We have developed a simple and physically clear picture of adiabatic rapid passage (ARP) in molecules in solution by careful examination of all the conditions needed for ARP. The relaxation effects were considered in the framework of the Landau-Zener model for random crossing of levels. The model enables us to include into consideration non-Markovian Gaussian-correlated noise. It explains all the numerical results obtained in the first paper of the series [B. D. Fainberg and V. A. Gorbunov, J. Chem. Phys. 117, 7222 (2002)], in particular, that for positive chirp pulse excitation relaxation favors more efficient population transfer with respect to the relaxation-free system with frozen nuclear motion. We also relate parameters of non-Markovian Gaussian-correlated noise with irreversible dephasing time of an optical transition by calculating the photon echo signal attenuation. (C) 2004 American Institute of Physics.