Bound-state dynamics, adiabatic

The adiabatic approximation, which is to be applied to bound-state dynamics, involves the separation of fast and slow motions. However, unlike the original application of the Bom-Oppenheimer approximation,77 in which fast electronic motion is separated from the slower nuclear one, there is no clear separation of time scales for nuclear motions. Nevertheless, there is now ample evidence to show that there are always states, to be termed adiabatic, which are accurately described by an adiabatic approximation.66,69-71 78... 

In this way r is singled out as the fast electronic coordinate. In the absence of prior knowledge we can, equally well, designate R as the fast coordinate. This gives rise to an alternative adiabatic breakdown of the Schrodinger equation, and exemplifies the nonuniqueness associated with the adiabatic separation of bound-state nuclear dynamics. 

Ultrafast excitation experiments and corresponding dynamical simulations reveal that on the molecular time scale caging is sensitive both to the detailed molecular structure of the solvent surrounding the molecule and to the dynamics of the dissociation process. As an example let us take excitation of U to an electronically bound state (B) that dissociates because of a non-adiabatic transition to a repulsive state, Figure 11.10. The transition is symmetry forbidden in the isolated homonuclear molecnle bnt allowed in solntion, where coupling to the solvent breaks the symmetry of the isolated molecule. ... 

Treating bound modes quantum mechanically, the adiabatic separation between s and u is equivalent to assuming that quantum states in bound modes orthogonal to s do not change throughout the reaction (as s progresses from reactants to products). The reaction dynamics is then described by motion on a one-mathematical-dimensional vibrationally and rotationally adiabatic potential... 

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