Method for identifying ground state stacking configuration of atomically thin two-dimensional nanomaterials

Abstract

The application relates to a method for identifying a ground state stacking configuration of an atomic-scale double-layer two-dimensional nanomaterial, and belongs to the field of two-dimensional nanomaterials. The application aims to solve the problem of poor accuracy of the previous method for identifying the ground state configuration. The lattice mismatch rate of any two single-layer two-dimensional nanomaterials is calculated, and the two single layers with a large lattice mismatch rate are matched, then the lattice of the two matched single-layer two-dimensional nanomaterials is selected to obtain a slip distance, a slip angle and a layer spacing, each slip distance, slip angle and layer spacing form a complete stacking configuration, the repeated complete stacking configurations in the multiple complete stacking configurations are removed, then the remaining complete stacking configurations are subjected to geometric optimization processing, the total energy of each complete stacking configuration after optimization is calculated, the total energy of the multiple complete stacking configurations after optimization is sorted from low to high, and the first stacking configuration is selected as the ground state stacking configuration. The application is used for accurately identifying the ground state stacking configuration.

Description

Technical Field

[0001] This invention relates to the field of two-dimensional nanomaterials. Background Technology

[0002] In recent years, two-dimensional (2D) nanomaterials have shown great application potential in electronics, energy storage, catalysis, and sensors due to their atomic-level thickness and unique physicochemical properties. Among them, monolayer 2D nanomaterials, with their high electron mobility and excellent mechanical properties, have been widely used in nanoelectronics and flexible electronic devices. Due to the introduction of interlayer interactions (such as van der Waals forces, hydrogen bonds, and electrostatic interactions), multilayer 2D nanomaterials exhibit significantly richer physicochemical properties compared to monolayer materials, such as tunable band gaps, extended optical absorption, and higher charge mobility. These properties make multilayer 2D nanomaterials even more promising in multiple application areas. Theoretical research results indicate that insulating monolayer boron nitride (h-BN) is primarily used as the gate dielectric in high-performance electronic devices, such as graphene-based field-effect transistors (FETs). Multilayer h-BN, however, not only retains the insulating properties of a monolayer but also exhibits layer-dependent (2-5 layer structure) optical properties, making it applicable to optoelectronic devices such as photodetectors, light-emitting diodes (LEDs), and optical modulators. Furthermore, multilayer molybdenum disellerate (MoTe2) exhibits a temperature-induced structural phase transition not found in monolayers; its crystal structure transforms from a monoclinic phase (2H) to an orthorhombic phase (1T') at 200-250 K. This significantly enhanced light absorption and emission properties make it a promising candidate for applications in photodetectors, lasers, and phase-change memories. Therefore, theoretical research on multilayer two-dimensional nanomaterials has become a key direction driving the development of next-generation high-performance materials.

[0003] Stacking engineering is a crucial technique in the research of novel multilayer two-dimensional nanomaterials. By controlling the stacking angle, stacking order, and interlayer slip at the atomic scale, stacking engineering can significantly alter the interlayer interactions of two-dimensional nanomaterials, thereby enabling precise control over various properties such as electronic, optical, magnetic, and mechanical properties, facilitating their application in multiple fields. For example, in twisted bilayer graphene (TBG), a small change in the stacking angle (1.1°) can induce a superconducting phase transition; precise control of the interlayer stacking order of phosphorene (such as AA or AB configurations) allows for continuous control of its band gap (0.78-1.04 eV); and interlayer slip can induce the band gap of MoS2 from a direct band gap to an indirect band gap, improving its carrier mobility and making it valuable for flexible electronic devices. However, the stability of the stacking configuration is often overlooked. Clearly, unstable "theoretical atomic-scale two-dimensional nanomaterials," even with numerous superior properties, are difficult to apply practically. Therefore, exploring the ground-state configuration of multilayer materials is not only the core key to unlocking the intrinsic properties of materials, but also the key to unleashing their application potential.

[0004] However, accurately and efficiently identifying the most stable stacking configurations in multilayer two-dimensional nanomaterials remains a significant challenge. The diversity of stacking order and interlayer slip results in a vast stacking configuration space for two-dimensional nanomaterials, exceeding the processing capabilities of traditional manual stacking methods, thus limiting their further development in practical applications. Clearly, traditional methods are inefficient and struggle to meet the demands within such a vast configuration space. Therefore, developing efficient, reliable, and universal algorithmic tools to identify the most stable stacking configurations in multilayer two-dimensional nanomaterials is crucial for promoting their practical application. In fact, researchers have made some progress in the automated generation and stable configuration screening of van der Waals double-layer stacking configurations. Barik et al., based on 520 monolayer materials in the C2DB database, automatically generated 760 van der Waals double-layer stacking configurations (mainly considering...) by performing interlayer slip operations along the high-symmetry direction of the lattice (a lattice is a solid material in which atoms are arranged in a certain periodic pattern in space; this regular arrangement of atoms forms a certain spatial geometry). The study investigated the interlayer spacing and established a corresponding database for researchers. Pakdel et al. screened 1052 stable monolayer materials from the C2DB database. Using AA stacking as the initial configuration and atomic lateral displacement difference as the interlayer slip vector, they generated 8451 van der Waals bilayer stacking configurations by applying the slip vector to the top layer structure. Based on this, they identified 133 potential bistable bilayer candidate materials that can undergo state transitions under specific conditions such as electric fields, mechanical strain, or thermal activation, demonstrating application value in sliding electronics. Although the above research has made some progress in developing high-throughput computational workflows for two-dimensional nanomaterial stacking engineering, there is still a significant gap from an efficient and universally applicable automated workflow for stacking engineering. First, regarding interlayer spacing control, the above research only considered van der Waals interactions. Electrostatic interactions, hydrogen bonding, and other interlayer interactions are also significant for regulating the novel physicochemical properties of multilayer two-dimensional nanomaterials. Secondly, previous studies have failed to conduct a comprehensive search for stacking order and interlayer slip paths, resulting in stacked structures that may not be the ground-state configuration. Therefore, existing methods for identifying the ground-state configuration are inaccurate, necessitating the development of a highly efficient workflow capable of globally searching all possible stacking configurations and accurately identifying the ground-state stacking configuration. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of poor accuracy in previous methods for identifying ground state configurations, and to propose a method for identifying the ground state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials.

[0006] A method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials, the method comprising the following:

[0007] Step 1: Determine whether any two monolayer two-dimensional nanomaterials belong to the same crystal system. If not, proceed to Step 2; if yes, proceed to Step 3.

[0008] Step 2: Convert the crystal system of the two monolayer two-dimensional nanomaterials to the same crystal system, and then proceed to step 3;

[0009] Step 3: Each monolayer two-dimensional nanomaterial has a lattice with a side length along the x-axis and a side length along the y-axis. Based on the lattice side lengths of any two monolayer two-dimensional nanomaterials, calculate the lattice mismatch rate of the two monolayer two-dimensional nanomaterials. If the lattice mismatch rate is greater than a preset value, proceed to step 4; if the lattice mismatch rate is less than a preset value, proceed to step 5.

[0010] Step 4: Scale the lattice of the two monolayer two-dimensional nanomaterials so that the lattice mismatch rate of the two monolayer two-dimensional nanomaterials after scaling is less than a preset value, then proceed to step 5.

