Method for identifying ground state stacking configuration of atomic-scale double-layer two-dimensional nano material

Abstract

The invention discloses a method for identifying a ground state stacking configuration of an atomic-scale double-layer two-dimensional nano material, and relates to the field of two-dimensional The objective of the invention is to solve the problem of poor accuracy of a conventional ground state configuration identification method. The lattice mismatch rate of any two single-layer two-dimensional nanometer materials is calculated, the two single layers with the large lattice mismatch rate are matched, then slip distances, slip angles and interlayer spacing are selected for the lattices of the two matched single-layer two-dimensional nanometer materials, and each slip distance, slip angle and interlayer spacing form a complete stacking structure. The method comprises the following steps: selecting a plurality of complete stacking configurations, removing repeated complete stacking configurations in the plurality of complete stacking configurations, performing geometric optimization processing on the remaining complete stacking configurations, calculating the total energy of each optimized complete stacking configuration, sorting the total energy of the plurality of optimized complete stacking configurations from low to high, and selecting a first stacking configuration as a ground state stacking configuration. The method is used for accurately identifying the ground state stacking configuration.

Description

Technical Field

[0001] The present invention relates to the field of two-dimensional nanomaterials. Background Art

[0002] In recent years, two-dimensional (2D) nanomaterials have shown great application potential in electronics, energy storage, catalysis, sensors and other fields due to their atomic-level thickness and unique physical and chemical properties. Among them, single-layer two-dimensional nanomaterials have been widely used in nanoelectronics and flexible electronic devices due to their high electron mobility and excellent mechanical properties. Due to the introduction of interlayer interactions (such as van der Waals forces, hydrogen bonds and electrostatic interactions), multilayer two-dimensional nanomaterials exhibit completely different and richer physical and chemical properties than single-layer materials, such as adjustable band gaps, extended optical absorption and higher charge mobility. These properties give multilayer two-dimensional nanomaterials a broader prospect in multiple application fields. Theoretical research results show that insulating single-layer boron nitride (h-BN) is mainly used as a gate dielectric in high-performance electronic devices (such as graphene-based field effect transistors (FETs)). Multilayer h-BN not only maintains the insulating properties of a single layer, but also has optical properties that are dependent on the number of layers (2-5 layers), and can be used in optoelectronic devices such as photodetectors, light-emitting diodes (LEDs), and optical modulators. In addition, multilayer molybdenum ditelluride (MoTe2) exhibits a temperature-induced structural phase transition that a single layer does not have. At 200-250K, its crystal structure transforms from a monoclinic phase (2H) to an orthorhombic phase (1T'). Its significantly improved light absorption and luminescence properties make it have application potential in the fields of light detection, lasers, and phase change memories. It can be seen that theoretical research on multilayer two-dimensional nanomaterials has become a key direction for promoting the development of a new generation of high-performance materials.

[0003] In the research of new multilayer two-dimensional nanomaterials, stacking engineering is an important technical means. By controlling the stacking angle, stacking order, and interlayer slip at the atomic scale, stacking engineering can significantly change the interlayer interaction mode of two-dimensional nanomaterials, thereby achieving precise control of various properties of two-dimensional nanomaterials, such as electronic, optical, magnetic, and mechanical properties, and promoting the application of two-dimensional nanomaterials in multiple fields. Taking twisted bilayer graphene (TBG) as an example, a slight change in the stacking angle (1.1°) can induce a superconducting phase transition; by precisely controlling the interlayer stacking order of phosphorene (such as AA or AB configuration), its band gap can be continuously controlled (0.78-1.04eV); and interlayer slip can induce the energy band of MoS from a direct band gap to an indirect band gap and improve its carrier mobility, making it valuable for application in flexible electronic devices. However, the important issue of the stability of the stacking configuration is often overlooked. Obviously, unstable "theoretical atomic-scale two-dimensional nanomaterials" will be difficult to achieve practical application even if they have many excellent properties. Therefore, exploring the ground state configuration of multilayer materials is not only the core key to unlocking the intrinsic properties of the materials, but also the key to unleashing their application potential.

[0004] However, accurately and efficiently identifying the most stable stacking configuration in multilayer two-dimensional nanomaterials still faces huge challenges. The diversity of stacking order and interlayer slippage leads to a huge stacking configuration space of two-dimensional nanomaterials, which exceeds the processing capabilities of traditional manual stacking methods, thus limiting its further development in practical applications. Obviously, traditional methods are inefficient and difficult to meet the needs in such a vast configuration space. Therefore, the development of efficient, reliable and universal algorithmic tools to identify the most stable stacking configuration in multilayer two-dimensional nanomaterials is crucial to promoting their practical applications. In fact, researchers have made certain progress in the automated generation and stable configuration screening of van der Waals bilayer stacking configurations. Based on 520 single-layer materials in the C2DB database, Barik et al. automatically generated 760 van der Waals bilayer stacking configurations (mainly considering the interlayer slip operation along the high symmetry direction of the lattice (lattice: a solid material arranged periodically in space according to certain regulations. This regular arrangement of atoms forms a certain spatial geometric shape, called a lattice). interlayer spacing), and established a corresponding database for researchers to use. Pakdel et al. screened out 1052 stable single-layer materials from the C2DB database, using AA stacking as the initial configuration and the atomic lateral displacement difference as the interlayer slip vector. By applying the slip vector to the top structure, 8451 van der Waals double-layer stacking configurations were generated. On this basis, they identified 133 potential bistable double-layer candidate materials that can undergo state transitions under specific conditions such as electric fields, mechanical strains or thermal activation, and show application value in sliding electronics. Although the above studies have made certain progress in the development of high-throughput computational workflows for two-dimensional nanomaterial stacking engineering, there is still a large gap from efficient and universal automated workflows for stacking engineering. First, in terms of interlayer spacing regulation, the above studies only considered van der Waals interactions. Other interlayer interactions, such as electrostatic interactions and hydrogen bonding, are also of great significance in regulating the novel physical and chemical properties of multilayer two-dimensional nanomaterials. Secondly, previous research efforts have failed to conduct a global exploration of the stacking order and interlayer slip paths, resulting in the possibility that the final stacking structure obtained may not be the ground state configuration. Therefore, previous methods for identifying the ground state configuration have poor accuracy, and there is an urgent need to develop a workflow that is both efficient and can globally search all possible stacking modes and accurately identify the ground state stacking configuration. Summary of the Invention

