A potentiostatically assisted electrochemical catalyst model

Abstract

The present application discloses a constant potential-assisted electrochemical catalyst model, including: obtaining the first work function required for electrons to be transferred from the electrode surface to the bulk pure aqueous solution; simulating different potential conditions based on introducing unequal charge amounts several times, and determining the first value of the first work function relative to the absolute potential of the standard hydrogen electrode; obtaining the first mapping relationship between the grand canonical free energy of the electrochemical system and the electrode potential; fitting the free energy and potential of each important species on the reaction path under different charge conditions with a quadratic function, and obtaining the second mapping relationship between the reaction free energy and activation free energy of all elementary reaction steps under isopotential conditions. The present application can give the dependence of the activation energy barrier on the potential in a wide potential range after calculating several isoelectronic reactions, and can simulate the electrochemical process under real reaction conditions, changing the problem that the traditional theoretical simulation model cannot accurately describe the energy changes of the electron transfer step in the chemical process.

Description

Technical Field

[0001] The present application belongs to the field of computational chemistry technology, and specifically relates to a constant potential-assisted electrochemical catalyst model. Background Art

[0002] As an important means of energy storage and conversion, electrochemical catalysis has been widely used in the fields of carbon dioxide reduction and nitrogen reduction in recent years. Catalysts are the core of electrocatalytic systems. The rational design of electrocatalysts is of great significance for accelerating the development of electrochemical urea synthesis. In recent years, theoretical research has developed rapidly in depth and breadth, continuously enriching people's understanding of the microscopic mechanism of electrocatalytic processes, and becoming an important booster for promoting the rational design of electrocatalytic materials.

[0003] Accurately describing the electrode-electrolyte solution interface is the key to designing efficient electrocatalysts. Usually, on the macroscopic metal electrode surface, that is, when the surface of the simulated unit cell tends to infinity, the chemical process occurring at any reactive center can be approximated as an isoelectric process, because the gain and loss of a finite number of electrons has a negligible effect on the work function of the infinite metal surface. However, on the finite-size surface of actual simulation, when the total number of electrons is conserved during the reaction, the electron transfer between the active species and the metal surface will cause a significant change in the surface work function. Therefore, the difference between traditional theoretical calculations and experimental process models makes it very difficult to accurately describe the performance of catalysts.

[0004] Based on constant potential conditions under an ideal surface, 2008 The research team proposed a cell-extrapolation method to achieve the correction of reaction energy from isoelectronic to isopotential processes ( Figure 1 ). They first simulated the initial state (IS), transition state (TS) and final state (FS) of the same reaction based on a series of slab models containing surfaces of different sizes, and obtained the isoelectronic energy difference ΔE and work function difference ΔΦ (equivalent to the potential difference) between the reaction species. Then, they extrapolated to an infinite surface through a nearly linear relationship to obtain the isopotential energy difference when ΔΦ→0eV. The calculation accuracy of the unit cell extrapolation method depends on the size and number of the selected slab models. The larger the model, the more reliable the extrapolation results can be, but the high computational cost imposed by this limits the practical application of this method.

[0005] In addition, the implicit solvent model based on the Poisson–Boltzmann equation also has important applications in simulating constant potential reactions. The Goddard group and the Head-Gordon group simultaneously proposed a constant potential DFT calculation method under the implicit solvent model. By iteratively optimizing the amount of charge injection in the system, the potential of the reaction system converges self-consistently to the target value, thereby establishing the dependence of the activation free energy and the potential under isopotential. However, the algorithm is currently limited to characterizing a single kinetic trajectory and has no statistical significance. Therefore, it is mainly used to observe the dynamic behavior of surface and interface adsorbed species and solvent molecules during the reaction process, and cannot be used to establish a free energy image of the reaction path. Summary of the invention

[0006] The present application provides a constant potential-assisted electrochemical catalyst model to solve the technical problem that the original model ignores the negative impact of environmental factors such as charge effect and pH effect on the simulation results.

