Nuclear motion inducing nonadiabatic transitions

We next study the geometrical aspects of the observed nonadiabatic transition. The observed nonadiabatic transitions originates from the matrix element of the nonadiabatic coupling operator KR X between the two adiabatic states H 3(R(t))) and 1 1 (R(i))). It is therefore pertinent, in the first instance, to study a spatial vector of = 

For the adiabatic functions expanded in the CSF basis set as = the nonadiabatic coupling is decomposed into 

Therefore, even if the transition through the above elements of X j are set to zero, the left hand side is not necessarily reduced to zero, because of the presence of the last term. In Fig. 7.7, we plot the first term on the right 

Chemical Theory Beyond the Born-Oppenheimer Paradigm 

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A large number of elementary molecular collision processes proceeding via (or in) excited electronic states are known at present. A prominent feature of all these is that as a rule they can not be interpreted (even at a very low kinetic energy of nuclei) in terms of the motion of a representative point over a multidimensional potential-energy surface. The breakdown of the Born-Oppenheimer approximation, which manifests itself in the so-called nonadiabatic coupling of electronic and nuclear motion, induces transitions between electronic states that remain still well defined at infinitely large intermolecular distances. 

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