A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density

TL;DR

This paper proposes a reformulation of time-dependent Kohn-Sham density-functional theory using the second time derivative of the density, resulting in a more transparent, time-local scheme that facilitates new approximations and clarifies the adiabatic approximation.

Contribution

It introduces a second-order, time-local reformulation of TDDFT based on the second derivative of the density, enhancing transparency and potential for new approximations.

Findings

Time-local second-order Kohn-Sham scheme derived

Clearer causal structure in the reformulated theory

Framework for constructing new exchange-correlation approximations

Abstract

The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle exactly, by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation potential as an implicit density functional. It is shown that this suggests a reformulation of TDDFT in terms of the second time derivative of the density, rather than the density itself. The result is a time-local Kohn-Sham scheme of second order in time whose causal structure is more transparent than that of the usual Kohn-Sham formalism. The scheme can be used to construct new approximations at the exchange-only level and beyond, and it offers a straightforward definition of the exact adiabatic approximation.