Least Squares Resolution
of Absorption Spectra

Introduction

A fundamental limitation of the semiclassical theory [of the interaction of matter with radiation] is its inability to predict spectral lineshapes for the transitions involved. The results of a conventional calculation of an electronic spectrum are the Born-Oppenheimer resonance frequency and the Franck-Condon electronic dipole strength (i.e., vertical difference of electronic energies in ground state and excited state at a given geometry, and the vibronic dipole strengths summed over all vibrational levels in the excited state) for each electronically excited state that may be chosen for consideration. No information about the individual vibronic transitions is obtained, and even if the resonance frequency and dipole strength were available for each such component its lineshape would still be unknown (this is probably Lorentzian in form, but the halfwidth is not computationally accessible); thus, the electronic envelope (bandshape) cannot in practice be obtained by superposition of its vibronic components.
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