Calculation method for oxygen evolution reaction overpotential of high-entropy alloy catalyst based on preferred occupation

Abstract

The application provides a high-entropy alloy catalyst oxygen evolution reaction overpotential calculation method based on preferred occupation, comprising the following steps: establishing a high-entropy alloy atom distribution supercell model based on the occupation fraction of various types of constituent elements of the high-entropy alloy on various sublattices and performing crystal structure relaxation, constructing a slab model according to the optimized structure model and performing R2 optimization; calculating the Gibbs reaction free energy change and site change of three intermediates on different types of adsorption sites, selecting a catalytic site, and obtaining the preferred element of different intermediates; and preliminarily screening a first nearest neighbor atom combination covering the preferred elements of different intermediates on the slab catalytic surface; obtaining the optimal catalytic site combination of different intermediates and obtaining the lowest overpotential for completing the catalytic reaction, calculating the lowest overpotential and the average overpotential of each optimal catalytic site combination. The application can more accurately construct a theoretical calculation model based on preferred occupation, so that the overpotential of the high-entropy alloy OER can be accurately predicted.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oxygen evolution reaction (OER) of high-entropy alloy catalysts, in particular to a method for calculating the overpotential of oxygen evolution reaction of high-entropy alloy catalysts based on preferred occupation. BACKGROUND

[0002] OER, as the anodic reaction of electrocatalytic water splitting, requires the participation of four electrons, and the efficiency of electrocatalytic water splitting is mainly limited by the high kinetic overpotential of anodic OER. Therefore, overcoming the large energy barrier and reducing the overpotential is the key requirement for designing high-performance electrocatalysts. The noble metal-based oxides IrO2 and RuO2 are currently practical electrocatalysts, however, their limited availability, high cost and low durability have severely limited their widespread application. Therefore, it is urgent to develop efficient and cost-effective catalysts to promote the development of water splitting applications.

[0003] High-entropy alloys (HEAs), also known as multi-principal element alloys (MPEAs), are characterized by equal or near-equal molar fractions of principal elements. The most obvious electrocatalytic effect of HEAs is that due to the different combinations of elements, the number of active sites increases with the growth of surface sites. A large number of different active sites on the catalytic surface provide different reaction types. With the increase in the number of active sites, the probability of encountering high catalytic active sites also rises significantly. Therefore, compared with single metals or binary alloys, HEAs can exhibit greater catalytic potential. In recent years, the application of HEAs as catalysts in the field of OER has attracted widespread attention. CoFeMoNi HEA catalysts exhibit an extremely low overpotential of 250 mV at a current density of 10 mA / cm2, and the catalytic activity is 89 mV lower than that of the most advanced IrO2 catalyst. HEAs / HEAs catalysts are significantly superior to commercial noble metal RuO2 catalysts. Therefore, HEAs catalysts have shown great potential, exceeding the catalytic activity of noble metal-based catalysts, and have great economic value in industry.

[0004] However, the exploration of HEAs as electrocatalysts is still in its early stages, especially regarding design and regulation strategies to improve catalytic performance. This is mainly because the synergistic effect of different elements in HEAs-based catalysts makes the catalytic mechanism unclear, and considering the time and money-consuming of experimental screening, reasonable theoretical calculation / prediction plays a key role in the development of HEAs-based catalysts. Among the limited HEAs catalysts, CoFeGaNiZn HEA has been quite comprehensively characterized, and some useful experimental data for OER catalysis have been obtained, such as the homogenization of FCC_CoFeGaNiZn HEA by Aditi et al. at 1273 K. In addition, the Zn atom has an abnormally low d-band center energy in CoFeGaNiZn HEA, making it worthy of attention in the study of OER mechanism.

[0005] Therefore, taking CoFeGaNiZn HEA as the research system can provide accurate information for constructing a theoretical model and verifying its reliability. This helps to more accurately explore the potential OER mechanism of HEAs. In addition, the screening of HEAs-based catalysts is heavily dependent on reliable catalytic “material banks”. The computational method based on density functional theory (DFT) is beneficial to determine the actual active sites of catalysis, thus providing a deeper understanding of the OER mechanism. Establishing a reliable atomic distribution of HEAs is a prerequisite for accurate prediction. Although it is generally believed that the constituent atoms are randomly distributed throughout the lattice, recently, some HEAs have shown ordered behavior. If a model is based on an unreasonable disordered crystal structure, i.e. the atoms on the lattice are completely randomly distributed, it may not reveal some unique or potential catalytic properties. For example, based on first-principles calculations, ordered CuFeNiPtRh HEA exhibits excellent electrocatalytic activity and CO tolerance for ethanol oxidation reaction (EOR) compared to disordered CuFeNiPtRh HEA. Therefore, if all metal atoms are assumed to be randomly or completely randomly occupied throughout the lattice when calculating catalytic performance, using quasi-random structure (SQS) or coherent potential approximation (CPA) simulation, some catalytic properties may be ignored.

