A method for calculating the energy barrier of local clusters of transition metal oxides and predicting the cycle life

Abstract

The application discloses a transition metal oxide local cluster energy barrier calculation and cycle life prediction method, relates to the cross technical field of quantum calculation and material science, and comprises the following steps: determining a plurality of candidate micro events of a transition metal oxide material; for each candidate micro event, intercepting a local cluster and passivating a broken bond, determining an active space and an electronic integral by adopting a quantum embedding strategy, solving energy based on the quantum variation algorithm, calculating a reaction energy barrier and an activation energy, and quantifying an uncertainty to obtain a statistical distribution; inputting the statistical distribution and working condition characteristics into an Arrhenius degradation mapping model to generate an overall degradation rate, a cycle life and a prediction interval thereof; and based on the prediction interval, dynamically selecting a key micro event with the life variance minimization as an objective, and iteratively executing to obtain a final reaction energy barrier and a cycle life. The application adopts the quantum variation algorithm and the local cluster strategy, obtains a high-precision energy barrier, and realizes cycle life prediction.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of quantum computing and materials science, and in particular to a method for calculating the local cluster energy barrier and predicting the cycle lifetime of transition metal oxides. Background Technology

[0002] Transition metal oxide materials, including layered, spinel, and rock salt phase structures, have wide applications in electrochemical energy storage systems, catalytic reactions, and ion transport devices. The microscopic events in these materials, such as ion diffusion processes, transition metal migration behavior, and oxygen vacancy generation or migration, are dominated by energy barriers, and their distribution characteristics directly affect the material's diffusion coefficient, structural stability, and cycle life performance. Currently, accurately calculating the energy barriers of these microscopic events and establishing an effective mapping relationship between them and battery cycle life is a pressing technical problem to be solved in material design and performance optimization.

[0003] Traditional first-principles calculations combined with the minimum energy path method (DFT+NEB) are commonly used techniques for simulating ion migration paths and calculating energy barriers. This method constructs a periodic supercell model and performs transition state searches to evaluate the energy barrier distribution of microscopic events, providing a theoretical basis for material property analysis.

[0004] However, the DFT+NEB method has significant limitations in strongly correlated transition metal oxide systems. Regarding the strong correlation characteristics, the correlation effect of transition metal d electrons introduces systematic biases in the characterization of energy barriers and transition states using conventional approximations such as the Generalized Gradient Approximation (GGA) or the DFT+U method. In terms of scale and cost, periodic supercell optimization is computationally expensive, and the computational cost increases exponentially with different doping types, defect configurations, and local environment combinations, leading to a sharp increase in computational cost. Regarding the mapping from mechanism to lifetime, the microscopic energy barrier calculation results usually remain at the material level, lacking an effective correlation model with battery cycle life. Finally, in terms of uncertainty quantification, factors such as initial state values, Hubbard model U-value parameters, and functional selection introduce significant uncertainties, which are detrimental to engineering decisions and applications.

[0005] Quantum variational algorithms solve for electronic structure and excited states in a quantum-classical hybrid loop by parameterizing quantum circuits, possessing a natural potential to handle many-body correlation effects. Combining embedded local cluster strategies with variational optimization methods, key energy barriers can be evaluated more accurately while controlling computational scale. Furthermore, coupling with lifetime prediction models provides a new technical approach for end-to-end prediction from microscopic mechanisms to macroscopic performance. Summary of the Invention

[0006] The technical problem to be solved by this invention is to address the shortcomings of existing technologies, and the following technical solution is provided: 1) In a first aspect, the present invention provides a method for calculating the local cluster energy barrier and predicting the cycle lifetime of transition metal oxides, the specific technical solution of which is as follows: S1. Identify multiple candidate micro-events in the transition metal oxide material; S2. For any candidate micro-event, take the atomic position involved in the candidate micro-event as the center, extract the corresponding local cluster within a preset radius, and passivate the end positions of the local clusters. Based on the passivated local clusters, determine the active space and electron integral of the local clusters using a quantum embedding strategy. Based on the active space and electron integral, obtain the statistical distribution of the reaction barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event, until the transition metal oxide material corresponding to each candidate micro-event is obtained. S3. Statistical distribution of reaction barrier and activation energy of transition metal oxide material corresponding to each candidate micro-event, together with operating condition characteristics, are input into a degradation mapping model based on Arrhenius rate kernel to generate the overall degradation rate and cycle life of transition metal oxide material, and output the overall prediction range of cycle life; S4. Based on the overall prediction range of cycle life, key micro-events are identified, key micro-events are used as candidate micro-events in S2, and S2 is returned to calculate the final reaction barrier and final cycle life.

[0007] The beneficial effects of the method for calculating local cluster energy barriers and predicting cycle lifetimes of transition metal oxides provided by this invention are as follows: By employing a quantum variational algorithm combined with a local cluster strategy to solve for the energy barrier, this method effectively overcomes the computational bias problem of the traditional DFT+NEB method in strongly correlated systems. Within a controllable computational scale, this method obtains reaction energy barriers and activation energies with near-chemical accuracy, providing high-quality mechanistic parameters for materials design. By generating the statistical distribution of the energy barrier through bootstrapping and outputting confidence intervals, explicit quantification and propagation of uncertainty are achieved, enhancing the reliability and engineering decision-making capability of the results. A degenerate mapping model based on the Arrhenius rate kernel establishes a physical correlation between the energy barrier distribution and cycle lifetime, enabling end-to-end prediction from microscopic mechanisms to macroscopic performance. An active learning mechanism aimed at minimizing lifetime uncertainty iteratively optimizes predictions by dynamically selecting key microscopic events, accelerating prediction convergence and reducing redundant computations within a limited computational budget. This method combines high accuracy, low cost, and interpretability, providing an effective theoretical tool and engineering guidance for the performance evaluation of transition metal oxide materials and cell design.

[0008] 2) In a second aspect, the present invention also provides a system for calculating the local cluster energy barrier and predicting the cycle lifetime of transition metal oxides, the specific technical solution of which is as follows: The system includes an event determination module, a statistical distribution determination module, a calculation module, and an iterative determination module. The event determination module is used to determine multiple candidate micro-events in the transition metal oxide material. The statistical distribution determination module is used to: for any candidate micro-event, extract the corresponding local cluster within a preset radius, centered on the atomic position involved in the candidate micro-event, passivate the break points of the local clusters, and, based on the passivated local clusters, determine the active space and electron integral of the local clusters using a quantum embedding strategy. Based on the active space and electron integral, obtain the statistical distribution of the reaction barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event, until each... The statistical distribution of the reaction barrier and activation energy of the transition metal oxide material corresponding to each candidate micro-event is calculated. The calculation module is used to input the statistical distribution of the reaction barrier and activation energy of the transition metal oxide material corresponding to each candidate micro-event, together with the operating condition characteristics, into a degradation mapping model based on the Arrhenius rate kernel to generate the overall degradation rate and cycle life of the transition metal oxide material, and output the overall prediction range of the cycle life. The iterative determination module is used to determine the key micro-events based on the overall prediction range of the cycle life, take the key micro-events as candidate micro-events, and repeatedly call the statistical distribution determination module and the calculation module to calculate the final reaction barrier and the final cycle life.

[0009] 3) In a third aspect, the present invention also provides an electronic device, the electronic device including a processor coupled to a memory, the memory storing at least one computer program, the at least one computer program being loaded and executed by the processor, so as to enable the electronic device to implement any of the above-mentioned methods for calculating the local cluster energy barrier and predicting the cycle lifetime of transition metal oxides.

[0010] 4) In a fourth aspect, the present invention also provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements the method for calculating the local cluster energy barrier and predicting the cycle lifetime of any of the above-mentioned transition metal oxides.

[0011] It should be noted that the beneficial effects of the technical solutions of the second to fourth aspects of the present invention and their corresponding possible implementations can be found in the above description of the technical effects of the first aspect and its corresponding possible implementations, and will not be repeated here. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating a method for calculating the local cluster energy barrier and predicting the cycle lifetime of transition metal oxides according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a system for calculating the local cluster energy barrier and predicting the cycle lifetime of a transition metal oxide according to an embodiment of the present invention. Detailed Implementation

[0013] like Figure 1 As shown in the figure, a method for calculating the local cluster energy barrier and predicting the cycle lifetime of a transition metal oxide according to an embodiment of the present invention includes the following steps: S1. Multiple candidate micro-events for transition metal oxide materials are identified. Specifically, the crystal structure file of the transition metal oxide material is imported, and multiple candidate micro-events are defined based on the crystal structure file. These candidate micro-events include at least two of the following types: ion migration, transition metal migration, oxygen vacancy generation, or oxygen vacancy migration. This avoids the limitations of single-event analysis. Moreover, the definition process is based on crystallographic rules and atomic site analysis, generating a structured list of candidate events, providing complete input for subsequent local cluster extraction and energy barrier calculation. By covering multiple micro-event types, the system can capture the main failure mechanisms of materials under different operating conditions, enhancing the comprehensiveness and reliability of lifetime prediction. This technical feature lays a solid foundation for subsequent quantum variational energy barrier solutions and physical modeling, supporting end-to-end prediction from microscopic mechanisms to macroscopic performance, and improving the guiding value for material design and cell optimization.

[0014] The specific implementation process for defining multiple candidate micro-events is as follows: 1) The system reads crystal structure files of transition metal oxide materials provided by the user through a file interface. These files typically use standard formats such as CIF or POSCAR and contain information on the material's lattice parameters, atomic coordinates, atom types, and symmetry. Parsing the crystal structure files allows for the extraction of lattice vectors and atomic position data, and the construction of a three-dimensional crystal model. During the parsing process, the integrity and format correctness of the file are verified to ensure that no data is misleadingly imported.

[0015] 2) Based on the resolved crystal structure, multiple candidate micro-events are automatically identified and defined. This step relies on pre-defined crystallographic rules and a materials database to analyze common structural types of transition metal oxides (such as layered, spinel, or rock salt phases). The atomic arrangement and site types in the crystal structure are scanned to identify possible micro-event locations. For example, in layered structures, octahedral and tetrahedral interstitial sites are marked; in spinel or rock salt phases, transition metal sites and oxygen sites are identified. Then, based on these sites, a list of candidate micro-events is generated, with event types including at least two of ion migration, transition metal migration, oxygen vacancy formation, or oxygen vacancy migration. The event definitions ensure coverage of major degradation mechanisms in the material, such as lithium ion migration between octahedrons and tetrahedrons, displacement of transition metal ions in the lattice, and formation and migration of oxygen vacancies between adjacent oxygen sites. Each candidate micro-event is specified with its event type, the atoms or sites involved, and possible initial and final states, providing a basis for subsequent local cluster extraction and energy barrier calculations.

