Adiabatic electronic wavefunctions

Finally, on the ground-state free energy surface, the evolving adiabatic electronic wavefunction during the CCB dissociation, expressed in terms of the VB state wavefunc-tions, is... 

Figure 5. Energy curves (hartree) for CH3F dissociation in vacuo (solid line) and in methanol (filled circles) against the CF distance (A). Curves A refer to the covalent structure, curves B to the ionic structure corresponding to HsC+F-, and curves AB to the adiabatic electronic wavefunction.

Figure 3.9 Ab initio d/dR and d2/dR2 matrix elements between the E, F and G, K adiabatic states of H2 Bl2 = (-hw 2ad), M2 = ( iad. y 2ad)r where 4>i and 2 are the adiabatic electronic wavefunctions for the E, F and G, K double-minimum states, respectively. Except for the smallest R values, Bi2(R) is Lorentzian. The relationships B12 = —B21 and (Ai2 — A2i) = Bi2 are not satisfied exactly because 4>iad ar d 4>2a

The geometric phase effect, the signature property of a conical intersection, requires that the adiabatic electronic wavefunction (chosen to be real-valued and continuous with respect to nuclear coordinates) change sign when... 

This adiabatic product function is not the only BO product that can be formulated. Since the adiabatic electronic wavefunctions depend parametrically on Q and i d /dQ is a differential operator, nonadiabatic... 

The absence of symmetry restrictions implies that it is difficult to make a strict separation of Franck-Condon and vibronic coupling effects. Suppose we have obtained accurate expressions for the adiabatic potential surfaces E (Q) and E (Q), for instance, by quantum-chemical calculations. To evaluate the effect of vibronic coupling between them, we wish to expand the adiabatic electronic wavefunctions in -independent wavefunctions. For nontotally symmetric modes the origin of this expansion is determined by symmetry, but for totally symmetric modes, it is not. It will thus be necessary to calculate for which value of Q the nonadiabatic coupling between the adiabatic potentials vanishes and to use this value as the origin. 

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 ... 

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