[0006] In fact, due to the differences in constituent atoms and sublattices, it is inevitable that there will be a preference for occupation of sublattices or even heterogeneous phase structures. In our view, under certain composition and heat treatment temperature, the occupation preference can be described by the site occupation fraction (SOFs) and can be quantitatively characterized, thus further reasonably predicting various properties. Therefore, it is necessary to determine the details of the constituent atoms distributed in the sublattice, including the local region and the entire lattice.

[0007] Our previous work utilized an internally built thermodynamic database involving temperature-dependent Gibbs free energies of end-member compounds to predict the SOFs of various HEAs. In this work, the site-preferential configurations of FCC_CoFeGaNiZn HEA were obtained based on the predicted SOFs, which enabled us to more reasonably and reliably predict the adsorption energies at different sites of the HEA. Therefore, based on the reasonable atomic distribution model, the adsorption sites and catalytic mechanism of FCC_CoFeGaNiZn HEA in OER catalysis can be more deeply understood. In this paper, the free energy changes and position changes of OH, O and OOH three intermediates on 171 adsorption sites of FCC_CoFeGaNiZn HEA surface were systematically studied. In addition, we elucidated the three intermediate free energies of HEAs in OER, the changes of adsorption sites, the changes of morphology on the catalytic surface, the actual active sites of the catalyst, the scaling relationship, and the calculation of the average overpotential of the HEA surface. The purpose of the present invention is to establish a reasonable and general method to explore and describe the OER mechanism of HEAs, so as to screen and improve the HEA catalyst. SUMMARY

[0008] The purpose of the present application is to propose a high-entropy alloy catalyst oxygen evolution reaction overpotential calculation method based on preferential site occupation. Based on the preferential site occupation, a theoretical calculation model can be constructed more accurately, so that the overpotential of the high-entropy alloy OER can be accurately predicted. This method can provide a reliable calculation method for OER overpotential calculation of other high-entropy alloy systems, so as to screen out high-entropy alloy catalysts with superior performance.

[0009] To achieve the above purpose, the technical scheme of the present application is: a high-entropy alloy catalyst oxygen evolution reaction overpotential calculation method based on preferential site occupation, comprising the following steps:

[0010] Step S1: modeling based on the phase structure of high-entropy alloy phases, calculating the phonon spectrum by density functional perturbation theory to obtain temperature-dependent Gibbs free energy, constructing a formatted Gibbs free energy database of end-member compounds, and calculating the site occupation fraction of each type of constituent element in the high-entropy alloy on different types of sublattices based on the database;

[0011] Step S2: based on the site occupation fraction data of each type of constituent element on the sublattice, an n x n x n supercell model of the high-entropy alloy atomic distribution block is established by expanding the cell, and based on the principle of total energy minimization, the crystal structure relaxation of the actual atomic distribution structure model in the high-entropy alloy is carried out to obtain an optimized structure model;

[0012] Step S3: According to the optimized structure model, the average d-band center energy of each type of component element of the high-entropy alloy is calculated, the element with the highest average d-band center energy is obtained as the element with significant catalytic potential, then the cross section of the optimized structure model is cut, the surface containing the most atoms of the element with the highest average d-band center energy is selected as the slab catalytic surface, and the remaining n-1 close-packed planes in the loop are placed below the slab catalytic surface to construct an n-layer slab model containing a vacuum layer;

[0013] Step S4: The R2 optimization of the constructed n-layer slab model containing a vacuum layer is carried out by using the selected dynamics method, and the atoms in the bottom n-1 layers are locked during the optimization process, and the surface layer atoms are released;

[0014] Step S5: The Gibbs reaction free energy change values ΔG *OH , ΔG *O , ΔG *OOH and site changes of three intermediates *OH, *O and *OOH on different types of adsorption sites are calculated, and the site type with the largest range of Gibbs reaction free energy change of the three intermediates *OH, *O and *OOH is selected as the catalytic site; the different types of adsorption sites include top, bridge and hollow sites, wherein the hollow sites include FCC-hollow and HCP-hollow sites;

[0015] Step S6: The average Gibbs reaction free energy change of three intermediates on different element catalytic sites is calculated to obtain the preferred element of different intermediates;

[0016] Step S7: The preferred element of each intermediate is selected, and a first near-neighbor atom combination covering the preferred elements of different intermediates is preliminarily screened out on the slab catalytic surface;

[0017] Step S8: The Gibbs reaction free energy change of three intermediates on each atomic site in the preliminarily screened atom combination is calculated to obtain the optimal catalytic site combination of different intermediates, and further obtain the lowest overpotential for completing the catalytic reaction, then the lowest overpotential of each optimal catalytic site combination is calculated, and the overpotentials of all combinations are summed and averaged to obtain the average overpotential.

[0018] The present application realizes the calculation of the OER overpotential of the high-entropy alloy catalyst based on the atomic preferred occupation behavior.

