Avoided surface crossings

Avoided Surface Crossings Using an Analytic Gradient Based Method. 

E. M. Evleth, Totally avoided surface crossings in amino radical-radical recombinations, Chem. Phys. Lett. 38 516 (1976) E. M. Evleth, J. T. Gleghorn, and E. Kassab, Clarification of the concept of avoided crossings in the NH bond rupture surfaces of excited ammonia, Chem. Phys. Lett., submitted. 

Figure 12 Plots of the energy surfaces appropriate to the D-B-A (left) and D -B-A (right) species as functions of the reaction coordinate along which the diabatic surfaces cross and the adiabatic surfaces undergo an avoided crossing (as shown) (appears as Figure 10.2 in ref. 12).

State crossing See avoided crossing, surface crossing. 

Spin-coupled calculations revealed crossing seams between potential energy surfaces arising from the I + 02(a) and I + 02 X) asymptotes. In a fully adiabatic treatment of this problem the surface crossings were avoided and somewhat difficult to locate. To facilitate interpretation of the adiabatic results, diabatic calculations were preformed with coupling between states from different asymptotes suppressed. Surface intersections were allowed and readily located using the diabatic treatment. 

Figure 7.13. Cross sections through the T, (n,jr ) and T, ( r, r ) triplet surfaces for the a cleavage of a) acetaldehyde, b) acrolein, and c) benzaldehyde, leading to the bent acyl radicals. In a) and b), the surface crossing that is avoided for nonplanar geometries determines the barrier height and the location of the transition state (by permission from Reinsch et al., 1988).

Class Diabatic reactionss proceed directly from the excited state to the ground state of the photoproduct via geometries, at which the two surfaces cross (conical intersections, Special Topic 2.5) or nearly cross (avoided crossings, funnels). In such reactions, no intermediates other than the excited state reached by absorption can usually be detected, because the molecule arrives on or near to a cusp of the ground-state surface and immediately proceeds to a stable product. 

Accidental degeneracy occurs whenever two potential-energy surfaces cross or touch as a function of some internal nuclear coordinate. They can cross or touch only if the total wavefunctions of both states transform as different irreducible represents of the appropriate point group. Otherwise, for finite systems there will invariably be some, perhaps small, interaction that will couple the two states and cause an avoided crossing. The same considerations also apply to orbital-based density-functional theory. 

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