Gaussian Expansions of Orbitals

Gaussian Expansions of Orbitals.

Using numerical calculations and analytic theory, we examine the convergence behavior of Gaussian expansions of several model orbitals. By following the approach of Kutzelnigg, we find that the errors in the energies of the optimal n-term even-tempered Gaussian expansions of s-type, p-type, and d-type exponential orbitals are εn s ∼ exp(−π(3n)), εn ∼ exp(−π(5n)), and εn ∼ exp(−π(7n)), respectiv...

Exact Gaussian expansions of Slater-type atomic orbitals

Three exact Slater-type function (STO) integral transforms are presented. The STO-NG basis set can then be developed using either only 1s Gaussian functions, the same Gaussian exponents for each shell, or using the first Gaussian of each symmetry. The use of any of these three alternatives depends only on appropriate numerical integration techniques.

Canonical tensor products as a generalization of Gaussian-type orbitals

GTOBAS: fitting continuum functions with Gaussian-type orbitals

GTOBAS is a program for fitting Gaussian-type orbitals (GTOs) to Bessel and Coulomb functions over a finite range. The exponents of the GTOs are optimized using the method of Nestmann and Peyerimhoff [J. Phys. B 23 (1990) L773]. The appended module NUMCBAS provides the numerical Bessel and Coulomb functions required as input for the program. The use of GTO continuum basis sets is particularly i...

Molecular integrals over spherical Gaussian-type orbitals: I

A novel derivation, involving the Fourier transform and the addition theorem of harmonic polynomials, is presented for multi-centre molecular integrals over spherical Gaussiantype orbitals. Compact closed-form formulae, consisting of vector-coupling coefficients and well known functions only, are obtained for all multi-centre molecular integrals. The resulting formulae manifest the angular and ...