[0019] Preferably, the crystal structure relaxation in step S2 is R3 optimization: optimizing the unit cell volume, unit cell shape and atomic position.

[0020] Preferably, the step S3 is specifically:

[0021] Method for obtaining slab catalytic surface from different types of closest packed planes based on first principle and d-band center theory: cutting the closest packed plane of the optimized structure to obtain n 2 (n is the expansion multiple) layers of closest packed plane, n consecutive closest packed planes constitute a cycle. When n tends to infinity, the physical and chemical properties of each closest packed plane tend to be consistent. However, due to limited computing resources, the expansion multiple of the unit cell is limited, which leads to large differences in the physical and chemical properties of different closest packed planes. Therefore, a surface with significant catalytic potential is selected from n types of closest packed planes as a slab catalytic surface using the d-band center theory, and the formula for calculating the d-band center is shown in formula (1):

[0022]

[0023] wherein x is the energy, p(x) is the energy-dependent electronic state density function, E f is the energy at the Fermi level. By calculating the d-band center energy of different atoms of different elements of the optimized structure, and taking the average value of the d-band center energy of each element, an element with significant catalytic potential (the element with the highest d-band center energy) is obtained. The closest packed plane containing the most of the element is selected as the slab catalytic surface.

[0024] Preferably, the step S5 is specifically:

[0025] For metal or alloy catalysts, there are four types of adsorption sites on the catalytic surface, namely top, bridge, FCC-hollow and HCP-hollow sites. The top site is located above the atom. The bridge site is located between two atoms. The FCC-hollow site is located above three atoms, and the site has no atoms in the lower layer. The HCP-hollow site is located above three atoms, but the site has atoms in the lower layer.

[0026] Firstly, three different adsorbed molecules (intermediates) were placed in different adsorption sites (top, bridge and hollow sites) of the optimized slab model to perform R2 optimization, and the total energy of the system was obtained, in which the intermediates were adsorbed on different sites. Then, the Gibbs free energy change and site relaxation change of different intermediates on different sites were calculated, in which the optimization process only allowed the adsorbed substances and the atomic layer of the slab model affected by the adsorbed substances to relax, and the lower layer of the slab model was fixed. Finally, the range of Gibbs free energy change of all optimized intermediates on different types of sites was analyzed, and the site type that could provide the largest range of Gibbs free energy change of three intermediates *OH, *O and *OOH was selected as the catalytic site of the three intermediates (considering the limited computing resources, all intermediates used the same type of catalytic site). The calculation of the adsorption energy of the three intermediates is shown in formulas (2), (3) and (4):

[0027]

[0028] In this model, the Gibbs free energy of e - +H + is equal to 1 / 2H2 at U=0V (where U is the electrode applied potential relative to CHE) and PH2=1bar. Where ΔE *OH , ΔE *O , ΔE *OOH are the adsorption energies of intermediates *OH, *O and *OOH, respectively, E* is the energy of the (111) crystal plane slab model in HEA, E *OH , E *O and E *OOH are the electronic energies of the slab model with intermediates *OH, *O and *OOH, respectively, is the energy of H2O at 298.15K, is the energy of H2 at 298.15K.

[0029] The calculation of the Gibbs free energy change (ΔG *OH , ΔG *O and ΔG *OOH ) of each step involving an electron transfer is shown in formulas (5), (6) and (7):

[0030] ΔG=ΔE+ΔZPE-TΔS+ΔG U +ΔG pH (5)

[0031] ΔG U =-eU (6)

[0032] ΔG pH= -kTln[H + ] = kTlnlO x pH (7)

[0033] where AG refers to AG *OH or AG *O or AG *OOH , AE is the adsorption energy, AZPE is the zero point energy correction, AS is the entropy change, AZPE and AS can be calculated by DFT and standard thermodynamic data, the free energy of gas phase water is calculated at 0.035 Bar, because this pressure corresponds to the equilibrium pressure of liquid water at 298 K. Under these conditions, the free energy of gas phase water is equal to that of liquid water. Since DFT calculations usually cannot adequately describe the high-spin ground state of oxygen molecules, the free energy of O2 molecules is calculated by the chemical reaction 2G(H2O) - 2G(H2) - G(O2) = -4.92 eV. The AZPE and AS values of *OH, *O and *OOH are determined using the vibrational frequencies of the adsorbed species. In the calculation process, the slab model atoms are fixed, only allowing the adsorbed species atoms to relax, and the temperature is set to 298.15 K. AG U is the external electric field energy, AG U = -eU, where U is the potential applied by the electrode, e is the elementary charge. AG pH is the correction value of free energy at any pH value, where k is the Boltzmann constant, for acidic conditions, pH is set to 0, [H + ] is the concentration of hydrogen ions.

