To better represent the solvation effects observed along reaction pathways, and of ionic species in general, a charge-dependent variable-radii smooth conductor-like screening model (VR-SCOSMO) is developed. This model is implemented and parameterized with a third order density-functional tight binding quantum model, DFTB3/3OB-OPhyd, a quantum method which was developed for organic and biological compounds, utilizing a specific parameterization for phosphate hydrolysis reactions. Unlike most other applications with the DFTB3/3OB model, an auxiliary set of atomic multipoles is constructed from the underlying DFTB3 density matrix which is used to interact the solute with the solvent response surface. The resulting method is variational, produces smooth energies, and has analytic gradients. As a baseline, a conventional SCOSMO model with fixed radii is also parameterized. The SCOSMO and VR-SCOSMO models shown have comparable accuracy in reproducing neutral-molecule absolute solvation free energies; however, the VR-SCOSMO model is shown to reduce the mean unsigned errors (MUEs) of ionic compounds by half (about 2-3 kcal/mol). The VR-SCOSMO model presents similar accuracy as a charge-dependent Poisson-Boltzmann model introduced by Hou et al. [J. Chem. Theory Comput. 6, 2303 (2010)]. VR-SCOSMO is then used to examine the hydrolysis of trimethylphosphate and seven other phosphoryl transesterification reactions with different leaving groups. Two-dimensional energy landscapes are constructed for these reactions and calculated barriers are compared to those obtained from ab initio polarizable continuum calculations and experiment. Results of the VR-SCOSMO model are in good agreement in both cases, capturing the rate-limiting reaction barrier and the nature of the transition state.