Estimation of Parameters in a Model Hamiltonian

Whenever a perturbation, predissociation, or autoionization is observed, its strength is governed by an off-diagonal matrix element. Although these matrix elements can frequently be calculated from, ab initio wavefunctions or estimated semiempirically from other perturbation-related information, experimentalists typically treat the perturbation matrix element as a purely empirical parameter of no interest other than its capacity to account for the spectrum. This book is based on the premise that perturbation matrix elements have intrinsic molecular structural significance, that their magnitudes are predictable, and that their measured values often provide unexpected clues to a global description of the electronic structure of a molecule. 

In Sections 5.2, 5.3 and 5.4, the orders of magnitude of all types of perturbation parameters are related to known or easily estimable quantities in order to provide a basis for predicting their absolute magnitudes, relative sizes, and inter- or intramolecular trends. 

The same electronic matrix elements that control the strength of perturbations also govern predissociation (Table 7.2) and, in reduced form, autoionization (Section 8.4). 

The vibrational part of the H matrix elements is much easier to calculate than the electronic one. Methods for such calculations are described in Section 5.1 for bound bound interactions and in Section 7.6 for bound continuum vibrational interactions. 

An understanding of observable properties is seldom trivial. Spectroscopic energy levels are, in principle, eigenvalues of an infinite matrix representation of H, which is expressed in terms of an infinite number of true de-perturbed molecular constants. In practice, this matrix is truncated and the observed molecular constants are the effective parameters that appear in a finite-dimension effective Hamiltonian. The Van Vleck transformation, so crucial for reducing H to a finite Heff, is described in Section 4.2. 

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