[0034] Preferably, the number of layers of the slab model upper layer of atoms affected by the adsorbed species is determined by calculating the differential charge density of the adsorbed species adsorbed on the slab model to observe the charge transfer between the adsorbed species and the slab model, so as to determine whether the adsorbed species has an effect on the upper layers of atoms of the slab model. For example, if the adsorbed species only affects the two layers of atoms on the upper surface of the slab model, then the adsorbed species and the two layers on the upper surface of the slab model are relaxed, while the bottom n-2 layers of atoms of the slab model remain fixed.

[0035] Preferably, the step S6 is specifically:

[0036] Method for determining the preferred element of different intermediates: Under the same overpotential path, different intermediates may exist on different catalytic sites, and the free energy change values (ΔG) of different intermediates on different element catalytic sites on the slab catalytic surface need to be calculated respectively, and then the average values of the free energy change values of all atoms of different elements on the surface are calculated respectively. According to the Sabatier principle, the adsorption strength of the element to the intermediate is too strong or too weak, which is not conducive to the catalytic reaction. Therefore, the element that makes the average free energy difference of the intermediate minimum and makes the average value as close to 0eV as possible is called the preferred element of the intermediate, that is, the element that helps to reduce the overpotential of the intermediate.

[0037] Preferably, the step S7 is specifically:

[0038] The method for screening different atomic combinations involved in OER is: first, the atomic combination must contain the preferred element of different intermediates, and second, the atomic combination only considers adjacent atoms (in the same overpotential path, the reaction of three intermediates across multiple strongly adsorbed hollow sites is challenging, which hinders their transfer to more distant sites).

[0039] Preferably, the step S8 is specifically:

[0040] For the preliminary screening of the atomic combination of OER, considering that the environment around different atoms of HEA is different, there may be interactions between atoms, which may cause the Gibbs free energy change of the intermediate on its preferred element not to be the minimum, so further calculation of the Gibbs free energy change of different intermediates on different sites is required to find the optimal route with the lowest energy for each step of the elementary reaction, so that the overpotential of the OER catalytic reaction is the lowest. The calculation of the overpotential of the three intermediates is shown in formula (8):

[0041] η OER = max{ΔG1, ΔG2, ΔG3, ΔG4} / e -1.23, (8)

[0042] Where ΔG1 is the energy required by the *OH intermediate in the first step of the OER reaction to be adsorbed on the slab model, ΔG1 = ΔG *OH ; ΔG2 is the energy required by the *O intermediate to be adsorbed on the slab model after the *OH intermediate is desorbed in the second step of the oxygen evolution reaction, ΔG2 = ΔG *O - ΔG *OH ; ΔG3 is the energy required by the *OOH intermediate to be adsorbed on the slab model after the *O intermediate is desorbed in the third step of the OER reaction, ΔG3 = ΔG *OOH - ΔG *O ; ΔG4 is the energy required by H+ The additional electric field energy required for O2 generation after desorption on the slab model, AG4=4.92-AG *OOH ; e is the basic charge, and according to the Nernst equation, the equilibrium potential of OER is 1.23 V (relative to CHE) when pH=0, and the theoretical overpotential (eta) is equal to the maximum gap (the step requiring the maximum potential in the four steps of the OER reaction) minus the ideal value 1.23.

[0043] Compared with the prior art, the present application has the following beneficial effects:

[0044] The present application is based on a more accurate theoretical calculation model of preferential occupation energy, which can accurately predict the overpotential of high-entropy alloy OER, thereby reducing the experimental cost. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 The schematic diagram of the thermodynamic model of the end group compound prototype AuCu3 of the FCC structure of the preferred embodiment of the present application is shown in the figure;

[0046] Figure 2 The schematic diagram of the thermodynamic calculation path of the FCC_CoFeGaNiZn high-entropy alloy of the FCC structure of the preferred embodiment of the present application is shown in the figure, wherein ①=②+③;

[0047] Figure 3 The trend graph of the occupation fraction of each type of constituent element of the FCC_CoFeGaNiZn high-entropy alloy of the preferred embodiment of the present application with temperature change is shown in the figure;

[0048] Figure 4 The schematic diagram of the 3x3x3 supercell sublattice occupation configuration of the FCC_CoFeGaNiZn high-entropy alloy constructed using the occupation fraction value at 1273K of the preferred embodiment of the present application is shown in the figure;

[0049] Figure 5 The schematic diagram of the d-band center energy distribution of the five elements of the FCC_CoFeGaNiZn high-entropy alloy constructed using the occupation fraction value at 1273K of the preferred embodiment of the present application is shown in the figure;

[0050] Figure 6 The schematic diagram of the different (111) crystal surface sections of the 3x3x3 supercell FCC_CoFeGaNiZn high-entropy alloy at 1273K occupation fraction of the preferred embodiment of the present application is shown in the figure;

[0051] Figure 7 The schematic diagram of the slab model after the (111) crystal surface section of the FCC_CoFeGaNiZn high-entropy alloy of the preferred embodiment of the present application is shown in the figure;

[0052] Figure 8Schematic diagram of four types of adsorption sites on the high-entropy alloy catalytic surface of a preferred embodiment of the present application;

