Quasiparticle Density-Matrix Representation of Nonlinear TDDFT Response Functions

TL;DR

This paper introduces a quasiparticle density-matrix approach in Liouville space for nonlinear TDDFT response, simplifying calculations by avoiding nonlinear integral equations and highlighting electronic coherence.

Contribution

It develops a collective-oscillator quasiparticle representation of nonlinear TDDFT response in Liouville space, providing explicit formulas that streamline response calculations.

Findings

Derived closed-form expressions for nonlinear density response.

Eliminated the need for solving nonlinear integral equations.

Revealed electronic coherence sizes explicitly.

Abstract

The time-dependent density functional (TDDFT) equations may be written either for the Kohn-Sham orbitals in Hilbert space or for the single electron density matrix in Liouville space. A collective-oscillator, quasiparticle, representation of the density response of many-electron systems which explicitly reveals the relevant electronic coherence sizes is developed using the Liouville space representation of adiabatic TDDFT. Closed expressions for the nonlinear density-density response are derived, eliminating the need to solve nonlinear integral equations, as required in the Hilbert space formulation of the response.