Quasidiabatic

The quasidiabatic framework is defined as the framework for which the conditions in Eqs. (10) are replaced by the following less stricked ones [81] ... 

Quasidiabatic framework, non-adiabatic coupling, adiabatic-to-diabatic transformation matrix, line integral approach, 53—57... 

A more general description of the effects of vibronic coupling can be made using the model Hamiltonian developed by Koppel, Domcke and Cederbaum [65], The basic idea is the same as that used in Section III.C, that is to assume a quasidiabatic representation, and to develop a Hamiltonian in this picture. It is a useful model, providing a simple yet accurate analytical expression for the coupled PES manifold, and identifying the modes essential for the non-adiabatic effects. As a result it can be used for comparing how well different dynamics methods perform for non-adiabatic systems. It has, for example, been used to perform benchmark full-dimensional (24-mode) quantum dynamics calculations... 

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. 

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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