Potential energy surfaces intersections

Let S be any simply connected surface in nuclear configuration space, bounded by a closed-loop L. Then, if 4>(r,R) changes sign when transported adiabatically round L, there must be at least one point on S at which (r, R) is discontinuous, implying that its potential energy surface intersects that of another electronic state. 

Because CASSCF is a full Cl, it can be considered in either an atomic orbital (AO) basis (valence bond [VB] theory) or symmetry-adapted molecular orbital (MO) theory. The two pictures are equivalent, but the VB method is more powerful because (as we discuss more fully below) it can explain why geometries change in excited states and why two potential energy surfaces intersect. In this respect, the VB picture is more appropriate for the reactivity problems we discuss here, whereas MO theory is still key to spectroscopy. 

Two recent papers by Letokhov (38) and by Moore (39) contain excellent and detailed discussions of the application of lasers to isotope separation. The approaches fall into two broad categories which may be characterized as one-step and two-step processes. The one-step process is particularly simple conceptually but not as generally applicable. It involves selective excitation of a suitable molecule to an upper pre-dlssoclative state. This upper state is a non-dissociative one whose potential energy surface intersects another surface corresponding to a dissociative state. Such a system is illustrated in Figure 13. If the dissociative lifetime is shorter than the radiative lifetime, then selective photo-excitation can produce isotopically enriched... 

Most treatments of nonadiabatic processes do not abandon the Born-Oppenheimer idea of nuclear motion on potential-energy surfaces, instead in a nonadiabatic process the nuclei move on more than one Born-Oppenheimer potential-energy surface. Nonadiabatic transitions between potential-energy surfaces occur when the nuclei encounter a region where two potential-energy surfaces are in close proximity. Regions where the potential-energy surfaces intersect linearly, conical intersections, are of preeminent importance. 

Conical intersection Case in which two potential energy surfaces intersect such that their separation decreases to zero linearly in the relevant nuclear coordinates. 

DETERMINATION OF POTENTIAL ENERGY SURFACE INTERSECTIONS AND DERIVATIVE COUPLINGS IN THE ADIABATIC REPRESENTATION... 

World Scientific, Singapore, 2004, pp. 129-174. Determination of Potential Energy Surface Intersections and Derivative Couplings in the Adiabatic Representation. 

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