[0016] 3) During the definition process, an algorithm is used to automatically generate a candidate set of events, avoiding biases caused by manual intervention. Specifically: The crystal structure files of transition metal oxide materials are parsed to extract lattice parameters, atomic coordinates, and atomic type information. After parsing, a three-dimensional crystal model is constructed, and the materials are classified using predefined structural templates (such as layered, spinel, or rock salt phases) from a crystallography database. Classification criteria include lattice symmetry, atomic arrangement pattern, and space group number. For example, layered structures typically exhibit two-dimensional layered arrangement, spinel structures display cubic symmetry, while rock salt phases exhibit face-centered cubic arrangement. The material's structure type is automatically determined by comparing the matching degree of lattice vectors and atomic positions with the template. Based on the structure type, a regular basis algorithm is applied to scan the crystal structure, generating candidate microscopic events. The algorithm first identifies all possible atomic sites and interstitial sites. For ion migration events, the algorithm calculates the migration paths of alkali metal ions (such as lithium or sodium). This is achieved by analyzing the connectivity of the interstitial network: the crystal space is partitioned using Delaunay triangulation or Voronoi diagrams, octahedral and tetrahedral interstitial sites are identified, and preliminary estimates of the energy barriers between sites are calculated. The energy barrier is calculated based on empirical potential functions of the local atomic environment, such as using bond valence and modeling or electrostatic potential analysis. The formula is expressed as: in, It is an approximation of the migration energy barrier. It is a force constant. It is the distance between atoms. This is the reference bond length. The algorithm filters paths with energy barriers below a threshold and marks them as candidate ion migration events.

[0017] For transition metal migration events, the algorithm focuses on the sites of transition metal atoms (such as nickel, cobalt, or manganese). It analyzes the coordination environment and local symmetry of the transition metal atoms to identify possible directions of displacement. This is achieved by calculating the local strain and bond angle deviation at the transition metal sites. The algorithm uses pre-simulations of molecular dynamics or static energy calculations to assess the stability of the transition metal atoms in the crystal lattice. For example, it calculates the embedding energy of each transition metal site. : ,in, It is the total energy. It is the lattice energy after removing that atom. These are the energies of isolated atoms. Sites with lower embedding energies are flagged as candidate events for potential migration.

[0018] For oxygen vacancy generation or migration events, the algorithm scans all oxygen sites and evaluates the vacancy formation energy and migration path. The vacancy formation energy is calculated based on local charge balance and bonding strength. : ,in, It is the energy of vacancy formation. It is energy containing vacancies. It is complete energy. This refers to the oxidation potential. The algorithm screens oxygen sites with lower formation energies as candidate vacancy generation events. For vacancy migration, the algorithm analyzes the connectivity between oxygen sites and calculates an approximation of the migration energy barrier, similar to ion migration methods.

[0019] When generating the event candidate set, at least two microscopic event types are ensured to be included. The algorithm achieves this through priority ranking: first, weight factors are assigned based on the importance of events to material degradation. For example, ion migration may have a higher weight in layered structures; oxygen vacancy events have a higher weight in rock salt phases. Then, the algorithm generates a structured list containing event types, involved atom indices, initial and final state coordinates, and local environment descriptors. The list output is in a machine-readable format, such as JSON or XML, facilitating subsequent use by the local cluster extraction module. The entire automated generation process relies on open-source computational materials science libraries, such as pymatgen or ASE, for crystal structure analysis and event prediction. The algorithm improves accuracy through iterative optimization, for example, by using historical data to train a simple machine learning model to refine event selection. Ultimately, the event candidate set comprehensively covers multiple microscopic event types, providing reliable input for subsequent energy barrier calculations.

[0020] For example, for ion migration events, feasible migration pathways are initially screened based on ion radius and site energy; for oxygen vacancy events, the local environment and bonding strength of oxygen sites are evaluated. A structured set of candidate micro-events is output, ensuring at least two types of micro-events are included to comprehensively capture the degradation behavior of materials. This process is logically clear, technically feasible, and lays the foundation for subsequent steps.

[0021] Crystal structure files are digital files that store crystallographic information about materials, commonly in formats such as CIF and POSCAR. The CIF format follows international crystallographic standards and includes data such as lattice constants, atomic coordinates, space group symmetry, and thermal vibration parameters. The POSCAR format is the input file used by the VASP software, explicitly listing lattice vectors and atomic positions. These files provide an atomic-level structural description of the material, serving as the fundamental input for computational simulations and ensuring structural accuracy and repeatability. Candidate micro-events refer to atomic-level processes that may occur in transition metal oxide materials, affecting their electrochemical performance and degradation behavior. Candidate micro-events are predefined based on crystal structure analysis and include types such as ion migration, transition metal migration, oxygen vacancy generation, or oxygen vacancy migration. An event list is automatically generated by scanning crystal sites and the local environment, ensuring coverage of multiple degradation mechanisms and providing a set of target events for subsequent quantum computing. Ion migration refers to the movement of alkali metal ions, such as lithium or sodium, between interstitial sites (e.g., octahedrons or tetrahedrons), driven by an electric field and concentration gradient. Transition metal migration refers to the displacement of transition metal ions (such as nickel, cobalt, and manganese) within the crystal lattice, which may lead to structural phase transitions or capacity decay. Oxygen vacancy formation refers to the process by which oxygen atoms are removed from the crystal lattice to form vacancies, usually accompanied by charge compensation; oxygen vacancy migration refers to the diffusion of these vacancies between oxygen sites. It is required to include at least two of these event types to comprehensively characterize the multiple degradation pathways of materials and avoid the limitations of single-event analysis.

[0022] S2. For any candidate micro-event, take the atomic position involved in the candidate micro-event as the center, extract the corresponding local cluster within a preset radius, and passivate the end of the bond break position of the local cluster. Based on the passivated local cluster, use a quantum embedding strategy to determine the active space and electron integral of the local cluster. Based on the active space and electron integral, obtain the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event. Continue until the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event are obtained. Among them, based on the active space and electron integral, the statistical distribution of the reaction energy barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event are obtained, including: Based on the active space and electron integral, the electronic Hamiltonian of the local cluster is constructed through secondary quantization. A measurable Pauli operator term representation is then generated via fermion-qubit mapping and symmetry transformation. A quantum variational algorithm is used to solve for the variational energy of the Pauli operator term representation, obtaining the energy of the candidate micro-event in each configuration along the path. Based on the energy of the candidate micro-event in each configuration along the path, the reaction barrier and activation energy of the corresponding transition metal oxide material are calculated. The statistical uncertainty of the reaction barrier and activation energy of the corresponding transition metal oxide material is quantified, yielding the statistical distribution of the reaction barrier and activation energy. Using a quantum variational algorithm to solve for the variational energy of the Pauli operator term representation can accurately obtain the energy of the candidate micro-event in each configuration along the path, thus reliably calculating the reaction barrier and activation energy. By statistically quantifying the uncertainty of the reaction barrier and activation energy, generating their statistical distribution, and outputting confidence intervals, the sources of uncertainty, such as quantum measurement noise, finite sampling, and model selection, are explicitly characterized, giving the barrier estimation a clear probability boundary. This process improves the accuracy and reliability of barrier calculation within a controllable computational scale, provides high-quality input data for subsequent degradation mapping models, and supports the accuracy of cycle lifetime prediction and the robustness of engineering decisions.

[0023] Specifically, taking the atomic position involved in the candidate microscopic event as the center, the corresponding local cluster is extracted within a preset radius. The specific implementation process is as follows: An event is read from a defined list of candidate microscopic events, and the atomic positions involved in that event are extracted. These atomic positions are determined based on the event type: for example, for ion migration events, the involved atomic positions include the coordinates of the starting and ending sites of the migrating ion; for transition metal migration events, the initial and post-displacement positions of the transition metal atoms are involved; for oxygen vacancy generation or migration events, the oxygen atom sites and their adjacent metal atom positions are involved. These positions are represented in three-dimensional Cartesian or fractional coordinates using atomic coordinate data from the crystal structure file. After extraction, the center point of these atomic positions is calculated. The center point is typically defined as the spatial geometric center of these positions, calculated using the following formula: in, These are the coordinates of the center point. It refers to the number of atoms involved. It is the first The coordinates of each atom. For events involving paths, such as migration paths, it is possible to calculate the center point of multiple images along the path, or select the position of the highest-energy transition state in the path as the center.

[0024] Using the calculated center point as the center, extract a local cluster within a preset radius. Preset radius. Typically between 6 and 12 angstroms, depending on configuration or user input. The interception process is achieved by traversing all atoms in the crystal structure and calculating the Euclidean distance of each atom to the center point. The distance calculation formula is: in, These are the coordinates of the center point. These are the coordinates of the atom to be checked. If the atom distance... If a specific atom is found to be present, it is included in the local cluster. Periodic boundary conditions are automatically handled to ensure that repeating lattice units are considered during truncation. For example, for crystal structures, lattice vectors are used to extend atomic coordinates, and the minimum mirror distance is calculated to avoid boundary effects. The truncated local cluster contains a principal region and an environment region: the principal region consists of atoms directly involved in the event, and the environment region consists of surrounding atoms providing electrostatic and structural background. The truncated local cluster is then structurally optimized and validated. Optimization includes adjusting atomic positions to eliminate local strain introduced by truncation, for example, by relaxing atomic coordinates using an energy minimization algorithm. The validation step checks the chemical rationality of the local cluster, ensuring bond lengths and bond angles are within reasonable ranges to avoid non-physical structures. The atom list, coordinates, and chemical bond information of the local cluster are output, preparing for subsequent end passivation. The entire truncation process is implemented using open-source computational materials science libraries such as pymatgen or ASE to ensure repeatability and accuracy. Through this process, a local cluster model is generated for each candidate microscopic event for subsequent quantum embedding and energy barrier calculations.

[0025] In this context, the atomic positions involved in candidate micro-events refer to the spatial coordinates of atoms directly related to a specific micro-event in transition metal oxide materials. These positions are obtained based on crystal structure file analysis and vary with the event type. For example, in ion migration events, the involved atomic positions include the initial and target site coordinates of migrating ions (such as lithium or sodium); in transition metal migration events, they include the coordinates of key points on the displacement path of transition metal atoms (such as nickel, cobalt, or manganese); and in oxygen vacancy generation or migration events, they include the coordinates of oxygen atom sites and their coordinating metal atoms. These positions define the spatial extent of the micro-event and serve as the central basis for identifying local clusters. A local cluster is a local set of atoms extracted from the overall crystal structure of a transition metal oxide, encompassing all atoms within a predetermined radius centered on the atomic positions involved in the candidate micro-event. Local clusters include a principal region and an environmental region: the principal region consists of atoms directly involved in the event, such as migrating ions or vacancy sites; the environmental region consists of surrounding atoms, providing electrostatic and structural background to maintain the local chemical environment. The purpose of truncating local clusters is to simulate microscopic events within a controllable computational scale, reducing the demand for quantum computing resources. Simultaneously, end passivation handles boundary breakage, ensuring the accuracy of quantum embedding. The local cluster model provides the structural foundation for subsequent construction of the electronic Hamiltonian and variational energy solutions.

