Parametric broadening of the molecular vibronic band due to zero-point oscillations and thermal fluctuations of interatomic bonds

Abstract

Numerous computations of the spectra of molecules are performed by mainstream methods based on the fundamental work by Lax [J. Chem. Phys. 20, 1752 (1952)] for smoothing a series of individual transitions represented by delta functions. There is an assumption that the linewidth of an individual rovibronic transition spectrum is many orders of magnitude smaller than the rovibronic bandwidth. However, the presence of rotational–vibrational structure in the molecular spectrum masks the broadening of each individual rovibronic transition. In this work, in the framework of harmonic approximation of potential energy surfaces, a new kind of contribution to homogenous broadening is considered to describe the optical spectrum of any single rovibronic transition. Its origin is in zero-point oscillations and thermal fluctuations around equilibrium positions of nuclei. Franck–Condon diagrams with slanting equidistant vibrational levels are proposed. Expressions of the spectral intensity of a single vibronic transition are derived from the first principles. This theory was used to estimate the broadening magnitude of the vibronic transition due to quantum uncertainty of nuclear coordinates of linear polymethine dyes with an extended π-electron system. It was shown that the calculated magnitude of the broadening is approximately two times smaller than the bandwidth observed in the experiment but it has the same order of magnitude. The value of such broadening depends on the environment that restricts the vibrational and rotational degrees of freedom of the molecule. It was demonstrated that an organic chromophore with an extended π-electron system can be considered to be a molecular optical parametric oscillator.