We present quantum mechanical calculations of the absorption line shape of an electron "solvated" in several sodalites. Photon absorption by the electron modifies the forces acting on the nuclei, setting the counterions in motion. This nuclear motion causes broadening and gives vibrational structure to the absorption spectrum of the electron. The major effort in the computation of the absorption spectrum is directed toward the evaluation of an overlap integral that evolves in time because of nuclear motion. The systems considered here have a very large number of nuclear degrees of freedom, and this makes a brute-force quantum mechanical calculation of the overlap impossible. Good results can be obtained with a method that exploits the fact that in a system with many degrees of freedom the overlap integral decays rapidly to zero, and can therefore be evaluated accurately and efficiently by short-time methods. The short-time method that seems most advantageous is the Gaussian wave packet (GWP) procedure proposed some time ago by Heller. This simplifies the nuclear dynamics and also substantially diminishes the number of electron energy calculations needed for determining the forces acting on the nuclei. When the GWP method is used, the electronic wave function is calculated only for a small number of nuclear configurations along the classical trajectory on which the center of the nuclear wave packet evolves. The present calculation is the first use of this method to compute the absorption spectrum of a complex system. We study the absorption line shape for an electron solvated in a dry sodalite, and in chloro-, bromo-, and iodo-sodalite. We find that the homogeneous linewidth due to the nuclear motion is narrower than that observed experimentally. This implies that the measured linewidth is due to inhomogeneous broadening. For the dry sodalite the main inhomogeneity is the disorder in the position of the counterions, and for halo-sodalites, the presence of defects introduced during synthesis. Our results imply that a careful synthesis can improve the contrast in displays based on the cathodochromic effects in zeolites.