Related papers: Analytical two-center integrals over Slater gemina…
In this paper we consider calculation of two-centre exchange integrals over Slater-type orbitals (STOs). We apply the Neumann expansion of the Coulomb interaction potential and consider calculation of all basic quantities which appear in…
We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
The Slater orbitals are the natural basis functions in quantum molecular calculations. Three-center repulsion Coulomb-exchange integrals over Slater orbitals are evaluated analytically with arbitrary orbital exponents, first for linear…
The use of Slater-type spinor orbitals in algebraic solution of the Dirac equation is investigated. The one- and two-center integrals constitute the matrix elements arising in generalized eigenvalue equation for one-electron atoms and…
The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab-initio calculations of molecules are evaluated over the non-integer Slater-type orbitals via ellipsoidal coordinates. These integrals…
In this paper, which constitutes the first part of the series, we consider calculation of two-centre Coulomb and hybrid integrals over Slater-type orbitals (STOs). General formulae for these integrals are derived with no restrictions on the…
A simple method is outlined for analytic evaluation of the basic 2-electron atomic integral with integrand containing products of atomic s-type Slater orbitals and exponentially correlated function of the form $r_{ij}…
This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on…
In previous work, the necessary integrals arising from correlated wavefunctions were expressed in forms suitable for numerical integration. For the evaluation of $r_{12}$ and $1/r_{12}$ integrals an analytic formula is derived.…
For general two-electron two-centre integrals over Slater-type orbitals (STOs), the use of the Neumann expansion for the Coulomb interaction potential yields infinite series in terms of few basic functions. In many important cases the…
In a recent paper Ozdogan (Z. Naturforsch, 59a(2004)743) published formulas for evaluating the two-center overlap and nuclear attraction integrals over integer and noninteger Slater type orbitals. The purpose of this article is to point out…
The comments of Guseinov are critically analyzed. Contrary to his comments, it is pointed out that our formula for two-center overlap integrals over Slater type orbitals have been derived independently, not derived from the earlier works of…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
The Slater-type orbital basis with non-integer principal quantum numbers is a physically and mathematically motivated choice for molecular electronic structure calculations in both non-relativistic and relativistic theory. The…
The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They…
The definition for the Slater-type orbitals is generalized. Transformation between an orthonormal basis function and the Slater-type orbital with non-integer principal quantum numbers is investigated. Analytical expressions for the linear…
We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach…
This work describes the fully analytical method for calculation of the molecular integrals over Slater-type orbitals with non-integer principal quantum numbers. These integrals are expressed through relativistic molecular auxiliary…