[0026] Specifically, end-blunting processing is performed on the broken bond positions of the local cluster. The specific implementation process is as follows: Automatic identification of bond-break sites in local clusters. A bond-break site refers to the atomic location at the boundary of a local cluster where a chemical bond is broken due to a truncation operation. Identification is achieved by analyzing the connectivity of atoms within the local cluster: all atomic pairs are scanned using a bond length thresholding method, the interatomic distances are calculated, and compared with a standard bond length database. For example, for transition metal oxides, standard bond length references include metal-oxygen bonds, oxygen-oxygen bonds, etc. If the interatomic distance is less than or equal to the threshold, a chemical bond is considered to exist; otherwise, it is marked as a bond-break. Special attention is paid to boundary atoms, i.e., those atoms that were bonded to other atoms in the lattice before truncation but lost their connectivity after truncation. The identification process is based on crystallographic rules and atomic coordination number calculations. For each boundary atom, its current coordination number is checked to see if it is lower than the typical value in a intact crystal. For example, oxygen atoms typically have a coordination number of 2 or 3 in intact oxides; if the coordination number decreases after truncation, it is marked as a bond-break site. Then, end passivation is performed. The passivation method uses hydrogen atoms or other end groups to saturate the bond-break site to simulate the intact valence state of the boundary atom. The specific steps include: For each bond-breaking position, determining the number of hydrogen atoms to be added based on the atom type and local chemical environment. For example, if the bond breaking involves an oxygen atom, adding a hydrogen atom forms a hydroxyl group; if the bond breaking involves a transition metal atom, hydrogen atoms may be added or the charge may be adjusted to maintain electroneutrality. When adding hydrogen atoms, standard bond length and bond angle parameters are used. For example, the oxygen-hydrogen bond length is set to approximately 0.96 Å, and the bond angle is referenced to the geometry of water or hydroxyl groups. The position calculation is based on a vector method: adding hydrogen atoms by extending the standard bond length along the bond-breaking direction from the bond-breaking atom position. The direction is determined by the local coordination geometry of the bond-breaking atom, such as using the direction of the uncoordinated orbitals of the bond-breaking atom or the average bond vector. The formula is expressed as: ,in, These are the coordinates of a hydrogen atom. These are the coordinates of the broken-bond atoms. It is the standard bond length. It is a unit direction vector.

[0027] Then, the passivated local clusters undergo structural optimization and verification. The optimization process adjusts the positions of hydrogen atoms and neighboring atoms using an energy minimization algorithm to eliminate local strain. For example, rapid relaxation is performed using molecular mechanics force fields or density functional theory to ensure bond lengths, bond angles, and dihedral angles are within reasonable ranges. The verification step checks whether all atoms in the passivated local cluster are saturated with valence states and assesses whether the total charge is neutral. It also checks for excessive strain or non-physical configurations, such as abnormally short atomic distances. If problems are found, the passivation parameters are iteratively adjusted, such as modifying hydrogen atom positions or adding additional end groups. The passivated local cluster structure is then output, including atomic coordinates, chemical bond information, and charge states. This process is implemented using open-source computational chemistry libraries, such as OpenBabel or RDKit, ensuring automation and reproducibility. Through end passivation, the boundary effects of the local clusters are effectively controlled, providing reliable input for subsequent quantum embedding and active space determination.

[0028] In this context, the bond-break sites of local clusters refer to the atomic sites involved in the breaking of chemical bonds due to separation from the overall transition metal oxide crystal during the truncation process. These sites are typically located in the boundary regions of the local clusters and involve atoms such as oxygen atoms, transition metal atoms, or other coordinating atoms. In the intact crystal, these atoms are connected to surrounding atoms by chemical bonds, but these bonds are broken after truncation, leading to unsaturated atomic valence states and local charge imbalances. Bond-break sites can introduce boundary spurious effects, such as non-physical electrostatic potentials or structural strains, affecting the accuracy of subsequent quantum computing. Identifying and addressing these bond-break sites is a key objective of end-passivation processing.

[0029] The specific implementation process is as follows: Based on the passivated local clusters, and using a quantum embedding strategy to determine the active space and electronic integral of the local clusters, the specific implementation process is as follows: The system receives a passivated local cluster as input. Passivation involves adding hydrogen or other end-groups to saturate bond-breaking positions, eliminating boundary spurious effects, and optimizing atomic coordinates to ensure structural rationality. A quantum embedding strategy is then applied to process this local cluster. This strategy divides the local cluster into two regions: an active region and an environment region. The active region contains atoms and orbitals directly involved in microscopic events, such as migrating ions, transition metal atoms, or oxygen vacancies and their nearest coordinating atoms; the environment region consists of surrounding atoms, providing electrostatic and structural background. The division is based on chemical rules and spatial distances; for example, with the event center as the reference, the radius of the active region is set to 3 to 5 Å, and the environment region covers the remaining portion. Embedding is achieved using density embedding theory or a hybrid quantum mechanical / molecular mechanical approach. In density embedding, the environment region provides an effective potential field through electron density projection; in the quantum mechanical / molecular mechanical approach, the active region uses high-precision quantum chemical calculations, while the environment region is described using classical force fields. The embedding potential field is solved through a self-consistent cyclic solution to ensure the continuity of electron density and potential energy at the boundary between the two regions. For example, density embedding is achieved by solving the Kohn-Sham equation coupled with the embedding potential: ,in, It is the effective Hamiltonian, which includes the active region Hamiltonian and the embedding potential term. It is a molecular orbital. It is orbital energy.

[0030] Then, the active space of the local cluster is determined based on the quantum embedding results. The active space refers to a set of molecular orbitals used for quantum variational calculations, typically chosen from orbitals close to the Fermi level to capture key electronic behaviors. First, the electronic structure of the local cluster is calculated, and the molecular orbital energy levels are obtained by solving the self-consistent field equations. After sorting the orbital energy levels by energy, the active orbital set is automatically selected. The selection criteria are based on an energy window: for example, centered on the highest occupied molecular orbital and the lowest unoccupied molecular orbital, expanding to include several occupied and unoccupied orbitals. The number of orbitals is set according to the configuration, typically 4 to 10 orbitals, to balance accuracy and computational cost. For transition metal oxides, d orbitals of transition metals and p orbitals of oxygen are preferentially selected because these orbitals play a dominant role in strongly correlated events. After the active space is determined, the orbital index, symmetry information, and occupancy number are output, providing input for the electronic integration calculation.

[0031] Then, the electron integrals of the local clusters are calculated. These electron integrals form the basis for constructing the second-order quantized Hamiltonian, and include single-electron and two-electron integrals. The single-electron integral describes the electron's kinetic energy and nuclear attraction potential, while the two-electron integral describes electron-electron interactions. Calculations are performed based on molecular orbitals in the active space. Quantum chemistry libraries such as PySCF or OpenMolcas are used to perform the integral calculations. The formula for the single-electron integral is: ,in, and These are molecular orbitals in the active space. It is a single-electron operator. A two-electron integral. The calculation formula is: ,in, It is a two-electron operator. The integral calculation takes into account relativistic effects and symmetry simplifications, such as using point group symmetry to reduce the number of integrals. The accuracy of the integral is also verified, for example, by checking the convergence and numerical stability of the integral. After the calculation is completed, the electronic integral is stored in matrix form, which facilitates the subsequent construction of the Hamiltonian.

[0032] Finally, the active space and electron integral are integrated to output structured data, including orbital sets, integral values, and related metadata. This process is automated to ensure repeatability and efficiency. The active space and electron integral are determined through a quantum embedding strategy, providing high-quality input for subsequent variational energy calculations and supporting the accuracy and reliability of the entire energy barrier calculation process.

[0033] Quantum embedding strategies are a method for calculating electronic structure, dividing the region into an active region handled by quantum mechanics and an environmental region handled by classical mechanics or lower precision. In energy barrier calculations for localized clusters in transition metal oxides, quantum embedding strategies are used to accurately describe the electronic behavior of local events while controlling computational costs. The strategy couples the two regions by embedding a potential field or boundary conditions, ensuring continuity of electron density and energy. Common implementations include density embedding theory and hybrid quantum mechanics / molecular mechanics approaches, where the active region uses high-precision quantum chemical calculations, and the environmental region uses force fields or electron density projections. Quantum embedding strategies effectively handle strongly correlated effects and boundary problems, providing a physical basis for determining the active space. The active space of a localized cluster refers to a set of molecular orbitals selected in quantum variational calculations to approximate the key electronic degrees of freedom of the cluster. The active space typically contains orbitals near the highest occupied molecular orbital and the lowest unoccupied molecular orbital, as well as specific orbitals involved in microscopic events, such as d orbitals in transition metals or p orbitals in oxygen. Determining the active space is based on electronic structure calculations and energy ordering, aiming to capture dominant chemical behavior with fewer orbitals. The size and composition of the active space affect computational accuracy and resource requirements. In transition metal oxides, the active space prioritizes strongly correlated orbitals to reduce performance bias.

[0034] Specifically, based on the active space and electronic integral, the electronic Hamiltonian of the local cluster is constructed through second quantization, and a measurable Pauli operator term representation is generated through fermion-qubit mapping and symmetry transformation. The specific implementation process is as follows: Based on the established active space and the calculated electronic integral, the electronic Hamiltonian of the local cluster is constructed through second-order quantization. The active space provides a set of selected molecular orbitals as basis functions, while the electronic integral contains the interaction parameters between these orbitals. The second-order quantization form expresses the electronic Hamiltonian as a combination of production and annihilation operators. Specifically, the electronic Hamiltonian is written as: in, It is a single-electron integral matrix element that describes the electron's orbital position. and The single-particle energy between them; It is a two-electron integral matrix element that describes the orbital Electron-electron interactions between them; and They are the orbits The fermion generation and annihilation operators are used. The operator expression is automatically constructed and regularly ordered to ensure numerical stability. During construction, the orbital ordering and spin degrees of freedom in the active space are considered. Typically, restricted basis sets are used for closed-shell states, or unrestricted basis sets are used for open-shell states to accurately describe the electronic states of transition metal oxides.

[0035] Mapping fermion Hamiltonians to qubit Hamiltonians is called fermion-qubit mapping. Standard mapping methods are used, such as the Jordan-Wigner transform or the Bravyi-Kitaev transform. The Jordan-Wigner transform maps each fermion mode to a qubit and introduces a chain operator to maintain anti-commutation relations: in, It is the first Pauli operators on qubits. The Bravyi-Kitaev transform reduces nonlocal correlations between qubits through more complex algebraic relations, typically producing sparser Hamiltonian representations. The mapping method is automatically selected based on the size of the active space and hardware constraints; for example, the Bravyi-Kitaev transform is preferred for larger active spaces to reduce the number of Pauli terms.

