Fully-Optimized Parameters for Mixed Ramp-Gaussian Basis Sets

The description of core electrons is important for calculating a number of chemical properties using computational quantum chemistry. Though many existing specialized all-Gaussian basis sets for core-dependent properties out-perform general-purpose all-Gaussian basis sets, the underlying deficiencies of Gaussian basis sets when describing the core region of the electronic wave function persist, which limits accuracy and increases computational cost. A promising alternative to traditional all-Gaussian basis sets are mixed ramp-Gaussian basis sets. Previous investigations which focused on simply replacing core basis functions with ramp functions failed to provide the anticipated improvements in performance. For the first time, we present parametrizations for fully optimized mixed ramp-Gaussian basis sets in the form of the $R_S-n$ basis sets. Using pseudo ramp functions to approximate the ramps, basis set performance for these new mixed ramp-Gaussian basis sets is evaluated. Through multiple benchmark studies, the importance of fully optimizing the nonpolarization Gaussian functions in mixed ramp-Gaussian basis sets is confirmed. These investigations also show mixed ramp-Gaussian basis sets to have significant promise for the efficient calculation of core-dependent properties.