On the temperature dependence of molecular line shapes due to linearly coupled phonon bands

Simple closed-form expressions of line-shape functions are derived for models of a two-level chromophore linearly coupled to harmonic oscillator baths on the basis of an accurate approximation for the coth(x/2) function. The expressions are valid for arbitrary temperature and can be extended to a general spectral density given by a sum of algebraic terms with exponential damping factors. Detailed analyses for three typical spectral densities reveal, in the strong-coupling limit, general temperature dependences of the line widths, and in the weak coupling limit, important features of temperature dependence.