoms, multiple different spatial arrangements and local coordination environments of atoms can be formed.

[0057] Using the geometrically optimized cluster structure as the initial configuration for machine learning molecular dynamics, thermal perturbation sampling was performed at 800 K, with a simulation time of 1 ps and a total of 5000 integration steps. Figure 4 The image shows the cluster structure Zn4Zr. 27 O 58 Energy distribution diagram after high-temperature MD thermal perturbation. The above parameters are only examples of specific implementation methods and do not constitute a limitation on the scope of protection of this invention.

[0058] During thermal perturbation, the spatial positions and local coordination relationships of Zn, Zr, and O atoms change, resulting in candidate configurations with different spatial arrangements and local atomic environments. Candidate configurations are extracted from molecular dynamics trajectories at preset time intervals, and structural optimization and similarity deduplication are performed on the extracted configurations to obtain candidate cluster structures with structural differences.

[0059] The optimized candidate structures are deduplicated and screened based on structural energy, atomic coordinate differences, local coordination environment, or structural similarity. Low-energy candidate structures with structural differences are retained to construct the initial population of the genetic algorithm.

[0060] Example 3: Global Structure Search using Genetic Algorithm

[0061] The candidate cluster structures obtained in Example 2 were used as the initial population for the genetic algorithm. Compared with the initial population of the genetic algorithm that was generated randomly, the initial population in this example was pre-optimized by the machine learning potential function and subjected to thermal perturbation sampling, thus containing more low-energy structures while retaining different spatial arrangements and local coordination structures.

[0062] For each cluster structure in the initial population, a machine learning potential function is used to evaluate the structure energy, and the structures are ranked according to their energy. Low-energy structures are selected as parent structures. Structural crossover is performed between the two parent structures. In this embodiment, structural crossover uses a spatial cutting-recombination method, that is, partial structural regions are selected from each of the two parent cluster structures and recombine to form new candidate structures.

[0063] Structural crossover can generate new offspring structures by combining selected spatial regions, local structural units, or atomic arrangements from two parent structures. After generating offspring structures through structural crossover, structural mutations are applied to some of these offspring structures. Structural mutations can be achieved by altering the spatial coordinates, local positions, or local structural relationships of Zn, Zr, and O atoms. The candidate structures obtained from structural crossover and structural mutation are then subjected to structural validity checks.

[0064] Candidate structures with excessively close interatomic distances or unreasonable structures are eliminated or corrected. Subsequently, a machine learning potential function is used for geometric optimization, and the energy of the optimized structure is calculated. Based on the structure energies calculated using the elemental machine learning potential function, the candidate structures are reordered, and low-energy structures are retained for the next generation of the population.

[0065] Repeat the following steps: selection → crossover → mutation → EMLP structure optimization → EMLP energy evaluation → low-energy structure retention, until the preset convergence condition is met. Figure 5 It is Zn4Zr 27 O 58 Energy evolution diagram of a population after 100 generations of cluster genetic algorithm iteration.

[0066] Example 4: First Principles Verification

[0067] Several low-energy candidate structures are selected from the structures obtained by the genetic algorithm for first-principles single-point computation. First, a corresponding first-principles computation structure file is created, and the appropriate computation parameters are set. Then, the low-energy candidate structures selected by the genetic algorithm are reordered using DFT single-point energies; the top-ranked structures are then subjected to DFT geometric optimization to determine the final stable structure of the Zn-Zr-O cluster.

[0068] Based on the first-principles calculation results, the low-energy candidate structures obtained by the genetic algorithm are reordered, and the structure with the lowest energy is selected as a stable candidate structure for the target size and element composition of the Zn-Zr-O cluster.

[0069] By comparing the structure energy ranking obtained from machine learning potential functions and first-principles calculations, the reliability of machine learning potential functions in screening low-energy structures in clusters can be verified.

[0070] Example 5: Stability analysis of Zn-Zr-O clusters of different sizes

[0071] The global structure search process described above was executed for Zn-Zr-O clusters of different sizes. Structural analysis was performed on the obtained stable structures, including the spatial distribution of Zn atoms, the surface enrichment of Zn atoms, the Zn coordination number, and the local coordination relationships between Zn-O and Zn-Zr.

[0072] For example, cluster structures with the same proportion but different numbers of Zn atoms can be constructed separately, and EMLP-MD thermal perturbation and global search using genetic algorithms can be performed independently on each size of cluster. Figure 6 , which represents the stable configurations of Zn-Zr-O clusters of different sizes under a 13%Zn / (Zn+Zr) ratio.

[0073] Based on the specific calculation results, the coordination and other coordination structure ratios of Zn atoms in clusters of different sizes can be further statistically analyzed, and the spatial distribution of Zn on the cluster surface and inside the cluster can be compared. Our results show that in some of the low-energy structures obtained in this embodiment, Zn atoms are mainly distributed in the cluster surface region, exhibiting a certain degree of surface dispersion. With changes in cluster size, the coordination number and local coordination environment of Zn atoms change.