[0053] Figure 9 Schematic diagram of different adsorption sites on the FCC_CoFeGaNiZn high-entropy alloy slab model surface of a preferred embodiment of the present application;

[0054] Figure 10 Schematic diagram of the site and energy change distribution after relaxation of the intermediate *OH of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst on three different types of different adsorption sites, respectively, of a preferred embodiment of the present application;

[0055] Figure 11 Schematic diagram of the site and energy change distribution after relaxation of the intermediate *O of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst on three different types of different adsorption sites, respectively, of a preferred embodiment of the present application;

[0056] Figure 12 Schematic diagram of the site and free energy change distribution after relaxation of the intermediate *OOH of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst on three different types of different adsorption sites, respectively, of a preferred embodiment of the present application;

[0057] Figure 13 Schematic diagram of the range distribution of the free energy of the three intermediates of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst on three different types of adsorption sites, of a preferred embodiment of the present application;

[0058] Figure 14 Schematic diagram of the distribution of the average free energy change value of the three different intermediates of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst on five different elements, of a preferred embodiment of the present application;

[0059] Figure 15 Rhombus configuration of four site clusters of a preferred embodiment of the present application;

[0060] Figure 16 Schematic diagram of the reaction combination containing three intermediate element tendencies on different top sites of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst, of a preferred embodiment of the present application;

[0061] Figure 17 Schematic diagram of the distribution of the free energy change value of the three intermediates of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst on different sites of the second reaction combination, respectively, of a preferred embodiment of the present application;

[0062] Figure 18The overpotential change diagram of the OER of the FCC_CoFeGaNiZn high-entropy alloy catalyst of the preferred embodiment of the present application in the optimal reaction combination. DETAILED DESCRIPTION

[0063] The present application is further described below in conjunction with the accompanying drawings and examples.

[0064] It should be noted that the following detailed description is illustrative only, and is intended to provide further description in order to provide a fuller enabling teaching of the examples in accordance with the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0065] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of examples in accordance with the present application; as used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise, and it is further to be understood that the terms "comprising", "including", and / or "containing" when used herein, specify the presence of stated features, steps, operations, devices, components and / or combinations thereof.

[0066] In this embodiment, the FCC structure of the FCC_CoFeGaNiZn high-entropy alloy is taken as an example to provide a calculation method for the overpotential of the oxygen evolution reaction of the high-entropy alloy catalyst based on the preferred occupation, with reference to Figures 1-18 , including the following steps:

[0067] Step S1: Based on the FCC single-phase structure of the high-entropy alloy, the prototype AuCu3 is seen from Figure 1 . The corresponding sublattice model AB3 is constructed, and the end group compound of the FCC_CoFeGaNiZn high-entropy alloy is established, which includes a total of 25 end group compounds, as shown in Figure 2

[0068] Through the phonon spectrum calculation based on the density functional perturbation theory, the corresponding relationship between the Gibbs free energy of the end group compound and the temperature is obtained, and the general formula G(T) = A + B x T x lnT + C x T^ 2 + D x T^ 3 + E x T^ -1 + F x T is fitted according to the calculation phase diagram (CALPHAD) thermodynamics, wherein A, B, C, D, E and F are constant terms that need to be fitted, T represents temperature (K), each constant term in the function relationship is obtained by fitting with MATLAB, and then the free energy of the element at the base state is subtracted to write the generated Gibbs free energy (ΔG) database in the format (.TDB), for example, the temperature-dependent Gibbs free energy expression of the element is: FUNCTION SERCO 1.0

[0069] ​- 681500 - 14.54*T*LN(T) - 0.009912*T**2 + 0.1033E-07*T**3 - 3.081E+04*T**(-1) + 71.78*T; the expression for the end group is: PARAMETER G(FCC, CO:FE; 0) 1.0

[0070] - 755700 - 12.13*T*LN(T) - 0.009343*T**2 + 9.877E-07*T**3 - 3.39E+04*T**(-1) + 56.47*T - 0.25*SER CO# - 0.75*SER FE#. Then, the occupation fractions of elements on sublattice are calculated from low temperature 300 K to high temperature 1500 K at different temperatures based on the database using Pandat software or Thermo-Calc, see Figure 3 .

[0071] Step S2: Using the obtained temperature-dependent occupation fraction data of different elements on sublattice of FCC_CoFeGaNiZn high-entropy alloy, the atomic arrangement model of FCC_CoFeGaNiZn high-entropy alloy phase at 1273 K occupation is constructed, see Figure 4 Based on the principle of total energy minimization, the structure model of the actual distribution of atoms in high-entropy alloy is relaxed (unit cell volume, unit cell shape, atomic position, stress tensor of primitive cell and force on atoms), and the optimized stable structure model is obtained.