[0007] In order to solve the above technical problems, a technical solution adopted in the present application is: a constant potential assisted electrochemical catalyst model, comprising:

[0008] Determine the bulk pure water solution as the potential reference zero point to obtain the first work function required for electrons to transfer from the electrode surface to the bulk pure water solution;

[0009] Determine a first value of the first work function relative to the absolute potential of a standard hydrogen electrode based on simulating different potential conditions by introducing different charges several times;

[0010] Based on the first value, a first mapping relationship between the grand canonical free energy of the electrochemical system and the electrode potential is obtained;

[0011] Based on the first mapping relationship, the free energy and potential of each important species on the reaction path under different charge conditions are fitted with a quadratic function to obtain the second mapping relationship between the reaction free energy and activation free energy of all elementary reaction steps under isopotential conditions.

[0012] Further, the method of determining the bulk pure aqueous solution as the potential reference zero point and obtaining the first work function required for electrons to transfer from the electrode surface to the bulk pure aqueous solution comprises:

[0013] The first work function is determined based on formula (1); formula (1) is:

[0014] W=-(E fermi -E ref ) (1);

[0015] Where W is the first work function, E ref is the potential of the reference zero point, E fermi is the electrode surface potential.

[0016] Furthermore, based on introducing different charges several times to simulate different potential conditions, a method for determining a first value of the first work function relative to the absolute potential of a standard hydrogen electrode includes:

[0017] The first value is determined according to formula (2); formula (2) is:

[0018]

[0019] Among them, U is the first value, e is the charge, U SHE is the absolute potential of the standard hydrogen electrode.

[0020] Further, based on the first value, a method for obtaining a first mapping relationship between the grand canonical free energy of the electrochemical system and the electrode potential includes:

[0021] Based on the results of the comparison and fitting of the calculated and experimental values ​​of the zero-charge potential of multiple metal crystal planes, the absolute potential of the standard hydrogen electrode was determined by fitting the linear PB model under the PBE functional.

[0022] According to formula (3), the first mapping relationship is determined; formula (3) is:

[0023] G(U)=E DFT +ZPE-TS-N e μ e (3);

[0024] Where T is temperature, S is entropy change, ZPE is the zero charge potential of the metal crystal surface, E DFT is the electron energy calculated by DFT method, N e μ e represents the contribution of all electronic chemical potentials to the free energy in the grand canonical ensemble, where N e is the total number of electrons in the system, μ e is the electronic chemical potential at the relative potential zero point.

[0025] Further, the first mapping relationship can be simplified according to formula (4); formula (4) is:

[0026] G(U)=E DFT +ZPE-TS-q(U+4.6) (4);

[0027] Where T is temperature, S is entropy change, q is the charge that deviates from the reference state of the number of electrons, that is, q = -(Ne-N0), -(U+4.6) is the surface electronic chemical potential with the bulk pure aqueous solution as the reference state, N e is the charge number of the system, and N0 is the charge number under standard conditions.

[0028] Further, based on the first mapping relationship, the free energy and potential of each important species on the reaction path under different charge conditions are fitted with a quadratic function to obtain a second mapping relationship between the reaction free energy and the activation free energy of all elementary reaction steps under isopotential conditions, including:

[0029] The second mapping relationship is determined according to formula (5); formula (5) is:

[0030] ΔGr(U)=ΔG(U=0)+ΔqU (5);

[0031] Here, ΔGr(U) is the reaction free energy, ΔG(U) is the activation free energy, and Δq is the inflow or outflow of charge in the constant potential reaction system.

[0032] The beneficial effects of the present application are as follows: Based on the implicit solvent model and density functional theory, the present application improves the existing constant charge method and proposes a new constant potential reaction free energy calculation method, which simulates the change of electrode potential by introducing an external charge to change the surface electronic chemical potential, and obtains the analytical expression of the system grand canonical free energy on the electrode potential through quadratic function fitting. The advantage of this scheme is that after calculating several isoelectronic reactions, the dependence of the activation energy barrier on the potential in a wide potential range can be given, which can simulate the electrochemical process under real reaction conditions, change the problem that the traditional theoretical simulation model cannot accurately describe the energy change of the electron transfer step in the chemical process, realize the rational design of efficient catalysts, and promote the development of related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the unit cell extrapolation method under constant potential conditions;

[0034] Figure 2 This is the spatial distribution image of various physical quantities in the Pt(111) electrode-electrolyte solution system under the implicit solvent model;