[0011] Step 5: Select the longest edge length from the four lattice edge lengths of the two monolayer two-dimensional nanomaterials as the maximum slip distance;

[0012] Step 6: Perform relative slipping of the two monolayer two-dimensional nanomaterial lattices with different angle and distance step sizes to obtain multiple slip stacking configurations. Select the slip angle step size and slip distance step size corresponding to the optimal slip stacking configuration from the multiple slip stacking configurations as the optimal slip angle step size and optimal slip distance step size, respectively. Select P times the optimal slip angle step size as candidate slip angles, and the candidate slip angles must be less than 360 degrees, P = 1, 2, 3...M, for a total of M candidate slip angles. Select F times the optimal slip distance step size as candidate slip distances, and the candidate slip distances must be less than the maximum slip. Given the distance condition F = 1, 2, 3...L, a total of L candidate slip distances are selected. One value is selected from each of the M candidate slip angles and L candidate slip distances to form a slip vector. Each monolayer two-dimensional nanomaterial has two surfaces, upper and lower. Two monolayer two-dimensional nanomaterials form four zero-slip stacking configurations. Each zero-slip stacking configuration is slipped according to each slip vector to obtain multiple slip stacking configurations. A Bayesian optimization algorithm is used to determine the optimal interlayer spacing between the two monolayer two-dimensional nanomaterials in each slip stacking configuration. All possible double-layer slip stacking configurations are generated based on each slip vector and the corresponding optimal interlayer spacing.

[0013] Step 7: Remove duplicate double-layer sliding stack configurations from multiple double-layer sliding stack configurations, and then perform geometric optimization on the remaining double-layer sliding stack configurations to obtain the total energy of each optimized double-layer sliding stack configuration. Sort the total energy of the multiple optimized double-layer sliding stack configurations from low to high, and select the first double-layer sliding stack configuration as the ground state stack configuration.

[0014] Preferably, in step 2, the crystal systems of the two monolayer two-dimensional nanomaterials are converted into the same crystal system. The specific process is as follows:

[0015] The crystal system of the monolayer two-dimensional nanomaterial with higher symmetry is taken as the target crystal system. The lattice basis vectors of the other monolayer two-dimensional nanomaterial are projected onto the Cartesian coordinate system to obtain an equivalent lattice. The equivalent lattice is transformed into a crystal system structure consistent with the target crystal system using the lattice reparameterization and rotation tensor method. The equivalent lattice is then mapped to the target crystal system. The mapped lattice belongs to the same crystal system as the other monolayer two-dimensional nanomaterial.

[0016] Preferably, in step 3, the lattice mismatch rate r m Represented as:

[0017]

[0018] In the formula, Max() is the maximum value function, Min() is the minimum value function, a1 and b1 are the side lengths of the lattice of a single-layer two-dimensional nanomaterial along the x-axis and y-axis, respectively, and a2 and b2 are the side lengths of the lattice of another single-layer two-dimensional nanomaterial along the x-axis and y-axis, respectively.

[0019] Preferably, in step 4, the process of scaling the lattice of the two single-layer two-dimensional nanomaterials is as follows:

[0020] Step 41, Supercell Expansion: Align the side lengths a1 along the x-axis and b1 along the y-axis of one monolayer two-dimensional nanomaterial lattice with the side lengths a2 along the x-axis and b2 along the y-axis of another monolayer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice composed of the maximum values ​​of a1 and a2 and b1 and b2. Align the side lengths a1 along the x-axis and b1 along the y-axis of one monolayer two-dimensional nanomaterial lattice with the side lengths b2 along the y-axis and a2 along the x-axis of another monolayer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice composed of the maximum values ​​of a1 and b2 and b1 and a2. Select the new lattice with the smallest area from the two new lattices as the candidate lattice. Perform cell expansion on the two monolayer two-dimensional nanomaterial lattices to obtain two expanded lattices, and both expanded lattices cover the area of ​​the candidate lattice.

[0021] Step 42, Periodicity Removal: Remove the periodicity in the x, y, and z directions from the two expanded lattices to obtain two non-periodic two-dimensional nanostructures;

[0022] Step 43, Crystal structure trimming: Using the candidate lattice size as the trimming frame, trim the two non-periodic two-dimensional nanostructures to obtain two trimmed two-dimensional nanostructures, and the atoms of the two trimmed two-dimensional nanostructures are complete atoms.

[0023] Step 44, Periodicity Restoration: Reconstruct the periodicity of each cut two-dimensional nanostructure in the x, y, and z directions to obtain two processed monolayer two-dimensional nanomaterial lattices.

[0024] Preferably, in step 6, the optimal sliding angle step size and sliding distance step size corresponding to the optimal sliding stacking configuration are selected from multiple sliding stacking configurations as the optimal sliding angle step size and optimal sliding distance step size, respectively. The specific process is as follows:

[0025] Calculate the bond length difference, bond angle difference, and total energy difference between the initial slip stack configuration and the slip stack configuration. Select the slip step size corresponding to 0 at the junction of bond length difference and non-zero bond angle difference, and the slip step size corresponding to 0 at the junction of total energy difference and non-zero bond angle difference. Select the minimum value from the three selected slip step sizes and take this value as the optimal slip step size. Take the slip angle and slip distance corresponding to this optimal slip step size as the optimal slip angle step size and slip distance step size.

[0026] Preferably, in step 6, a Bayesian optimization algorithm is used to determine the optimal interlayer spacing between the two monolayer two-dimensional nanomaterials in each slip-stacking configuration. The specific process is as follows:

[0027] Step 61: For each sliding stack configuration, randomly select a preset number of interlayer spacings within a preset interlayer spacing range;

[0028] Step 62: Calculate the total energy corresponding to each interlayer spacing according to first principles, and use the interlayer spacing and the corresponding total energy as the data of the i-th round dataset, with the initial value of i being 1;

[0029] Step 63: Split the i-th round dataset into a training set and a test set. Use the training set to train the GPR model and obtain the trained GPR model. Input each interlayer spacing in the test set into the trained GPR model in sequence to predict the corresponding total energy and calculate the standard deviation of the obtained total energy.

[0030] Step 64: Determine whether the standard deviation is below the preset threshold. If yes, proceed to step 65; otherwise, proceed to step 66.

[0031] Step 65: Select the interlayer spacing corresponding to the minimum total energy in the interlayer spacing-total energy curve fitted by the GPR model as the optimal interlayer spacing for this stacking configuration.

[0032] Step 66: Determine the interlayer spacing for the next round based on the standard deviation, so that i = i + 1, and proceed to step 62.

[0033] The beneficial effects of this invention are:

[0034] This invention first evaluates the lattice matching of any two monolayer two-dimensional nanomaterials and corrects monolayers with high lattice mismatch rates. This reduces stress and defects at the interface of the subsequently generated bilayer slip stack configuration, preventing delamination or breakage and significantly improving structural stability. Next, slip operations are performed on the two matched zero-slip stacked monolayer two-dimensional nanomaterials. Due to different slip distances and angles, various slip stack configurations are generated. Based on the optimized slip angle and slip distance step sizes, this invention generates multiple sets of slip vectors and uses a Bayesian optimization algorithm to match the optimal interlayer spacing for each slip stack configuration. This ultimately achieves a global search for slip stack configurations of this type of material, generating all possible bilayer slip stack configurations. Finally, this invention selects one bilayer slip stack configuration as the ground state stack configuration by calculating the total energy. Therefore, this invention can obtain a structurally stable ground state stack configuration, and its identification method has high accuracy.

