Machine Learning-Aided First Principles Calculations of Free Energies

The free energy of atoms and molecules in condensed matter is an extremely important property. Knowledge of free energy allows quantitative evaluation of a wide variety of physical properties, such as coexistence points of different phases, concentration of minority species, redox levels of atoms and molecules in condensed matter, and thermodynamic stability of reaction intermediates. However, accurate first-principles calculations of free energies are extremely challenging. Since free energies are not observable, the free energy difference between a known system and a real system of interest must be calculated in large-scale molecular dynamics simulations using thermodynamic perturbation theory (TPT) or thermodynamic integration theory (TI). Recently, machine-learned force fields (MLFFs) have enabled efficient computation of free energies [1-3]. By using MLFFs as surrogate models, computationally difficult TI from a known system to a real system becomes feasible. Errors in MLFF can also be corrected by TPT and TI. Machine-learned models can be also used to correct inexpensive low-level first-principles results, such as results by semi-local exchange-correlation functionals, to obtain accurate but expensive theoretical results [4]. Here, we show three applications of the ML-framework to the free energies in aqueous solutions and interfacial systems: hydration free energies of ions in water, redox potentials of transition metal ions in water, and hydration free energies of adsorbates on the surface of platinum catalysts. All examples demonstrate that MLFFs enable efficient statistical sampling necessary for accurate computations of free energies.<br/>[1] R. Jinnouchi, F. Karsai, and G. Kresse, <i>Phys. Rev. B</i> <b>100</b> 014105 (2019).<br/>[2] R. Jinnouchi, F. Karsai, and G. Kresse, <i>Phys. Rev. B</i> <b>101</b> 060201(R) (2020).<br/>[3] R. Jinnouchi, F. Karsai, C. Verdi, and G. Kresse, <i>J. Chem. Phys.</i> <b>154</b> 094107 (2021).<br/>[4] P. Liu, C. Verdi, F. Karsai, and Georg Kresse, <i>Phys. Rev. B</i> <b>105</b>, L060102 (2022).