# Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA

## TL;DR

This paper introduces a cubic-scaling separable resolution-of-the-identity method for all-electron Gaussian basis calculations, enabling efficient RPA correlation energy computations with maintained accuracy.

## Contribution

It develops a novel density fitting scheme using quadratures over real-space points that preserves atomic orbital use and scales cubically for all-electron RPA calculations.

## Key findings

- Accurate Fock exchange and MP2 energies demonstrated.
- Cubic scaling in operations for RPA correlation energies.
- Small crossover point with standard RI-RPA implementation.

## Abstract

We explore a separable resolution-of-the-identity formalism built on quadratures over limited sets of real-space points designed for all-electron calculations. Our implementation preserves in particular the use of common atomic orbitals and their related auxiliary basis sets. The set up of the present density fitting scheme, i.e. the calculation of the system specific quadrature weights, scales cubically with respect to the system size. Extensive accuracy tests are presented for the Fock exchange and MP2 correlation energies. We finally demonstrate random phase approximation (RPA) correlation energy calculations with a scaling that is cubic in terms of operations, quadratic in memory, with a small crossover with respect to our standard RI-RPA implementation.