[0035] This invention not only provides an efficient global search tool for the study of bilayer slip stacking configurations of ground-state two-dimensional nanomaterials and lays a methodological foundation for establishing a universal prediction model for multilayer material structures, but also promotes the practical application of novel two-dimensional nanomaterials in high-performance devices. Attached Figure Description

[0036] Figure 1 A flowchart illustrating the method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials;

[0037] Figure 2 Flowchart for candidate lattice determination in the rescaling step (only for cases where the mismatch rate between two monolayers is >5%);

[0038] Figure 3 This diagram illustrates the method for calculating bond length and bond angle differences in stacked configurations of bilayer two-dimensional nanomaterials. Figure 3 (a) is a sliding angle of 0° and a sliding distance of Top and side views of the AA stacked configuration. Figure 3 (b) is a sliding angle of 0° and a sliding distance of j. Top and side views of the stacked configuration. Figure 3 (c) is a sliding angle of 0° and a sliding distance of... Top and side views of the stacked configuration. Figure 3 (d) represents a sliding angle of i° and a sliding distance of... The top and side views of the stacked configuration are shown. In the figures, L0 and θ0 represent the representative B1-B2 bond length and bond angle (∠B1B2B3) in the upper layer of the initial stacked configuration, respectively. n and θ mThese represent the representative B1-B2 bond lengths and bond angles (∠B1B2B3) in the upper layer of a double-slip stacked configuration, respectively. i and s j Let |ΔL| and |Δθ| represent the slip angle and slip distance, respectively, and let |ΔL| and |Δθ| represent the absolute values ​​of the bond length difference and bond angle difference between the initial stacking configuration and the slipped stacking configuration, respectively.

[0039] Figure 4 The figure shows the test results for the bond length difference |ΔL|, bond angle difference |Δθ|, and total energy difference |ΔE| in the bilayer borene stacked configuration. Figure 4 (a) represents the sliding distance step size s j The bond length difference |ΔL| test plot, Figure 4 (b) is s j The bond angle difference |Δθ| test diagram, Figure 4 (c) is s j Total energy difference |ΔE| test graph; Figure 4 (d) represents the slip angle w i The bond length difference |ΔL| test plot, Figure 4 (e) is w i The bond angle difference |Δθ| test diagram, Figure 4 (f) is w i The total energy difference |ΔE| test plot, where P represents the selected critical point;

[0040] Figure 5 The optimal interlayer spacing d for a Bayesian-optimized two-layer stacked configuration i Prediction flowchart;

[0041] Figure 6 This is a schematic diagram of the fitting of the Gaussian process regression model to the relationship between interlayer spacing and total energy.

[0042] Figure 7 A schematic diagram of the sampling function workflow (relationship between expected improvement (EI) and interlayer spacing under different iteration rounds);

[0043] Figure 8 The figures show a top view, a side view, and the binding energy of a monolayer borone. Figure 8 (a) Figure 8 (b) Figure 8 (c) Figure 8 (d) Figure 8 (e) Figure 8 (f) and Figure 8 (g) represent monolayers of α7-, α8-, α1-, α-, α5-, χ3-, and β-, respectively. 12 - Top and side views of borene;

[0044] Figure 9The geometric structures of three bilayer borenes at 300K, along with their potential energy and phonon scattering spectra during a 6ps molecular dynamics (AIMD) simulation.

[0045] In the picture, Figure 9 (a) Figure 9 (d) and Figure 9 (g) Top and side views of the bilayer α7-α8-borene, bilayer α5-α8-borene and bilayer α7-α7-borene models at 300K, respectively; Figure 9 (b) Figure 9 (e) and Figure 9 (h) represents the potential energy of the bilayer α7-α8-borene, bilayer α5-α8-borene, and bilayer α7-α7-borene systems during a 6ps AIMD simulation time;

[0046] Figure 9 (c) Figure 9 (f) and Figure 9 (i) Phonon scattering spectra of bilayer α7-α8-borene, bilayer α5-α8-borene and bilayer α7-α7-borene systems (Atomic Line Graph Neural Network (ALIGNN));

[0047] Figure 10 Potential energy diagrams of bilayer α7-α8-borene, bilayer α5-α8-borene, and bilayer α7-α7-borene systems at different temperatures over a 6ps AIMD simulation time;

[0048] In the picture, Figure 10 (a) Figure 10 (d) and Figure 10 (g) represents the potential energy of the bilayer α7-α8-borene, bilayer α5-α8-borene and bilayer α7-α7-borene systems at 500K for 6ps AIMD simulation time;

[0049] Figure 10 (b) Figure 10 (e) and Figure 10 (h) represents the potential energy of the bilayer α7-α8-borene, bilayer α5-α8-borene and bilayer α7-α7-borene systems at 1000K within a 6ps AIMD simulation time;

[0050] Figure 10 (c) Figure 10 (f) and Figure 10 (i) represents the potential energy of the bilayer α7-α8-borene, bilayer α5-α8-borene and bilayer α7-α7-borene systems at 2000 K within a 6ps AIMD simulation time. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0054] Example:

[0055] A method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials, characterized in that the method includes the following:

[0056] Step 1: Determine whether any two monolayer two-dimensional nanomaterials belong to the same crystal system. If not, proceed to Step 2; if yes, proceed to Step 3.

[0057] Step 2: Convert the crystal system of the two monolayer two-dimensional nanomaterials to the same crystal system, and then proceed to step 3;

[0058] Step 3: Each monolayer two-dimensional nanomaterial has a lattice with a side length along the x-axis and a side length along the y-axis. Based on the lattice side lengths of any two monolayer two-dimensional nanomaterials, calculate the lattice mismatch rate of the two monolayer two-dimensional nanomaterials. If the lattice mismatch rate is greater than a preset value, proceed to step 4; if the lattice mismatch rate is less than a preset value, proceed to step 5.

[0059] Step 4: Scale the lattice of the two monolayer two-dimensional nanomaterials so that the lattice mismatch rate of the two monolayer two-dimensional nanomaterials after scaling is less than a preset value, then proceed to step 5.

[0060] Step 5: Select the longest edge length from the four lattice edge lengths of the two monolayer two-dimensional nanomaterials as the maximum slip distance;

[0061] Step 6: Perform relative slipping of the two monolayer two-dimensional nanomaterial lattices with different angle and distance step sizes to obtain multiple slip stacking configurations. Select the slip angle step size and slip distance step size corresponding to the optimal slip stacking configuration from the multiple slip stacking configurations as the optimal slip angle step size and optimal slip distance step size, respectively. Select P times the optimal slip angle step size as candidate slip angles, and the candidate slip angles must be less than 360 degrees, P = 1, 2, 3...M, for a total of M candidate slip angles. Select F times the optimal slip distance step size as candidate slip distances, and the candidate slip distances must be less than the maximum slip. Given the distance condition F = 1, 2, 3...L, a total of L candidate slip distances are selected. One value is selected from each of the M candidate slip angles and L candidate slip distances to form a slip vector. Each monolayer two-dimensional nanomaterial has two surfaces, upper and lower. Two monolayer two-dimensional nanomaterials form four zero-slip stacking configurations. Each zero-slip stacking configuration is slipped according to each slip vector to obtain multiple slip stacking configurations. A Bayesian optimization algorithm is used to determine the optimal interlayer spacing between the two monolayer two-dimensional nanomaterials in each slip stacking configuration. All possible double-layer slip stacking configurations are generated based on each slip vector and the corresponding optimal interlayer spacing.

[0062] Step 7: Remove duplicate double-layer sliding stack configurations from multiple double-layer sliding stack configurations, and then perform geometric optimization on the remaining double-layer sliding stack configurations to obtain the total energy of each optimized double-layer sliding stack configuration. Sort the total energy of the multiple optimized double-layer sliding stack configurations from low to high, and select the first double-layer sliding stack configuration as the ground state stack configuration.