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

[0006] A method for identifying the ground state stacking configuration of a double-layer two-dimensional nanomaterial at the atomic scale, the method comprising the following:

[0007] Step 1: determine whether any two single-layer 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 systems of the two monolayer two-dimensional nanomaterials into the same crystal system, and then proceed to step 3;

[0009] Step 3: The lattice of each single-layer two-dimensional nanomaterial has a side length along the x-axis and a side length along the y-axis. Based on the lattice side lengths of any two single-layer two-dimensional nanomaterials, the lattice mismatch ratio of the two single-layer two-dimensional nanomaterials is calculated. If the lattice mismatch ratio is greater than a preset value, step 4 is executed; if the lattice mismatch ratio is less than the preset value, step 5 is executed.

[0010] Step 4: scaling the lattices of the two single-layer two-dimensional nanomaterials so that the lattice mismatch rate of the two single-layer two-dimensional nanomaterials after scaling is less than a preset value, and then executing Step 5;

[0011] Step 5, selecting the maximum side length from the four lattice side lengths of the two monolayer two-dimensional nanomaterials as the maximum slip distance;

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

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

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

[0015] The crystal system of the single-layer two-dimensional nanomaterial with higher symmetry among the two single-layer two-dimensional nanomaterials is taken as the target crystal system, and the lattice basis vectors of the other single-layer two-dimensional nanomaterial are projected into 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 by using lattice reparameterization and rotation tensor method to obtain an equivalent lattice. The equivalent lattice is mapped to the target crystal system. The mapped lattice belongs to the same crystal system as the crystal system of the other single-layer two-dimensional nanomaterial.

[0016] Preferably, in step 3, the lattice mismatch ratio r m Expressed as:

[0017]

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

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

[0020] Step 41, supercell expansion: aligning the side length a1 along the x-axis and the side length b1 along the y-axis of a single-layer two-dimensional nanomaterial lattice with the side length a2 along the x-axis and the side length b2 along the y-axis of another single-layer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice consisting of the maximum values ​​of a1 and a2 and the maximum values ​​of b1 and b2; aligning the side length a1 along the x-axis and the side length b1 along the y-axis of a single-layer two-dimensional nanomaterial lattice with the side length b2 along the y-axis and the side length a2 along the x-axis of another single-layer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice consisting of the maximum values ​​of a1 and b2 and the maximum values ​​of b1 and a2; selecting the new lattice with the smallest area from the two new lattices as a candidate lattice; performing cell expansion processing on the two single-layer two-dimensional nanomaterial lattices respectively to obtain two expanded lattices, and both expanded lattices cover the area of ​​the candidate lattice;

[0021] Step 42, periodicity removal: removing 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: trimming the two non-periodic two-dimensional nanostructures using the candidate lattice size as a trimming frame to obtain two trimmed two-dimensional nanostructures, wherein the atoms in the two trimmed two-dimensional nanostructures are intact atoms;

[0023] Step 44, periodicity recovery: reconstruct the periodicity of each cropped two-dimensional nanostructure in the x, y and z directions to obtain two processed single-layer two-dimensional nanomaterial lattices.

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

[0025] Calculate the bond length difference, bond angle difference and total energy difference between the initial slip stacking configuration and the slip stacking configuration, select the slip step corresponding to 0 in the junction where the bond length difference is equal to 0 and not equal to 0, select the slip step corresponding to 0 in the junction where the bond angle difference is equal to 0 and not equal to 0, and the slip step corresponding to 0 in the junction where the total energy difference is equal to 0 and not equal to 0, select a minimum value from the selected 3 slip step lengths, and use this value as the optimal slip step length, and use the slip angle and slip distance corresponding to the optimal slip step length as the optimal slip angle step length and slip distance step length.

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

[0027] Step 61: Randomly select a preset number of interlayer spacings within a preset interlayer spacing range for each sliding stacking configuration;

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

[0029] Step 63: Split the i-th round data set into a training set and a test set, train the GPR model using the training set to obtain a trained GPR model, input each inter-layer spacing in the test set into the trained GPR model in sequence, predict the corresponding total energy, and calculate the standard deviation of the obtained total energies;

[0030] Step 64: Determine whether the standard deviation is below a preset threshold. If yes, proceed to step 65; if no, 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 of the stacking configuration;

[0032] Step 66: Determine the next round of interlayer spacing based on the standard deviation, set i=i+1, and execute step 62.

[0033] The beneficial effects of the present invention are:

[0034] The present invention first evaluates the lattice matching of any two single-layer two-dimensional nanomaterials and corrects the single layer with a large lattice mismatch rate. The advantages are: reducing the stress and defects at the interface of the subsequently generated double-layer slip stacking configuration, avoiding delamination or rupture of the stacking configuration, and thus significantly improving its structural stability; next, the two matched zero-slip stacked single-layer two-dimensional nanomaterials are subjected to a slip operation. Due to the different slip distances and slip angles, a variety of slip stacking configurations will be generated. Based on obtaining the optimized slip angle step and slip distance step, the present invention generates multiple groups of slip vectors, and uses the Bayesian optimization algorithm to match the optimal interlayer spacing for each slip stacking configuration, ultimately realizing a global search of the slip stacking configuration of this type of material, and generating all possible double-layer slip stacking configurations; finally, the present invention selects one double-layer slip stacking configuration as the ground state stacking configuration by calculating the total energy; therefore, the present invention can obtain a ground state stacking configuration with stable structure, and the recognition method of the present invention is highly accurate.

