Vibronic approach in the theory of the excitonic spectra of molecular crystals

The excitonic and vibronic spectra of a molecular chain have been studied on using a complete vibronic approach (without separation in Hilbert subspaces) which has been developed in this paper. The methods of canonical transformations and Green's functions are applied to find out analytical expressions as continued fractions for the linear optical susceptibility near the frequencies of the Frenkel exciton and its first and/or subsequent three vibronic replicas. The approximation of the dynamical theory, i.e., the case of a narrow exciton band compared with the energy of the vibrational quantum, is modified to treat vibronic spectra with totally symmetric phonons by considering both the linear and quadratic exciton-phonon coupling. The excitonic and vibrational parameters for anthracene, naphthalene, and benzene crystals as well as for three other models of molecular chains have been used in calculating the linear absorption spectra of the one-dimensional models of those crystals. The main results concern the shape of the absorption maxima and the manifestations of joint and unbound exciton-phonon configurations in the one-, two-, and three-phonon vibronic spectra depending on the dominant impact of the linear or (and) quadratic exciton-phonon coupling. The picture of the calculated spectra has been compared with the data of previous theoretical studies. It agrees with the available experimental data on the linear absorption in the three aromatic crystals.