Parametric Broadening of the Electronic-Vibrational Spectrum of a Molecule Caused by Zero-Point Vibrations and Thermal Fluctuations of Interatomic Bonds

Abstract

The existence in the Born–Oppenheimer approximation of a fundamentally new type of broadening of the spectral line of the electronic vibrational–rotational (rovibronic) transition in a molecule, caused by zero-point vibrations and thermal fluctuations of atomic nuclei near their equilibrium positions during vibrational–rotational motion inside the molecule, is discovered. A quantitative description in the harmonic approximation is obtained to describe the shape and width of the electron transition line corresponding to this type of broadening, which is called parametric, since the energy of any rovibronic level and transition between levels depends parametrically on the current instantaneous position of nuclei, which move much more slowly than electrons. To take this effect into account, Franck-Condon diagrams with oblique (bent) levels of vibrational energy are proposed. From the point of view of the Copenhagen interpretation of quantum mechanics, the parametric broadening exists due to the difference between an open (i.e. experimentally measured) quantum system from an isolated (unobservable) one. The magnitude of this broadening is estimated on the example of the 0–0 transition in a series of polymethine dye monomers. The estimate showed that the magnitude of the parametric broadening of the indicated zero-phonon line is comparable with the broadening observed in the experiment. The existing quantum chemical methods for calculating molecular spectra do not take into account the parametric broadening. They smooth the quasi-continuum of closely spaced rovibronic transitions, approximately calculating their common envelope, but do not consider the broadening of a single transition. The creation of a theory of parametric broadening will contribute to the development of intramolecular converters of energy from nuclei to electrons and vice versa, sensing nanoprobes, and quantum radio, photoacoustic and acousto-optic, and transceiving or converting devices of molecular size.