[0035] This invention not only provides an efficient global search tool for the study of double-layer slip stacking configurations of ground-state two-dimensional nanomaterials, lays a methodological foundation for establishing a universal multilayer material structure prediction model, but also promotes the practical application of new two-dimensional nanomaterials in high-performance devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flowchart of the method for identifying the ground-state stacking configuration of atomic-scale double-layer two-dimensional nanomaterials;

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

[0038] Figure 3 This is a schematic diagram of the calculation method for the bond length difference and bond angle difference of the stacking configuration of double-layer two-dimensional nanomaterials. In the figure, Figure 3 (a) is the sliding angle of 0° and the sliding distance of Top and side views of the AA stacking configuration, Figure 3 (b) The sliding angle is 0° and the sliding distance is j Top and side views of the stacked configuration, Figure 3 (c) The sliding angle is 0° and the sliding distance is Top and side views of the stacked configuration, Figure 3 (d) is the sliding angle i° and the sliding distance is The top view and side view of the stacking configuration, in which L0 and θ0 represent the representative B1-B2 bond length and bond angle (∠B1B2B3) in the upper layer of the initial stacking configuration, respectively. n and θ mrepresent the representative B1-B2 bond length and bond angle (∠B1B2B3) in the upper layer of the double-layer slip stacking configuration, w i and s j represent the slip angle and slip distance, respectively; |ΔL| and |Δθ| represent the absolute value of the difference in bond length and bond angle between the initial stacking configuration and the slipped stacking configuration, respectively;

[0039] Figure 4 This is a test diagram of the bond length difference |ΔL|, bond angle difference |Δθ| and total energy difference |ΔE| of the double-layer boron olefin stacking configuration. In the figure, Figure 4 (a) is the sliding distance step s j Bond length difference |ΔL| test graph, 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) is the slip angle w i Bond length difference |ΔL| test graph, Figure 4 (e) is w i The bond angle difference |Δθ| test diagram, Figure 4 (f) is w i Total energy difference |ΔE| test diagram, P represents the selected critical point;

[0040] Figure 5 is the optimal interlayer spacing d of the double-layer stacking configuration based on Bayesian optimization i Prediction flow chart;

[0041] Figure 6 Schematic diagram of the fitting of the Gaussian process regression model to the relationship between interlayer spacing and total energy;

[0042] Figure 7 Schematic diagram of the sampling function workflow (the relationship between the expected improvement (EI) value and the inter-layer spacing under different iteration rounds);

[0043] Figure 8 The top view, side view and binding energy of a single-layer borophene are shown in the figure. Figure 8 (a) Figure 8 (b) Figure 8 (c) Figure 8 (d) Figure 8 (e) Figure 8 (f) and Figure 8 (g) Monolayer α7-, α8-, α1-, α-, α5-, χ3-, and β 12 -Top and side views of borophene;

[0044] Figure 9The geometric structures of three types of bilayer borophene at 300K, the potential energy and phonon scattering spectra within 6ps of AIMD simulation time;

[0045] In the figure, Figure 9 (a) Figure 9 (d) and Figure 9 (g) Top view and side view of the bilayer α7-α8-borophene, bilayer α5-α8-borophene, and bilayer α7-α7-borophene models at 300K, respectively; Figure 9 (b) Figure 9 (e) and Figure 9 (h) Potential energies of bilayer α7-α8-borophene, bilayer α5-α8-borophene, and bilayer α7-α7-borophene systems within 6 ps AIMD simulation time, respectively;

[0046] Figure 9 (c) Figure 9 (f) and Figure 9 (i) Phonon scattering spectra of bilayer α7-α8-borophene, bilayer α5-α8-borophene, and bilayer α7-α7-borophene systems (atomic line graph neural network (ALIGNN)).

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

[0048] In the figure, Figure 10 (a) Figure 10 (d) and Figure 10 (g) Potential energies of bilayer α7-α8-borophene, bilayer α5-α8-borophene, and bilayer α7-α7-borophene systems at 500K within 6ps AIMD simulation time;

[0049] Figure 10 (b) Figure 10 (e) and Figure 10 (h) Potential energies of bilayer α7-α8-borophene, bilayer α5-α8-borophene, and bilayer α7-α7-borophene systems at 1000K within 6ps AIMD simulation time;

[0050] Figure 10 (c) Figure 10 (f) and Figure 10 (i) Potential energies of bilayer α7-α8-borophene, bilayer α5-α8-borophene, and bilayer α7-α7-borophene systems at 2000 K within 6 ps AIMD simulation time. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0052] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other.

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

[0054] Example:

[0055] A method for identifying the ground state stacking configuration of a double-layer two-dimensional nanomaterial at the atomic scale, characterized in that the method comprises the following steps:

[0056] Step 1: determine whether any two single-layer 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 systems of the two monolayer two-dimensional nanomaterials into the same crystal system, and then proceed to step 3;

[0058] Step 3: The lattice of each single-layer two-dimensional nanomaterial has a side length along the x-axis and a side length along the y-axis. Based on the lattice side lengths of any two single-layer two-dimensional nanomaterials, the lattice mismatch ratio of the two single-layer two-dimensional nanomaterials is calculated. If the lattice mismatch ratio is greater than a preset value, step 4 is executed; if the lattice mismatch ratio is less than the preset value, step 5 is executed.

[0059] Step 4: scaling the lattices of the two single-layer two-dimensional nanomaterials so that the lattice mismatch rate of the two single-layer two-dimensional nanomaterials after scaling is less than a preset value, and then executing Step 5;

[0060] Step 5, selecting the maximum side length from the four lattice side lengths of the two monolayer two-dimensional nanomaterials as the maximum slip distance;

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

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

[0063] Specifically, this embodiment is implemented based on Python programming, which can automatically generate all possible double-layer slip stacking configurations of any two given single-layer two-dimensional nanomaterials and efficiently identify their ground-state stacking configurations. The workflow is as follows: Figure 1As shown, the process involves five steps: (i) Python library import and single-layer material input, (ii) maximum slip distance calculation, (iii) slip angle and distance step calculation, (iv) mirror transformation and upper-layer slip, and (v) structure optimization and ground-state stacking configuration identification. Function names are written in the "function name" format, with Pymatgen and ASE used for crystal operations and Numpy for mathematical calculations. The specific process is as follows: 17 Pymatgen functions, including "Structure," "Poscar," "CifWriter," and "StructureMatcher," are called for operations such as crystal structure analysis, geometry file format conversion, and equivalent structure identification. Four Numpy functions, including "Dot," "Add," "Max()," and "Min()," are called for basic numerical computations such as matrix multiplication, element-wise addition, and maximum and minimum value extraction, providing efficient mathematical support for subsequent lattice parameter transformation and structure screening. DFT calculations are performed by invoking first-principles software (such as DFTB+, VASP, and CASTEP) through the four functions integrated into ASE: "Calculators," "Dftbplus," "Castep," and "Vasp." Working collaboratively with these 25 core functions, BiLayerStacker fully automates the entire process, from structural analysis and numerical computation to first-principles calculations.