[0035] Figure 3 It is the coordinate diagram of the constant potential model;

[0036] Figure 4 A schematic diagram of a flow chart of an embodiment of a constant potential-assisted electrochemical catalyst model of the present application;

[0037] Figure 5 This is a schematic diagram showing that the first work function and the absolute electrode potential of the present application both use the bulk solution as the potential reference zero point;

[0038] Figure 6 It is a steady-state and transition-state configuration diagram of the CO2 chemical adsorption process in Example 1 of the present application;

[0039] Figure 7*CO2 and *CO2 in Example 1 of this application δ- A graph showing the functional relationship between the system's free energy and potential;

[0040] Figure 8 The corresponding relationship diagram of the free energy-potential of the basic reaction of the center of pyridine-type FeN4 when the pH is 1 in Example 2 of the present application;

[0041] Fig. 9 This is a corresponding relationship diagram of the free energy-potential of the basic reaction of the center of pyridine-type FeN4 when the pH is 13 in Example 2 of the present application;

[0042] Fig.10 This is a corresponding relationship diagram of the free energy-potential of the basic reaction of the center of the pyridine type FeN4-OH when the pH is 1 in Example 2 of the present application;

[0043] Fig.11 This is a corresponding relationship diagram of the free energy-potential of the basic reaction of the center of pyridine-type FeN4-OH when the pH is 13 in Example 2 of the present application;

[0044] Fig.12 This is a graph showing the variation of the adsorption free energy of *OH at the FeN4-OH center with pH and potential in Example 2 of the present application;

[0045] Fig.13 This is a graph showing the change in charge transfer value of the adsorbate at the FeN4-OH center with pH value in Example 2 of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with specific embodiments.

[0047] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways than those described herein. Therefore, the present invention is not limited to the specific embodiments of the following disclosure.

[0048] See also Figure 2 , Figure 2The spatial distribution image of various physical quantities in the Pt(111) electrode-electrolyte solution system under the implicit solvent model. The solvation model: The development of the full-space implicit solvent model provides a simple and easy constant potential calculation scheme for electrochemical reaction simulation. The implicit solvent model, as the name suggests, is to disperse the solvent molecules and electrolyte ions, and express the solvation effect as the interaction between the dielectric constant and ion charge density continuously distributed in space and the solute system. When additional charges are introduced into the system to simulate the potential conditions, the counter charge is composed of equal amounts of electrolyte ions in the solution. The distribution images of the dielectric constant, electrostatic potential and electrolyte charge density are obtained by self-consistently solving the Poisson equation. In order to simplify the solution in the actual model, it is usually assumed that the ion concentration in the solution presents a static Boltzmann distribution with respect to the electrostatic potential.

[0049] See also Figure 3 , Figure 3 The coordinate diagram of the constant potential model. The constant potential model: When the system is at the equilibrium potential U0, the free energy of the reactant A*+H+(aq)+e- and the intermediate state A*+H* are equal, such as Figure 3 As shown. Based on this equation, the model assumes that the total reaction and the final state of the reaction have the same activation free energy, which can be understood as the approximate overlap of the potential energy surfaces of the reactants and the intermediate states. However, the correctness of the physical image behind it still requires more rigorous demonstration. Under the premise of this assumption, this method avoids the isopotential correction caused by the gain and loss of electrons in the electrochemical reaction, and simplifies the model to the problem of finding a transition state of an atypical electrochemical reaction (combination of surface adsorbed states A* and H*). This provides a very concise and efficient research solution for exploring complex electrochemical processes, such as multi-electron reduction of CO2.

[0050] In order to achieve an accurate description of the activation free energy at constant potential with high efficiency, this application proposes a new calculation scheme, which combines the implicit solvation model and constant charge calculation to achieve a dynamic description of the catalytic process.

[0051] In the actual calculation, we still optimize the geometric structures of reactants, products and transition states based on the constant charge method, and inject external charges into the reaction system to simulate the potential environment. Similarly, the charges are expressed by the electrolyte ions in the implicit solvent model, and the spatial distribution of their charge density and electrostatic potential is obtained by self-consistently solving the linear PB equation. After several isoelectronic calculations, the calculation formula of the electrode potential U and the grand canonical free energy G relative to SHE is used.