[0036] Then, a symmetry transformation is performed on the mapped qubit Hamiltonian, specifically by using tapering techniques to simplify the Hamiltonian using conserved quantities. First, the symmetries of the Hamiltonian are identified, such as particle number conservation, spin symmetry, or point group symmetry. For each symmetry, the corresponding set of Pauli operators is found, and these symmetries are converted into additional Z operator constraints using Klein transformations or similar methods. In practice, symmetry generators are constructed, and a set of reciprocal Pauli operators is selected as a new basis, such that the Hamiltonian exhibits a block diagonal form under these bases. For example, for particle number conservation, the Hamiltonian can be simplified by eliminating two qubits through transformation: in, It is a simplified Pauli operator tensor product. These are the corresponding coefficients. This step significantly reduces the number of qubits and the complexity of the Pauli terms.

[0037] Generate measurable Pauli operator terms, and the simplified Hamiltonian is represented as a linear combination of Pauli operators: Each of them It is the Pauli operator tensor product (e.g.) wait), The coefficients are real numbers. This refers to the number of terms. Pauli terms are grouped and rearranged to optimize measurement efficiency. Grouping is based on operator commutation relations: mutually commuting Pauli terms are grouped together so that terms in the same group can be measured in the quantum circuit via a single basis transformation. A graph coloring algorithm or a greedy algorithm is used to achieve efficient grouping, minimizing the total number of measurements. Finally, a list of grouped Pauli terms is output, including the coefficients, operator sequence, and measurement basis information for each term, providing standardized input for subsequent variational energy solutions.

[0038] Specifically, a quantum variational algorithm is used to solve the variational energy of the Pauli operator term representation to obtain the energy of the candidate micro-event in each configuration of the path. Based on the energy of the candidate micro-event in each configuration of the path, the reaction energy barrier and activation energy of the corresponding transition metal oxide material are calculated. The specific implementation process is as follows: The system receives the generated Pauli operator term representations, which are measurable forms of the electronic Hamiltonian in qubit form. Each Pauli operator term representation contains the grouped Pauli operator tensor product and its coefficients. Variational energy solutions are performed for each configuration along the reaction path of the candidate microscopic event. The reaction path consists of multiple discrete image configurations generated between the initial and final states using interpolation methods.

[0039] The implementation of the quantum variational algorithm comprises three main stages: construction of a parameterized quantum circuit, configuration of a classical optimizer, and calculation of the energy expectation value. The parameterized quantum circuit employs either a hardware-efficient circuit or a chemically based circuit such as UCCSD. Taking a hardware-efficient circuit as an example, the circuit consists of multiple layers of single-qubit rotation gates and two-qubit entangled gates, with the gate parameters forming an optimizable vector θ. The circuit output state is... Its energy expectation is estimated by measuring the Pauli term: The circuit is executed on a quantum processor or simulator, and multiple measurements are performed on each Pauli term in groups to obtain an estimate of the expected value.

[0040] Optimization algorithms such as L-BFGS or SPSA are configured to iteratively update parameters θ to minimize the energy E(θ). A convergence threshold is set for the optimization process; iteration stops when the energy change or gradient norm falls below a set value. This optimization process is executed independently for each path configuration, ultimately obtaining the ground-state energy estimate for that configuration. To improve accuracy, error mitigation techniques such as zero-noise extrapolation are employed, extrapolating measurement results under different noise levels to a noise-free energy value.

[0041] After obtaining the energies of candidate micro-events at each configuration along the path, the reaction barrier and activation energy are calculated. The reaction barrier is defined as the difference between the energy of the transition state configuration and the energy of the initial state configuration. in, Represents the transition state configuration energy. This represents the initial configuration energy. The activation energy is obtained by fitting energy barrier values ​​at multiple temperatures using Arrhenius analysis. The transition state positions in the energy profile are automatically identified, typically corresponding to the energy peaks, and verified by numerical differentiation.

[0042] Among them, quantum variational algorithms are a class of quantum-classical hybrid algorithms that work in conjunction with parameterized quantum circuits and classical optimizers. The core of the algorithm is to construct a parameterized quantum circuit to prepare a trial wavefunction, obtain the expected energy value through measurement, and use a classical optimizer to adjust the parameters to find the ground state energy. In the calculation of energy barriers of local clusters in transition metal oxides, quantum variational algorithms are used to solve for the ground state energy of the electron Hamiltonian, effectively handling strong correlations and adapting to current noisy quantum hardware. Common implementations include variational quantum eigenvalue solvers and adaptive variational algorithms, which obtain chemically accurate energies with limited quantum resources through iterative optimization. The energy of a candidate micro-event at each configuration of the path refers to the electronic ground state energy corresponding to each image configuration in the micro-event reaction path. The reaction path describes the continuous change of atomic positions from the initial state through the transition state to the final state; each configuration is a specific atomic arrangement obtained by discretizing the path. The energy calculation is based on the electron Hamiltonian of the local cluster and is solved using a quantum variational algorithm. These energy values ​​constitute the energy profile of the reaction path, used to identify transition states and calculate energy barriers. They are key physical quantities that connect atomic-scale events with macroscopic material properties.

[0043] Specifically, the statistical uncertainty of the reaction energy barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event is quantified to obtain the statistical distribution of the reaction energy barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event. The specific implementation process is as follows: Sources of uncertainty in the reaction barrier calculation process are identified and collected. These sources include quantum measurement noise, finite sampling error, differences in active space selection, variations in embedding mode, and the sensitivity of the initial parameters of the classical optimizer. For each source of uncertainty, a corresponding sampling strategy is designed. For example, for quantum measurement noise, multiple independent energy estimates are obtained by increasing the number of measurements; for differences in active space selection, multiple reasonable active space variants are generated near the orbital energy window.

[0044] Then, a bootstrap sampling method is used to generate the statistical distribution of the reaction barrier. The specific steps are as follows: samples are randomly drawn with replacement from the original energy calculation data to form multiple bootstrap sample sets. Each bootstrap sample set contains energy estimates for each configuration along the path, and the reaction barrier is calculated based on these values. ,in, It is the reaction energy barrier of the b-th bootstrap sample set. and These are the energy estimates of the transition state and the initial state in the sample set, respectively. By repeating this process extensively (typically more than 1000 times), a sample set of reaction energy barriers is obtained. The statistical distribution of the reaction energy barrier is formed.

[0045] Then, the statistical distribution of the activation energy is derived based on the statistical distribution of the reaction barrier. The activation energy is obtained by fitting the reaction barrier at multiple temperatures using the Arrhenius relation. First, the above bootstrap sampling process is repeated under different temperature conditions to obtain the reaction barrier distribution at each temperature. For each bootstrap sample set b, linear regression is performed: in, It is the rate of degradation. It refers to the pre-factor. Let be the activation energy of the b-th sample set, R be the gas constant, and T be the absolute temperature. Fitting is performed using the least squares method. and The relationship is such that the slope is... Thus obtain Repeat this process for all bootstrap sample sets to obtain the sample set of activation energies. This leads to a statistical distribution of activation energy.

[0046] Finally, descriptive statistical analysis and interval estimation were performed on these two statistical distributions. The mean, variance, skewness, and kurtosis of the reaction barrier and activation energy distributions were calculated. Based on the sample distribution, 95% confidence intervals were constructed using the quantile method. in, and These are the 2.5% and 97.5% quantiles of the sample, respectively. The output provides complete statistical distribution characteristics and confidence intervals, offering probabilistic input for subsequent lifespan prediction.

[0047] The statistical distribution of the reaction barrier refers to the set of reaction barrier values ​​obtained through multiple independent calculations or samplings, exhibiting certain probability distribution characteristics. In the calculation of the barrier of localized clusters in transition metal oxides, the statistical distribution of the reaction barrier reflects the degree of influence of various error sources and sources of variation on the barrier estimation. This distribution is usually obtained through statistical methods such as bootstrapping and includes information such as the central tendency, dispersion, and shape characteristics of the reaction barrier. The statistical distribution of the reaction barrier provides a basis for quantifying uncertainty in barrier prediction, extending point estimation to probabilistic estimation and supporting more reliable engineering decisions. The statistical distribution of the activation energy refers to the probability distribution of the activation energy estimate obtained through statistical methods. In the study of transition metal oxide materials, the activation energy is usually obtained by fitting the reaction barrier at different temperatures to the Arrhenius relation. The statistical distribution of the activation energy considers the uncertainty of the reaction barrier and the variability of the fitting process, and is constructed through multiple sampling and fitting operations. This distribution characterizes the reliability and possible fluctuation range of the activation energy estimate, serving as an important bridge connecting microscopic barriers and macroscopic lifetime prediction, and providing probabilistic input for degradation rate modeling.

[0048] S3. Input the statistical distribution of the reaction barrier and activation energy of the transition metal oxide material corresponding to each candidate micro-event, along with the operating condition characteristics, into a degradation mapping model based on the Arrhenius rate kernel to generate the overall degradation rate and cycle life of the transition metal oxide material, and output the overall predicted range of the cycle life. Specifically: For each candidate micro-event, the statistical distributions of its reaction barrier and activation energy are read. These distributions are stored as a sample set containing multiple independent estimates of the barrier and activation energy. Simultaneously, operating condition characteristic parameters are obtained, including operating temperature, voltage window upper and lower limits, particle size distribution, and morphological descriptors. These input data are standardized to ensure dimensional uniformity and numerical stability. Then, a degradation mapping calculation based on the Arrhenius rate kernel is performed. The core of the degradation mapping model is to construct a multi-event coupled degradation rate equation. For each candidate micro-event i, based on its activation energy statistical distribution and reaction barrier statistical distribution, combined with the operating temperature T, the baseline degradation rate of that event is calculated: in, It is the degradation rate of candidate micro-event i in the b-th sample. This refers to the pre-factor, which is related to the reaction energy barrier. R is the activation energy of candidate micro-event i in the b-th sample, R is the gas constant, and T is the operating temperature.

[0049] Subsequently, a condition characteristic correction factor is introduced, and the voltage window correction is achieved by the difference between the window voltage and the material's steady-state potential: Where β is a material-dependent voltage sensitivity parameter, and V is the operating voltage. This is the reference voltage. Particle size correction is based on Oswald's ripening theory: Where D is the characteristic particle size, and γ is the size effect index. Morphology correction is quantified by the shape factor η.

[0050] The overall degradation rate is obtained by weighted summation of the rates of each event: Weighting factors The relative contribution of each micro-event to the overall degradation is determined through sensitivity analysis. After obtaining the sample distribution of the overall degradation rate, the cycle lifetime is calculated using a capacity decay model. The evolution of capacity retention over time is expressed as: in, Let m be the initial capacity and m be the time exponent factor. Solve for... The corresponding time , as the cycle lifetime estimate for the b-th sample.

[0051] Finally, an overall prediction interval is constructed based on the cycle lifetime estimates of all samples. This involves assembling the cycle lifetime sample set. Sort in ascending order, and use the 2.5% and 97.5% quantiles as the 95% prediction interval: It also outputs the statistical characteristics of the overall degradation rate and the distribution parameters of cycle life, providing complete prediction results for material design and cell applications.