[0063] Specifically, this embodiment is implemented based on Python programming, which can automatically generate all possible bilayer slip stacking configurations for any two given monolayer two-dimensional nanomaterials and efficiently identify their ground-state stacking configurations. Its workflow is as follows: Figure 1As shown, the process includes five steps: (i) Python library import and single-layer material input, (ii) maximum slip distance calculation, (iii) slip angle and distance step size calculation, (iv) mirror transformation and upper-layer slip, and (v) structure optimization and ground-state stacking configuration identification. Function names in this paper are written using the "function name" format, where Pymatgen and ASE are used for crystal operations, and NumPy is used for mathematical calculations. The specific process is as follows: 17 functions in Pymatgen, including "Structure", "Poscar", "CifWriter", and "StructureMatcher", are called for crystal structure analysis, geometric structure file format conversion, and equivalent structure identification. Four functions in NumPy, including "Dot", "Add", "Max()", and "Min()", are called for basic numerical calculation tasks such as matrix multiplication, element-wise addition, and extraction of maximum and minimum values, providing efficient mathematical support for subsequent lattice parameter transformation and structure selection. By utilizing four functions integrated into ASE—"Calculators," "Dftbplus," "Castep," and "Vasp"—BiLayerStacker calls first-principles calculation software (such as DFTB+, VASP, and CASTEP) to perform DFT calculations. Through the collaborative work of 25 core functions, BiLayerStacker achieves a fully automated workflow from structural analysis and numerical computation to first-principles calculations.

[0064] Steps 1, 2, and 4 accomplish the following: Figure 1 Part (i) of the process; steps 3 and 5 implement the following: Figure 1 Part (ii) of the process; Step 6 implements the following: Figure 1 The process in part (iii) and part (iv) is as follows; step 7 implements... Figure 1 Part (v) of the process.

[0065] Among all the generated bilayer two-dimensional nanomaterial slip stacking configurations, although some configurations differ in geometric arrangement (such as different interlayer slip positions or different stacking orders), from the perspective of physical essence and symmetry, they may actually be equivalent. The atomic arrangement of such configurations can be mapped to each other through spatial symmetry operations (such as translation, rotation or mirror transformation), which leads to them exhibiting completely consistent characteristics in energy, electronic structure and other physicochemical properties. Therefore, these configurations are essentially redundant structures. If they are not identified and deduplicated, they may introduce duplicate information in subsequent performance screening or computational analysis, reducing research efficiency and configuration diversity. Therefore, step 7 is to delete duplicate configurations.

[0066] The core purpose of geometry optimization is to bring materials to their optimal state by adjusting the position, shape, or arrangement of atoms or molecules, thereby providing a reliable structural basis for subsequent physicochemical property analysis.

[0067] The entire process for generating all possible bilayer slip stack configurations in this embodiment is as follows: input two monolayer materials — evaluate lattice matching — calculate the maximum slip distance — generate slip vectors — generate four zero-slip stack configurations (due to the different chemical environments of the upper and lower surfaces of the monolayer materials) — adjust the interlayer spacing using Bayesian optimization — apply slip vectors — generate all bilayer slip stack configurations — deduplication, geometry optimization, and total energy sorting — ground state configuration.

[0068] Further specifying, in step 2, the crystal systems of the two monolayer two-dimensional nanomaterials are converted into the same crystal system. The specific process is as follows:

[0069] The crystal system of the monolayer two-dimensional nanomaterial with higher symmetry is taken as the target crystal system. The lattice basis vectors of the other monolayer two-dimensional nanomaterial are projected onto the Cartesian coordinate system to obtain an equivalent lattice. The equivalent lattice is transformed into a crystal system structure consistent with the target crystal system using the lattice reparameterization and rotation tensor method. The equivalent lattice is then mapped to the target crystal system. The mapped lattice belongs to the same crystal system as the other monolayer two-dimensional nanomaterial.

[0070] Specifically, when two monolayer materials belong to different crystal systems (e.g., hexagonal and cubic), the lattice basis vectors of the monolayer materials are standardized, and dynamic symmetry matching is used to achieve equivalent lattice mapping between materials of different crystal systems. For example, when the two input monolayer materials belong to triclinic and cubic crystal systems respectively, the cubic crystal system is set as the target crystal system due to its higher symmetry. First, the original lattice basis vectors of the triclinic monolayer are projected to the Cartesian coordinate system through coordinate transformation to obtain Cartesian coordinate lattice parameters equivalent to the original triclinic crystal system. Based on this, techniques such as lattice reparameterization and rotation tensor are used to construct an equivalent lattice structure that is symmetry compatible with the target crystal system (cubic crystal system). Finally, the equivalent lattice is mapped to the target crystal system, completing the compatibility conversion from a low-symmetry crystal system to a high-symmetry target crystal system; the converted crystal system retains the volume and symmetry information of its original lattice. After the lattice transformation is completed, the lattice mismatch rate r of the two monolayers is calculated based on the new lattice parameters and the lattice parameters of the high-symmetry crystal system material. m .

[0071] Further specifying, in step 3, the lattice mismatch rate r m Represented as:

[0072]

[0073] In the formula, Max() is the maximum value function, Min() is the minimum value function, a1 and b1 are the side lengths of the lattice of a single-layer two-dimensional nanomaterial along the x-axis and y-axis, respectively, and a2 and b2 are the side lengths of the lattice of another single-layer two-dimensional nanomaterial along the x-axis and y-axis, respectively.

[0074] Specifically, to avoid periodic boundary problems, the mismatch rate of the two lattices is calculated. Max() is the maximum value function, used to select the maximum value among the given variables; Min() is the minimum value function, used to select the minimum value among the given variables.

[0075] When r m When r is less than 5%, the "maximum slip distance calculation" module will be triggered via a conditional branch. m When the percentage is ≥5%, the structure is scaled twice to ensure that the upper and lower single-layer structures satisfy r. m For a lattice matching condition of <5%, the secondary scaling process comprises four key steps: (a) supercell expansion, (b) periodic removal, (c) lattice structure trimming, and (d) periodic restoration.

[0076] Further restrictions,

[0077] In step 4, the process of scaling the lattice of the two monolayer two-dimensional nanomaterials is as follows:

[0078] Step 41, Supercell Expansion: Align the side lengths a1 along the x-axis and b1 along the y-axis of one monolayer two-dimensional nanomaterial lattice with the side lengths a2 along the x-axis and b2 along the y-axis of another monolayer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice composed of the maximum values ​​of a1 and a2 and b1 and b2. Align the side lengths a1 along the x-axis and b1 along the y-axis of one monolayer two-dimensional nanomaterial lattice with the side lengths b2 along the y-axis and a2 along the x-axis of another monolayer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice composed of the maximum values ​​of a1 and b2 and b1 and a2. Select the new lattice with the smallest area from the two new lattices as the candidate lattice. Perform cell expansion on the two monolayer two-dimensional nanomaterial lattices to obtain two expanded lattices, and both expanded lattices cover the area of ​​the candidate lattice.

[0079] Step 42: Remove the periodicity in the x, y, and z directions from the two expanded lattices to obtain two non-periodic two-dimensional nanostructures.

[0080] Step 43, Crystal structure trimming: Using the candidate lattice size as the trimming frame, trim the two non-periodic two-dimensional nanostructures to obtain two trimmed two-dimensional nanostructures, and the atoms in the two trimmed lattices are all complete atoms;

[0081] Step 44, Periodicity Restoration: Reconstruct the periodicity of each cut two-dimensional nanostructure in the x, y, and z directions to obtain two processed monolayer two-dimensional nanomaterial lattices.

