  Atomic radii and charges are two major parameters used in implicit solvent
electrostatics and energy calculations. The optimization problem for charges
and radii is under-determined, leading to uncertainty in the values of these
parameters and in the results of solvation energy calculations using these
parameters. This paper presents a new method for quantifying this uncertainty
in implicit solvation calculations of small molecules using surrogate models
based on generalized polynomial chaos (gPC) expansions. There are relatively
few atom types used to specify radii parameters in implicit solvation
calculations; therefore, surrogate models for these low-dimensional spaces
could be constructed using least-squares fitting. However, there are many more
types of atomic charges; therefore, construction of surrogate models for the
charge parameter space requires compressed sensing combined with an iterative
rotation method to enhance problem sparsity. We demonstrate the application of
the method by presenting results for the uncertainties in small molecule
solvation energies based on these approaches. The method presented in this
paper is a promising approach for efficiently quantifying uncertainty in a wide
range of force field parameterization problems, including those beyond
continuum solvation calculations.The intent of this study is to provide a way
for developers of implicit solvent model parameter sets to understand the
sensitivity of their target properties (solvation energy) on underlying choices
for solute radius and charge parameters.