[0052] Operating condition characteristics refer to the external operating conditions and internal structural parameters faced by transition metal oxide materials during actual use. These characteristics include the operating temperature range, charge / discharge voltage window, particle size distribution of active materials, and particle morphology. Operating condition characteristics directly affect the dynamic processes of microscopic events within the material and serve as a crucial bridge connecting the intrinsic properties of the material with its practical application performance. In lifetime prediction models, operating condition characteristics serve as important input parameters to correct theoretical predictions based on the intrinsic properties of the material, making them more consistent with real-world application scenarios. The degradation mapping model based on the Arrhenius rate kernel is a physics-driven mathematical model that links the energy barrier characteristics of microscopic events with macroscopic degradation behavior through the Arrhenius relation. The core of the model is the Arrhenius rate equation, which correlates activation energy and temperature with the reaction rate constant. In the cycle lifetime prediction of transition metal oxides, this model integrates the contributions of multiple microscopic events, considering the energy barrier distribution and operating conditions of each event, and obtains the overall degradation rate through weighted superposition. By introducing correction factors such as voltage, size, and morphology, the model makes the prediction results more reflective of the complex environment in real-world applications. The overall degradation rate is the combined performance decay rate of transition metal oxide materials under the combined effects of multiple micro-events. It is obtained by weighted summation of the degradation rates of each candidate micro-event, with the weights reflecting the relative importance of each event to the overall degradation. The overall degradation rate is a comprehensive indicator, incorporating the combined effects of the material's intrinsic properties and external operating conditions, directly determining the material's capacity decay rate and cycle life. In prediction models, the overall degradation rate is expressed in statistical distribution form, reflecting the uncertainty of the prediction results. The overall prediction range of cycle life is the fluctuation range of the cycle life estimate obtained based on statistical methods. The prediction range considers multiple sources of uncertainty, including uncertainties in the reaction barrier and activation energy, variability in operating conditions, and model errors. It is usually expressed in confidence interval form; for example, a 95% prediction interval indicates a 95% confidence that the actual cycle life falls within this range. The prediction range provides a basis for risk assessment in engineering applications, supporting risk-based decision-making and robust optimization design.

[0053] S4. Based on the overall prediction interval of cycle lifetime, identify key micro-events, use them as candidate micro-events in S2, and return to execute S2 to calculate the final reaction energy barrier and final cycle lifetime.

[0054] Based on the overall prediction interval of cycle lifetime, and aiming to minimize the variance of cycle lifetime, a dynamic selection criterion based on the reduction of expected variance is used to identify key micro-events from multiple candidate micro-events, thus achieving optimized allocation of computational resources. This technique, by quantitatively analyzing the contribution of each candidate micro-event to lifetime uncertainty, prioritizes the event with the largest reduction in expected variance for refined calculation. This dynamic screening method effectively identifies the micro-events with the most significant impact on lifetime prediction, avoiding redundant calculations for secondary events. Under limited computational budgets, this strategy accelerates the convergence process between lifetime prediction results and confidence intervals, improving prediction efficiency. Simultaneously, by iteratively optimizing the energy barrier calculation accuracy of key micro-events, the uncertainty of lifetime prediction is continuously reduced, enhancing the reliability and engineering applicability of the entire prediction system and providing more accurate guidance for material design and cell development. The variance of cycle lifetime refers to the statistical dispersion of the predicted cycle lifetime values ​​of transition metal oxide materials calculated based on quantum variational algorithms, reflecting the range of uncertainty in the lifetime prediction results. This variance originates from multiple uncertainties, including quantum measurement noise, finite sampling error, differences in active space selection, and fluctuations in operating conditions. It is quantified through bootstrapping and statistical modeling. The variance of cycle lifetime serves as the optimization objective in the active learning process. Minimizing this variance guides the selection and calculation of key micro-events, improves the stability and engineering applicability of the lifetime prediction model, and provides a reliable confidence boundary assessment for materials design and cell development.

[0055] The specific implementation process of S4 is as follows: During initialization, the statistical distributions of the reaction barriers and activation energies of the transition metal oxide materials corresponding to each candidate micro-event have been obtained through the aforementioned steps, along with the overall prediction interval of the cycle life generated based on these distributions and operating condition characteristics. The overall prediction interval of the cycle life is represented in the form of a statistical distribution, such as a 95% confidence interval, and the variance of the cycle life is calculated as the current uncertainty measure. The iterative optimization objective is set to minimize the variance of the cycle life, and stopping conditions are configured, including a variance threshold (e.g., the cycle life variance is no greater than 5% to 10% of the estimated life), a continuous iteration variance reduction threshold (e.g., less than 2%), and a maximum number of iterations (e.g., 5 to 10 rounds). First, a dynamic selection criterion based on the expected variance reduction is used to evaluate the potential impact of each candidate micro-event on the cycle life variance. For each candidate micro-event, the statistical distribution of its reaction barrier is extracted, including the barrier mean and variance. Then, sensitivity analysis is used to estimate the sensitivity of the cycle life to changes in the barrier of this event. In specific implementation, the barrier of candidate micro-event i is perturbed, for example, by introducing a small deviation in the barrier distribution, and the cycle life index is recalculated. The perturbation method is based on the standard deviation of the energy barrier distribution, for example, setting the perturbation amplitude to... ,in It is a scaling factor (e.g., 0.1 to 0.5). This represents the standard deviation of the energy barrier distribution for candidate micro-event i. Multiple Monte Carlo samplings are performed, adjusting the energy barrier value of candidate micro-event i in each sampling while keeping the energy barriers of other events constant. The degradation mapping model is then rerun to generate a new cycle lifetime distribution. The sensitivity of cycle lifetime to the energy barrier of candidate micro-event i is then expressed. The approximate calculation is performed using the ratio of the change in lifetime to the change in energy barrier: in, This represents the sensitivity of cycle lifetime to changes in the energy barrier of candidate micro-event i. This represents the mean change in cycle life. This represents the magnitude of the perturbation to the energy barrier of candidate micro-event i. Sensitivity The larger the value, the more significant the impact of the energy barrier fluctuations of candidate micro-event i on lifetime prediction.

[0056] Calculate the expected variance reduction for each candidate microevent. The expected variance reduction is defined as the reduction in lifetime variance that may result from refining the current event's energy barrier variance. Refining refers to reducing the variance of the event's energy barrier by increasing the number of measurements using the quantum variational algorithm, re-optimizing the path, or employing a more precise embedding strategy. Assume that the energy barrier variance of candidate microevent i can be reduced from the current... Reduce to Then the expected reduction in lifetime variance The estimate is: ,in, This represents the expected decrease in variance of candidate micro-event i. This represents the sensitivity of cycle lifetime to changes in the energy barrier of candidate micro-event i. This represents the current energy barrier variance of candidate micro-event i. Let represent the energy barrier variance after refinement of candidate micro-event i. Estimates based on historical data or theoretical models, such as by analyzing the relationship between the number of measurements and variance, assuming that variance is inversely proportional to the number of measurements. ,in To increase the proportion of measurements. Calculate for all candidate micro-events. Values, and sort them for selection. The biggest events are considered key micro-events.

[0057] When identifying key micro-events, the following conditions must be met: ① Key micro-events must have a high expected variance reduction. , usually choose The events that rank first or among the top few in value. ② The energy barrier variance of key micro-events. It needs to exceed the set threshold to ensure that the refinement operation is meaningful. ③ The absolute value of the lifetime sensitivity to key micro-events. The number of key micro-events must be significantly greater than other events; events with negligible impact on lifetime should be avoided. ④ The number of key micro-events is limited by the computational budget; typically, one to two events are selected per iteration to ensure sufficient refinement.

[0058] After identifying the key micro-events, these events are selected as candidate micro-events in step S2, and the process returns to step S2. In step S2, the key micro-events undergo a second round of local cluster extraction, end-face passivation, quantum embedding strategy to determine the active space and electron integral, construction of the electron Hamiltonian, variational energy calculation, and quantization of the energy barrier statistical uncertainty. Refinement operations include increasing the number of measurements in the variational quantum eigenvalue solver to improve energy estimation accuracy, or re-optimizing the path image to more accurately capture transition states. After refinement, the statistical distributions of the reaction energy barrier and activation energy of the key micro-events are updated. Subsequently, the degradation mapping model is rerun based on the updated energy barrier distribution to generate a new overall cycle lifetime prediction interval and calculate the new cycle lifetime variance. The iteration stopping condition is then checked. ① If the cycle lifetime variance decreases to a set threshold (e.g., variance not exceeding 5% of the estimated lifetime), the iteration stops. ② If the decrease in cycle lifetime variance is less than 2% in two consecutive iterations, the iteration stops. ③ If the maximum number of iterations is reached (e.g., 10 iterations), the iteration stops.

[0059] Otherwise, continue to the next iteration, recalculate the expected variance reduction, and identify new critical micro-events. After iteration, output the final reaction barrier and final cycle lifetime. The final reaction barrier is obtained by integrating the refined critical micro-event barrier distributions, and the final cycle lifetime is taken from the mean of the cycle lifetime distribution of the last iteration, along with the converged prediction interval. Through this process, under limited computational resources, the micro-events that contribute the most to lifetime uncertainty are prioritized, effectively reducing prediction variance and improving the reliability of the results.

[0060] The final reaction barrier refers to the statistical distribution of the reaction barrier obtained by the system after multiple rounds of iterative optimization based on a dynamic selection criterion of reduced expected variance, which refines the calculation of key micro-events. This result integrates the barrier distribution characteristics of all key micro-events, including the average value, variance, and confidence interval of events such as lithium-ion migration, transition metal migration, or oxygen vacancy migration. The final reaction barrier is obtained by solving the energies of each path configuration using a quantum variational algorithm, and after uncertainty quantification and active learning optimization, it has a clear statistical confidence boundary and can accurately reflect the energy characteristics of micro-events in strongly correlated systems of transition metal oxide materials, providing reliable mechanistic parameters for material design and performance evaluation. The final cycle lifetime refers to the range of cycles in which the capacity of a transition metal oxide material decays to 80% of its rated value, predicted by an Arrhenius-type degradation mapping model based on the refined statistical distribution of the reaction barrier and operating conditions. This lifetime index gradually converges through multiple rounds of iterative optimization, fully considering multiple influencing factors such as the uncertainty of the barrier distribution, temperature, voltage window, particle size, and morphology, and outputs a lifetime prediction result with a confidence interval. Ultimate cycle lifetime enables an end-to-end mapping from quantum-level energy barrier calculations to macroscopic performance, providing directly applicable engineering metrics for cell design, material selection, and usage strategy formulation.

[0061] Although the steps have been numbered in the above embodiments, they are only specific embodiments given by the present invention. Those skilled in the art can adjust the execution order of the steps according to the actual situation, which is also within the protection scope of the present invention. It can be understood that some embodiments may include some or all of the above embodiments.

