Polarized basis sets of Slater‐type orbitals: H to Ne atoms

Abstract

We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.

Inelastic low-energy collisions of electrons with HeH+: Rovibrational excitation and dissociative recombination

“…In this calculation, bound electron orbitals are described by the Slater type basis (STO) of triple-zeta quality (abbreviated as VB2 in Ref. [22]). Our zero-energy quantum defects were determined by matching the R-matrix, evaluated at 10 meV, to the Coulomb functions at distances beyond the boundary radius.…”

Generation of basis sets with high degree of fulfillment of the Hellmann‐Feynman theorem

“…As in the search of the VB1 basis set, 15 for H and Li we have taken as a main reference the corresponding homonuclear diatomics. Furthermore, we have found that, in Li and Be, the extensions significantly affect the energies in molecules containing these atoms, i.e.…”

“…In this work we present a procedure for improving the degree of fulfillment of the electrostatic theorem and apply it to the improvement of the previously reported VB1 15 …”

“…The results of Figure 3 are illustrative of the trends in this respect. Plates 3a-3d show the energy derivative and the corresponding components of the electrostatic forces acting on the C and O nuclei obtained with the VB1, CVB1, VB2, and CVB2 basis sets 15 at RHF level. Comparison of these results with those presented in Figure 3e (corresponding to FVB1 also at RHF level) clearly illustrates the improvement associated to the basis set extension.…”

Analytical method for the representation of atoms‐in‐molecules densities

“…This study was limited to molecules with atoms of the first two rows of the periodic table because, at present, STO basis sets including polarization are only available for them. 25 All the calculations in this work have been made in the RHF framework, using experimental equilibrium geometries, with the VB1 Slater basis sets. 25 The calculation of the integrals was carried out with our own package for STO molecular integrals (SMILES).…”