[0064] Steps 1, 2, and 4 achieve Figure 1 Part (i) of the process; steps 3 and 5 implement Figure 1 Part (ii) of the process; step 6 is to achieve Figure 1 The process of part (iii) and part (iv) in step 7 is implemented Figure 1 The process in part (v) of this document.

[0065] Among all the generated double-layer two-dimensional nanomaterial slip stacking configurations, although some configurations have differences in geometric arrangement (such as different interlayer slip positions or different stacking orders), from the perspective of physical nature and symmetry, they may actually be equivalent. The atomic arrangements of such configurations can be mapped to each other through spatial symmetry operations (such as translation, rotation or mirror transformation), which leads to them showing completely consistent characteristics in energy, electronic structure and other physical and chemical 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, so duplicate configurations should be deleted in step 7.

[0066] The core purpose of geometric optimization is to make the material reach the optimal state by adjusting the position, shape or arrangement of the atomic or molecular structure, thereby providing a reliable structural basis for subsequent physical and chemical property analysis.

[0067] The entire process of generating all possible double-layer slip stacking 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 stacking configurations (due to the different chemical environments of the upper and lower surfaces of the monolayer materials) - use Bayesian optimization to adjust the interlayer spacing - apply slip vectors - generate all double-layer slip stacking configurations - deduplication, geometric optimization and total energy sorting - ground state configuration.

[0068] Further defined, in step 2, the crystal systems of the two monolayer two-dimensional nanomaterials are converted into the same crystal system, and the specific process is:

[0069] The crystal system of the single-layer two-dimensional nanomaterial with higher symmetry among the two single-layer two-dimensional nanomaterials is taken as the target crystal system, and the lattice basis vectors of the other single-layer two-dimensional nanomaterial are projected into 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 by using lattice reparameterization and rotation tensor method to obtain an equivalent lattice. The equivalent lattice is mapped to the target crystal system. The mapped lattice belongs to the same crystal system as the crystal system of the other single-layer two-dimensional nanomaterial.

[0070] Specifically, when the crystal systems to which the two monolayer materials belong are inconsistent (such as hexagonal and cubic systems), the lattice basis vector matrix of the monolayer material is standardized, and combined with dynamic symmetry matching, equivalent lattice mapping between heteromorphic materials is achieved. For example, when the two input monolayer materials belong to the triclinic system and the cubic system, the cubic system is set as the target crystal system because of its higher symmetry. First, the original lattice basis vector of the triclinic monolayer is projected to the Cartesian coordinate system by coordinate transformation to obtain the rectangular coordinate lattice parameters equivalent to the original triclinic system. On this basis, the lattice reparameterization and rotation tensor techniques are used to construct an equivalent lattice structure that is symmetric with the target crystal system (cubic system). Finally, the equivalent lattice is mapped to the target crystal system to complete the compatibility conversion of the low-symmetry crystal system to the 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 ratio 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 define, in step 3, the lattice mismatch ratio r m Expressed as:

[0072]

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

[0074] Specifically, to avoid the periodic boundary problem, the mismatch ratio of the two lattices is calculated. Max() is a maximum function used to select the maximum value of a given variable; Min() is a minimum function used to select the minimum value of a given variable.

[0075] When r m <5%, the "maximum slip distance calculation" module will be triggered through the conditional branch. m ≥5%, the structure is scaled twice to make the upper and lower single-layer structures meet r m Under the lattice matching condition of <5%, the secondary scaling process consists of four key steps: (a) supercell expansion, (b) periodicity removal, (c) lattice structure trimming, and (d) periodicity restoration.

[0076] Further limiting,

[0077] In step 4, the process of scaling the lattices of the two single-layer two-dimensional nanomaterials is as follows:

[0078] Step 41, supercell expansion: aligning the side length a1 along the x-axis and the side length b1 along the y-axis of a single-layer two-dimensional nanomaterial lattice with the side length a2 along the x-axis and the side length b2 along the y-axis of another single-layer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice consisting of the maximum values ​​of a1 and a2 and the maximum values ​​of b1 and b2; aligning the side length a1 along the x-axis and the side length b1 along the y-axis of a single-layer two-dimensional nanomaterial lattice with the side length b2 along the y-axis and the side length a2 along the x-axis of another single-layer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice consisting of the maximum values ​​of a1 and b2 and the maximum values ​​of b1 and a2; selecting the new lattice with the smallest area from the two new lattices as a candidate lattice; performing cell expansion processing on the two single-layer two-dimensional nanomaterial lattices respectively to obtain two expanded lattices, and both expanded lattices cover the area of ​​the candidate lattice;

[0079] Step 42: removing 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: trimming the two non-periodic two-dimensional nanostructures using the candidate lattice size as a trimming frame to obtain two trimmed two-dimensional nanostructures, wherein the atoms in the two trimmed lattices are intact atoms;

[0081] Step 44, periodicity recovery: reconstruct the periodicity of each cropped two-dimensional nanostructure in the x, y and z directions to obtain two processed single-layer 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 be determined first so that they can simultaneously meet the lattice matching conditions and the minimum integer multiple expansion requirements. n and b n (n=1, 2) can be aligned with the x or y direction of the lower (upper) layer respectively, Figure 2 Two lattice alignments are automatically enumerated in Figure 2 For each alignment, two new sets of lattice parameters ( Figure 2 Parts II and III of the , namely:

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

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

[0086] Wherein, (a1', b1') and (a2', b2') represent the new lattice parameters used for the two-layer stacking configuration generated in the two lattice alignment modes. Since the unit 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 stacking configuration construction, in order to reduce the consumption of computing resources while ensuring physical rationality, the set of lattice parameters corresponding to the smallest unit cell area is used as the lattice parameters (a1', b1') for the subsequent pre-construction of the double-layer slip stacking configuration. new and b new ; Figure 2 After determining the lattice parameters used for the double-layer stacking configuration, the upper and lower monolayers are expanded by integer multiples of the lattice parameters along the x-direction and y-direction respectively until they can completely cover the a-shaped structure in both directions. new and b new The defined area.

