The use of scaled STO basis sets. SCF calculations on the ground states of helium, beryllium and neon

Abstract

LCAO SCF calculations are presented for the ground states of helium, beryllium and neon using universal even-tempered, even-tempered and Clementi–Roetti basis sets. Gross uniform scaling of all exponents for the basis sets considered here (with the exception of the Clementi–Roetti single and double-zeta basis sets) leads to the appearance of multiple minima along selected cuts through the energy hypersurface in exponent space. The calculated energies and orbital expectation values 〈rⁿ〉(n=–1, 1, 2, 3), at the respective minimum energy values of the scaling factor, are in very close agreement with the Hartree–Fock values for nearly all choices of basis set. However, the orbital cusp values, and expectation values involving δ(r_i) and p⁴_i, show a greater degree of sensitivity to the choice of scale factor. Furthermore, a similar pattern of results for helium and beryllium is obtained when grossly scaled Clementi–Roetti or Raffenetti basis sets for neon are used. In the case of neon, when basis sets with small numbers of primitive functions are used, significant improvements in the calculated expectation values may be obtained by differentially scaling the exponents of the s- and p-type basis atomic orbitals.