[0052] See also Figure 4 , Figure 4 This is a schematic flow diagram of an embodiment of a constant potential-assisted electrochemical catalyst model of the present application. The model includes:

[0053] Step S1. Determine the bulk pure water solution as the potential reference zero point, and obtain the first work function required for electrons to transfer from the electrode surface to the bulk pure water solution.

[0054] For details, see Figure 5 , Figure 5 Schematic diagram of the first work function and absolute electrode potential using the bulk solution as the potential reference zero point. Taking the bulk pure water solution as the potential reference zero point (Eref), the first work function W required for electrons to transfer from the electrode surface to the bulk solution, the formula (1) of the first work function is:

[0055] W=-(E fermi -E ref ) (1);

[0056] Where W is the first work function, E ref is the potential of the reference zero point, E fermi is the electrode surface potential.

[0057] Step S2: Determine a first value of the first work function relative to the absolute potential of a standard hydrogen electrode based on simulating different potential conditions by introducing different amounts of charge several times.

[0058] Specifically, by introducing different charges into the system several times to simulate different potential conditions, the first work function is relative to the first value of the absolute potential of the standard hydrogen electrode (USHE), in units of V vs. SHE. The formula (2) for the first value is:

[0059]

[0060] Among them, U is the first value, e is the charge, U SHE is the absolute potential of the standard hydrogen electrode.

[0061] Step S3. Based on the first value, a first mapping relationship between the grand canonical free energy of the electrochemical system and the electrode potential is obtained.

[0062] Specifically, according to the results of the comparison and fitting of the calculated values ​​and experimental values ​​of the zero charge potential (PZC) of multiple metal crystal planes in the literature, the linear PB model was used to fit U under the PBE functional. SHE The value is 4.6 V. According to formula (3), the first mapping relationship between the grand canonical free energy of the electrochemical system and the electrode potential is obtained; formula (3) is:

[0063] G(U)=E DFT +ZPE-TS-N e μ e (3);

[0064] Where T is temperature, S is entropy change, ZPE is the zero charge potential of the metal crystal surface, E DFTis the electron energy calculated by the DFT (Discrete Fourier Transform) method, N e μ e represents the contribution of all electronic chemical potentials to the free energy in the grand canonical ensemble, where N e is the total number of electrons in the system, μ e is the electronic chemical potential at the relative potential zero point.

[0065] Formula (3) can be simplified as formula (4):

[0066] G(U)=E DFT +ZPE-TS-q(U+4.6) (4)

[0067] Where q is the charge that deviates from the reference state of the electron number, that is, q = -(N e -N0), -(U+4.6) is the surface electron chemical potential with reference to the bulk pure aqueous solution, N e is the charge number of the system, and N0 is the charge number under standard conditions.

[0068] Step S4. Based on the first mapping relationship, the free energy and potential of each important species on the reaction path under different charge conditions are fitted with a quadratic function to obtain a second mapping relationship between the reaction free energy and activation free energy of all elementary reaction steps under isopotential conditions.

[0069] Specifically, it is found through testing that the free energy and potential of the system approximately satisfy a quadratic function relationship. Therefore, we fit the free energy and potential of each important species (including transition state) on the reaction path under different charge conditions with a quadratic function, and further obtain the analytical expressions of the reaction free energy ΔGr(U) and activation free energy ΔG(U) of all elementary reaction steps under isopotential conditions, i.e., the second mapping relationship. The second mapping relationship is determined according to formula (5); the formula (5) is:

[0070] ΔGr(U)=ΔG(U=0)+ΔqU (5);

[0071] Here, ΔGr(U) is the reaction free energy, ΔG(U) is the activation free energy, and Δq is the inflow or outflow of charge in the constant potential reaction system.

[0072] When ΔG(U) represents the reaction free energy, Δq can be specifically expressed as the amount of electron transfer from reactants to products during urea synthesis, which is similar to the expression of the hydrogen electrode method, but more applicable.

