Correction methods for first-principles calculations of the solution enthalpy of gases and compounds in liquid metals

Liquid metals (LMs) have a wide range of engineering applications, such as in coolants, batteries, and flexible electronics. While accurate calculation methods for thermodynamic properties based on density functional theory (DFT) have been extensively developed for solid materials, including methods to correct identified systematic errors, almost no attempt has been made for LMs. In the present study, four correction methods for the first-principles calculation of the solution enthalpy of gases and compounds in LMs are proposed, namely, Correction-1, using the experimental binding energy of an impurity gas molecule; Correction-2, additionally using the experimental enthalpy of formation of a solid compound composed of LM and gas-impurity elements; Correction-3, using the concept of the fitted elemental-phase reference energies (FERE) method; and Correction-4, using the concept of the coordination corrected enthalpies (CCE) method. The performance of each method is examined with hydrogen, nitrogen, oxygen, and iodine gases and their sodium compounds in liquid sodium, and the operating principle of each method is clarified. In general, the four correction methods effectively reduce the calculation error, and Correction-2 reduces the error to less than 10 kJ mol^-1, while the uncorrected errors are up to several tens of kJ mol^-1. This study demonstrates that, with appropriate correction, the DFT calculation of the solution enthalpy of impurities in LMs can achieve the same level of accuracy as in precise experiments.