High-order density-matrix perturbation theory

TL;DR

This paper introduces a straightforward formalism for calculating high-order derivatives of the electronic density matrix in density functional theory, simplifying derivations and handling electric-field perturbations effectively.

Contribution

It proposes a novel approach that avoids wavefunction perturbation expansion, enabling easier computation of high-order derivatives and electric-field effects in insulators.

Findings

Simplifies derivation of high-order density matrix derivatives

Facilitates treatment of electric-field perturbations in insulators

Provides a unified formalism for density matrix derivatives

Abstract

We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the Kohn-Sham wavefunctions. It has the following advantages: (i) it allows a simple derivation for the expression for the high order derivatives of the density matrix; (ii) in extended insulators, the treatment of uniform-electric-field perturbations and of the polarization derivatives is straightforward.