Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

An approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent was studied. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom. It also suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function.