Variable atomic radii for continuum-solvent electrostatics calculation.

We have developed a method to improve the description of solute cavity defined by the interlocking-sphere model for continuum-solvent electrostatics calculations. Many models choose atomic radii from a finite set of atom types or uses an even smaller set developed by Bondi [J. Phys. Chem. 68, 441 (1964)]. The new model presented here allowed each atom to adapt its radius according to its chemical environment. This was achieved by first approximating the electron density of a molecule by a superposition of atom-centered spherical Gaussian functions. The parameters of the Gaussian functions were then determined by optimizing a function that minimized the difference between the properties from the model and those from ab initio quantum calculations. These properties included the electrostatics potential on molecular surface and the electron density within the core of each atom. The size of each atom was then determined by finding the radius at which the electron density associated with the atom fell to a prechosen value. This value was different for different chemical elements and was chosen such that the averaged radius for each chemical element in a training set of molecules matched its Bondi radius. Thus, our model utilized only a few adjustable parameters-the above density cutoff values for different chemical elements-but had the flexibility of allowing every atom to adapt its radius according to its chemical environment. This variable-radii model gave better solvation energy for 31 small neutral molecules than the Bondi radii did, especially for a quantum mechanics/Poisson-Boltzmann approach we developed earlier. The improvement was most significant for molecules with large dipole moment. Future directions for further improvement are also discussed.