[0087] (b) Periodic removal:

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

[0089] (c) Lattice structure tailoring:

[0090] The lattice parameters used to obtain the double-layer stacking configuration (a new and b new ) and complete the supercell expansion, first define a "cropping box": the length of the "cropping box" in the x and y directions is a new and b new .by The "cropping box" is translated within the aperiodic two-dimensional nanostructure with a step size of 1.5, ensuring that the cropping box does not exceed the boundary of the aperiodic two-dimensional nanostructure. At each translation position, the atomic distribution at the "cropping box" boundary is detected. Only when the returned cropping region is free of atoms at the edge, the upper and lower monolayers are cropped at that position. The goal of cropping is to find the optimal cropping position where no atoms lie on the cropping box edge.

[0091] (d) Periodic recovery:

[0092] After completing the automatic cutting of the upper and lower single-layer structures, according to the lattice parameters (a new and b new )Reconstruct the periodic unit cell, where a=a new , b=b new , The lattice angles α, β, and γ inherit the values ​​of the original structure, restoring the periodicity of the trimmed two-dimensional nanostructure. The modified upper and lower monolayers serve as input for the subsequent generation of a bilayer slip stacking configuration.

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

[0094] Calculate the initial stacking configuration (( Figure 3 (a) and (c)) and the slip stacking configuration (( Figure 3The bond length difference, bond angle difference and total energy difference of (b) and (d)) are selected, and the slip step corresponding to the bond length difference being equal to 0 and not equal to 0 at the junction, the slip step corresponding to the bond angle difference being equal to 0 and not equal to 0 at the junction, and the slip step corresponding to the total energy difference being equal to 0 and not equal to 0 at the junction are selected. A minimum value is selected from the selected three slip steps, and the value is taken as the optimal slip step, and the slip angle and slip distance corresponding to the optimal slip step are taken as the optimal slip angle step and slip distance step.

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

[0096] Step 61: Randomly select a preset number of interlayer spacings within a preset interlayer spacing range for each sliding stacking configuration;

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

[0098] Step 63: Split the i-th round data set into a training set and a test set, train the GPR model using the training set to obtain a trained GPR model, input each inter-layer spacing in the test set into the trained GPR model in sequence, predict the corresponding total energy, and calculate the standard deviation of the obtained total energies;

[0099] Step 64: Determine whether the standard deviation is below a preset threshold. If yes, proceed to step 65; if no, 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 of the stacking configuration;

[0101] Step 66: Determine the next round of interlayer spacing based on the standard deviation, set i=i+1, and execute step 62.

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

[0103] In order to complete the efficient global search of the slip stacking configuration of double-layer two-dimensional nanomaterials, the strategy of "fixing the lower layer and sliding the upper layer" is adopted. Since two-dimensional nanomaterials have strict periodic boundaries, if the slip distance exceeds the reasonable range, it is easy to cause repeated configurations or lattice mismatch, thereby reducing work efficiency. To this end, the slip distance threshold of the upper structure is automatically determined. By analyzing the lattice parameters of the upper and lower single-layer structures (i.e., a1, b1 and a2, b2), the lattice parameter with the largest length is extracted and defined as the maximum slip distance (d max=Max(a1,b1,a2,b2)). In the subsequent stacking configuration generation process, the sliding distance in any direction is limited to less than d max , thereby reducing the generation of repeated structures and significantly improving the efficiency of global search.

[0104] Slide angle and distance step calculation:

[0105] Appropriate slip angle and distance step are the key to completing the global search of double-layer slip stacking configurations. On the one hand, too large a step size will lead to an incomplete search range and fail to cover all possible slip stacking configurations, resulting in the omission of the true ground state double-layer stacking configuration; while too small a step size can ensure a global search, but it will lead to the generation of a large number of repeated configurations, which not only wastes computing resources but also reduces work efficiency. In summary, in order to simultaneously ensure the globalization and search efficiency of the double-layer slip stacking configuration search, the optimal slip distance step (s) and slip angle step (w) are automatically determined. Taking the key structural parameters (bond length and bond angle) of the configuration and the change in total energy as evaluation indicators, a series of candidate step combinations (w i ,s j ) to evaluate its performance in stacking configuration resolution and configuration repeatability. Specifically, the evaluation criteria for s and w are "minimum repeat step length", that is, the maximum step length selected before the sliding step length increases to the critical value that first triggers a significant change in the geometry or energy of the stacking configuration. Taking bilayer α7-borophene as an example ( Figure 3 ), the specific process of pre-test is as follows:

[0106] Sliding distance step test:

[0107] The initial configuration is a double-layer α7-borophene stacked with AA (w i =0°; Figure 3 (a)), the optimal interlayer spacing value predicted by the Bayesian optimization algorithm is the preset interlayer spacing (see "(iv) Mirror image change and upper layer slip" section for details), The step length is 13 double-layer slip stacking configurations are automatically generated within the range ( Figure 3 (b)) and perform geometry optimization on them; their 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 (a)-(c) are shown. When s j Increase from 0 to When |ΔL| and |ΔE| show obvious fluctuations ( Figure 4 (a) and (c)), and when s j When it reaches 0.5, |Δθ| shows obvious fluctuations ( Figure 4 (b)); Considering |ΔL|, |Δθ| and |ΔE|, select As the "minimum repetition distance step". A large number of repeated configurations will be generated; if This will result in the omission of the true ground-state double-layer stacking configuration.

[0108] Slip angle step test:

[0109] by w i = 0° double-layer α7 borophene slip stacking configuration is the initial configuration ( Figure 3 (c)), the optimal interlayer spacing value tested is used as the preset interlayer spacing (see "(iv) Mirror image change and upper layer slip" section for details), and 11 double-layer slip stacking configurations are automatically generated in the range of 0-10° with a step size of 1° ( Figure 3 (d)) and perform geometry 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 (f)) changes, such as Figure 4 (d)-(e) are shown. When w i When increasing from 0° to 4°, |ΔL| and |ΔE| show obvious fluctuations ( Figure 4 (d) and (f)), and when w i When it reaches 5°, |Δθ| shows obvious fluctuations ( Figure 4 (e)); Comprehensively consider |ΔL|, |Δθ| and |ΔE|, and select w i =3° as the “minimum repetition distance step”. If w i <3°, a large number of repeated configurations will be generated; if w i >3°, the true ground-state double-layer stacking configuration will be missed.

