A cubic scaling algorithm for excited states calculations in particle-particle random phase approximation

TL;DR

This paper presents an efficient cubic-scaling algorithm for excited state calculations in particle-particle RPA, enabling application to larger systems by reducing computational cost while maintaining accuracy.

Contribution

It introduces an $O(N^3)$ algorithm using density fitting and eigensolvers, improving efficiency for low-lying excitation calculations in pp-RPA.

Findings

Achieves cubic scaling for pp-RPA excited state calculations.

Maintains accuracy with a reduced orbital subset.

Enables application to larger molecules and solids.

Abstract

The particle-particle random phase approximation (pp-RPA) has been shown to be capable of describing double, Rydberg, and charge transfer excitations, for which the conventional time-dependent density functional theory (TDDFT) might not be suitable. It is thus desirable to reduce the computational cost of pp-RPA so that it can be efficiently applied to larger molecules and even solids. This paper introduces an $O(N^3)$ algorithm, where $N$ is the number of orbitals, based on an interpolative separable density fitting technique and the Jacobi-Davidson eigensolver to calculate a few low-lying excitations in the pp-RPA framework. The size of the pp-RPA matrix can also be reduced by keeping only a small portion of orbitals with orbital energy close to the Fermi energy. This reduced system leads to a smaller prefactor of the cubic scaling algorithm, while keeping the accuracy for the low-lying excitation energies.