[0072] Step S3: According to the optimized structure model, the d-band center energy of different atoms of different elements of FCC_CoFeGaNiZn high-entropy alloy is calculated, and the average value of the d-band center energy of each element is obtained, to obtain the element with significant catalytic potential (the element with the highest average d-band center energy), as shown in Figure 5 Ga element shows the highest average d-band energy (1.655 eV) among the elements in CoFeGaNiZn HEA, which indicates that it is the most active element, and the presence of Ga may have a potential positive impact on the environment of the surrounding local site. Then, the (111) surface of FCC_CoFeGaNiZn high-entropy alloy is cut, and 9 layers of (111) surface are obtained, see Figure 6 Since it is 3x3x3 supercell, therefore three consecutive (111) surfaces constitute a cycle, we choose the second layer (or the fifth layer or the eighth layer) with the most Ga atoms in the 9 (111) layers as the slab surface, and place the remaining two (111) surfaces in the cycle under the slab surface, to construct a 3-layer, 108-atom and vacuum layer slab model, see Figure 7.

[0073] Step S4: The constructed 3-layer slab model containing a vacuum layer is subjected to crystal structure relaxation (R2 optimization: optimization of cell shape and atomic positions) using the selective dynamics method. The atoms in the bottom 2 layers are locked during the optimization, and the surface layer atoms are released.

[0074] Step S5: The free energy change values (ΔG *OH , ΔG *O , and ΔG *OOH ) and site changes of three intermediates (*OH, *O, and *OOH) on different types of adsorption sites (top, bridge, and FCC-hollow) are calculated. The site type with the largest range of Gibbs reaction free energy change of the three intermediates *OH, *O, and *OOH is selected as the catalytic site.

[0075] For the FCC_CoFeGaNiZn high-entropy alloy, there are three types of adsorption sites on the catalytic surface, namely top, bridge, and FCC-hollow sites, as shown in Figure 8 . The top site is located above an atom. The bridge site is located between two atoms. The FCC-hollow site is located above three atoms, and the site has no atoms in the lower layer.

[0076] First, three different adsorption molecules (intermediates) are placed on three different types of different adsorption sites of the optimized slab model to perform R2 optimization, respectively, to obtain the total energy of the system with different intermediates adsorbed on different sites. Then, the free energy change and site relaxation change of different intermediates on different sites are calculated, wherein only the adsorption material and surface atoms are allowed to relax during the optimization, and the bottom two layers of the slab are fixed. Finally, the energy change range of all optimized intermediates of different types of sites is analyzed, and the site type that can provide appropriate adsorption strength is selected as the catalytic site. The energy change range of the three intermediates is shown in Figures 9-13 . Considering the limited computing resources, only the top site is considered for all intermediates.

[0077] Step S6: Calculate the average Gibbs reaction free energy change of three intermediates on different element catalytic sites to obtain the preferred element of different intermediates.

[0078] Under the same overpotential pathway, different intermediates can exist on different catalytic sites, and the average Gibbs free energy change of different intermediates on different element catalytic sites needs to be calculated respectively. According to the Sabatier principle, too strong or too weak adsorption of elements on intermediates is not conducive to the progress of the catalytic reaction. Therefore, the average Gibbs free energy difference of different intermediates on different elements must be minimized, and the average value should be as close as possible to the free energy change of the slab (0 eV), where the element that helps to reduce the overpotential of the intermediate is called the preferred element. As shown in Figure 14 , for *OH, the best element for the *OH intermediate is Zn, and Ni is the second choice. The average energy difference between the best Zn element and the second best Ni element is 0.124 eV, which indicates that some of the top sites of Ni can still have similar activity to the top sites of Zn. Therefore, Ni elements need to be considered. The free energy difference of Co, Fe and Ga relative to Zn reaches 0.361 eV, indicating that the similarity of activity of these three elements to the top sites of Zn is limited. Similarly, the same method is applied to the other two intermediates *O and *OOH. For the *O intermediate, Ga is the best element, and the free energy of the other four elements relative to Ga is more than 0.350 eV. For the *OOH intermediate, the best element is Fe, and Co is the second best element, with a free energy difference of 0.139 eV. The difference between elements Ga, Ni and Zn and the best element Fe exceeds 0.336 eV.

[0079] Step S7: selecting the preferred elements of each intermediate, and preliminarily screening the first near-neighbor atomic combination on the slab surface covering the preferred elements of different intermediates;

[0080] Screening different atomic combinations involved in the OER catalytic reaction, firstly, the atomic combination must contain the preferred elements of different intermediates, and secondly, the atomic combination only considers adjacent atoms (in the same overpotential pathway, the reaction of the three intermediates across multiple strongly adsorbed hollow sites is challenging, which hinders their transfer to a farther site, see Figure 15 ). Considering that the best element for the *OH intermediate is Zn, and Ni is the second choice, the best element for the *O intermediate is Ga, and the best element for the *OOH intermediate is Fe, Co is the second best element, four atomic top sites are identified on the slab surface, and a total of fourteen groups of site combinations are found, see Figure 16 .