[0082] Specifically, (a) supercell expansion:

[0083] Before implementing supercell expansion, the lattice parameters (side lengths) of the supercell to be expanded in the x and y directions must first be determined so that they simultaneously satisfy the lattice matching condition and the requirement of minimum integer multiple expansion. This is because the lattice basis vectors a of the upper (lower) layer... n and b n (n = 1, 2) can be aligned with the x or y direction of the lower (upper) layer respectively. Figure 2 The code automatically enumerates two lattice alignment methods, such as... Figure 2 As shown in sections I and II. For each alignment, two new sets of lattice parameters are generated by obtaining the maximum values ​​of the lattice parameters ((a1, b1) and (a2, b2)) in the x and y directions. Figure 2 Parts II and III of the text, namely:

[0084] Formula 2: a1' = Max(a1,a2), b1' = Max(b1,b2)

[0085] Formula 3: a2' = Max(a1,b2), b2' = Max(a2,b1)

[0086] In the formula, (a1', b1') and (a2', b2') represent the new lattice parameters used in the two lattice alignment modes to generate the double-layer stacked configuration. Since the cell areas (S1 and S2) corresponding to the two sets of new lattice parameters ((a1', b1') and (a2', b2')) may be different, considering that large-scale slip and geometry optimization operations are required in the subsequent stacked configuration construction, in order to reduce the consumption of computational resources while ensuring physical rationality, the set of lattice parameters with the smallest corresponding cell area is used as the lattice parameters (a1', b1') for the subsequent pre-constructed double-layer slip stacked configuration. new and b new ; Figure 2 After determining the lattice parameters used in the double-layer stacked configuration, the lattice parameters of the upper and lower monolayers are extended by integer multiples along the x and y directions, respectively, until they completely cover the structure of the upper and lower monolayers in both directions. new and b new The defined area.

[0087] (b) Periodic removal:

[0088] After the supercell expansion is complete, the periodicity of the upper and lower monolayers needs to be temporarily removed to facilitate subsequent pruning operations. The program reads the input upper and lower monolayer structures, which contain lattice vectors and periodicity information. The periodicity (in the x, y, and z directions) of the upper and lower monolayer structures is then removed.

[0089] (c) Lattice structure trimming:

[0090] The lattice parameters (a) used to obtain the double-layer stacked configuration new and b new After completing the supercell expansion, first define a "clipping box": the length of the "clipping box" in the x and y directions is a. new and b new .by The step size is used to translate a "cutting box" within the aperiodic two-dimensional nanostructure, ensuring that the cutting box does not exceed the boundary of the aperiodic two-dimensional nanostructure. At each translation position, the atomic distribution on the boundary of the "cutting box" at that position is detected; only when there are no atoms on the edge of the returned cutting region, cutting operations are performed on the upper and lower monolayers at that position. The purpose of cutting is to find the optimal cutting position where no atoms are located on the edge of the cutting box.

[0091] (d) Periodic recovery:

[0092] After completing the automated cutting of the upper and lower single-layer structures, based on the lattice parameters (a new and b new Reconstruct a periodic unit cell, where a = a new b = b new , The lattice angles α, β, and γ inherit the values ​​from the original structure, restoring the periodicity of the trimmed two-dimensional nanostructure. The corrected upper and lower monolayers are then used as inputs for generating subsequent bilayer slip-stacking configurations.

[0093] Further specifying, in step 6, the optimal sliding angle step size and sliding distance step size are selected from multiple sliding stacking configurations as the optimal sliding angle step size and optimal sliding distance step size, respectively. The specific process is as follows:

[0094] Calculate the initial stacking configuration (( Figure 3 (a) and (c)) with slip stacking configuration (( Figure 3(b) and (d) are given the bond length difference, bond angle difference, and total energy difference. The slip step size corresponding to the bond length difference equal to 0 and the bond angle difference equal to 0 and the total energy difference equal to 0 is selected. The minimum value among the three selected slip step sizes is chosen as the optimal slip step size. The slip angle and slip distance corresponding to the optimal slip step size are chosen as the optimal slip angle step size and slip distance step size.

[0095] Further specifying, in step 6, a Bayesian optimization algorithm is used to determine the optimal interlayer spacing between the two monolayer two-dimensional nanomaterials in each slip-stacking configuration. The specific process is as follows:

[0096] Step 61: For each sliding stack configuration, randomly select a preset number of interlayer spacings within a preset interlayer spacing range;

[0097] Step 62: Calculate the total energy corresponding to each interlayer spacing according to first principles, and use the interlayer spacing and the corresponding total energy as the data in the i-th round dataset, with the initial value of i being 1;

[0098] Step 63: Split the i-th round dataset into a training set and a test set. Use the training set to train the GPR model and obtain the trained GPR model. Input each interlayer spacing in the test set into the trained GPR model in sequence to predict the corresponding total energy and calculate the standard deviation of the obtained total energy.

[0099] Step 64: Determine whether the standard deviation is below the preset threshold. If yes, proceed to step 65; otherwise, proceed to step 66.

[0100] Step 65: Select the interlayer spacing corresponding to the minimum total energy in the interlayer spacing-total energy curve fitted by the GPR model as the optimal interlayer spacing for this stacking configuration.

[0101] Step 66: Determine the interlayer spacing for the next round based on the standard deviation, so that i = i + 1, and proceed to step 62.

[0102] Specifically, the maximum slip distance is calculated as follows:

[0103] To achieve efficient global search for the slip stacking configuration of bilayer two-dimensional nanomaterials, a strategy of "fixing the lower layer and slipping the upper layer" is adopted. Since two-dimensional nanomaterials have strict periodic boundaries, if the slip distance exceeds a reasonable range, it can easily lead to repetitive configurations or lattice mismatch, thus reducing efficiency. Therefore, the slip distance threshold of the upper layer structure is automatically determined. By analyzing the lattice parameters of the upper and lower monolayer structures (i.e., a1, b1 and a2, b2), the lattice parameter with the longest length is extracted and defined as the maximum slip distance (d). max=Max(a1,b1,a2,b2)). During subsequent stacking configuration generation, the slip distance in any direction is limited to less than d. max This reduces the generation of repetitive structures and significantly improves the efficiency of global search.

[0104] Slide angle and distance step calculation:

[0105] Appropriate slip angle and distance step size are crucial for completing the global search of double-layer slip stack configurations. On the one hand, an excessively large step size will result in an incomplete search range, failing to cover all possible slip stack configurations and causing omissions of the true ground-state double-layer stack configuration; on the other hand, while an excessively small step size can ensure a global search, it will lead to the generation of a large number of duplicate configurations, wasting computational resources and reducing efficiency. Therefore, to simultaneously ensure the globalization and efficiency of the double-layer slip stack configuration search, the optimal slip distance step size (s) and slip angle step size (w) are automatically determined. Using the key structural parameters of the configuration (bond length and bond angle) and the change in total energy as evaluation indicators, a series of candidate step size combinations (w) are analyzed. i ,s j Pre-testing was conducted to evaluate its performance in resolving stacked configurations and the repeatability of configurations. Specifically, the evaluation criterion for s and w was the "minimum repeatability step size," that is, the maximum step size selected before the glide step size increases to a critical value that first causes a significant change in the geometry or energy of the stacked configuration. Taking bilayer α7-boronene as an example ( Figure 3 The specific process for its pre-test is as follows:

