  Within the context of FSSH dynamics, one often wishes to remove the angular
component of the derivative coupling between states $\left|J\right>$ and
$\left|K\right>$. In a set of previous papers, Truhlar {\em et al.} posited one
approach for such a removal based on direct projection, while we isolated a
second approach by constructing and differentiating rotationally invariant
basis. Unfortunately, neither approach was able to demonstrate a {\em
one-electron operator} $\hat{O}$ whose matrix element
$\left<J|\hat{O}|K\right>$ was the angular component of the derivative
coupling. Here, we show that a one-electron operator can in fact be constructed
efficiently in a semi-local fashion. The present results yield physical insight
into designing new surface hopping algorithms and be of immediate use for FSSH
calculations.
