Alchemical thermodynamic integration for ab initio free-energy calculations in solutions

We develop an alchemical thermodynamic integration scheme that couples ab initio force calculators on the fly during Monte Carlo and molecular dynamics simulations. The implementation is validated against existing hybrid-Hamiltonian approaches. The scheme yields ab initio free energies of high-pressure Fe-Ni and ambient Li-Na liquid solutions that agree with previous calculations and reproduce the experimentally observed Li-Na miscibility gap. The code has an efficiency comparable to standard ab initio molecular dynamics. These results establish this scheme as a practical alchemical-integration framework for first-principles free-energy calculations in solutions.