Two-electron Molecular Integrals Research Articles

Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule

We report on accurate variational calculations of the Born–Oppenheimer potential for excited states of the hydrogen molecule with , and Φ symmetries. The obtained potential energy curves reach the relative precision of or better along internuclear distances of 0.01–20 au. Calculations rely on the recursive evaluation of two-centre two-electron molecular integrals with exponential functions in arbitrary precision arithmetics. Our results for most of the states are the first-ever reported, and for the previously calculated states constitute an improvement by several orders of magnitude.

Evaluation of two-electron integrals for explicit r12 theories

We present a practical scheme for the evaluation of nonstandard two-electron molecular integrals that appear in ab initio theories employing explicitly correlated wave functions with linear r12 terms (“linear r12” methods). In contrast with previous efforts, the target integrals are evaluated recursively via intermediates formulated solely in terms of Cartesian Gaussian functions. All working equations fit conveniently the framework of highly efficient Head-Gordon and Pople method of evaluation of electron repulsion integrals. Thus, only straightforward modifications of existing codes that employ HGP or HGP–PRISM scheme are necessary to implement our approach. High potential of the pathway is realized in a robust practical implementation.

New translation method for STOs and its application to calculation of two-center two-electron integrals

The new translation method for Slater-type orbitals (STOs) previously tested in the case of the overlap integral is extended to the calculation of two-center two-electron molecular integrals. The method is based on the exact translation of the regular solid harmonic part of the orbital followed by the series expansion of the residual spherical part in powers of the radial variable. Fair uniform convergence and stability under wide changes in molecular parameters are obtained for all studied two-center hybrid, Coulomb, and exchange repulsion integrals. Ten-digit accuracy in the final numerical results is achieved through multiple precision arithmetic calculation of common angular coefficients and Gaussian numerical integration of some of the analytical formulas resulting for the radial integrals. c 2000 John Wiley & Sons, Inc. Int J Quantum Chem 79: 91-100, 2000

Calculation of many-centre two-electron molecular integrals with STO

A program for the calculation of two-electron molecular integrals between real Slater-type orbitals (STO) is reported.The program is mainly intended for comparison purposes, to analyze and test the results provided by other algorithms. However, it can be used in actual molecular calculations of small systems. The integrals are obtained by means of Gaussian expansions of the STO. Expansions that enable to attain an accuracy of at least ten decimal places in the integrals are included.

Ab initio SCF calculations on [V10O28]6−: A benchmark for the classical calculation and processing of molecular integrals on large Gaussian basis sets

AbstractA vector efficient implementation of the McMurchie and Davidson algorithm for the calculation of one‐ and two‐electron molecular integrals is presented, as available in the Cray version of the ASTERIX program system. The implementation and performance of a vector‐oriented strategy for the generation and processing of the P supermatrix is also discussed. This program system has been applied to the ab initio SCF computation of the ground‐state wave function for the [V10O28]6− ion, with a basis set of triple‐zeta quality for the valence shell of oxygen generating 1404 GTOS and 574 CGTOS for the complete system. The performance and the bottlenecks of the integral calculation are discussed as a function of the integral classes. Two‐dimensional maps of the electrostatic potential are presented for this molecule and compared to experimental information about proton fixation.

General recurrence formulas for molecular integrals over Cartesian Gaussian functions

General recurrence formulas for various types of one- and two-electron molecular integrals over Cartesian Gaussian functions are derived by introducing basic integrals. These formulas are capable of dealing with (1) molecular integrals with any spatial operators in the nonrelativistic forms of the relativistic wave equations, (2) those with the kernel of the Fourier transform, (3) those with arbitrarily defined spatial operators so far as the integrals can be expressed in terms of the basic integrals, and (4) any order of their derivatives with respect to the function centers in the above integrals. Thus, the present formulation can cover a large class of molecular integrals necessary for theoretical studies of molecular systems by ab initio calculations, and furthermore provides us with an efficient scheme of computing them by virtue of its recursive nature.

Program for the four-index transformation of two-electron molecular integrals from an atomic to a molecular basis

Program for the four-index transformation of two-electron molecular integrals from an atomic to a molecular basis

Field and field gradient integrals based on Gaussian type orbitals

A program for the calculation of two-electron molecular integrals between real Slater-type orbitals (STO) is reported.The program is mainly intended for comparison purposes, to analyze and test the results provided by other algorithms. However, it can be used in actual molecular calculations of small systems. The integrals are obtained by means of Gaussian expansions of the STO. Expansions that enable to attain an accuracy of at least ten decimal places in the integrals are included.

Evaluation of Molecular Integrals by a Numerical Method

Numerical integration in elliptical coordinates is proposed as a convenient method for the computation of most types of two-electron molecular integrals including some types of three- and four-centre integrals, and in some cases, of one-electron two- and three-centre integrals. This method removes a great deal of the burden of analysis and in addition lifts many of the restrictions on the form of the orbitals which are imposed by existing methods. For Slater-type orbitals general formulae are given to facilitate the calculation of two-centre Coulomb integrals, hybrid repulsion integrals and certain three-centre integrals. Explicit expressions are listed for integrals involving orbitals of the first, second and third quantum shell.