Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

TL;DR

This paper introduces a molecular-orbital-free algorithm for calculating excited states in time-dependent perturbation theory, significantly reducing computational complexity and enabling large-scale optical property simulations.

Contribution

It presents a novel non-linear conjugate gradient method using a variational approach that avoids molecular orbital calculations, improving efficiency for large systems.

Findings

Algorithm is robust and efficient for large systems.

Convergence is influenced by initial guess quality and noise sensitivity.

Method is extensible to other time-dependent theories.

Abstract

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.