An Implicit Solvent Model for SCC-DFTB with Charge-Dependent Radii

Motivated by the need to rapidly explore the potential energy surface of chemical reactions that involve highly charged species, we have developed an implicit solvent model for approximate density functional theory, SCC-DFTB. The solvation free energy is calculated using a popular model that employs Poisson-Boltzmann for electrostatics and a surface-area term for nonpolar contributions To balance the treatment of species with different charge distributions, we make the atomic radii that define the dielectric boundary and solute cavity depend on the solute charge distribution Specifically, the atomic radii are assumed to be linearly dependent on the Mulliken charges and solved self-consistently together with the solute electronic structure Benchmark calculations indicate that the model leads to solvation free energies of comparable accuracy to the SM6 model (especially for ions), which requires much more expensive DFT calculations. With analytical first derivatives and favorable computational speed, the SCC-DFTB-based solvation model can be effectively used, in conjunction with high-level QM calculations, to explore the mechanism of solution reactions This is illustrated with a brief analysis of the hydrolysis of monomethyl monophosphate ester (MMP) and trimethyl monophosphate ester (TMP) Possible future improvements are also briefly discussed.