Assessment of free energies from electrostatic embedding density functional tight binding-based/molecular mechanics in periodic boundary conditions

Electrostatic embedding Quantum mechanics / molecular mechanics (QM/MM) methods in periodic boundary conditions can successfully describe the condensed phase reactivity of a fragment treated at the QM level with an atomistic description of an electrostatic environment treated at the MM level. The computational cost of ab initio QM methods limits the phase space sampling, affecting thus statistical quantities like free energies. Here, we explore the accuracy of the semi-empirical density-functional based tight-binding (DFTB) method by comparing the free energy profiles from several methods and parameters in the DFTB/MM to ab initio QM/MM free energy simulations. We show that DFTB2 correctly describes the free energy barrier of cis/trans isomerization of proline in water, the intramolecular proton transfer in pterin, and the nucleophilic fluoride substitution of chloromethane, showing a qualitatively good agreement with respect to experimental or ab initio simulations. DFTB3 describes well the free energy barriers but tends to favor weak endothermic reactions. None of the tested DFTB methods is able to predict a simultaneous water-assisted proton transfer for pterin, predicting rather a sequential proton transfer involving ionic water intermediates