Rational Design of atomic gaussian basis sets for Ab initio calculations of the dipole polarizabilities and hyperpolarizabilities. I. Optimized polarization sets for the first-row atoms from B to F

Abstract

The rational design rules for atomic Gaussian basis sets, tailored for the calculations of molecular polarizabilities ${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$ and hyperpolarizabilities ${\mathit{\beta }}_{\mathit{i}\mathit{j}\mathit{k}}$ at the SCF level, are elaborated. The sequence of the optimized polarization sets (2d), (3d), (4d), (3d1f), (4d3f) for the first-row atoms from B to F is constructed, the optimization technique is supposed to provide a rapid convergence of both ${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$ and ${\mathit{\beta }}_{\mathit{i}\mathit{j}\mathit{k}}$ with the size of the polarization set. Adding of these polarization sets to the [6s4p] and [6s5p] substrates, derived from the energy-optimized (10s6p) primitive set of Huzinaga, gives the [6s4pNdMf] and [6s5pNdMf] bases families. They are combined with the corresponding [4sNpMd] and [5sNpMd] bases for Hydrogen built up in the same manner. The convergence of SCF results with the size of the basis set has been thoroughly investigated by the examples of H₂CO, CH₃CN, and HCN molecules. It has been established that both ${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$ and ${\mathit{\beta }}_{\mathit{i}\mathit{j}\mathit{k}}$ values converge to their saturation limits at the [6s4p3d/4s3p] level. This basis set provides the results, which are very close to near HF limit values, estimated with the most sophisticated polarized Gaussian basis sets used up to now.