Indeterminacies of Fitting Parameters in Molecular Spectroscopy

Abstract

AbstractAnalyses of molecular spectra often use the idea of aneffective Hamiltonian, in which the dynamical variables are the degrees of freedom involved in the spectrum, and the effects of the other degrees of freedom are represented by the values of various parameters. However, it may not be possible to determine all these parameters by empirical fits of the spectra because different parameters may make indistinguishable contributions to the eigenvalues of the Hamiltonian. This article reviews a number of examples of such indeterminacies, including applications to vibration–rotation spectra of diatomic molecules, without or with corrections for the breakdown of the Born–Oppenheimer approximations; electron‐spin structure in diatomic molecules; centrifugal distortion in asymmetric‐top molecules; vibration–rotation resonances in polyatomic molecules; vibration–rotation interactions in degenerate vibrational states; and internal rotation. The discussion of these indeterminacies involves unitary transformations that are expanded as infinite series. This procedure may break down if the convergence of the series is slow. The study of near‐singularities of least‐squares matrices associated with the presence of indeterminacies is also discussed.