On the accuracy of the algebraic approximation for diatomic molecules

Methods in Computational Molecular Physics

“…Analogous expressions derived within the UGA formalism may be found in a paper by Robb and Niazi (1984). The N-electron spin integrals appearing in equations (67) and (68) have been calculated by Karwowski (1975) and, within the unitary group approach, by Kent and Schlesinger (1990). As we see, within the symmetric-group based formalism, the way transitionjdensity matrix elements (63) and (64) depend upon the spin coupling scheme is reflected by the form of the U~ matrices only.…”

“…By using systematic sequences of even-tempered basis sets of either Gaussian-type functions [47,48] or exponential-type functions [65][66][67], atomic self-consistent field energies which are, in fact, often more accurate than those obtained by finite difference techniques can be obtained. For diatomic molecules, the accuracy achieved in fully numerical self-consistent field caIculations can be matched by calculations performed within the algebraic approximation when elliptical basis functions are employed [68][69][70]. Basis set expansions provide a compact representation of self-consistent field wave functions.…”

“…where S is a hermitian operator, and one takes the exponential as its Taylor series: (68) In practice, one derives in the contact transformation Sand not P. One can then write Eq.…”

Generation of systematic sequences of even‐tempered basis sets: Empirical generating formulae

“…The late 1970s and early 1980s saw the introduction 43–48 of sequences of basis sets and the systematic approach to the basis set limit. By the late 1980s, the finite basis set expansion or algebraic approximation had been refined to the point where it could be shown to match the accuracy achieved in finite difference Hartree–Fock calculations for small (i.e., few‐electron) diatomic molecules 49, 50. At the same time, it was demonstrated that similar techniques could be exploited for the corresponding relativistic problems—the Dirac–Hartree–Fock and the Dirac–Hartree–Fock–Breit models 51–53.…”

On the accuracy of the algebraic approximation in electronic structure calculations for the ground states of H32+ and H43+ using basis sets of atom-centred Gaussian-type functions

“…Over the past decade, it has also been demonstrated that finite basis set expansions can provide equivalent or superior approximations for Hartree-Fock wave functions for atoms and diatomic molecules. By using systematic sequences of even-tempered basis (44)(45)(46). Basis set expansions provide a compact representation of self-consistent field wave functions.…”