[0106] Slip distance step test:

[0107] The initial configuration is a bilayer α7-boronene with stacked AA layers (w i =0°; Figure 3 (a) The optimal interlayer spacing predicted by the Bayesian optimization algorithm is used as the preset interlayer spacing (see "(iv) Mirror Transformation and Upper Layer Slippage" section for details). The step size is 13 double-layer slip stack configurations are automatically generated within the range. Figure 3 (b)) and perform geometric optimization on it; its bond length difference (|ΔL|); Figure 3 (b) and Figure 4 (a)), bond angle difference (|Δθ|); Figure 3 (b) and Figure 4 (b) and the total energy difference between the slip stacking configuration and the initial stacking configuration (|ΔE|). Figure 4 (c) changes, such as Figure 4 As shown in (a)-(c). When s j Increase from 0 to At that time, |ΔL| and |ΔE| showed significant fluctuations. Figure 4 (a) and (c)), while when s j When |Δθ| reaches 0.5, |Δθ| shows significant fluctuations. Figure 4 (b)); Taking into account |ΔL|, |Δθ| and |ΔE|, select As the "minimum repetition distance step size". If we take This will result in a large number of repetitive configurations; if we take This would result in the omission of the true ground-state double-layer stacked configuration.

[0108] Slide angle step size test:

[0109] by w i The initial configuration is a bilayer α7 borene with a slip stacking configuration of 0°. Figure 3 (c) Using the optimal interlayer spacing value obtained from the test as the preset interlayer spacing (see “(iv) Mirror Transformation and Upper Layer Slip” section for details), 11 double-layer slip stacking configurations are automatically generated in a step size of 1° within the range of 0-10°. Figure 3 (d)) and perform geometric optimization on it; its bond length difference (|ΔL|); Figure 3 (d) and Figure 4 (d)), bond angle difference (|Δθ|); Figure 3 (d) and Figure 4 (e) and the total energy difference between the slip stacking configuration and the initial stacking configuration (|ΔE|); Figure 4 The changes in (f) are as follows: Figure 4 As shown in (d)-(e). When w i As the angle increases from 0° to 4°, |ΔL| and |ΔE| show significant fluctuations. Figure 4 (d) and (f)), while when w i When the angle reaches 5°, |Δθ| shows significant fluctuations. Figure 4 (e)); Considering |ΔL|, |Δθ| and |ΔE|, select w i =3° is used as the "minimum repetition distance step size". If we take w... i If the angle is less than 3°, a large number of repeating configurations will be generated; if w is taken... i If the angle is greater than 3°, it will result in the omission of the true ground-state double-layer stacked configuration.

[0110] Mirror transformation and upper-level slip:

[0111] Two-dimensional nanomaterials exhibit numerous non-planar configurations, meaning they possess varying degrees of wrinkling within their surfaces. This results in different chemical environments on the upper and lower surfaces of these materials. Therefore, when studying the stacking configurations of bilayer two-dimensional nanomaterials, both the upper and lower surfaces of the two monolayers must be considered to ensure that the generated configuration space fully covers all possible interlayer interactions. Based on this, four stacking combinations were analyzed: “TD”, “TD’”, “T’D”, and “T’D’”, as shown below. Figure 1 As shown in section iv. Here, "T" and "D" represent the upper and lower single-layer structures of the input, respectively, while "T'" and "D'" represent the mirror flip structures of the upper (T) and lower (D) single-layer structures relative to the xy plane, respectively.

[0112] All possible combinations of interlayer interactions were considered. First, a mirror-flipped structure (T′ and D′) of the upper (T) and lower (D) layers relative to the xy plane was constructed; second, with... The initial interlayer spacing merges the upper layer (T or T′) and the lower layer (D or D′), thereby generating four stacking combinations (w i =0°; ), that is, “TD”, “TD′”, “T′D” and “T′D′” ( Figure 1 (Part IV). Next, the optimal interlayer spacing d is determined using the Bayesian optimization (BO) algorithm. i ( Figure 5 The average interlayer spacing of the four double-layer stacking configurations is set to d. i Then, place it at the middle position in the z-direction. Finally, keep the lower layer stationary and apply the slip vector V(w,S) to the upper layer to generate all possible double-layer slip stack configurations, thus achieving a global search for double-layer slip stack configurations.

[0113] The Bayesian optimization algorithm is used for each two-layer slip stack configuration (“TD”, “TD’”, “T’D”, and “T’D’”); w i =0°; Determine the optimal interlayer spacing (d) i ), and the obtained d i As the initial stacking configuration ("TD", "TD'", "T'D" and "T'D'"); w i =0°; The initial interlayer spacing is determined by the Bayesian optimization algorithm, which involves four key steps: (1) total energy calculation and initial dataset construction, (2) dataset partitioning and Gaussian process regression model training, (3) sampling point selection and first-principles calculation, and (4) model iterative optimization and optimal spacing determination.

[0114] (1) Total energy calculation and initial dataset construction:

[0115] For each stacking configuration ("TD", "TD′", "T′D", and "T′D′"); w i =0°; ),exist Twelve interlayer spacing values ​​(d) are randomly selected within the range, and corresponding double-layer slip stack configurations are automatically generated accordingly. Based on this, first-principles calculations are performed on the above configurations to obtain the total energy (E). total Finally, for each group (d, E) total The data is paired and organized to construct the initial dataset. Figure 5 The middle (1) section provides data support for the fitting of the subsequent Gaussian process regression (GPR) model and the iterative sampling of Bayesian optimization.

[0116] (2) Dataset partitioning and GPR model training:

[0117] After establishing the initial dataset, it was divided into training and test sets in an 8:2 ratio. A GPR model was then trained based on the training set to fit the interlayer spacing (d) and total energy (E). total The relationship between ) Figure 5 Middle (2) part and Figure 6 The GPR model can not only predict total energy, but also provide confidence intervals. Figure 6 The purple shading (represented by the standard deviation σ(d)) measures the uncertainty of a prediction: a larger confidence interval (larger standard deviation) indicates higher uncertainty; a smaller confidence interval indicates a more reliable prediction. Furthermore, Figure 6 The interlayer spacing versus total energy curve fitted to the GPR model. A larger confidence interval indicates higher uncertainty in that region, and vice versa. The Bayesian optimization algorithm prioritizes sampling points with higher uncertainty to improve model accuracy.

[0118] (3) Sampling point selection and first-principles calculation:

[0119] After initially fitting the GPR model, the Expected Improvement (EI) sampling function is introduced. Figure 7 The interlayer spacing value (d) that best improves the prediction performance of the GBP model is selected as the sampling point d for the next round. next The EI value is calculated based on both the mean μ(d) and standard deviation σ(d) of the current GPR model's prediction of total energy. In each iteration, the interlayer spacing d corresponding to the peak of the EI curve is selected. next Using these as new sample points, first-principles calculations are performed to obtain the true total energy E. total Then add it to the training set and retrain the GPR model. Figure 5 (Part 2) After selecting the sampling point, the corresponding total energy is obtained by first-principles calculation, and the new sample (d) is used. next E total ) are included in the training set to update the GPR model ( Figure 5 (Part 3). The above "sampling-update" process continues, and the model's predictive ability is constantly enhanced.

