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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…

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…

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…

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 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 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…

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 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…

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…

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary…

In this paper methods for calculations of multi-center integrals of squared Coulomb potentials and Slater-type orbitals (STO) are derived. These integrals are necessary for accurate lower bounds to energy levels of molecular systems. All…

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…

The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…

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…

A unified formula for analytical evaluation of two-center exchange, hybrid and coulombic type integrals is presented.

Single-center two-electron integration is an important core technology in ab initio calculation of atomic and molecular structures. Therefore, this paper reviews and optimizes the method of Zhao et al., and draws a conclusion: Because this…

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…

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb and long-range Ewald operators) are employed in quantum chemical calculations. We derive a…

Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…

Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…