Quasidiabatic basis

The singularity at the conical intersection can be made to vanish if only two conditions are fulfilled by the quasidiabatic basis bp = cp and bp = cp. Since we have two independent coordinates R and Rp these conditions can be met. In general, the quasidiabatic basis can perform more efficiently than just removing the singularity as one approaches the conical intersection. 

It is clear from (A.8) and (A.9) that the gradient difference and derivative coupling in the adiabatic representation can be related to Hamiltonian derivatives in a quasidiabatic representation. In the two-level approximation used in Section 2, the crude adiabatic states are trivial diabatic states. In practice (see (A.9)), the fully frozen states at Qo are not convenient because the CSF basis set l Q) is not complete and the states may not be expanded in a CSF basis set evaluated at another value of Q (this would require an infinite number of states). However, generalized crude adiabatic states are introduced for multiconfiguration methods by freezing the expansion coefficients but letting the CSFs relax as in the adiabatic states ... 

Owing to Eq. (35), there is no reason to expect that a strictly diabatic basis exists. Nevertheless, one can construct quasidiabatic states which are extremely useful in solving and understanding many relevant problems abundantly discussed in the literature. With their help it is possible to remove a substantial part of the derivative couplings and make the group-Born-Oppenheimer Eq. (26) more transparent and better amenable to explicit numerical calculations. That part of the derivative couplings which can be removed by an unitary transformation U( (R) is called... 

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