Crude adiabatic electronic wavefunction

To overcome the difficulty associated with this singularity, so-called crude-adiabatic electronic wavefunctions have been introduced into the literature.Here, wavefunctions Qo) = for a fixed nuclear configuration Qo are used in the expression (4) for any Q of interest ... 

In this representation, the molecular wavefunction is expanded using the electronic wavefunctions with the contiguration fixed at the reference configuration Rq. This representation is called a crude adiabatic (CA) representation and the basis Ro) the electronic basis. The other representation, the Born-Oppenheimer (BO) representation, is defined as... 

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. 

The divergence of nonadiabatic couplings in Eq. 8.7 leads to computational problems in fuU quantum treatments, like those reviewed in this chapter, due to the difficulty to integrate them over the vibrational wavefunctions. Different strategies have been proposed to face these problems. Probably the most traditional solution is to work within the so-called crude-adiabatic approximation, where the electronic wavefunctions at a fixed nuclear configuration go are used in the expansion in Eq. 8.5,... 

The electronic wavefunction in the crude adiabatic approximation is defined according to Equation 1.18 at a specific nuclear configuration q and therefore it does not... 

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