Shape of the Absorption and Fluorescence Spectra of Condensed Phases and Transition Energies

Miguel Lagos and Rodrigo Paredes

General integral expressions for the temperature dependent profile of the spectral lines of photon absorption and emission by atomic or molecular species in a condensed environment are derived with no other hypothesis than: (a) The acoustic vibrational modes of the condensed host medium constitute the thermodynamic energy reservoir at a given constant temperature, and local electronic transitions modifying the equilibrium configuration of the surroundings are multiphonon events, regardless the magnitude of the transition energy. (b) Electron--phonon coupling is linear in the variations of the bond length. The purpose is to develop a theoretical tool for the analysis of the spectra, allowing to grasp highly accurate information from fitting the theoretical lineshape function to experiment, including those spectra displaying wide features. The method is illustrated by applying it to two dyes, Lucifer Yellow CH and Coumarin1, which display fluorescent maxima of 0.51 and 0.41 eV FWHM. Fitting the theoretical curves to the spectra gives that the neat excitation energies are 2.58 eV ± 2.5% and 3.00 eV ± 2.0%, respectively.