Zero‐phonon line profiles in Markovian and non‐Markovian schemes in high‐temperature systems: Applications to glassy water and ethanol

Abstract

AbstractThis 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. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009