Redox potentials and solvation free energies energies from an efficient electrostatic embedding QM/MM thermodynamic integration approach

Periodic boundary condition-adapted formulations of quantum mechanics/molecular mechanics (QM/MM) methods enable the extraction of accurate free energies, provided that efficient phase-space sampling is achieved. In this work, we develop a thermodynamic integration scheme based on an electrostatic embedding QM/MM approach for efficiently computing solvation energies and redox potentials in condensed-phase systems. This method is compatible with both ab initio DFT and semi-empirical DFTB QM/MM frameworks in periodic boundary conditions (PBC). Our PBC-adapted QM/MM model employs a mixed particle–mesh Ewald (PME) scheme for QM–MM interactions and an Ewald pair potential for QM–QM interactions, enhancing computational efficiency. For solvation free energies, we introduce two coupling parameters to decouple electrostatic and van der Waals interactions. Redox potentials are computed using a fractional electron occupation scheme interpolating between N- and N±1-electron states. The method is applied to aqueous solvation of amino acid analogues and to redox processes in water, yielding results in good agreement with experimental data. This approach enables robust and accurate free energy predictions in realistic condensed-phase environments.