Quantum Chemistry Based Battery Electrochemistry: The Effect of Entropy and Anode Surface Structure
Authors: Kateris Nikolaos , Wang Hai 
Published: August 2024

Lithium-sulfur (Li-S) battery is a promising battery technology, thanks to their high energy density and the use of inexpensive materials. A Li-S battery typically consists of a Li anode, a sulfur cathode or sulfur-based catholyte, and an organic solvent for lithium polysulfides (Li2S
x
). Upon discharge, Li2S
x
chains accept Li and undergo successive chain shortening events, with the final discharge product being Li2S. Li2S is however insoluble in typical organic solvents and its irreversible precipitation leads to the impairment of Li-S batteries. The addition of phosphorus pentasulfide (P2S5) to a Li2S
x
catholyte has been experimentally and theoretically shown to form complexes with sulfur chains, which can accommodate Li2S, thus overcome the problem of Li2S precipitation and improving battery cyclability. [1]
Quantum chemistry and specifically density functional theory (DFT) calculations have been used to predict molecular structures and electrochemical potentials for Li-S batteries, as well as other electrochemical systems. Here we present a series of DFT calculations (uB3LYP/6-31+G(2df,p)) using the P2S5-Li2S8 system as a case study to highlight considerations critical to reliable electrochemical predictions. Here, we focus on entropy, atomic structure of metal anode surface sites, and the level of DFT theory.
The level of theory used throughout this study (uB3LYP/6-31+G(2df,p)) was chosen after careful comparison with other levels of theory, with varying methods and functionals (HF, B3LYP, M06, M11) and basis sets (3-21G, 6-31G(d), 6-31+G(2df,p), 6-311G(d), 6-311+G(2df,p), cc-pVTZ). The B3LYP functional with the 6-31+G(2df,p) or cc-pVTZ basis set performed best in predicting electrochemical potentials in agreement with the cyclic voltammetry experiments, as well as the nuclear magnetic resonance spectra. In addition, different solvents, all with similar dielectric constants, were considered and the resulting impact on E
0 was found to be negligible.
The standard electrochemical potential for a full-cell reaction (E
0) is directly related to the Gibbs free energy of the reaction (ΔG
0): ΔG
0 = –nFE
0, where n is the number of electrons transferred and F is the Faraday constant. Gibbs free energy comprises an electronic energy (E
elec), a temperature dependent sensible enthalpy (H
sens) and a temperature dependent entropy term (–TS). Often, the sensible enthalpy and entropy terms are neglected and reaction Gibbs free energy is approximated as the difference of electronic energy between products and reactants. Our results for reactions involving lithium polysulfide chains and sulfur chains anchored on phosphorus groups indicate that, even at room temperature, the entropy term has a significant contribution to E
0 (of 0.2-0.3 V). Importantly, without considering this contribution, theoretically predicted electrochemical potentials do not match experimental results from cyclic voltammetry.
Additionally, atomic structures of different surface sites impact the evaluation of E
0. Several surface sites, as shown in Fig. 1a, were simulated for the atom to be reacted (shown transparent in Fig. 1a), while keeping the rest of the atoms stationary. The Gibbs free energy of reaction was calculated for each site and its effect on E
0 was compared with that of the standard thermodynamic result for bulk Li(s), as shown in Fig. 1b. We found that as pexted, Li atoms in the ‘lone’ or ‘pair’ configuration react more readily. In the case of the ‘lone’ Li, E
0 increases by 0.35 V.
In summary, DFT was used to identify the complexation and reaction mechanisms governing P2S5-Li2S8 catholyte batteries. In the calculation of electrochemical potentials for this system, we identified that special care should be taken to the temperature dependence of Gibbs free energy of reactions, the variation of local surface sites for the metal anode, and the level of DFT theory used. These considerations will aid the understanding of Li-S and other battery chemistry.
[1] Wang, P., Kateris, N., Li, B., Zhang, Y., Luo, J., Wang, C., Zhang, Y., Jayaraman, A.S., Hu, X., Wang, H. and Li, W., 2023. High-Performance Lithium–Sulfur Batteries via Molecular Complexation. Journal of the American Chemical Society, 145 (2023) 18865–18876.

Figure 1