Broadband infrared and Raman probes of excited-state vibrational molecular dynamics; Simulation protocols based on loop diagram

Vibrational motions in electronically excited states can be observed by either time and frequency resolved infrared absorption or by off resonant stimulated Raman techniques. Multipoint correlation function expressions are derived for both signals. Three representations for the signal which suggest different simulation protocols are developed. These are based on the forward and the backward propagation of the wavefunction, sum over state expansion using an effective vibration Hamiltonian and a semiclassical treatment of a bath. We show that the effective temporal ($\Delta t$) and spectral ($\Delta\omega$) resolution of the techniques is not controlled solely by experimental knobs but also depends on the system dynamics being probed. The Fourier uncertainty $\Delta\omega\Delta t>1$ is never violated.