Note that Ω i (see Eq. 23) is an independent variable of the nuclear DOFs, {R, P }. Thus, the first term on the right hand side of Eq. 95, which is independent of both R and P , must be equal to r s dΩi dt •[B i ] w , whereas the remaining terms on the right hand side of Eq. 95, which in principle depends on R and P , must be equal to