Zero-Phonon Line Profiles in Markovian and Non-Markovian Schemes in High-Temperature Systems: Applications to Glassy Water and Ethanol

摘要

This article mainly presents applications of previously derived formulas by the author to experimental systems whereby the Markovian and non-Markovian multimode Brownian oscillator (MBO) model and their consequent dynamics are explored. These applications include computing the zero-phonon line (ZPL) widths of aluminum phthalocyanine tetrasulphonate (APT) in glassy films of water and ethanol, which are compared to those of the Ohmic MBO model-calculated ZPL widths at different temperatures. The analytical forms of the ZPL width and Franck-Condon factors (FCF) derived from the high-temperature limit underdamped MBO model absorption line shape (Toutounji, Chem Phys, 2003, 293, 311) are recovered from the finite-temperature MBO model, which includes Matsubara terms (Toutounji and Small, J Chem Phys, 2002, 117, 3848). As the applicability of the Ohmic MBO model at low temperatures is questionable, the corresponding low-temperature (T) Markovian dynamics is discussed. A formula for the Ohmic MBO model ZPL FCF at T = 0 is presented. It is established that this formula reduces to e(-s), S is Huang-Rhys factor, at T = 0, which further ratifies our previous conclusion (Toutounji and Small, J Chem Phys, 2002, 117, 3848) that the bath modes are completely thwarted from contributing to the ZPL profile at this T. Hayes-Small theory of linear absorption and hole-burning line shapes is discussed and compared to that of the MBO model and other line shapes. Overdamped Ohmic MBO model is briefly discussed. Illustrative calculations are presented.