13.1: The Displaced Harmonic Oscillator Model Here we will discuss the displaced harmonic oscillator, a widely used model that describes the coupling of nuclear motions to electronic states. Although it has many applications, we will look at the specific example of electronic absorption experiments, and thereby gain insight into the vibronic structure in absorption spectra. 13.2: Coupling to a Harmonic Bath The displaced harmonic oscillator model is readily generalized to many vibrations or a continuum of nuclear motions. Coupling to a continuum, or a harmonic bath, is the starting point for developing how an electronic system interacts with a continuum of intermolecular motions and phonons typical of condensed phase systems. 13.3: Semiclassical Approximation to the Dipole Correlation Function The semiclassical approximation is a useful representation of the dipole correlation function when one wants to describe the dark degrees of freedom (the bath) using classical molecular dynamics simulations.