Radial subshell splittings and double-zeta functions in many-electron atoms

When the electron-electron interaction is explicitly considered in many-electron atoms, the average subshell radiusnl splits into two different radii, inner radius nl and outer radius >nl, where n and l are the principal and azimuthal quantum numbers. For the 102 atoms He through Lr in their ground states, the radii nl and nl are systematically examined at the Hartree-Fock limit level. For a subshell nl, two exponents zetanl(est) estimated from these radii have good linear correlations with variationally determined exponents zetanl(var) of double-zeta Slater-type functions.     

Long-Range multicenter integrals with slater functions: Gauss transform-based methods

The separation of the short- and long-range terms in the potentials generated by pairs of Slater functions is reformulated in the context of the Gauss transform method. Analytic expressions of the long-range potentials (in closed form) are derived for equal exponents and generalized (as expansion series) for different exponents. Additionally, the representation of these potentials from small sets of charges or lowest-order multipoles is examined, paying special attention to their values and optimal positions. Finally, numerical tests of the formal developments are presented. It is concluded that the long-range three- and four-center integrals can be calculated with high accuracy in a simple and relatively inexpensive manner. © John Wiley & Sons, Inc.     

Asymptotic formulas for Coulomb and hybrid integrals with slater type functions

Asymptotic expressions are obtained for two-center Coulomb and hybrid integrals with Slater functions. Results of numerical test of these expressions are presented. The use of asymptotic formulas in LCAO-MO calculations of electronic molecular structure substantially reduces the computation time. V.I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 2, pp. 12–15, March–April, 1994. Translated by L. Chernomorskaya     

A mixed basis set of slater and gaussian functions for molecular calculations

A procedure for using simultaneously Slater and Gaussian basis functions in molecular calculations is presented here. The analytic expressions of the integral prototypes involving both Slater and Gaussian functions are explicitly derived.     

The use of slater orbitals in variational calculations involving one-electron green's functions

In this paper an application of a minimum principle proposed for electronic systems by Hall, Hyslop and Rees, [1] and [2], is considered. It is shown that the evaluation of the required two-centre molecular integrals involving one-electron Green's functions may be facilitated by the introduction of a particular class of trial functions. These functions incorporate the potential energy of the system as a weighting factor and Slater-type orbitals are then used as a basis set. The evaluation of the resulting integrals is discussed and illustrative calculations for the H ₂ ⁺ ion are presented.     

Hulthén and slater type 2d functions in some excited configurations of sulphur and phosphorus

It is shown that a substantial energy improvement is gained by the variational use of Hulthén orbitals, instead of single Slater orbitals, in the 3d shells of some excited configurations of sulphur and phosphorus. The energies obtained are close to those attained with two-term Slater functions. In some cases the radial distribution functions from Hulthén orbitals are as good an approximation of SCF radial distributions as those from two-term Slater orbitals. Single term 2d functions with only one parameter are found to give almost identical energies and radial distribution functions as those obtained from two-parameter Hulthén orbitals. It is shown that the relationship between one-term 2d orbitals and Hulthén orbitals gives a method of enforcing nuclear cusp conditions on the former with little effect on the energy.     

SCA calculations of the inner shell ionization with Dirac-Fock electronic wave functions

The theory of inner shell ionization for arbitrary atomic shells is reviewed. Emphasis is onL- andM-shells in order to show how the proper screening formalism entering the electronic form factor affects the ionization probabilities. The radial wavefunctions in the form factor are computed as relativistic Hartree-Fock orbitals for both bound and continuum states. The continuum orbitals were evaluated in theV(N–1) potential with correct exchange. These results are then compared with the previous ones using screened hydrogen-like wavefunctions and also with the experimental data in some cases.     

Molecular integrals with an arbitrary many-electron operator in the slater atomic orbital basis

Formulas are derived for molecular integrals with an arbitrary many-electron operator. Final results are expressed in terms of overlap integrals and one-center many-electron integrals.Baku University. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 446–449, July–August, 1991. Original article submitted October 12, 1990.