Efficient Free Energies from a Simplified Electrostatic Embedding QM/MM Approach Based on Electrostatic Potential Fitted Operators
Résumé
Periodic boundary condition (PBC)-adapted formulations of quantum mechanics/molecular mechanics (QM/MM) methods allow for the accurate computation of free energies, provided a sufficient phase-space sampling. In this work, we develop a robust and efficient QM/MM approach based on Electrostatic Potential Fitted (ESPF) charge operators. The method combines smooth particle-mesh Ewald summation to describe QM-MM electrostatic interactions and the Ewald pair potential to treat long-range QM-QM interactions. It is fully compatible with both ab initio DFT and semi-empirical DFTB QM/MM frameworks under PBC. We demonstrate the efficiency of the approach by implementing a thermodynamic integration (TI) scheme to compute solvation free energies and redox potentials in condensedphase systems. For solvation energies, we introduce two separate coupling parameters to independently decouple electrostatic and van der Waals interactions. For redox potentials, a coupling parameter is introduced directly into the density matrix, interpolating between the N-and N±1-electron states via fractional occupations. We apply this framework to compute solvation free energies and redox potentials in water for a set of amino acid analogues and aromatic ketones, obtaining results in qualitative agreement with experimental data. This work paves the way for routine free energy calculations using electrostatic embedding QM/MM methodologies.
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