Evaluation Of Two-electron Integrals Research Articles

Numerical evaluation of two-electron integrals for molecular Rydberg states in systems with two active electrons

In molecular systems such as alkali dimers the two-electron wavefunction can be constructed using a limited number of configurations formed by products of two one-electron orbitals φ of the molecular ion. Starting from numerical values of the wavefunctions φ computed on a grid of points, we propose a numerical evaluation of the two-electron integrals by considering a multiple quadrature in which the innermost integral is expressed by means of an hypergeometric function. The method is well adapted to configurations involving Rydberg or continuum orbitals φ.

An analytical algorithm for the evaluation of two-electron integrals in diatomics: A test calculation with an elliptical basis set

A purely analytical method designed to compute the two-electron integrals that appear in anab-initio calculation of the electronic structures of diatomic molecules using elliptical basis set is presented. Test calculations are successfully carried out on LiH molecule.

An algorithm for evaluation of two-electron integrals by numerical integration method

An algorithm for evaluation of two-electron integrals by numerical integration method

Methods for efficient evaluation of integrals for Gaussian type basis sets

Methods are described that allow for an efficient evaluation of two-electron integrals over contracted Gaussian lobe functions. The improvement in computational speed is achieved by avoiding the computation of integrals that are: 1. sufficiently small on numerical reasons, 2. zero by symmetry, 3. identical to other integrals by symmetry. Examples of the effectiveness of these techniques are included. We also report the timings for a further processing of two-electron integrals in a Hartree Fock and correlation energy computation.

The orbital-product expansion method for the evaluation of two-electron integrals applied to a calculation on MnO 4−

A previously described method for the evaluation of multi-centre integrals using gaussian function expansions of orbital products is rigorously tested. The ground state of the permanganate ion was studied by an ab initio SCF MO calculation using a minimal basis set of contracted gaussian functions of near Hartree-Fock accuracy. The two-electron integrals were estimated with considerable accuracy from moment-constrained expansions of the unique orbital products. The effect of errors in the integral estimation was considered.

Gaussian expansions of orbital products for the evaluation of two-electron integrals

A method is described for evaluating multicenter integrals over contracted gaussian-type orbitals by the use of gaussian expansion of orbital products. The expansions are determined by the method of non-linear least squares with constraints. There is no restriction upon the symmetry of the orbital product and the method is applicable to all products arising from s, p and d-type orbitals. Results are given to indicate the accuracy of the method.

The evaluation of two-electron integrals using gaussian expansions of orbital products

A method for the evaluation of two-electron integrals using gaussian expansions of orbital products is discussed. The basis orbitals are taken to be contracted gaussian-type functions. The orbital product expansions are obtained by fitting a set of gaussian functions to the exact orbital product using the method of non-linear least squares. The imposition of constraints upon the expansions, such that the charge, dipole and quadrupole moments have their exact values, is described. A simple method for the generation of the starting approximations is presented. Molecular symmetry is used in order to reduce the number of least-squares fits that have to be obtained for a given molecule, and the method of obtaining the two-electron integrals from the orbital product expansions is described. The accuracy of the method applied to ab initio calculations and its advantages over other methods are discussed.