A Simple One-Electron Expression for Electron Rotational Factors

Within the context of FSSH dynamics, one often wishes to remove the angular component of the derivative coupling between states |J> and |K>. In a set of previous papers, Truhlar 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 one-electron operator Ô whose matrix element 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.