[0110] Mirror image changes and upper layer sliding:

[0111] In two-dimensional nanomaterials, there are a large number of non-"purely flat" configurations, that is, there are more or less wrinkles in the surface; this will lead to different chemical environments on the upper and lower surfaces of these materials. Therefore, when studying the stacking configuration of double-layer two-dimensional nanomaterials, both the upper and lower surfaces of the two single layers should be taken into account to ensure that the generated configuration space can fully cover all possible interlayer interactions. Based on this, four stacking combinations are analyzed: "TD", "TD'", "T'D" and "T'D'", such as Figure 1 As shown in part iv of the figure, “T” and “D” represent the upper and lower single-layer structures of the input, respectively, while “T'” and “D'” represent the mirror-flipped structures of the upper (T) and lower (D) single layers relative to the xy plane.

[0112] All possible combinations of interlayer interactions are considered. First, the mirror-image flip structures (T′ and D′) of the upper (T) and lower (D) layers relative to the xy plane are constructed; secondly, The initial interlayer spacing of the upper layer (T or T′) and the lower layer (D or D′) are merged to generate four stacking combinations (w i =0°; ), that is, “TD”, “TD′”, “T′D” and “T′D′” ( Figure 1 Part iv). Again, the optimal layer spacing d is determined by the Bayesian optimization (BO) algorithm. i ( Figure 5 ), and the average interlayer spacing of the four double-layer stacking configurations is set as d i ; and place it in the middle position in the z direction. Finally, fix the lower layer and apply the slip vector V(w,S) to the upper layer to generate all possible double-layer slip stacking configurations, realizing a global search for double-layer slip stacking configurations.

[0113] The Bayesian optimization algorithm is used to find the optimal solution for each double-layer slip stacking configuration (“TD”, “TD’”, “T’D” and “T’D’”; w i =0°; ) to determine the optimal interlayer spacing (d i ), the obtained d i As the initial stacking configuration ("TD", "TD'", "T'D" and "T'D'"); w i =0°; ). The Bayesian optimization algorithm for determining the optimal interlayer spacing includes 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 data set construction:

[0115] For each stacking configuration ("TD", "TD'", "T'D" and "T'D'"; w i =0°; ),exist 12 interlayer spacing values ​​(d) are randomly selected within the range, and the corresponding double-layer slip stacking configuration is automatically generated based on them. On this basis, the first-principles calculation is performed on the above configuration to obtain the total energy (E total ). Finally, each group (d,E total ) data were paired and sorted to construct the initial data set ( Figure 5 (1) in the middle), providing data support for the subsequent Gaussian process regression (GPR) model fitting and Bayesian optimization iterative sampling.

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

[0117] After the initial dataset is established, it is divided into a training set and a test set in a ratio of 8:2, and the GPR model is trained based on the training set to fit the relationship between the interlayer spacing (d) and the total energy (E total ) Figure 5 (2) part and Figure 6 The GPR model can not only predict the total energy, but also provide a confidence interval ( Figure 6 The purple shaded band in the middle), that is, the standard deviation σ(d), is used to measure the uncertainty of the prediction: the larger the confidence interval (the larger the standard deviation), the higher the uncertainty; the smaller the confidence interval, the more reliable the prediction. In addition, Figure 6 This is the interlayer spacing-total energy curve fitted by the GPR model. A larger confidence interval indicates greater uncertainty in the model in that region, and vice versa. The Bayesian optimization algorithm prioritizes sampling points with greater uncertainty to improve model accuracy.

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

[0119] After the initial fitting of the GPR model, the expected improvement (EI) sampling function is introduced ( Figure 7 ), select the inter-layer spacing value (d) with the best prediction performance of the improved GBP model as the next round of sampling point d next The calculation of the EI value depends on the predicted mean μ(d) and standard deviation σ(d) of the total energy by the current GPR model. In each iteration, the interlayer spacing d corresponding to the peak of the EI curve is selected. next As a new sample point, perform first-principles calculations to obtain the true total energy E total , then add it to the training set and retrain the GPR model ( Figure 5 After selecting the sampling point, the corresponding total energy is obtained by first principle calculation, and the new sample (d next ,E total ) into the training set and used to update the GPR model ( Figure 5 The above “sampling-updating” process continues, and the model’s predictive ability continues to improve.

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

[0121] As the GPR model is updated in successive rounds and the training samples are continuously expanded, the fitting accuracy of the entire prediction model to the total energy function continues to improve. 3 eV), indicating that the model has fully learned the search space and the Bayesian optimization process is terminated. Finally, the layer spacing with the lowest total energy is output as the optimal layer spacing d for the stacking configuration. i ( Figure 1 (iv) of the annex.

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

[0123] To improve the efficiency of geometric optimization of bilayer slip stacking structures, duplicate configurations were removed and the selected configurations were saved as POSCAR and CIF files. Based on this, the remaining bilayer stacking configurations were then geometrically optimized using computational software such as DFTB+ or VASP, which are called from the ASE library. Ultimately, the top 30 lowest-energy configurations were automatically selected as output, from which one was selected as the ground state.

