Deep neural network based quantum simulations and quasichemical theory for accurate modeling of molten salt thermodynamics

Abstract

With dual goals of efficient and accurate modeling of solvation thermodynamics in molten salt liquids, we employ ab initio molecular dynamics (AIMD) simulations, deep neural network interatomic potentials (NNIP), and quasichemical theory (QCT) to calculate the excess chemical potentials for the solute ions Na⁺ and Cl^- in the molten NaCl liquid. NNIP-based molecular dynamics simulations accelerate the calculations by 3 orders of magnitude and reduce the uncertainty to 1 kcal mol^-1. Using the Density Functional Theory (DFT) level of theory, the predicted excess chemical potential for the solute ion pair is -178.5 ± 1.1 kcal mol^-1. A quantum correction of 13.7 ± 1.9 kcal mol^-1 is estimated via higher-level quantum chemistry calculations, leading to a final predicted ion pair excess chemical potential of -164.8 ± 2.2 kcal mol^-1. The result is in good agreement with a value of -163.5 kcal mol^-1 obtained from thermo-chemical tables. This study validates the application of QCT and NNIP simulations to the molten salt liquids, allowing for significant insights into the solvation thermodynamics crucial for numerous molten salt applications.

Fig. 1. Validation of NNIP-MD simulations in comparison with AIMD simulations. Panel (a) is the NNIP-MD interaction energy extrapolation. The energies are calculated for 1000 configurations sampled with/without a (coupled/uncoupled) solute ion (Na⁺/Cl⁻) at the center of a cavity of radius 4 Å in the molten NaCl liquid of 64 solvent ion pairs. Panel (b) and (c) are radial distribution functions (g(r)) calculated over the configurations for LR contributions, where curves are from NNIP-MD simulations. Symbols are from AIMD simulations. Panel (b) is for the uncoupled sampling (without the solute ion centered in the cavity of 4 Å). Panel (c) is for the coupled sampling (with the solute ion at the center of the cavity).

Fig. 2. The process of excess chemical potential calculation for the systems of solute Na⁺ and Cl⁻ ions with 256 solvent ion pairs. Panel (a) and Panel (b) are for the long-ranged (LR) contributions to the solvation free energy of the solute ions Na⁺ and Cl⁻, respectively. The logarithms of the distribution of interaction energies from uncoupled (right, blue) and coupled (left, black) configurations are presented with the mean value ε and standard deviation σ. The right dashed curves and the left dash-dotted curves are the Gaussian fit to both distributions. Panel (c) is for the packing (PK) and minus the Inner-Shell (IS) cumulative contributions for both solute ions. Along with the expansion of the cavity with(IS)/without(PK) the solute ions at the center, the coupling parameter γ increases from 0 to 1. The IS and PK contributions are listed in Table 1. Panel (d) is the distributions of interaction energy corrections ε_DFT − ε_MP2 for the solute ion with 7 and 17 solvent ion pairs. The sampling is over 400 cluster configurations carved from DFT simulation trajectories. The DFT calculation is under Periodic Boundary Conditions (PBC) in a cell of size 25.4 Å.

Fig. 3. The Born–Haber cycle scheme for Na⁺ and Cl⁻ ion solvation. The ions are assumed to be solvated from the ideal gas state (g) to liquid state (l) with number density ρ_o = 15.61(nm)⁻³ and T₁ = 1150 K (NVT ensemble). The ideal gas of ions are changed into the NPT ensemble with pressure ρ_o = 1 bar and temperature of 1150 K. Then the temperature of the ideal gases is reduced to T₀ = 298.15 K isobarically. At room temperature the sodium ion is changed to the sodium atom and chloride ion to the chlorine radical. Both atoms are then changed into elements, respectively. The solid state (s) NaCl is formed from component elements at room temperature and 1 bar pressure. Then the solid salt are heated isobarically into the liquid phase (l) at T₁ = 1150 K. The change of free energy from the NVT ensemble (ρ_o,T₁) to the NPT ensemble (p_o,T₁) of the liquid molten NaCl(l) is neglected. All of the Gibbs free energy changes are from thermodynamic tables, and the total change of the solvation free energy is −163.5 kcal mol⁻¹.