Time-dependent density functional theory using atomic orbitals and the self-consistent Sternheimer equation

Abstract

We present the implementation of linear-response time-dependent density functional theory based on the self-consistent Sternheimer equation and employing a basis set of numerical pseudo-atomic orbitals. We demonstrate this method by presenting test calculations on systems of increasing size ranging from benzene to chlorophyll a, and by comparing our results with those obtained within Casida's formalism and with previous calculations. We provide a detailed assessment of the accuracy of this method, both in relation to the use of local orbitals for describing electronic excitations and to the handling of the frequency response using Pade approximants. We establish a simple criterion for estimating a priori the accuracy of the basis set in the calculation of optical spectra. We show that the computational cost of this method scales quadratically with the system size.