Theoretical Prediction of a Bi-Doped β-Antimonene Monolayer as a Highly Efficient Photocatalyst for Oxygen Reduction and Overall Water Splitting

The photo-/electrocatalysts with high activities for the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and the oxygen reduction reaction (ORR) are of significance for the advancement of photo-/electrochemical energy systems such as solar energy to resolve the global energy crisis, reversible water electrolyzers, metal–air batteries, and fuel cells. In the present work, we have systematically investigated the photochemical performance of the 2D β-antimonene (β-Sb) monolayer. From density functional theory investigations, β-Sb with single-atom doping possesses a trifunctional photocatalyst with high energetics and thermal stabilities. In particular, it is predicted that the performance of the HER activity of β-Sb will be superior to most of the 2D materials. Specifically, β-Sb with single atom replacement has even superior that the reference catalysts IrO2(110) and Pt(111) with relatively low overpotential values for ORR and OER mechanisms. The superior catalytic performance of β-Sb has been described by its electronic structures, charge transfer mechanism, and suitable valence and conduction band edge positions versus normal hydrogen electrode. Meanwhile, the low overpotential of multifunctional photocatalysts of the Bi@β-Sb monolayer makes them show a remarkable performance in overall water splitting (0.06 V for HER, 0.25 V for OER, and 0.31 V for ORR). In general, the Bi@β-Sb monolayer may be an excellent trifunctional catalyst that exhibits high activity toward all electrode reactions of hydrogen and oxygen.


I. COMPUTATIONAL DETAILS ABOUT HER, OER AND ORR
The reactions mechanism of HER, OER and ORR activities are investigated by calculating the reaction free energy of each step.

A. ∆G for HER
The standard hydrogen electrode (U SHE ) was theoretically defined in solution [pH = 0, p(H 2 ) = 1 bar]. The overall HER pathway can be described by, where H + (aq.) + e − is an initial state, H * an intermediate adsorbed, and H 2 (g) is the final product. Here, " * " represents the lowest adsorption site for intermediates, (aq.) and (g) represents the aqueous solution and gas phases, respectively. The Gibbs free energy of the adsorption of intermediate hydrogen (∆G H * )on the catalyst is a key descriptor for the HER mechanism of the catalyst [1] and is defined by, in which ∆E H is the hydrogen adsorption energy and defined as, where E nH * , E (n−1)H * shows the investigated energy of the catalysts with nH and (n-1)H adsorption. ∆E ZP E and T ∆S H * are the difference of zero-point energy and difference in entropy between adsorbed and gas phases, respectively. Contributions from catalysts both ∆E ZP E and T ∆S H * are small and neglected, and the vibration frequencies of the H * adsorbed on the catalysts are not sensitive to coverage [2]. Therefore, ∆E ZP E is described by And the value of ∆S H is defined as, where 1 2 S 0 H 2 is the entropy of H 2 under the standard condition and the value is 130 mol −1 K −1 [3].
The ideal value for HER is ∆G H * = 0. Also, the smaller | ∆G H * |, the better HER performance will be.
The theoretical overpotential η HER for HER [5] which is determined by ∆G H * , In the acidic environment, the overall OER could be described in Eqn. (6), which happens on the cathode of water splitting and the metal air battery during charge [4], The OER mechanism proceeds through a 4e − transferred reaction pathway as follows, where * refers to the active site on the catalysts. (g) and (l) represents the gas and liquid phase of oxygen and water molecules, respectively.
The ORR reaction mechanism occurs via elementary steps takes the reverse direction of OER mechanism [6], In the acidic solution, the ORR proceeds via the 4e − -transfer pathway can be written as below, * + O 2 (g) + H + + e − − → OOH * (13) The theoretically Gibbs free energy difference (∆G OH * , ∆G O * , and ∆G OOH * ) of each step involving one e − transfer is defined by the following equation, Here, ∆E, ∆ZP E, and ∆S displayed the energy difference of adsorption, zero-point energy and entropy between adsorbed state and freestanding state, respectively. The values of ∆E was calculated by DFT, and the values for ∆ZP E, and ∆S were investigated through DFT calculations and the standard thermodynamic data, as presented in Table S1. ∆G U =-eU, where e is the elementary charge, U is the applied electrode potential. And the last term ∆G pH =-k B T ln[H + ]=pH×k B T ln10 originating from the effect of pH value of the electrolyte. The free energy changes during 4e − pathways for OER could be expressed as; ∆G 1 =∆G OH * , ∆G 2 =∆G O * -∆G OH * , ∆G 3 =∆G OOH * -∆G O * , and ∆G 4 =4.92-∆G OOH * . And for ORR steps; ∆G a =∆G OOH * -4.92, ∆G b =∆G O * -∆G OOH * , ∆G c =∆G OH * -∆G O * , and ∆G d =∆G OH * .
The overpotential (η OER/ORR ) that could be used to evaluate the catalytic performance of REOs and ORR obtained from the following equations;