[0062] like Figure 2As shown, an embodiment of the present invention provides a system 200 for calculating the local cluster energy barrier and predicting the cycle lifetime of a transition metal oxide, comprising an event determination module 201, a statistical distribution determination module 202, a calculation module 203, and an iteration determination module 204. The event determination module 201 is used to determine multiple candidate micro-events of the transition metal oxide material. The statistical distribution determination module 202 is used to: for any candidate micro-event, extract the corresponding local cluster within a preset radius, centered on the atomic position involved in the candidate micro-event, perform end passivation treatment on the bond-breaking positions of the local cluster, and, based on the passivated local cluster, determine the active space and electron integral of the local cluster using a quantum embedding strategy; and, based on the active space and electron integral, obtain the reaction of the transition metal oxide material corresponding to the candidate micro-event. The statistical distribution of the energy barrier and the statistical distribution of the activation energy are obtained until the statistical distribution of the reaction energy barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event are obtained; the calculation module 203 is used to: input the statistical distribution of the reaction energy barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event, together with the operating condition characteristics, into the degradation mapping model based on the Arrhenius rate kernel, generate the overall degradation rate and cycle life of the transition metal oxide material, and output the overall prediction range of the cycle life; the iterative determination module 204 is used to: determine the key micro-events based on the overall prediction range of the cycle life, take the key micro-events as candidate micro-events, and repeatedly call the statistical distribution determination module 202 and the calculation module 203 to calculate the final reaction energy barrier and the final cycle life.

[0063] Optionally, in the above technical solution, the statistical distribution determination module 202 is further specifically used for: constructing the electronic Hamiltonian of the local cluster through secondary quantization based on the active space and electronic integral, generating a measurable Pauli operator term representation through fermion-qubit mapping and symmetry transformation, solving the variational energy of the Pauli operator term representation using a quantum variational algorithm to obtain the energy of the candidate micro-event in each configuration of the path, and calculating the reaction barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event based on the energy of the candidate micro-event in each configuration of the path; quantifying the statistical uncertainty of the reaction barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event to obtain the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event.

[0064] Optionally, in the above technical solution, the event determination module 201 is specifically used to: import the crystal structure file of the transition metal oxide material, and define multiple candidate micro-events based on the crystal structure file. The multiple candidate micro-events include at least two micro-event types among ion migration, transition metal migration, oxygen vacancy generation, or oxygen vacancy migration.

[0065] Optionally, in the above technical solution, the iterative determination module 204 is further specifically used to: determine key micro events from multiple candidate micro events based on the overall prediction interval of cycle lifetime, with the goal of minimizing the variance of cycle lifetime, using a dynamic selection criterion based on the reduction of expected variance.

[0066] In another embodiment, the system of the present invention includes: a structure and event definition module, a local cluster extraction and embedding module, a Hamiltonian and measurement generation module, a variational energy and path solving module, an optimization and error mitigation module, an energy barrier statistics and uncertainty module, a physical property lifetime prediction module, a database and active learning module, and a visualization and interface module. The structure and event definition module is responsible for importing crystal structure files of transition metal oxide materials, including standard crystallography files such as CIF and POSCAR formats. The module parses the lattice parameters, atomic coordinates, atom types, and symmetry information in these files to construct a complete three-dimensional crystal structure model. Based on the constructed crystal structure, the module identifies multiple candidate micro-events, including different types such as lithium-ion migration, sodium-ion migration, transition metal migration, oxygen vacancy migration, and oxygen vacancy generation. The module automatically identifies possible event sites in the crystal, analyzes them according to crystallographic rules and material databases, and generates a structured list of candidate micro-events. Each candidate micro-event explicitly specifies the event type, the atoms or sites involved, and possible initial and final states, providing a complete input definition for subsequent local cluster extraction and energy barrier calculations.

[0067] The local cluster extraction and embedding module extracts a corresponding local cluster within a preset radius of 6-12 Å for each candidate micro-event, centered on the atomic positions involved in the event. The extracted local cluster comprises a principal region and an environmental region. The principal region consists of atoms directly involved in the micro-event, while the environmental region consists of surrounding atoms to provide the necessary electrostatic and structural background. The module performs end passivation treatment on the bond-breaking positions of the local cluster using hydrogen atom addition, and eliminates boundary spurious effects by adding hydrogen atoms to saturate the valence states of boundary atoms. The module supports a hybrid quantum mechanical / molecular mechanical approach and density embedding strategy, determining the active space and electronic integral of the local cluster through self-consistent calculations. The embedding process divides the local cluster into an active region and an environmental region. The active region is characterized using ab initio electronic structure, while the environmental region is treated with a classical potential. The two regions are compatible at the boundary through constraint and potential energy coupling terms, preparing for the construction of the electronic Hamiltonian.

[0068] The Hamiltonian and measurement generation module is used to construct the electronic Hamiltonian of the local cluster through second-order quantization, based on a defined active space and calculated electronic integrals. The electronic Hamiltonian is represented as a combination of the generation and annihilation operators: in, It is a single-electron integral matrix element. It is a two-electron integral matrix element. The construction process uses Jordan-Wigner transform or Bravyi-Kitaev transform to realize fermion-qubit mapping, and utilizes symmetries such as particle number conservation for tapering dimensionality reduction. The module automatically merges and rearranges Pauli terms, performs grouping optimization based on operator commutation relations, and generates Hamiltonian representations that can be measured on quantum circuits, reducing the number of coherent measurement rounds of observables and improving computational efficiency.

[0069] The variational energy and path solving module calculates the energy of the Hamiltonian using a variational quantum eigenvalue solver. The quantum circuit employs parametric quantum circuits such as unitary coupled clusters with single and dual excitations, adaptive variational quantum eigenvalue solvers, or high-efficiency hardware circuits. For each configuration on the reaction path, the module independently performs variational energy solving, constructs a parametric quantum circuit, and iterates in a closed loop with a classical optimizer until energy convergence or a preset threshold is met. Path solving considers multiple discrete image points, including initial, transition, and final states, and constructs a complete energy profile by stitching together the variational energies of each image. The full path energy profile, composed of the variational energies of each configuration, is used to identify transition state locations and calculate the reaction energy barrier.

[0070] The optimization and error mitigation module offers a choice of algorithms such as L-BFGS, BFGS, and SPSA through classic optimizers to optimize the parameters of variable quantum circuits. The optimization process uses a hierarchical convergence criterion, automatically switching optimization strategies when the energy descent rate or gradient norm reaches a threshold. Noise mitigation employs techniques such as zero-noise extrapolation, extrapolating noise-free energy values ​​from measurements at multiple noise levels. The module dynamically adjusts the optimization strategy based on the convergence criterion, configuring higher sampling numbers for critical structures to ensure the stability and accuracy of the energy solution.

[0071] The barrier statistics and uncertainty module performs bootstrapping sampling for different initial values, embedding methods, and activity space selections, generating multiple independent barrier estimates. Based on the sample set of barrier differences, the module calculates the mean and variance, and constructs a 95% confidence interval. The statistical process uniformly considers sources of uncertainty such as quantum measurement noise, finite sampling, and model selection, forming a sample distribution of the barrier difference ΔE through multiple initial values, multiple sampling, and the bootstrapping method. This distribution-level result is passed to the subsequent lifetime model in the form of a random variable, providing a reliable barrier prediction interval.

[0072] The physical property lifetime prediction module employs an Arrhenius-type kernel function model, mapping the energy barrier distribution and operating condition characteristics to degradation rates and lifetime indices. Input features include operating temperature, voltage window, particle size, and morphology parameters. The model generates the capacity retention curve of the electrochemical system, obtains the lifetime index by solving for the lifetime point when the capacity decays to 80% of the rated value, and provides the corresponding lifetime range to reflect model uncertainty. The kernel function uses an Arrhenius-type temperature-dependent kernel and incorporates inputs such as voltage window and particle size morphology to characterize the hazard rate of major failure pathways.

[0073] The database and active learning module establish a four-dimensional database of materials, defects, energy barriers, and lifetimes to store all calculation and prediction results. Based on the expected improvement benefits, the module designs a sampling strategy aimed at reducing lifetime prediction variance or increasing expected improvement, prioritizing clusters and events that contribute the most to lifetime uncertainty for the next round of quantum solution and model update. Through a cycle of sampling, calculation, update, and resampling, an efficient iterative learning mechanism is formed, enabling lifetime predictions and their confidence intervals to converge quickly, avoiding redundant calculations on clusters with limited contributions.

[0074] The visualization and interface module provides visualization capabilities for path energy profiles, density of states, and potential surfaces. It supports exporting traceable reports containing raw parameters and environmental conditions, as well as a Python application programming interface, facilitating result analysis and system integration. Visualizations include energy barrier distribution and its confidence interval, capacity retention curves, and lifetime point intervals, helping users understand prediction results and make horizontal comparisons and trade-offs between different material or operating condition schemes.

[0075] The specific work steps are as follows: ① Local Cluster Construction: Initial values ​​for candidate paths are generated based on the target microscopic event, and key chemical structures along the path are selected. Local clusters are extracted within a given radius, and the edge environment is passivated. The construction process ensures that the local clusters accurately reflect the local environment of the microscopic event while controlling the computational scale. Local cluster construction includes specific operations such as generating initial values ​​for candidate paths based on the target event, extracting clusters within a given radius, and passivating the edge environment. ② Determination of Quantum Hamiltonian and Active Space: The active orbital set is determined by the energy levels near the highest occupied orbital and the lowest unoccupied orbital. The electronic Hamiltonian is constructed through secondary quantization, and the qubit Hamiltonian is obtained through fermion-qubit mapping and symmetry transformation. Pauli terms are grouped and measured to optimize the Hamiltonian, reducing quantum resource requirements. Specifically, this includes determining the active orbital set from the lowest unoccupied orbital to the energy levels near the highest occupied orbital; performing secondary quantization, fermion-qubit mapping, and symmetry transformation to obtain the Hamiltonian; and grouping and measuring the Hamiltonian through Pauli terms. ③ Variational-Path Joint Solution: Using variational circuits, including unitary coupled clusters with single and double excitations, optimization algorithms are employed. Zero-noise extrapolation and other measurement error correction methods are used for the structure of each path to obtain the energy of all structures within the path. The overall change of the path is studied, and indicators such as the transition state energy are obtained. For each structure in the path, a parameterized quantum circuit is constructed and iterated in a closed loop with a classical optimizer until energy convergence or a preset threshold is met. ④ Uncertainty Assessment: The mean, variance, and 95% confidence interval of the energy barrier difference are output. After obtaining the energy of each structure in the path, the calculated energy barrier difference ΔE is affected by various factors such as quantum measurement noise, finite sampling numbers, and noise mitigation residuals, exhibiting statistically fluctuating random variables. The assessment process involves multiple independent experimental runs and repeated measurements to collect a sample set of energy barrier differences. The mean and variance are calculated to reflect the central tendency and fluctuation amplitude of the results. Based on statistical assumptions, a 95% confidence interval is constructed to characterize the reliability of the true energy barrier difference within this interval. ⑤ Lifetime Prediction: Based on energy barrier characteristics and operating conditions, a kernel function for the degradation process is constructed and embedded into a lifetime prediction hazard rate model. This model generates a capacity retention curve for the electrochemical system, identifying the lifetime point where capacity decays to approximately 80%. A range is provided for this lifetime point to reflect the uncertainty of the prediction results. The lifetime prediction process couples the energy barrier distribution and operating conditions to a mechanism-based degradation kernel function, generating the overall degradation rate and cycle lifetime. ⑥ Continued Learning and Iterative Learning: Based on the lifetime prediction results, uncertainty and sensitivity analyses are performed on the energy barrier and operating conditions to identify which clusters or events contribute most to lifetime estimation. Based on this determination, relevant cluster structures or key evolutionary events are preferentially selected from candidate paths for the next round of quantum energy calculation and modeling updates.In this way, the prediction model is dynamically revised after each round of calculation, allowing the capacity maintenance curve and lifetime point estimate to gradually converge, reducing redundant calculations and improving the reliability and stability of the prediction. Ultimately, this forms a data-driven, iterative learning mechanism that improves lifetime prediction accuracy while ensuring computational efficiency.

