Probabilities of Electronically Adiabatic Processes

The possibility of describing an elementary process in the adiabatic approximation means that the representative point in the configuration space of the nuclei always remains on one certain potential energy surface. It follows that the potential energy surfaces of the reactant and product molecules are parts of a common potential energy surface of the system. 

The most general symmetry group of Hgi is connected with the symmetry of the potential caused by the symmetric configuration of the nuclei. The correlation of the electronic states for this t e of symmetry is considered in [112, 189, 287, 288, 339]. 

If the magnetic interaction is strong, i.e. comparable with the electrostatic interaction of electrons (as is the case with atoms and molecules of heavy elements), the electronic states cannot be classified according to the total electron spin and the Wigner rule is invalid. 

If the spin-orbital coupling is sufficiently small, the Wigner rule is only approximately valid. The spin-orbital coupling may be considered then as a perturbation responsible for transitions between the electronic states of different multiplicity. 

It should be noted that the same symmetry of the initial and the final electronic states is a necessary but not sufficient condition for the adiabatic character of the process. It has also to be estimated whether the initial and final electronic terms actually belong to the same potential energy surface. For qualitative estimations of this sort, it appears useful to further simplify Hei- In particular, if the electrostatic interaction between electrons is neglected, the change of the molecular electronic structure on rapproachment of the molecules is described by the variation of the one-electron molecular orbitals the electronic energy is then given by the sum of the one-electron energy levels. 

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