# Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

## TL;DR

This paper introduces a cubic scaling algorithm for RPA correlation energy calculation that leverages Cauchy's integral formula and interpolative separable density fitting to significantly reduce computational cost.

## Contribution

The authors develop a novel cubic scaling algorithm for RPA correlation energy using Cauchy's integral formula and interpolative separable density fitting, improving efficiency over previous methods.

## Key findings

- Achieves cubic computational scaling for RPA correlation energy calculations.
- Uses a geometrically convergent quadrature rule for the integral.
- Reduces computational cost via interpolative separable density fitting.

## Abstract

We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in $\chi^0$ by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.