Rational Design of atomic Gaussian basis sets for Ab initio Calculations of the dipole polarizabilities and hyperpolarizabilities II. Moderate Size Basis Sets for the First-Row Atoms from B to F

Abstract

The design rules, elaborated earlier in the first paper of this series for the construction of 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 tested here by the example of the basis set families, generated from the energy-optimized (9s5p) parent set. Adding the polarization sets to contracted sp substrates of various flexibility, we generate the [4s3pNdMf], [5s3pNdMf] and [6s4pNdMf] bases families, which are combined with the corresponding [3sNpMd] and [4sNpMd] bases for Hydrogen. The SCF results for H₂CO, CH₃CN, and HCN molecules, obtained with (11s7p3d/6s3p)/[6s4p3d/4s3p], are used as a benchmark here. The contraction flexibility is shown to affect the convergence of both ${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$ and ${\mathit{\beta }}_{\mathit{i}\mathit{j}\mathit{k}}$ values only insignificantly, slightly increasing the uncertainties of the calculated data. The smallest [4s3p3d/3s3p] basis is recommended for the calculation of (hyper)polarizabilities of large molecules within the SCF approximation. For the conjugated organic molecules with dominant ÏĂ-electron polarization rather reliable SCF results are obtained at the [4s3p2d/3s] level. So, for p-nitroaniline this basis set reproduces the results obtained with [6s4p3d/4s3p] basis with the error 1% for ${\mathit{\alpha }}_{\mathit{i}\mathit{j}}$ and 3% for dominant longitudinal hyperpolarizability ${\mathit{\beta }}_{\mathit{z}\mathit{z}\mathit{z}}$ .