Resolution of the identity approximation applied to PNOF correlation calculations

TL;DR

This paper introduces DoNOF-RI, an efficient implementation of the resolution of the identity approximation in PNOF calculations, significantly reducing computational costs while maintaining accuracy for molecular systems.

Contribution

The work develops the algebra for RI approximation in PNOF, reducing computational scaling and enabling faster, more accurate correlation calculations.

Findings

Significant reduction in arithmetic and memory scaling.

Fast convergence to exact results after initial approximation.

Demonstrated speed-ups in PNOF7-RI over PNOF7.

Abstract

In this work, the required algebra to employ the resolution of the identity approximation within Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from fifth-order to fourth-order, and the memory scaling is reduced from fourth-order to third-order, allowing significant computational time savings. After the DoNOF-RI calculation has fully converged, a restart with four-center electron repulsion integrals can be performed to remove the effect of the auxiliary basis set incompleteness, quickly converging to the exact result. The proposed approach has been tested on cycloalkanes and other molecules of general interest to study the numerical results as well as the speed-ups achieved by PNOF7-RI when compared with PNOF7.