[0124] Verification and application:

[0125] In order to evaluate the effectiveness of this embodiment, double-layer borophene was selected as the test object. Borophene, as an emerging two-dimensional nanomaterial, has attracted widespread attention from researchers due to its structural diversity and unique physical and chemical properties. Borophene's excellent properties such as ultra-high thermal conductivity, excellent mechanical properties, twisted Dirac fermions and phonon-mediated superconductivity make it an ideal material for stacking engineering research. In previous studies, scholars have synthesized a variety of single-layer borophene, such as α-, β-, β1-, β8-, β- on metal substrates such as Cu(111), Ag(111) / (110) / (100), Al(111), Au(111) and Ir(111) by molecular beam epitaxy (MBE), atomic layer deposition (ALD) and chemical vapor deposition (CVD). 12 -、β 13-, δ3-, δ6-, χ6- and χ3-borene, etc. However, although these single-layer borene structures show good stability on the substrate, their stability decreases rapidly after exposure to air or peeling from the substrate, which seriously limits their practical application in devices. In 2021, Liu et al. and Chen et al. successfully synthesized double-layer α-borene and β-borene on Ag (111) substrate and Cu (111) substrate respectively using MBE technology. 12 The discovery of α-borophene marks a significant advance in the study of multilayer borophene. Although the experimentally prepared double-layer borophene exhibits slightly higher thermodynamic stability than single-layer borophene, it also suffers from poor stability when exposed to air or peeled from a substrate, limiting its practical application in devices. Furthermore, the experimentally obtained borophene configurations are not always the most thermodynamically 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 borophene configuration space. This phenomenon highlights the irreplaceable role of theoretical research in borophene configuration design. Recent theoretical research by Wang et al. demonstrated a positive correlation between the number of layers and the stability of α-, α5-, α7-, and α8-borophene, revealing the important role of layer number in the stability of borophene materials. In summary, exploring new independent multilayer (e.g., double-layer) borophene configurations with improved structural stability will not only facilitate the experimental preparation of multilayer borophene but also provide a theoretical basis for structural control in stacking engineering. However, no studies have yet been reported on the global search and ground-state configuration identification of double-layer borophene slip stacking configurations. Therefore, systematically revealing the slip stacking mode and stable configuration construction rules of double-layer borophene from a theoretical perspective will promote the practical application of borophene materials in devices.

[0126] In this study, seven typical monolayer borophene structures (α, α1, α5, α7, α8, β 12 and χ3; Figure 8 ) as input, exploring 28 different combinations of bilayer borophene stacking configurations (Tables 1 and 2), generating approximately 320,000 bilayer borophene slip stacking configurations. Based on this, the top 30 configurations with the lowest total energy in each combination were automatically selected. Finally, the resulting 840 bilayer borophene slip stacking configurations were submitted to the DMol3 module for geometry optimization. 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 example.

[0127] Table 1 The number of bilayer borophene stacking structures generated under 28 different input monolayer combinations (N S ), sliding angle step (w, °) and sliding distance step Optimal layer spacing and the highest value among the top 30 binding energies (E bmax ,

[0128] eV / atom) and the lowest value (E bmin , eV / atom)

[0129]

[0130]

[0131] The geometry optimization results show that the 840 bilayer borophene slip stacking configurations output all have very high binding energies, with values ​​ranging from 6.111 to 6.567 eV / atom, which is close to the binding energy range of 6.159 to 6.563 eV / atom reported in the literature (Tables 1 and 2). 7AB -The geometry and binding energy of borophene configuration (E b =6.563eV / atom) is completely consistent, confirming that the double-layer α 7AB -borophene stacking configuration is indeed the ground state configuration. n -B m Indicates that the upper layer is A n , the lower layer is B m In addition, the binding energy values ​​of the output double-layer α-α-borene configuration, double-layer α5-α5-borene configuration and double-layer α8-α8-borene configuration are 6.435, 6.563 and 6.563 eV / atom, respectively, which are higher than the double-layer α reported in the literature. AB -、α 5AB - and α 8AB -The highest values ​​of the binding energy of the borophene configuration are 6.431, 6.562 and 6.560 eV / atom, respectively; this indicates that the previously reported stacking configurations are not the local energy minima in the stacking configuration space, and bilayer α7-α8-, α5-α8- and α7-α7-borophene are the ground state structures of the corresponding configuration space.

[0132] It is noteworthy that the binding energies of the two new types of bilayer α7-α8- and α5-α8-borophene (6.567 eV / atom (bilayer α7-α8-borophene); 6.566 eV / atom (bilayer α5-α8-borophene)) both exceed the highest binding energy of bilayer borophene reported in the literature (6.563 eV / atom). 7AB -borene)), indicating that bilayer α7-α8- and α5-α8-borene are the most thermodynamically stable bilayer borene stacking configurations reported so far. In addition, the molecular dynamics (AIMD) simulation and phonon scattering spectrum analysis results of bilayer α7-α8- and α5-α8-borene at 300K ( Figure 9; 300K) showed that both have excellent thermodynamic and kinetic stability. In addition, AIMD simulations under 500K, 1000K and 2000K conditions ( Figure 10 ) The results show that bilayer α7-α8-, α5-α8- and α7-α7-borophene all have good thermal stability, further confirming the high thermodynamic and kinetic stability of these new configurations. The predicted bilayer borophene slip stacking configuration not only refreshes the upper limit of the binding energy of bilayer borophene reported in the literature, but also provides a clear target for experimental realization. It can be seen that the above verification further confirms the wide applicability of the atomic-scale double-layer two-dimensional nanomaterial ground state stacking configuration identification method in this study in the bilayer borophene system, demonstrating its powerful ability in global search and ground state identification of double-layer slip stacking configurations.

[0133] Table 2 shows the binding energy (E) of double-layer borophene 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 Double-layer borophene configuration

[0134]

[0135] Therefore, the method of this embodiment successfully identified two highly stable double-layer borene configurations (double-layer α7-α8- and α5-α8-borene). Since these two materials have high thermal stability, high transmittance (>83%) and excellent electrical conductivity (conductivity>10 5 S / m), so it has great application potential in transparent conductive film materials.