[0081] Step S8: calculating the Gibbs free energy change of the three intermediates on each atomic site in the preliminarily screened atomic combination, obtaining the optimal catalytic site combination suitable for different intermediates, and further obtaining the lowest overpotential for the completion of the catalytic reaction.

[0082] For the atomic combination of the OER catalytic reaction for preliminary screening, considering that the environment around the different atoms of HEA is different, there may be interactions between atoms, which leads to the Gibbs free energy change of intermediates on their preferred elements not necessarily being the minimum, so further calculation of the Gibbs free energy change of different intermediates on different sites is required, and the energy change is as shown in Figure 17 The lowest energy optimal route on each step primitive is found, so that the overpotential of the OER catalytic reaction is the lowest, as shown in Figure 18 Based on the overpotential of the 14 combinations, the average overpotential is calculated to be 0.349 V, which is closer to the experimental overpotential of 0.37 V (10 mA / cm2current density) than the value of 0.28 V using the special quasi-random structure (SQS).

[0083] The above only describes the preferred embodiments of the present application, and any equivalent changes and modifications made within the scope of the patent application of the present application shall be included in the scope of the present application.

Claims

1. A method for calculating the overpotential of oxygen evolution reaction of high-entropy alloy catalysts based on preferred occupation, characterized in that, The method comprises the following steps: Step S1: modeling based on the phase structure of the high-entropy alloy phase, calculating the phonon spectrum by the density functional perturbation theory, obtaining the temperature-dependent Gibbs free energy, constructing the formatted end group compound generation Gibbs free energy database, and calculating the occupation fraction of each type of constituent element in the high-entropy alloy on different types of sublattices based on the database; Step S2: n×n×n cell expansion is performed based on the occupation fraction data of each type of constituent element on the sublattice to establish a high-entropy alloy atomic distribution block cell model, and a crystal structure relaxation is performed on the structure model of the actual distribution of atoms in the high-entropy alloy based on the total energy minimization principle to obtain an optimized structure model; Step S3: according to the optimized structure model, the average d-band center energy of each type of constituent element of the high-entropy alloy is calculated, the element with the highest average d-band center energy is obtained as an element with significant catalytic potential, then the surface of the optimized structure model is cut, the surface containing the most atoms of the element with the highest average d-band center energy is selected as the slab catalytic surface, and the remaining n-1 closest packed surfaces in the loop are placed below the slab catalytic surface to construct an n-layer slab model containing a vacuum layer; Step S4: R2 optimization is performed on the constructed n-layer slab model containing a vacuum layer by using a selected dynamic method, and the atoms of the bottom n-1 layers are locked during the optimization process, and the surface layer atoms are released; Step S5: calculating the Gibbs free energy change values ΔG of three intermediates *OH, *O and *OOH on different types of adsorption sites *OH , ΔG *O , ΔG *OOH and site changes, selecting the site type with the largest range of Gibbs free energy change of the three intermediates *OH, *O and *OOH as the catalytic site; the different types of adsorption sites include top, bridge and hollow sites, wherein the hollow sites include FCC-hollow and HCP-hollow sites; Step S6: the average Gibbs reaction free energy change of the three intermediates on different element catalytic sites is calculated to obtain the preferred element of each intermediate; Step S7: the preferred element of each intermediate is selected, and a first nearest neighbor atom combination covering the preferred elements of different intermediates is preliminarily screened out on the slab catalytic surface; Step S8: the Gibbs reaction free energy change of the three intermediates on each atom site in the preliminarily screened atom combination is calculated to obtain the optimal catalytic site combination of different intermediates, and the lowest overpotential for completing the catalytic reaction is further obtained, then the lowest overpotential of each optimal catalytic site combination is calculated, and the overpotentials of all combinations are summed and averaged to obtain the average overpotential.

2. The method of claim 1, wherein the method is for calculating the overpotential of oxygen evolution reaction (OER) of a high-entropy alloy catalyst based on preferred site occupation. The crystal structure relaxation in step S2 is specifically R3 optimization: optimizing the cell volume, cell shape and atom position.

3. The method of claim 1, wherein the method is a method of calculating overpotential of oxygen evolution reaction (OER) of a high-entropy alloy catalyst based on preferred occupation. Step S3 is specifically: The d-band center energy of different atoms of different elements of the optimized structure model is calculated, and the average d-band center energy of each type of constituent element is obtained by averaging the d-band center energy of each element: where x is the energy, p(x) is the energy-dependent electronic density of states function, E f is the energy at the Fermi level; The most dense plane of the optimized structure model is cut to obtain n 2 layers of the most dense plane, n is the expansion multiple, n continuous most dense planes constitute a cycle, the element with the highest average d-band center energy is selected as the element with significant catalytic potential, and the most dense plane containing the most of the element is selected as the slab catalytic surface.

4. The method of claim 1, wherein the method is a method of calculating overpotential of oxygen evolution reaction (OER) of a high-entropy alloy catalyst based on preferred occupation. The R2 optimization in step S4 is specifically optimizing the cell shape and atom position.

