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

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