Semiclassical Molecular Dynamics for Spectroscopic Calculations

We present some historical and recently developed techniques to perform semiclassical spectroscopy calculations with both ground and excited state dynamics. The illustrated topics begin with a derivation of the basic semiclassical van Vleck propagator starting from Feynman's path integral formulation, followed by the description of the initial value representation formalism and a derivation of the Heller–Herman–Kluk–Kay semiclassical propagator. The chapter continues by introducing the time averaging technique and its very recent developments consisting in the multiple coherent, divide-and-conquer, and mixed semiclassical approaches. The main features of each method are described through examples with the intent of helping readers have a gentle learning curve. The chapter ends with a workflow chart, a few representative applications, a summary, and some conclusions.