[0120] (4) Model iterative optimization and determination of optimal spacing:

[0121] As the GPR model is updated round by round and the training samples are continuously expanded, the fitting accuracy of the entire prediction model to the total energy function continues to improve. When the confidence intervals of all candidate interlayer spacing points converge to below the preset threshold (σ < 5 × 10⁻⁶), the accuracy improves. 3 When the value reaches eV, it indicates that the model has fully learned the search space, and the Bayesian optimization process terminates. Finally, the interlayer spacing with the lowest current total energy is output as the optimal interlayer spacing d for this stacking configuration. i ( Figure 1 (Part (iv))

[0122] (5) Structural optimization and ground-state stacking configuration identification:

[0123] To improve the efficiency of geometry optimization for double-layer sliding stacked structures and remove duplicate configurations, the selected configurations are saved as POSCAR and CIF format files. Based on this, computational software such as DFTB+ or VASP, called from the ASE library, is used to perform geometry optimization on the remaining double-layer stacked configurations. Finally, the 30 configurations with the lowest energy are automatically selected as output based on the optimized configurations, and one configuration is chosen as the ground state configuration.

[0124] Verification and Application:

[0125] To evaluate the effectiveness of this embodiment, bilayer borene was selected as the test object. Borene, as an emerging two-dimensional nanomaterial, has attracted widespread attention from researchers due to its structural diversity and unique physicochemical properties. Its ultra-high thermal conductivity, excellent mechanical properties, and distorted Dirac fermions and phonon-mediated superconductivity make it an ideal material for stacking engineering research. In previous studies, researchers have synthesized various monolayer borenes, such as α-, β-, β1-, β8-, and β-, on metal substrates such as Cu(111), Ag(111) / (110) / (100), Al(111), Au(111), and Ir(111), using techniques such as molecular beam epitaxy (MBE), atomic layer deposition (ALD), and chemical vapor deposition (CVD). 12 -、β 13α-, δ3-, δ6-, χ6-, and χ3-borenes, etc. However, although these monolayer borene structures exhibit good stability on the substrate, their stability rapidly decreases after exposure to air or peeling from the substrate, severely limiting their practical application in devices. In 2021, Liu et al. and Chen et al. successfully synthesized bilayer α-borenes and β-borenes on Ag(111) and Cu(111) substrates, respectively, using MBE technology. 12 The discovery of α-boronenes marks a significant advancement in the research of multilayer boronenes. Although the experimentally prepared bilayer boronenes exhibit slightly higher thermodynamic stability than monolayer boronenes, they still suffer from poor stability when exposed to air or peeled from a substrate, thus limiting their practical application in devices. Furthermore, the experimentally obtained boronene configurations are not always the thermodynamically most stable structures predicted theoretically, reflecting that experimental approaches are often constrained by kinetic conditions and substrate-induced effects, making it difficult to fully reveal the optimal solution in the boronene configuration space; this phenomenon highlights the irreplaceable role of theoretical research in boronene configuration design. Recent theoretical studies by Wang et al. have shown a positive correlation between the number of layers and the stability of α-, α5-, α7-, and α8-boronenes, revealing the crucial role of layer number in the stability of boronene materials. In summary, exploring novel independent multilayer (e.g., bilayer) boronene configurations with superior structural stability will not only promote the experimental preparation of multilayer boronenes but also provide a theoretical basis for structural control in stacking engineering. However, no research has yet been reported on global searches and ground-state configuration identification for bilayer boronene slip stacking configurations. Therefore, systematically revealing the construction rules of the slip stacking mode and stable configuration of bilayer borene from a theoretical perspective will promote the practical application of borene materials in devices.

[0126] This study utilizes seven typical monolayer borone structures (α, α1, α5, α7, α8, β... 12 and χ3; Figure 8 Using this as input, 28 different combinations of bilayer borene stacking configurations were explored (Tables 1 and 2), generating approximately 320,000 bilayer borene glide stacking configurations. Based on this, the top 30 configurations with the lowest total energy from each combination were automatically selected. Finally, the 840 bilayer borene glide stacking configurations were submitted to the DMol3 module for geometry optimization, from which the configuration with the lowest total energy was selected as the most stable ground-state stacking configuration, thus verifying the reliability of the results of this embodiment.

[0127] Table 1 shows the number of bilayer borene stacking configurations generated under 28 different input monolayer combinations (N). S ), sliding angle step size (w, °) and sliding distance step size Optimal interlayer spacing And the highest value among the top 30 binding energies (E) bmax ,

[0128] eV / atom) and minimum value (E bmin (eV / atom)

[0129]

[0130]

[0131] Geometric optimization results show that all 840 output bilayer borene slip stacking configurations possess high binding energies, ranging from 6.111 to 6.567 eV / atom, which is similar to the reported binding energy range of 6.159 to 6.563 eV / atom in the literature (Tables 1 and 2). The bilayer α7-α7-borene configuration is similar to the reported bilayer α... 7AB -Geometric and binding energy of borene configuration (E b =6.563eV / atom) is completely consistent, confirming the bilayer α 7AB -The stacked configuration of borones is indeed the ground state configuration. In this study, A n -B m Indicates that the upper layer is A n The lower layer is B. m The bilayer α-borene configuration was also observed. Furthermore, the binding energies of the exported bilayer α-α-borene, bilayer α5-α5-borene, and bilayer α8-α8-borene configurations were 6.435, 6.563, and 6.563 eV / atom, respectively, all higher than those reported in the literature for bilayer α-borene. AB -、α 5AB - and α 8AB The highest binding energies for the α7-α8-, α5-α8-, and α7-α7-borene configurations are shown (6.431, 6.562, and 6.560 eV / atom, respectively). This indicates that the previously reported stacked configurations are not the local energy minima in the stacked configuration space, and that the bilayer α7-α8-, α5-α8-, and α7-α7-borenes are the ground state structures in the corresponding configuration space.

[0132] Notably, the two novel bilayer α7-α8- and α5-α8-boronenes exhibit binding energies (6.567 eV / atom for bilayer α7-α8-boronene and 6.566 eV / atom for bilayer α5-α8-boronene) that were produced both exceed the highest reported binding energy for bilayer boronenes (6.563 eV / atom) in the literature. 7AB The results show that bilayer α7-α8- and α5-α8-borenes represent the most thermodynamically stable bilayer borene stacking configurations reported to date. Furthermore, molecular dynamics (AIMD) simulations and phonon scattering spectroscopy analyses of bilayer α7-α8- and α5-α8-borenes at 300 K yielded... Figure 9Both (at 300K) and (at 500K) indicate excellent thermodynamic and kinetic stability. Furthermore, AIMD simulations at 500K, 1000K, and 2000K (at 300K) also demonstrate this. Figure 10 The results show that bilayer α7-α8-, α5-α8-, and α7-α7-boronenes all possess good thermal stability, further confirming the high thermodynamic and kinetic stability of these new configurations. The predicted bilayer boronene slip stacking configurations not only break the upper limit of the binding energy reported in the literature for bilayer boronenes but also provide a clear target for experimental realization. Therefore, the above verification further confirms the wide applicability of the atomic-scale bilayer two-dimensional nanomaterial ground-state stacking configuration identification method in this study in bilayer boronene systems, demonstrating its powerful ability in global search and ground-state identification of bilayer slip stacking configurations.

[0133] Table 2 shows the binding energies (Ebinding energy) of bilayer borenes reported in this study and previous literature. b eV / atom; PBE); A n -B m Indicates that the upper layer is A n The lower layer is B. m bilayer borone configuration

[0134]

[0135] Therefore, the method of this embodiment successfully identified two highly stable bilayer borene configurations (bilayer α7-α8- and α5-α8-borene), due to their high thermal stability, high transmittance (>83%), and excellent electrical conductivity (>10). 5 With a density of S / m, it has great application potential in transparent conductive thin film materials.

