Quasidiabatic state

As opposed to a conical intersection, f (Qo) = AE(Qo) > 0 at the FC point. However with quasidiabatic states fiiDo) = 0. As a consequence, the second-order variation of the adiabatic energy difference satisfies... 

In this appendix we generalise the expressions of the diabatic quantities first introduced in Sec. 2 for the ideal case of an exact two-level problem to a more realistic description. In a normal situation, the Hamiltonian has an infinite number of eigenstates, and there is no finite number of strictly diabatic states [76] that can describe a given pair of adiabatic states [77-80]. Instead, one can define a unitary transformation of the adiabatic states generating two quasidiabatic states characterised by a residual non-adiabatic coupling, as small as possible, but never zero (see, e.g., [5,24,32-35]). In practice, the electronic Hilbert space is always truncated to a finite number of configurations. In what follows, we consider the case of MCSCF wavefunctions and make use of generalised crude adiabatic states adapted to this. 

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... 

Pacher T, Cederbaum LS, Kdppel H (1993) Adiabatic and quasidiabatic states in a gauge theoretical framework. Adv Chem Phys 84 293... 

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 ... 

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