Conserving Approximations in Time-Dependent Density Functional Theory

TL;DR

This paper introduces a variational approach-based method for improving the accuracy of linear response functions in time-dependent density functional theory, ensuring conservation laws and applicable to solids and nano-systems.

Contribution

It develops a new variational technique for successively better approximations to response functions in TDDFT, grounded in many-body perturbation theory and conserving physical laws.

Findings

Response functions obey conservation laws such as particle and momentum conservation.

Multiple levels of response functions with different sophistication are presented.

Applicable to optical response calculations of solids and nano-scale systems.

Abstract

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.