(362k) Grand Canonical Potential Kinetics (GCP-K) for Electrochemical Reactions from Quantum Mechanics

Traditional density functional theory (DFT) is always performed with a fixed number of electrons which is unable to appropriately address the electrochemical conditions of applied potential. So, it is important to modify the existing quantum mechanics calculation method to a constant potential-based method in order to simulate exact experimental conditions. Here, we develop constant potential-based method called the grand canonical potential kinetics (GCP-K) formulation based on thermodynamics from quantum mechanics calculations to allow the reaction barriers to change continuously as a function of applied potential, leading directly to current versus potential relation.^1-4 In this talk, I will be presenting GCP-K methodology development and its application to elucidate the reaction mechanism and kinetics for hydrogen evolution reaction (HER) on transitions metal chalcogenides (TMDs) and CO₂ reduction reaction (CO₂RR) for atomically dispersed Ni single-atom catalysts alone with experimental comparison.

The GCP-K arises from the minimization of the fixed charge based free energy, F (n), using a Legendre transformation to grand canonical free energy, G (n; U), allowing the thermodynamic free energy for heterogeneous electrochemical reactions to depend on the applied potential (U) (Fig. 1)

G(n;U) = F (n) - ne(U_SHE-U)

Where G is the grand canonical free energy, which depends on applied voltage U vs SHE, n is the number of electrons, e is the unit electronvolt in energy, F is DFT energy as a function of n, and U_SHE = µ_e,SHE/e is the chemical potential of electron at the standard hydrogen electrode (SHE) condition. The signs are analogous to experimental value i.e., U= - 0.1 V corresponds to -0.1 V vs SHE. The GCP-K methods allows change of the geometry at the transition states and the charge transfer from electrode to adsorbed species continuously as a function of applied potential alone the reaction pathways.

In the first application of our GCP-K method, we predict the HER activity (current as a function of U) as a function of Te vacancy concentration for the basal plane of both the 2H and 1T′ phases of MoTe₂ with experimental validation. This method allows us to describe the transition state energy barrier change with applied potential as a result of structural change. The energy barrier further converted into the turnover frequency (TOF) and current density as a function of potential using a micro-kinetics model. To validate the accuracy of the GCP-K predictions, our experimental collaborator synthesized both phases of MoTe₂ monolayer materials and created controlled Te vacancy by applying Ar plasma. Using GCP-K method, we predict an overpotential of 535 and 565 mV to achieve current density of 10 mA cm^-2 for 1T′-MoTe₂ and 2H-MoTe₂ containing 1.14 x 10¹⁴ cm^-2 and 3.45 x 10¹³ cm^-2 Te vacancies respectively. Which shows good agreement with experimental overpotentials of 561 and 634 mV for 1T′-MoTe₂ and 2H-MoTe₂ containing similar vacancy concentrations ( 1.28 x 10¹⁴ cm^-2 and 3.54 x 10¹³ cm^-2).

In the last part of presentation, I will be talking about GCP-K application for CO₂RR on Ni-single atom catalysts (Ni-SACs). We applied the GCP-K method to determine the reaction mechanism and kinetics for CO₂RR on different nitrogen coordination such as Ni-N₂C₂, Ni-N₃C₁, and Ni-N₄. We find each site has unique reaction kinetics with Ni-N₂C₂ initiates current at early potential and produces U_onset =-0.84 V, with a Tafel slope of 52 mV dec^−1, a faradic efficiency (FE) of 98%, and TOF = 3903 h^−1 per Ni site. On the other hand, Ni-N₃C₁ shows an onset potential of -0.92 V, with higher Tafel slope of 62 mV dec^−1, a lower FE = 78% and TOF = 2940 h^−1 per Ni site. Finally, Ni-N₄ dominant for U < −1.05 V producing 10 mA cm^−2 at -1.03 V applied potential with a Tafel slope of 55 mV dec^−1, a FE = 99% faradic efficiency, and TOF = 3944 h^−1 per Ni site. These predicted results show reasonable agreement with experience experimental studies.

In order to help guide identification of the sites in experimental synthesized Ni-SACs, we predict the CO vibrational frequencies for various sites. The CO stretch for CO bound to Ni is 1985 cm^−1 at -1.0 V on Ni-N₂C₂ site and 1942 cm^−1 at -1.25 V on Ni-N₄ site. As compared with literature, Ni-N₂C₂ site shows best fit with experiment, but we expect that synthesized Ni-SACs have different proportions of all three Ni sites and the resulted overall activity originates from each of them.

References

1. Yufeng Huang et al., Reaction mechanism for the hydrogen evolution reaction on the basal plane sulfur vacancy site of MoS₂ using grand canonical potential kinetics, J. Am. Chem. Soc. 2018, 140, 48, 16773–16782.

2. Md Delowar Hossain et al., Reaction Mechanism and Kinetics for CO₂ Reduction on Nickel Single Atom Catalysts from Quantum Mechanics; Comm., 2020, 11 (1), 1-14.

3. Jie Song et al., Reaction Mechanism and Strategy for Optimizing the Hydrogen Evolution Reaction on Single-Layer 1T′ WSe₂ and WTe₂ Based on Grand Canonical Potential Kinetics; ACS Appl. Mater. Interfaces, 2021, 13, 46, 55611–55620.

4. Md Delowar Hossain et al., The Kinetics and Potential Dependence of the Hydrogen Evolution Reaction Optimized for the Basal Plane Te Vacancy Site of MoTe₂, 2023, Chem Catal., 100489.