[0136] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. A method for identifying the ground state stacking configuration of atomic-scale double-layer two-dimensional nanomaterials, characterized in that: The method includes the following: Step 1: determine whether any two single-layer 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 systems of the two monolayer two-dimensional nanomaterials into the same crystal system, and then proceed to step 3; Step 3: The lattice of each single-layer two-dimensional nanomaterial has a side length along the x-axis and a side length along the y-axis. Based on the lattice side lengths of any two single-layer two-dimensional nanomaterials, the lattice mismatch ratio of the two single-layer two-dimensional nanomaterials is calculated. If the lattice mismatch ratio is greater than a preset value, step 4 is executed; if the lattice mismatch ratio is less than the preset value, step 5 is executed. Step 4: scaling the lattices of the two single-layer two-dimensional nanomaterials so that the lattice mismatch rate of the two single-layer two-dimensional nanomaterials after scaling is less than a preset value, and then executing Step 5; Step 5, selecting the maximum side length from the four lattice side lengths of the two monolayer two-dimensional nanomaterials as the maximum slip distance; Step 6: Perform relative sliding of the two monolayer two-dimensional nanomaterial lattices with different angle steps and different distance steps to obtain multiple slip stacking configurations, select the slip angle step and slip distance step corresponding to the optimal slip stacking configuration from the multiple slip stacking configurations as the optimal slip angle step and the optimal slip distance step, respectively, select P times the optimal slip angle step as the candidate slip angle, and the candidate slip angle satisfies less than 360 degrees, P = 1, 2, 3 ... M, and select M candidate slip angles in total, select F times the optimal slip distance step as the candidate slip distance, and the candidate slip distance satisfies less than the maximum slip Distance condition, F = 1, 2, 3 ... L, a total of L candidate slip distances are selected, and one value is selected from each of the M candidate slip angles and L candidate slip distances to form a set of slip vectors. Each single-layer two-dimensional nanomaterial has two surfaces, an upper surface and a lower surface. Two single-layer two-dimensional nanomaterials form a total of four zero-slip stacking configurations. Each zero-slip stacking configuration is slipped according to each slip vector to obtain multiple slip stacking configurations. The Bayesian optimization algorithm is used to determine the optimal interlayer spacing for the two single-layer two-dimensional nanomaterials in each slip stacking configuration. All possible double-layer slip stacking configurations are generated based on each set of slip vectors and the corresponding optimal interlayer spacing. Step 7. Remove the repeated double-layer slip stacking configurations from the multiple double-layer slip stacking configurations, and then perform geometric optimization on the remaining double-layer slip stacking configurations to obtain the total energy of each optimized double-layer slip stacking configuration. Sort the total energies of the optimized multiple double-layer slip stacking configurations from low to high, and select the first double-layer slip stacking configuration as the ground state stacking configuration.

2. The method for identifying the ground state stacking configuration of a double-layer two-dimensional nanomaterial at the atomic scale 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 single-layer two-dimensional nanomaterial with higher symmetry among the two single-layer two-dimensional nanomaterials is taken as the target crystal system, and the lattice basis vectors of the other single-layer two-dimensional nanomaterial are projected into 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 by using lattice reparameterization and rotation tensor method to obtain an equivalent lattice. The equivalent lattice is mapped to the target crystal system. The mapped lattice belongs to the same crystal system as the crystal system of the other single-layer two-dimensional nanomaterial.

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

4. The method for identifying the ground state stacking configuration of atomic-scale double-layer two-dimensional nanomaterials according to claim 1, characterized in that: In step 4, the process of scaling the lattices of the two single-layer two-dimensional nanomaterials is as follows: Step 41, supercell expansion: aligning the side length a1 along the x-axis and the side length b1 along the y-axis of a single-layer two-dimensional nanomaterial lattice with the side length a2 along the x-axis and the side length b2 along the y-axis of another single-layer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice consisting of the maximum values ​​of a1 and a2 and the maximum values ​​of b1 and b2; aligning the side length a1 along the x-axis and the side length b1 along the y-axis of a single-layer two-dimensional nanomaterial lattice with the side length b2 along the y-axis and the side length a2 along the x-axis of another single-layer two-dimensional nanomaterial lattice, respectively, to obtain a new lattice consisting of the maximum values ​​of a1 and b2 and the maximum values ​​of b1 and a2; selecting the new lattice with the smallest area from the two new lattices as a candidate lattice; performing cell expansion processing on the two single-layer two-dimensional nanomaterial lattices respectively to obtain two expanded lattices, and both expanded lattices cover the area of ​​the candidate lattice; Step 42: removing 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: trimming the two non-periodic two-dimensional nanostructures using the candidate lattice size as a trimming frame to obtain two trimmed two-dimensional nanostructures, wherein the atoms in the two trimmed lattices are intact atoms; Step 44, periodicity recovery: reconstruct the periodicity of each cropped two-dimensional nanostructure in the x, y and z directions to obtain two processed single-layer two-dimensional nanomaterial lattices.

5. The method for identifying the ground state stacking configuration of an atomic-scale double-layer two-dimensional nanomaterial according to claim 1 or 4, characterized in that: In step 6, the sliding angle step and sliding distance step corresponding to the optimal sliding shape are selected from multiple sliding shapes as the optimal sliding angle step and the optimal sliding distance step, respectively. The specific process is as follows: Calculate the bond length difference, bond angle difference and total energy difference between the initial slip stacking configuration and the slip stacking configuration, select the slip step corresponding to 0 in the junction where the bond length difference is equal to 0 and not equal to 0, select the slip step corresponding to 0 in the junction where the bond angle difference is equal to 0 and not equal to 0, and the slip step corresponding to 0 in the junction where the total energy difference is equal to 0 and not equal to 0, select a minimum value from the selected 3 slip step lengths, and use this value as the optimal slip step length, and use the slip angle and slip distance corresponding to the optimal slip step length as the optimal slip angle step length and slip distance step length.

6. The method for identifying the ground state stacking configuration of atomic-scale double-layer 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 two monolayer 2D nanomaterials in each slip stacking configuration. The specific process is as follows: Step 61: Randomly select a preset number of interlayer spacings within a preset interlayer spacing range for each sliding stacking configuration; Step 62: Calculate the total energy corresponding to each interlayer spacing according to the first principles, and use the interlayer spacing and the corresponding total energy as the data of the i-th round data set, where the initial value of i is 1; Step 63: Split the i-th round data set into a training set and a test set, train the GPR model using the training set to obtain a trained GPR model, input each inter-layer spacing in the test set into the trained GPR model in sequence, predict the corresponding total energy, and calculate the standard deviation of the obtained total energies; Step 64: Determine whether the standard deviation is below a preset threshold. If yes, proceed to step 65; if no, 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 of the stacking configuration; Step 66: Determine the next round of interlayer spacing based on the standard deviation, set i=i+1, and execute step 62.

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