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We introduce a hybrid Gaussian charge distribution model (HGM) that partitions the molecular electron density into overlapping spherical atomic domains. The semi-empirical HGM consists of atom-centered spherical Gaussian functions and discrete point charges, which are optimized to reproduce the electrostatic potential on the molecular surface as well as the number of electrons in atom-centered and certain off-atom-centered  spherical regions as closely as possible. In contrast, our previous Gaussian charge distribution model [J. Chem. Phys.  129 , 014509 (2008)] contained only spherical Gaussian functions and was not required to reproduce the number of electrons in off-atom-centered regions. Variable van der Waals (vdW) radii fluctuating around the Bondi radii are derived from the HGM based on the isodensity contour concept and further employed to define the molecular cavity in our quantum mechanical/Poisson–Boltzmann/surface area model as well as the polarizable continuum model. The variable vdW radii produce more accurate solvation free energies for 31 neutral molecules than the Bondi radii for both continuum solvent models (CSM) consistently. Moreover, for H atoms, the linear dependence of the atomic radii on the atomic partial charges is identified.

Variable van der Waals Radii Derived From a Hybrid Gaussian Charge Distribution Model for Continuum-Solvent Electrostatic Calculations