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Potential Energy Surfaces and Conical Intersections

Adiabatic and Diabatic Surfaces

Thus far, we have been concerned with potential energy surfaces derived under the Born-Oppenheimer approximation (see section 3.1), also known as the adiabatic approximation. Hence, such surfaces are referred to as adiabatic potential energy surfaces.
Avoided crossings are typical of adiabatic surfaces and arise because the adiabatic electronic states corresponding to the surfaces are often mixtures of two simple molecular orbital (i.e., covalent) or valence bond (i.e., ionic) electronic structures (cf. the NaCl example used in section 11 to explain the non-crossing rule), where the original energy functions do cross.
A surface where actual intersections are substituted for the avoided crossings is termed a diabatic surface.
If the nuclei are assumed to move slowly, then they are likely to follow a single, adiabatic energy surface, even in the region of an avoided crossing. If the nuclei have sufficient velocity, then the Born-Oppenheimer approximation breaks down and the nuclei may effectively “ignore” the gap in the avoided crossing and simply cross over to the other adiabatic surface, adopting that configuration. This is termed non-adiabatic behaviour can be modelled, to some extent, by a diabatic representation. Figure 12.1 goes someway to illustrating the adiabatic and diabatic representations of a polyatomic surface:

Figure 12.1
Figure 12.1 - Close -up view of the S1S2 conical intersection in pyrazine in the Q6aQ10a space. Adiabatic surfaces are shown in (a), the diabatic diagonal elements H11 (*) and H22 (ππ*) are shown in (b). The diabatic coupling element H12 is shown in (c) [33]
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[33] Woywod et al., “S1–S2 Conical Intersection in Pyrazine”, J. Chem. Phys., 100, 1408, 1994