5. The method of claim 1, wherein the method is a method of calculating overpotential of oxygen evolution reaction (OER) of a high-entropy alloy catalyst based on preferred occupation. Step S5 is specifically: First, the three different intermediates are placed in different adsorption sites of the optimized slab model for R2 optimization, and the adsorption energy and the Gibbs reaction free energy change of the different intermediates adsorbed on the different sites are obtained through the adsorption energy and the Gibbs reaction free energy calculation formula; Then the Gibbs free energy change of different intermediates on different sites and the site relaxation change are counted, wherein the optimization process only allows the relaxation of the adsorbed material and the atomic layer of the upper layer of the slab model affected by the adsorbed material, and the atoms of the lower layer of the slab model are fixed; Finally, the range of the Gibbs free energy change of the intermediates on all optimized sites of different types is analyzed, and the site type that can provide the largest range of the Gibbs free energy change of the three intermediates *OH, *O and *OOH is selected as the catalytic site of the three intermediates; The calculation of the adsorption energy of the three intermediates is shown in formulas (2), (3) and (4): wherein, ΔE *OH , ΔE *O , ΔE *OOH are the adsorption energies of the intermediates *OH, *O and *OOH, respectively, E * is the energy of the (111) slab model in the high-entropy alloy, E *OH , E *O and E *OOH are the electronic energies of the slab models with the intermediates *OH, *O and *OOH, respectively, is the energy of H2O at 298.15 K, is the energy of H2 at 298.15 K; the Gibbs free energy change ΔG for each step involved in the electron transfer *OH , ΔG *O , and ΔG *OOH are calculated as shown in equations (5), (6), (7): AG = AE + ΔZPE - TΔS + AG U + AG pH (5) AG U = -eU (6) AG pH = -kT ln[H + ] = kT ln 10 x pH (7) where AG refers to AG *OH or AG *O or AG *OOH , AE, AZPE and AS are the adsorption energy, zero-point energy correction and entropy change of the corresponding intermediate, respectively, the values of AZPE and AS of *OH, *O and *OOH are determined using the vibrational frequencies of the adsorbate species, in the calculation process, the slab model atoms are fixed, only allowing the adsorbate atoms to relax, the temperature T is set to 298.15 K; AG U is the energy of the applied electric field, U is the potential applied by the electrode, e is the elementary charge; AG pH is the correction value of the free energy at any pH value, k is the Boltzmann constant, [H + ] is the concentration of hydrogen ions.

6. The method of claim 5, wherein the method is based on the preferential site occupation of high-entropy alloy catalysts for oxygen evolution reaction overpotential calculation. The number of layers of the atomic layer of the upper layer of the slab model affected by the adsorbed material is determined by calculating the differential charge density of the adsorbed material adsorbed on the slab model to observe the charge transfer between the adsorbed material and the slab model, and to determine whether the adsorbed material has an effect on the upper layer of the slab model.

7. The method of claim 1, wherein the method is a method of calculating overpotential for oxygen evolution reaction (OER) of a high-entropy alloy catalyst based on preferred occupation. The determination of the preferred element of the different intermediates in step S6 is: the free energy change value of the different intermediates on the different element catalytic sites of the slab catalytic surface is calculated, and then the average value of the free energy change value of all atoms of the different elements on the surface is calculated, so that the average free energy difference of the intermediate is minimized, and the element whose average value is as close to 0eV as possible is the preferred element of the intermediate.

8. The method for calculating the overpotential of oxygen evolution reaction of high-entropy alloy catalysts based on preferred site selection according to claim 1, characterized in that, The first near-neighbor atomic combination covering the preferred element of the different intermediates is preliminarily screened out on the slab catalytic surface based on the following principle in step S7: the screened atomic combination must contain the preferred element of the different intermediates, and the atomic combination only considers the adjacent atoms of the preferred element of the different intermediates.

9. The method for calculating the overpotential of oxygen evolution reaction of high-entropy alloy catalysts based on preferred site selection according to claim 1, characterized in that, The step S8 is specifically: For the preliminarily screened atomic combination of the oxygen evolution reaction, the Gibbs free energy change of different intermediates on different sites is calculated, and the optimal route with the lowest energy on each step primitive is found, so that the overpotential of the OER is the lowest, and the calculation of the overpotential of the three intermediates is shown in formula (8): η OER = max{ΔG1,ΔG2,ΔG3,ΔG4} / e -1.23 (8) where AG1 is the overpotential energy required for the first step *OH intermediate to adsorb on the slab model, AG1 = AG *OH ; AG2 is the overpotential energy required for the second step *OH intermediate to desorb on the slab model, AG2 = AG *O - AG *OH ; AG3 is the overpotential energy required for the third step *O intermediate to desorb on the slab model, AG3 = AG *OOH - AG *O ; AG4 is the overpotential energy required for the fourth step H + to desorb on the slab model, AG4 = 4.92 - AG *OOH ; e is the elementary charge.

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