An extension of the Kubo-Greenwood formula for use in molecular simulations

TL;DR

This paper extends the Kubo-Greenwood formula to better calculate electronic conductivity in molecular simulations, removing the need for artificial broadening and addressing contributions from degenerate and resonant states.

Contribution

The authors develop an improved Kubo-Greenwood formula that accounts for degenerate and resonant states without artificial broadening, enhancing its applicability in molecular simulations.

Findings

Finite contributions from degenerate states at low frequencies.

No need for broadening parameters in the DC limit.

Single-particle excited states dominate the conventional KGF.

Abstract

We discuss the foundations and extend the range of applicability of the widely used Kubo-Greenwood formula (KGF) for the electronic conductivity. The conductivity is derived from the current density, and only the probability amplitude rather than the transition probability is used. It is shown that the contribution to the conductivity from degenerate states in a low or zero frequency external electric field and the contribution from states near resonance with a finite frequency external field are finite. The improved conductivity expression does not include the familiar "energy conserving" delta function, and no artificial broadening parameter for delta function is required for the DC limit. We explored two methods of computing current density. We discuss the role of many-electron statistics in computing the conductivity in single-particle approximations, and we show that the conventional KGF is due to the contribution from single-particle excited states.