Calculation of the molecular integrals with the range-separated correlation factor

TL;DR

This paper introduces a recursive, flexible scheme for calculating molecular integrals with a range-separated correlation factor, improving the efficiency and precision of explicitly correlated quantum chemical computations.

Contribution

A novel recursive method for computing five types of molecular integrals with a range-separated correlation factor, adaptable to various correlation functions.

Findings

Efficient recursive algorithm for integral calculation.

Flexible approach allowing arbitrary correlation factors.

Enhanced control over computational precision.

Abstract

Explicitly correlated quantum chemical calculations require calculations of five types of molecular integrals beyond the standard electron repulsion integrals. We present a novel scheme, which utilises general ideas of the McMurchie-Davidson technique, to compute these integrals when the so-called \range-separated" correlation factor is used. This correlation factor combines the well-known short range behaviour, resulting from the electronic cusp condition, with the exact long-range asymptotics found for the helium atom [M. Lesiuk, B. Jeziorski, and R. Moszynski, J. Chem. Phys. $\textbf{139}$, 134102 (2013)]. Almost all steps of the presented procedure are formulated recursively, so that an efficient implementation and control of the precision are possible. Additionally, the present formulation is very flexible and general, and it allows for use of an arbitrary correlation factor in the electronic structure calculations with minor or no changes.