Methods of Deperturbation

There are two sides to the deperturbation process the Hamiltonian model and the partially assigned and analyzed spectrum. The molecular Hamiltonian operator must be organized in a way that, of the infinite number of molecular bound states and continua, emphasis is placed on the finite subset of levels sampled in the spectrum under analysis. A computational model is constructed in which the unknown information about the relevant states is represented by a set of adjustable parameters that may be systematically varied, until an acceptable match between calculated and observed properties is obtained. 

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A fundamental difficulty with the theory of autoionisation is that the so-called prediagonalised state does not exist as such. This is a standard situation in perturbation theory, where the unperturbed Hamiltonian is simply a mathematical convenience, because the system cannot physically be deperturbed. It does, however, have the serious consequence that one cannot, at first sight, check the theory in any quantitative sense. Methods of overcoming this limitation will be described in chapter 8... 

Even after the perturbers are grouped into classes and the relative vibrational numbering within a class established, it may still be premature to apply the matrix element method. Knowledge of the perturber s electronic symmetry is necessary, because this determines the J-dependence of the perturbation matrix element. The matrix element at the perturbation culmination that one determines from a local graphical treatment of the J-levels near the crossing can be quite different from the one obtained from a least-squares fit of energy levels (Tv,j) for all J-values to a model Hamiltonian. It is the value of the matrix element in the deperturbation model, not the local magnitude of the matrix element, to which the matrix element method applies. In order to illustrate this point, three types of perturbations, of the SiO A1n state will be... 

Unfortunately these methods are seldom directly applicable to van der Waals spectra, but the present paper shows how the underlying ideas may be adapted. One major difficulty is that Franck-Cordon restrictions almost invariably preclude the observation of a progression of van der Waals stretching bands. Hence the sequence of vibrational term v ues required by the conventional methods is unavailable. Secondly, although the HX motions in A— HX complexes have useful analogies with electronic motions, their adiabatic separation from the van der Waals modes is often far from complete. Consequently inversion for the full potential function may require a preliminary deperturbation of the spectrum. Nevertheless remarkable results may be obtained in favourable cases, as exemplified below for the Ar...HF system. 

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