[0076] To facilitate a thorough understanding and implementation of this invention, a practical and readily applicable implementation scheme is provided below. This scheme is suitable for calculating energy barriers and predicting cycle lifetimes for microscopic events such as ion migration, transition metal displacement, and oxygen vacancy generation or migration in various transition metal oxide systems, including layered, spinel, or rock salt phases. To ensure engineering usability, the implementation process considers computational scale, noise mitigation, and the output of result confidence boundaries, and provides data interfaces to support material and cell design iterations. In terms of system deployment, the computing platform adopts a quantum-classical hybrid architecture. The classical computing side is configured with a structure preprocessing and molecular embedding module, a Hamiltonian generation and grouping module, an optimizer, and an uncertainty assessment module; the quantum computing side connects to a superconducting quantum processor or a noisy medium-scale quantum device such as an ion trap, or its high-fidelity simulator to execute variable quantum circuits. To adapt to different quantum hardware, the variational circuit library includes unitary coupled cluster single and double excitation circuits, adaptive variable quantum eigenvalue solver circuits, and hardware-efficient circuits. The classical optimizer covers the L-BFGS algorithm, the BFGS algorithm, and the SPSA algorithm, and error mitigation provides zero-noise extrapolation and readout calibration methods. The system establishes and maintains a four-dimensional database of material defect barrier lifetimes, storing all calculation process and result data. In the structure and event definition stage, crystallographic files such as CIF or POSCAR files of the target transition metal oxide material are imported into the system, and candidate microscopic events and initial values ​​of reaction pathways are determined based on the research objectives. For layered cathode materials, lithium-ion or sodium-ion migration events between octahedral tetrahedral sites are defined; for spinel or rock salt phase structures, displacement events of transition metals between octahedral tetrahedrons, or migration events of oxygen vacancies between adjacent coordination polyhedra, are defined. The system automatically generates a list of candidate microscopic events, ensuring that at least two types of microscopic events are included. In the local cluster extraction and embedding stage, the main region and surrounding region are extracted with a preferred radius of 6 to 12 Å, centered on the atomic positions involved in the candidate microscopic events, and the broken chemical bonds are passivated by hydrogenation and other end-passivation treatments to eliminate boundary spurious effects. For an accurate description of the impact of the electrochemical environment, a hybrid quantum mechanical-molecular mechanical approach or a density embedding strategy is employed: the active region is characterized using ab initio electronic structure methods, while the environmental region is treated with classical potential functions; the electron density continuity between the two regions is achieved at the boundary through constraint conditions and potential energy coupling terms. This stage outputs the candidate orbital set, electron integral, and boundary condition parameters for the active space. In the quantum Hamiltonian construction stage, several pairs of molecular orbitals close to the highest occupied orbital and the lowest unoccupied orbital are first selected as the active space based on the self-consistent field reference state. Freezing of the kernel and orbital selection are then performed based on charge conservation, spin symmetry, and point group symmetry to control the required number of qubits while ensuring computational accuracy. Subsequently, a second quantization process is performed, converting the electronic Hamiltonian into a qubit operator through the Jordan-Wigner transform or Bravyi-Kitaev mapping, and tapering dimensionality reduction operations are performed using symmetries such as particle number conservation.To reduce quantum measurement overhead, Pauli terms are optimized through grouping and rearrangement to decrease the number of coherent measurement rounds for observables. In the joint solution stage of variational energy and path, for each configuration image in the reaction path, a parameterized quantum circuit is constructed and iterated in a closed loop with a classical optimizer until energy convergence or a preset threshold is met. For transition metal-oxide systems with strong electron correlation, an adaptive variational quantum eigenvalue solver is preferred to construct a compact quantum circuit with a progressively increasing operator pool; for larger systems sensitive to quantum gate depth, a hardware-efficient circuit is used to adapt to practical quantum devices. The full-path energy profile is stitched together from the variational energy results of each image. To suppress the amplification effect of quantum hardware noise on energy differences, a zero-noise extrapolation technique is introduced in the measurement stage, and a higher sampling number is configured for key structures near the transition state. In the energy barrier statistics and uncertainty quantification stage, sources of uncertainty such as quantum measurement noise, finite sampling error, and the choice of active space or embedding mode are uniformly incorporated into the statistical framework. A sample distribution of the energy barrier difference ΔE is generated using multiple initial values, multiple sampling times, and a bootstrap method. The mean and variance are calculated, and a 95% confidence interval is given. This distribution-level result is passed to the subsequent lifetime prediction model as a random variable, ensuring that engineering decisions not only rely on point estimates but also have clear confidence boundaries. In the lifetime prediction stage, the energy barrier distribution and operating condition characteristic parameters are coupled to a mechanism-based degradation kernel function. The kernel function adopts an Arrhenius-type temperature dependence and incorporates inputs such as voltage windows, particle size, and morphological features to characterize the hazard rate function of the main failure paths. Subsequently, a capacity retention curve is generated at the system level, and the lifetime point at which the capacity decays to approximately 80% of the rated value is identified based on this curve. The corresponding lifetime interval is also output to reflect the model uncertainty. This curve can be used not only for lifetime prediction but also for cross-sectional comparison and engineering trade-offs between different material systems or operating condition schemes. In the closed-loop phase of active learning and database-driven learning, the width or variance of the aforementioned lifetime interval is used as the target metric to evaluate the marginal contribution of each candidate local cluster and micro-event to lifetime uncertainty. Cluster structures with the highest information gain are prioritized for the next round of quantum energy calculation and model update. A cyclical workflow of sampling, calculation, update, and resampling ensures rapid convergence between lifetime prediction and its confidence interval, avoiding redundant calculations on clusters with limited contribution to lifetime prediction. Structural parameters, energy barrier data, and lifetime results from all iterations are continuously integrated into the four-dimensional database, forming reusable data assets.

[0077] In a specific application scenario, the migration process of lithium ions between octahedral tetrahedral octahedral sites in layered transition metal oxide cathode materials is studied. First, local clusters are extracted within a radius of 8 to 10 Å based on crystallographic files and subjected to hydrogen passivation. A density embedding strategy is used to explicitly describe the active layer, with the nearest neighbor layer serving as the environmental region. Then, several orbitals near the Fermi level are selected to form the active space, and Bravyi-Kitaev mapping and symmetry tapering are performed for dimensionality reduction. Next, an adaptive variable quantum eigenvalue solver is used as the primary method, supplemented by unitary coupled cluster single and double excitations, to solve for the variational energy at 7 to 9 image points along the path. Zero-noise extrapolation and adaptive measurement number allocation are used to stabilize the energy estimate. Then, the mean, variance, and 95% confidence interval of the energy barrier difference are statistically output using the bootstrap method. Finally, under given operating temperature and voltage windows, capacity retention curves are generated, and lifetime points and lifetime ranges are given, providing quantitative basis for cathode material design optimization and cell operating window setting.

[0078] In another specific application scenario, the generation or migration process of oxygen vacancies in spinel or rock salt phase structures is taken as the research object. The same local cluster extraction and embedding process as described above is employed, but the coverage of transition metal d orbitals and oxygen p orbitals is appropriately expanded in the selection of the active space to enhance the accurate characterization of strong correlation effects and charge transfer features. After the energy path solution is completed, the energy barrier distribution superimposed with particle size and morphology factors is input into the degenerate kernel function to obtain a family of lifetime curves under different operating temperatures, rate performance, and upper voltage limits. These curves are used for multi-objective operating condition optimization and thermal management strategy formulation.

[0079] In terms of measurement overhead and noise co-control, the system prioritizes the commutative Pauli term clustering strategy when grouping Hamiltonian Pauli terms, and dynamically adjusts the number of samples with the estimated variance of each cluster as the weight. A higher measurement budget is configured for image points near the transition state, and multi-stretch factor extrapolation is performed with zero noise extrapolation to offset the system error dominated by decoherence. The classical optimizer sets a hierarchical convergence criterion, and automatically switches the optimization strategy when the energy descent rate or gradient norm reaches the threshold, so as to improve the overall convergence efficiency and numerical stability of the path.

[0080] In terms of visualization and result delivery, the system outputs path energy profiles, transition state configurations, energy barrier distributions and their confidence intervals, capacity retention curves and lifetime point intervals, and generates traceable reports containing original parameters and environmental conditions. The application programming interface supports batch calls to perform parallel evaluations of combinations of multiple material systems, multiple defect types, and multiple operating conditions, thereby completing candidate material screening and process window recommendations within a controllable computational budget.

[0081] The modules in this embodiment can be centrally deployed on the same workstation or computing cluster, or distributed across different hardware platforms after decoupling by functional modules. Substitutions to details such as the active space selection method, quantum mapping method, and circuit template design do not alter the core technical essence of this invention, which focuses on local cluster construction, quantum variational energy barrier solution, path energy calculation, lifetime mapping modeling, and active learning optimization. As long as the aforementioned statistical analysis and physical modeling chain is followed, energy barrier results with confidence boundaries can be obtained in strongly correlated transition metal oxide systems and robustly extrapolated to cycle lifetime prediction.

[0082] It should be noted that the above implementation scheme explicitly propagates the uncertainty of the energy barrier to the lifetime model in a distributed manner, solving the technical pain points of large energy barrier deviation, high computational cost, and difficulty in establishing an interpretable mapping relationship with battery cycle life in strongly correlated systems under the traditional DFT+NEB computation framework. Furthermore, through an active learning mechanism aimed at minimizing lifetime uncertainty and a four-dimensional database system, it achieves efficient convergence and scalable engineering applications under limited computational budgets. This implementation scheme can be directly applied to engineering scenarios such as new material screening, cell structure design, and usage strategy formulation. It can also be fused across modalities with existing experimental characterization data or other mechanistic simulation data to further improve prediction accuracy and result reliability.

