Generalization of the adiabatic electronic states

Equation (2.11) defines the standard adiabatic electronic states and the potential energy surfaces associated with them. Yet, there can exist other definitions depending on the choice of the electronic Hamiltonian. 

In his early study of nonadiabatic transitions of a diatomic molecule due to the Coriolis coupling, H. Nakamura proposed a new electronic Hamiltonian [290], in which a part of the rotational interactions is explicitly taken into account as 

Likewise, recalling Eq. (2.6), one may want to define an electronic Hamiltonian matrix 

Another interesting idea to generahze the adiabatic states arises from Eq. (2.9). By replacing the quantmn mechanical momentum operators for nuclei (Pfc) with their classical coimterparts (P/t), one obtains another electronic Hamiltonian 

The adiabatic states that diagonalize this Hamiltonian seem to dramatically reduce the magnitude of the nonadiabatic couplings among them. In return, these adiabatic electronic states depend not only on the nuclear positions but the momenta [368]. 

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