[0073] The present application can handle the process of non-proton coupled electron transfer, such as partial reduction of CO2 and N2 to chemical adsorption state. When ΔG(U) represents the activation free energy, similarly, Δq can be understood as the number of electron transfers from the reactant to the transition state. Different from most electrochemical calculation methods that regard Δq as a constant independent of the potential, Δq is expressed as a linear function of the potential U here, which can be attributed to the consideration of the influence of the potential on the polarization effect.

[0074] Embodiment 1

[0075] See also Figure 6-7 , Figure 6 It is the steady state and transition state configuration diagram during CO2 chemical adsorption; Figure 7 For *CO2 and *CO2 δ- A functional relationship diagram of the system free energy and potential. This example is an analysis of the stability of CO2 adsorption. As the initial step of the reduction process, the adsorption of CO2 on the surface of metallic copper is crucial to determining the selectivity of the product. Under gas phase conditions, the process of CO2 obtaining an electron and reducing it to generate CO2- is thermodynamically unfavorable, and the reaction energy is about 0.5eV. However, in traditional calculation models, since the charge effect is ignored, the adsorption values ​​of CO2 often deviate from the experimental values, and it is impossible to compare the stable structures of CO2 adsorption under different voltage conditions.

[0076] Therefore, to solve this problem, this paper uses a constant potential model to optimize the physical and chemical adsorption states of CO2 on the Cu(211) surface at different potentials, and obtains a stable configuration consistent with the AIMD simulation of the Cu(100) surface.

[0077] As Figure 6 As shown, the physically adsorbed CO2* is almost parallel to the surface and maintains a linear configuration, while *CO2δ- bonds with the Cu atoms at the step site to form a mixed coordinated bent configuration. Figure 7The quadratic function curves of the free energy and potential of the two adsorption states are shown in Figure 1. The intersection of the two curves means that when the potential is negative to -0.27V vs. SHE, the stability order of *CO2δ- and *CO2 will be reversed, so a more negative potential is conducive to the stability of the chemical adsorption state. In contrast, AIMD calculations based on the Cu(100) surface show that at a potential of -0.79V vs. SHE, *CO2 is still 0.39eV more stable than *CO2δ-, which indicates that the Cu(211) surface has a more positive reversal potential than Cu(100), which should be attributed to the fact that the step-site atoms with high crystal plane index are more reactive and thus more tightly bound to the chemical adsorption state. With the transformation of CO2 from physical adsorption to chemical adsorption, about 0.4 electrons are transferred from the metal surface to *CO2δ- under isoelectric conditions, which explains why a more negative potential is conducive to improving the relative stability of *CO2δ-. The activation free energy is much less affected by the potential, which means that the electron transfer is mainly completed after the formation of the transition state. Therefore, the kinetic rate of the chemical adsorption process on the Cu(211) surface mainly depends on the intrinsic properties of the crystal surface, and the coverage ratio of *CO2 and *CO2δ- when reaching thermodynamic equilibrium has a strong dependence on the potential.

[0078] Embodiment 2

[0079] See also Figure 8-13 , Figure 8 The corresponding relationship diagram of free energy-potential of the basic reaction of the center of pyridine FeN4 when the pH is 1; Fig. 9 The free energy-potential correspondence diagram of the basic reaction of the center of pyridine FeN4 when the pH is 13; Fig.10 The corresponding relationship diagram of free energy and potential of the basic reaction of the center of pyridine FeN4-OH when the pH is 1; Fig.11 The corresponding relationship diagram of free energy and potential of the basic reaction of the center of pyridine FeN4-OH when the pH is 13; Fig.12 The adsorption free energy of *OH on FeN4-OH center varies with pH and potential; Fig.13 This is a graph showing the change in charge transfer value of the adsorbate at the FeN4-OH center with pH value.

[0080] This example simulates the oxygen reduction process using a constant potential method. Since the effects of pH and surface charge are ignored, the accuracy of the traditional equal charge method is affected.