[0083] This invention addresses the problems of large systematic biases and high computational costs in calculating transition states and energy barriers using traditional DFT+NEB methods in strongly correlated transition metal-oxide systems. It proposes an integrated "local cluster-quantum variational-path" energy barrier solution framework for strongly correlated systems. This framework focuses on microscopic events, truncating local clusters with radius R and passivating their ends. It then determines the active space using a hybrid quantum mechanical / molecular mechanical approach or density embedding strategy. Based on the active space and electron integral, a second-order quantized Hamiltonian is constructed, and measurable Pauli terms are generated through fermion-qubit mapping and symmetry tapering. Variational quantum eigenvalue solvers, adaptive variational quantum eigenvalue solvers, unitary coupled cluster single / double excitations, or efficient hardware circuits are used to solve for the energies of various path configurations in a quantum-classical hybrid loop. This framework achieves migration and phase transition energy barriers with chemical precision within a controllable computational scale, providing high-quality mechanistic parameters for subsequent lifetime modeling, while significantly reducing the resource cost of full-scale hypercell computation. Key protective elements include local cluster extraction and embedding strategies, mapping and tapering processes, and the combined implementation of variational circuit libraries. This invention addresses the problem that quantum measurement noise, finite sampling, embedding methods, and active space selection lead to uncertainties in the energy barrier difference ΔE, making it difficult to directly use for engineering decisions. This invention proposes an explicit quantification and propagation method for energy barrier statistics and uncertainty. This method generates a sample distribution of the energy barrier difference ΔE through bootstrapping, outputs the mean, variance, and 95% confidence interval of ΔE, and passes ΔE as a random variable to the subsequent lifetime prediction model. This method provides mechanistic parameters with confidence boundaries for engineering design, enhancing the reproducibility of calculation results and the reliability of engineering decisions. Key protective elements include the generation process of the ΔE confidence interval and its distribution-level input interface in subsequent lifetime modeling. This invention also addresses the problem that microscopic mechanism calculation results are difficult to extrapolate to cell cycle life and lack interpretable mapping relationships. This invention constructs a physical kernel function model from energy barrier distribution to cycle life. This model employs an Arrhenius-type kernel function to map energy barrier distribution, operating temperature T, voltage window, particle size, and morphological features to degradation rate k, and provides a lifetime prediction interval. This achieves end-to-end prediction from microscopic mechanisms to macroscopic performance, outputting a lifetime quantification index directly usable in engineering. Key protection points include the kernel function form, input feature set, and lifetime interval solution process. Addressing the problem of exponential growth in the combination of local clusters and reaction paths coupled with limited computational budget, this invention proposes an active learning and four-dimensional database system aimed at minimizing lifetime uncertainty. This system establishes a four-dimensional database of materials, defects, energy barriers, and lifetime, and designs a sampling strategy aimed at reducing lifetime prediction variance. It prioritizes clusters and events that contribute the most to lifetime uncertainty for the next round of quantum solution and model update, forming an iterative optimization mechanism. This accelerates the convergence speed of lifetime prediction results and their confidence intervals within a limited computational budget, reducing redundant computation.Key protective elements include the sampling objective function and workflow orchestration for lifetime uncertainty. This invention addresses the problem that quantum measurement costs and hardware noise jointly limit computational accuracy and efficiency. It proposes a coordinated control strategy for measurement overhead and noise. This strategy optimizes the grouping and rearrangement of the Hamiltonian Pauli terms, combining error mitigation techniques such as zero-noise extrapolation with the convergence criteria of classical optimizers to dynamically allocate the number of measurements for each Pauli term group. This improves the estimation accuracy of the energy-bar difference under a given number of samplings, supporting the stability of the upper-level lifetime prediction model. Key protective elements include the coupled scheduling strategy of Pauli term grouping-rearrangement and zero-noise extrapolation error mitigation in Hamiltonian measurement. This invention overcomes the shortcomings of traditional DFT+NEB methods in strongly correlated systems, such as large computational bias, high cost, and difficulty in extrapolating to lifetime prediction, by introducing a quantum variational algorithm to solve the energy barrier in transition metal oxide localized cluster systems and establishing a mapping relationship from microscopic mechanisms to cycle lifetimes using physical kernel functions. This system achieves near-chemically accurate energy barrier results within a controllable computational scale, and can quantitatively characterize and transfer its uncertainty, thus providing confidence boundaries for lifetime prediction and improving the repeatability and reliability of the results. Simultaneously, by dynamically selecting the clusters and events that contribute most to lifetime prediction, redundant calculations are reduced while ensuring computational efficiency, gradually converging the lifetime prediction curve and lifetime point estimate, continuously optimizing prediction performance. The invention integrates energy barrier calculation and electrochemical lifetime prediction for strongly correlated systems, offering advantages such as high accuracy, low cost, interpretability, and scalability, demonstrating clear engineering application value and promising prospects. This invention addresses the problems of large deviations, high costs, and difficulty in extrapolating to lifetime prediction in existing technologies for strongly correlated scenarios. The proposed integrated system and method of "local cluster construction, quantum variational energy barrier solution, physical modeling, and result acquisition" achieves near-chemically accurate energy barriers within a controllable computational scale, transforming energy barrier distribution into lifetime prediction and engineering-usable indicators, and providing data to guide material and cell design iterations.

[0084] It should be noted that the beneficial effects of the local cluster energy barrier calculation and cycle lifetime prediction system 200 for transition metal oxides provided in the above embodiments are the same as the beneficial effects of the local cluster energy barrier calculation and cycle lifetime prediction method for transition metal oxides provided in the above embodiments. In addition, the system and method embodiments provided in the above embodiments belong to the same concept, and the specific implementation process can be found in the method embodiments, which will not be repeated here.

[0085] An electronic device according to an embodiment of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for calculating the local cluster energy barrier and predicting the cycle lifetime of any of the above-mentioned transition metal oxides.

[0086] An embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method for calculating the local cluster energy barrier and predicting the cycle lifetime of any of the above-mentioned transition metal oxides.

[0087] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the energy barrier of local clusters of transition metal oxides and predicting the cycle life, characterized in that, include: S1. Identify multiple candidate micro-events for transition metal oxide materials; S2. For any candidate micro-event, take the atomic position involved in the candidate micro-event as the center, extract the corresponding local cluster within a preset radius, and passivate the end of the bond break position of the local cluster. Based on the passivated local cluster, use a quantum embedding strategy to determine the active space and electron integral of the local cluster. Based on the active space and the electron integral, obtain the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event, until the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event is obtained. S3. Input the statistical distribution of the reaction energy barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event, together with the operating condition characteristics, into the degradation mapping model based on the Arrhenius rate kernel to generate the overall degradation rate and cycle life of the transition metal oxide material, and output the overall prediction range of the cycle life. S4. Based on the overall prediction range of the cycle lifetime, determine the key micro events, use the key micro events as candidate micro events in S2, and return to execute S2 to calculate the final reaction energy barrier and the final cycle lifetime. Several candidate micro-events for transition metal oxide materials were identified, including: Import the crystal structure file of the transition metal oxide material, and define multiple candidate micro-events based on the crystal structure file. These candidate micro-events include at least two of the following types: ion migration, transition metal migration, oxygen vacancy generation, or oxygen vacancy migration. Based on the overall predicted range of the cycle lifetime, determine key micro-events, including: Based on the overall prediction range of the cycle lifetime, with the goal of minimizing the variance of the cycle lifetime, a dynamic selection criterion based on the reduction of expected variance is used to determine key micro-events from the multiple candidate micro-events.

2. The method for calculating the local cluster energy barrier and predicting the cycle lifetime of a transition metal oxide according to claim 1, characterized in that, Based on the active space and the electron integral, the statistical distribution of the reaction energy barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event are obtained, including: Based on the active space and the electronic integral, the electronic Hamiltonian of the local cluster is constructed through secondary quantization, and a measurable Pauli operator term representation is generated through fermion-qubit mapping and symmetry transformation. The variational energy of the Pauli operator term representation is solved using a quantum variational algorithm to obtain the energy of the candidate micro-event in each configuration of the path. Based on the energy of the candidate micro-event in each configuration of the path, the reaction barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event are calculated. The statistical uncertainty of the reaction barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event is quantified to obtain the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event.

3. A system for calculating local cluster energy barriers and predicting cycle lifetimes of transition metal oxides, characterized in that, It includes an event determination module, a statistical distribution determination module, a calculation module, and an iteration determination module; The event determination module is used to: determine multiple candidate micro-events of transition metal oxide materials; The statistical distribution determination module is used to: for any candidate micro-event, take the atomic position involved in the candidate micro-event as the center, extract the corresponding local cluster within a preset radius, passivate the end position of the bond break of the local cluster, and determine the active space and electronic integral of the local cluster based on the passivated local cluster using a quantum embedding strategy. Based on the active space and the electronic integral, obtain the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to the candidate micro-event, until the statistical distribution of the reaction barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event is obtained. The calculation module is used to: input the statistical distribution of the reaction energy barrier and the statistical distribution of the activation energy of the transition metal oxide material corresponding to each candidate micro-event, together with the operating condition characteristics, into a degradation mapping model based on the Arrhenius rate kernel, generate the overall degradation rate and cycle life of the transition metal oxide material, and output the overall prediction range of the cycle life. The iterative determination module is used to: determine key micro events based on the overall prediction interval of the cycle lifetime, take the key micro events as candidate micro events, and repeatedly call the statistical distribution determination module and the calculation module to calculate the final reaction energy barrier and the final cycle lifetime. The event determination module is specifically used to: import the crystal structure file of the transition metal oxide material, and define multiple candidate micro-events based on the crystal structure file. The multiple candidate micro-events include at least two of the following micro-event types: ion migration, transition metal migration, oxygen vacancy generation, or oxygen vacancy migration. The iterative determination module is further specifically used to: based on the overall prediction interval of the cycle lifetime, with the goal of minimizing the variance of the cycle lifetime, and using a dynamic selection criterion based on the reduction of expected variance to determine key micro-events from the multiple candidate micro-events.

4. The system for calculating local cluster energy barriers and predicting cycle lifetimes of transition metal oxides according to claim 3, characterized in that, The statistical distribution determination module is further specifically used for: constructing the electronic Hamiltonian of the local cluster through secondary quantization based on the active space and the electronic integral, generating a measurable Pauli operator term representation through fermion-qubit mapping and symmetry transformation, solving the variational energy of the Pauli operator term representation using a quantum variational algorithm to obtain the energy of the candidate micro-event in each configuration of the path, and calculating the reaction energy barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event based on the energy of the candidate micro-event in each configuration of the path; The statistical uncertainty of the reaction energy barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event is quantified to obtain the statistical distribution of the reaction energy barrier and activation energy of the transition metal oxide material corresponding to the candidate micro-event.

5. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method for calculating the local cluster energy barrier and predicting the cycle lifetime of a transition metal oxide as described in any one of claims 1 to 2.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method for calculating the local cluster energy barrier and predicting the cycle lifetime of a transition metal oxide as described in any one of claims 1 to 2.

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