Nuclear dynamics adiabatic states, conical intersections

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

We refer to Chapter 4 for a detailed discussion on the definition and explicit construction of diabatic states. The diabatic representation is generally advantageous for the computational treatment of the nuclear dynamics if the adiabatic potential-energy surfaces exhibit degeneracies such as conical intersections. Moreover, the diabatic representation often reflects more clearly than the Born ppenheimer adiabatic representation the essential physics of curve crossing problems and is thus very useful for the construction of appropriate model Hamiltonians for polyatomic systems. 

When considering reaction paths on the PE surfaces of excited states, as required for the rationalization of photochemistry [4], two major additional complications arise. First, reliable ab initio energy calculations for excited states are typically much more involved than ground-state calculations. Secondly, multi-dimensional surface crossings are the rule rather than the exception for excited electronic states. The concept of an isolated Born-Oppenheimer(BO) surface, which is usually assumed from the outset in reaction-path theory, is thus not appropriate for excited-state dynamics. At surface crossings (so-called conical intersections [5-7]) the adiabatic PE surfaces exhibit non-differentiable cusps, which preclude the application of the established methods of mathematical reaction-path theory [T3]. As an alternative to non-differentiable adiabatic PE surfaces, so-called diabatic surfaces [8] may be introduced, which are smooth functions of the nuclear coordinates. However, the definition of these diabatic surfaces and associated wave functions is not unique and involves some subtleties [9-11]. 

Comparing equations (7a) and (7b) shows that the existence of a conical intersection fundamentally alters the nuclear Schrodinger equation even in the adiabatic, = 1, limit. Paradoxically then, as the result of a conical intersection, an electronic state can influence nuclear dynamics despite the fact that nuclear motion never occurs on the corresponding... 

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