[0081] Therefore, the application established a constant potential-implicit solvent model to evaluate the oxygen reduction performance of Fe-NC catalysts. The model takes into account several approximate effects of electrode potential (U) and solution environment (pH) on the electrochemical reaction. For the reaction intermediates involved in the oxygen reduction process, the relationship between energy (E) and U can be fitted as a quadratic function. Figure 8 and Fig. 9 The free energy changes of the elementary steps of the pristine FeN4 center at pH = 1 and 13 are shown, respectively. The limiting potential of the *OH intermediate reduction step is the lowest, and therefore, it is the potential-determining step (PDS) for the Fe-NC catalyst. Due to the strong adsorption of *OH by the FeN4 center, it exhibits poor ORR activity under both acidic and alkaline conditions.

[0082] The confinement potential of FeN4-OH center under alkaline conditions is reduced from Fig.12 As can be seen from the graph, the adsorption free energy of *OH (ΔG*OH) decreases with increasing pH, corresponding to stronger *OH adsorption at higher pH values. Therefore, the electron transfer capacity between the catalyst and the adsorbate is stronger in alkaline media ( Fig.13 ).

[0083] In summary, this application improves the existing constant charge method based on the implicit solvent model and density functional theory, and proposes a new constant potential reaction free energy calculation method, which simulates the change of electrode potential by introducing external charge to change the surface electronic chemical potential, and obtains the second mapping relationship of the system grand canonical free energy on the electrode potential through quadratic function fitting. The advantage of this solution is that after calculating several isoelectronic reactions, the dependence of the activation energy barrier on the potential in a wide potential range can be given, which can simulate the electrochemical process under real reaction conditions, change the problem that the traditional theoretical simulation model cannot accurately describe the energy change of the electron transfer step in the chemical process, realize the rational design of efficient catalysts, and promote the development of related fields.

[0084] The above description is only an embodiment of the present application and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly used in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for constructing a constant potential-assisted electrochemical catalyst model, characterized in that: The following steps are involved: The bulk pure water solution is determined as a potential reference zero point, and a first work function required for electrons to be transferred from the electrode surface to the bulk pure water solution is obtained; wherein the first work function is determined based on formula (1); the formula (1) is: W=-(E fermi -HAVE BEEN ref )(1); Where W is the first work function, E ref is the potential of the reference zero point, E fermi is the potential of the electrode surface; Based on simulating different potential conditions by introducing different amounts of charge several times, a first value of the first work function relative to the absolute potential of the standard hydrogen electrode is determined; wherein the first value is determined according to formula (2); formula (2) is: Wherein, U is the first value, e is the charge, and U SHE is the absolute potential of the standard hydrogen electrode; Based on the first value, a first mapping relationship between the grand canonical free energy of the electrochemical system and the electrode potential is obtained; wherein the first mapping relationship includes: Based on the results of the comparison and fitting of the calculated and experimental values ​​of the zero-charge potential of multiple metal crystal planes, the absolute potential of the standard hydrogen electrode was determined by fitting the linear PB model under the PBE functional. According to formula (3), the first mapping relationship is determined; the formula (3) is: G(U)=E DFT +ZPE-TS-N e μ e (3); Where T is temperature, S is entropy change, ZPE is the zero charge potential of the metal crystal surface, E DFT is the electron energy calculated by DFT method, N e μ e represents the contribution of all electronic chemical potentials to the free energy in the grand canonical ensemble, where N e is the total number of electrons in the system, μ e is the electronic chemical potential at the relative potential zero point; Based on the first mapping relationship, the free energy and potential of each important species on the reaction path under different charge conditions are fitted with a quadratic function to obtain a second mapping relationship between the reaction free energy and activation free energy of all elementary reaction steps under isopotential conditions; wherein the second mapping relationship is determined according to formula (5); the formula (5) is: ΔGr(U)=ΔG(U=0)+ΔqU (5); Here, ΔGr(U) is the reaction free energy, ΔG(U) is the activation free energy, and Δq is the inflow or outflow of charge in the constant potential reaction system.

2. The method according to claim 1, characterized in that The first mapping relationship is simplified according to formula (4); the formula (4) is: G(U)=E DFT +ZPE-TS-q(U+4.6) (4); Where T is temperature, S is entropy change, and q is the charge that deviates from the reference state of the number of electrons, that is, q = -(N e -N0), -(U+4.6) is the surface electron chemical potential with reference to the bulk pure aqueous solution, N e is the system charge number, and N0 is the charge number under standard conditions.

Images