The derivative coupling describes the fact that the Born-Oppenheimer potential surfaces E J (R) and E K (R) are coupled due to nuclear motion, represented by the operator ∇R . The general solution to the coupled nuclear-electronic problem involves a vibronic Schrödinger equation, rather than the purely electronic one in Eq. ( ), the latter of which describes the uncoupled Born-Oppenheimer approximation. Unless ∂ Ĥ/∂x happens to vanish by symmetry along a particular coordinate x, then electronic states J and K will be strongly coupled in regions where the energy gap