[0074] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited to the above embodiments. Those skilled in the art can adjust or equivalently replace the Zn-Zr-O cluster structure dataset construction method, machine learning potential function model, molecular dynamics sampling conditions, genetic algorithm search parameters, and first-principles verification method according to actual application needs without departing from the technical concept and solution of the present invention.

[0075] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still modify, transform, or optimize the specific implementation methods based on the principles and concepts disclosed in the technical solutions of the present invention. All equivalent substitutions, simple changes, or improvements that do not depart from the technical spirit of the present invention made in accordance with the technical solutions of the present invention should be included within the scope of protection of the present invention.

Claims

1. A global structure search method for Zn-Zr-O clusters based on the collaborative optimization of element-wise machine learning potential functions and genetic algorithms, characterized in that, Includes the following steps: S1. Construct a Zn-Zr-CHO structure dataset containing different compositions, sizes, and spatial configurations; the Zn-Zr-CHO element machine learning potential function is a unified machine learning potential function that includes the interactions of Zn, Zr, C, H, and O elements. When performing structure search for Zn-Zr-O clusters, the relevant interactions of Zn, Zr, and O elements in the potential function are called according to the elemental composition of the target cluster to perform structure optimization, molecular dynamics sampling, and energy evaluation. S2. First-principles calculations are used to obtain the system energy and atomic force information corresponding to the structure, and a general element-based machine learning potential function is trained based on the structure-energy-force database. S3. Generate a random Zn-Zr-O initial cluster structure according to the target composition, and optimize the structure using the element machine learning potential function; S4. Using the element machine learning potential function, molecular dynamics thermal perturbation sampling is performed to obtain candidate structures with different spatial arrangements and local coordination environments; S5. Perform structural optimization, similarity deduplication, and low-energy screening on the candidate structures to construct the initial population for the genetic algorithm; S6. Select, crossover, and mutate the initial population using a genetic algorithm, optimize the structure and evaluate the energy using the element machine learning potential function, and perform multiple generations of iteration; S7. Select the target structure from the low-energy candidate structures obtained through iteration, and perform high-precision verification and sorting using first-principles calculations to obtain a stable Zn-Zr-O cluster structure.

2. The method according to claim 1, characterized in that, The general machine learning potential function is a machine learning potential function established based on the local atomic environment and interaction relationship between Zn, Zr, C, H and O elements. It extensively samples the potential energy surface by randomly generating structures with different elemental compositions, atomic numbers and spatial arrangements, and uses the system energy and atomic forces obtained by first-principles calculations for training.

3. The method according to claim 2, characterized in that, The local atomic environment employs a stochastic exploration virtual chemical optimization strategy to optimize the randomly generated Zn-Zr-CHO structure, thereby obtaining structures with different element combinations, interatomic distances, and local coordination relationships; the element machine learning potential function is fitted using an E(3) equivariant graph neural network.

4. The method according to any one of claims 1 to 3, characterized in that, The structure dataset is filtered and deduplicated. The filtering includes filtering based on one or more indicators such as structure energy, atomic force, interatomic distance, local coordination environment, and structure similarity, in order to obtain a dataset for training and validating element-wise machine learning potential functions.

5. The method according to claim 1, characterized in that, The molecular dynamics thermal perturbation sampling includes: using the cluster structure optimized by the element machine learning potential function as the initial configuration, performing molecular dynamics simulation at a preset temperature; extracting candidate structures from the simulation trajectory at preset time intervals, and performing structural optimization and similarity deduplication on the candidate structures to obtain candidate structures with different spatial configurations and local coordination environments.

6. The method according to claim 1 or 5, characterized in that, Candidate structures optimized by element-wise machine learning potential function, deduplicated by structural similarity, and screened for low energy are used as the initial population of the genetic algorithm. The fitness of individuals is determined based on structural energy, so that low-energy structures have a higher retention priority.

7. The method according to claim 1, characterized in that, The crossover operation of the genetic algorithm includes combining spatial regions, local structural units, or atomic arrangements of two parent clusters; the mutation operation also includes perturbing or rearranging the positions of local structural units.

8. The method according to claim 7, characterized in that, For a target Zn-Zr-O cluster with a fixed elemental composition and number of atoms, the number of atoms of Zn, Zr and O remains unchanged during the crossover and mutation process of the genetic algorithm, and the generated candidate structures are optimized by checking the inter-atom distance and the elemental machine learning potential function structure.

9. The method according to claim 1, characterized in that, The first principle high-precision verification includes: selecting a preset number of structures from the low-energy candidate structures obtained by the genetic algorithm for first principle single-point energy calculation, performing preliminary screening based on the calculation results, performing first principle geometric optimization on the screened candidate structures, and reordering them based on the optimized system energy to obtain a stable structure of the target Zn-Zr-O cluster.

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