  From the change in kinetic energy induced by an external field, we discuss
the applicable conditions for the Mott-Davis and Moseley-Lukes form of the
Kubo-Greenwood formula (KGF) for the electrical conductivity which has been
implemented in \textit{ab initio} codes. We show that the simplified KGF is
suitable only for computing the AC conductivity at sufficiently high frequency
and when the gradient of the carrier density is small.
