Linear-scaling time-dependent density-functional theory in the linear response formalism

TL;DR

This paper introduces a linear-scaling TDDFT implementation in the linear response formalism, enabling efficient calculation of optical spectra for large molecules and nanostructures by using two sets of localised orbitals.

Contribution

It presents a novel double representation approach with in situ optimisation, avoiding issues with unoccupied state spanning and achieving linear computational scaling.

Findings

Good agreement with traditional TDDFT results for organic molecules

Demonstrates linear scaling of computational cost with system size

Successfully applied to carbon nanotubes

Abstract

We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on a system of carbon nanotubes.