Optical response functions for condensed systems with linear and quadratic electron-vibration coupling

Understanding the similarities and differences between optical coherence loss of electronic transitions of chromophores in glasses and in the glass forming solvent requires, in part, linear response (2-point correlation) functions, J(t;T). An approximate excited state vibrational Hamiltonian (H_e) which accounts for both linear and quadratic electron-phonon coupling is derived that is acceptable for mode frequency changes smaller than 30%. The associated linear response function for the case of no damping is obtained. A response function that includes damping is proposed for systems whose modes are either linearly or quadratically coupled. It is the product of three response functions, two of which are phononic and associated with linear and quadratic modes. The third response function is electronic with a dephasing frequency γ_el that is the width of the zero-phonon line. The total response function yields single-site absorption spectra in which folding of the widths of multi-phonon and sequence transitions occurs. Applications of the new response functions are made to the temperature dependence of single-site absorption and hole-burned spectra of the special pair band of the bacterial reaction center and the temperature dependence of the single site absorption spectrum of Al-phthalocyanine tetrasulphonate in glassy ethanol.