[0136] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials, characterized in that, The method includes the following: Step 1: Determine whether any two monolayer two-dimensional nanomaterials belong to the same crystal system. If not, proceed to Step 2; if yes, proceed to Step 3. Step 2: Convert the crystal system of the two monolayer two-dimensional nanomaterials to the same crystal system, and then proceed to step 3; Step 3: Each monolayer two-dimensional nanomaterial has a lattice with a side length along the x-axis and a side length along the y-axis. Based on the lattice side lengths of any two monolayer two-dimensional nanomaterials, calculate the lattice mismatch rate of the two monolayer two-dimensional nanomaterials. If the lattice mismatch rate is greater than a preset value, proceed to step 4; if the lattice mismatch rate is less than a preset value, proceed to step 5. Step 4: Scale the lattice of the two monolayer two-dimensional nanomaterials so that the lattice mismatch rate of the two monolayer two-dimensional nanomaterials after scaling is less than a preset value, then proceed to step 5. Step 5: Select the longest edge length from the four lattice edge lengths of the two monolayer two-dimensional nanomaterials as the maximum slip distance; Step 6: Perform relative slipping of the two monolayer two-dimensional nanomaterial lattices with different angle and distance step sizes to obtain multiple slip stacking configurations. Select the slip angle step size and slip distance step size corresponding to the optimal slip stacking configuration from the multiple slip stacking configurations as the optimal slip angle step size and optimal slip distance step size, respectively. Select P times the optimal slip angle step size as candidate slip angles, and the candidate slip angles must be less than 360 degrees, P = 1, 2, 3...M, for a total of M candidate slip angles. Select F times the optimal slip distance step size as candidate slip distances, and the candidate slip distances must be less than the maximum slip. Given the distance condition F = 1, 2, 3...L, a total of L candidate slip distances are selected. One value is selected from each of the M candidate slip angles and L candidate slip distances to form a slip vector. Each monolayer two-dimensional nanomaterial has two surfaces, upper and lower. Two monolayer two-dimensional nanomaterials form four zero-slip stacking configurations. Each zero-slip stacking configuration is slipped according to each slip vector to obtain multiple slip stacking configurations. A Bayesian optimization algorithm is used to determine the optimal interlayer spacing between the two monolayer two-dimensional nanomaterials in each slip stacking configuration. All possible double-layer slip stacking configurations are generated based on each slip vector and the corresponding optimal interlayer spacing. Step 7: Remove duplicate double-layer sliding stack configurations from multiple double-layer sliding stack configurations, and then perform geometric optimization on the remaining double-layer sliding stack configurations to obtain the total energy of each optimized double-layer sliding stack configuration. Sort the total energy of the multiple optimized double-layer sliding stack configurations from low to high, and select the first double-layer sliding stack configuration as the ground state stack configuration.

2. The method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials according to claim 1, characterized in that, In step 2, the crystal systems of the two monolayer two-dimensional nanomaterials are converted into the same crystal system. The specific process is as follows: The crystal system of the monolayer two-dimensional nanomaterial with higher symmetry is taken as the target crystal system. The lattice basis vectors of the other monolayer two-dimensional nanomaterial are projected onto the Cartesian coordinate system to obtain an equivalent lattice. Using the lattice reparameterization and rotation tensor method, the equivalent lattice is transformed into a crystal system structure consistent with the target crystal system to obtain an equivalent lattice. The equivalent lattice is then mapped to the target crystal system. The mapped lattice belongs to the same crystal system as the other monolayer two-dimensional nanomaterial.

3. The method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials according to claim 1, characterized in that, In step 3, the lattice mismatch rate r m Represented as: In the formula, Max() is the maximum value function, Min() is the minimum value function, a1 and b1 are the side lengths of the lattice of a single-layer two-dimensional nanomaterial along the x-axis and y-axis, respectively, and a2 and b2 are the side lengths of the lattice of another single-layer two-dimensional nanomaterial along the x-axis and y-axis, respectively.

4. The method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials according to claim 1, characterized in that, In step 4, the process of scaling the lattice of the two monolayer two-dimensional nanomaterials is as follows: Step 41, Supercell Expansion: Align the side lengths a1 along the x-axis and b1 along the y-axis of one monolayer two-dimensional nanomaterial lattice with the side lengths a2 along the x-axis and b2 along the y-axis of another monolayer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice composed of the maximum values ​​of a1 and a2 and b1 and b2. Align the side lengths a1 along the x-axis and b1 along the y-axis of one monolayer two-dimensional nanomaterial lattice with the side lengths b2 along the y-axis and a2 along the x-axis of another monolayer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice composed of the maximum values ​​of a1 and b2 and b1 and a2. Select the new lattice with the smallest area from the two new lattices as the candidate lattice. Perform cell expansion on the two monolayer two-dimensional nanomaterial lattices to obtain two expanded lattices, and both expanded lattices cover the area of ​​the candidate lattice. Step 42: Remove the periodicity in the x, y, and z directions from the two expanded lattices to obtain two non-periodic two-dimensional nanostructures. Step 43, Crystal structure trimming: Using the candidate lattice size as the trimming frame, trim the two non-periodic two-dimensional nanostructures to obtain two trimmed two-dimensional nanostructures, and the atoms in the two trimmed lattices are all complete atoms; Step 44, Periodicity Restoration: Reconstruct the periodicity of each cut two-dimensional nanostructure in the x, y, and z directions to obtain two processed monolayer two-dimensional nanomaterial lattices.

5. The method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials according to claim 1 or 4, characterized in that, In step 6, the optimal sliding angle step size and optimal sliding distance step size are selected from multiple sliding shapes. The specific process is as follows: Calculate the bond length difference, bond angle difference, and total energy difference between the initial slip stack configuration and the slip stack configuration. Select the slip step size corresponding to 0 at the junction of bond length difference equal to 0 and non-zero, the slip step size corresponding to 0 at the junction of bond angle difference equal to 0 and non-zero, and the slip step size corresponding to 0 at the junction of total energy difference equal to 0 and non-zero. Select the minimum value from the three selected slip step sizes and take this value as the optimal slip step size. The slip angle and slip distance corresponding to this optimal slip step size are taken as the optimal slip angle step size and slip distance step size.

6. The method for identifying the ground-state stacking configuration of atomic-scale bilayer two-dimensional nanomaterials according to claim 5, characterized in that, In step 6, the Bayesian optimization algorithm is used to determine the optimal interlayer spacing between the two monolayer two-dimensional nanomaterials in each slip stack configuration. The specific process is as follows: Step 61: For each sliding stack configuration, randomly select a preset number of interlayer spacings within a preset interlayer spacing range; Step 62: Calculate the total energy corresponding to each interlayer spacing according to first principles, and use the interlayer spacing and the corresponding total energy as the data of the i-th round dataset, with the initial value of i being 1; Step 63: Split the i-th round dataset into a training set and a test set. Use the training set to train the GPR model and obtain the trained GPR model. Input each interlayer spacing in the test set into the trained GPR model in sequence to predict the corresponding total energy and calculate the standard deviation of the obtained total energy. Step 64: Determine whether the standard deviation is below the preset threshold. If yes, proceed to step 65; otherwise, proceed to step 66. Step 65: Select the interlayer spacing corresponding to the minimum total energy in the interlayer spacing-total energy curve fitted by the GPR model as the optimal interlayer spacing for this stacking configuration. Step 66: Determine the interlayer spacing for the next round based on the standard deviation, so that i = i + 1, and proceed to step 62.

Images