Quasi-classical approaches to vibronic spectra revisited

The framework to approach quasi-classical dynamics in the electronic ground state is well established and is based on the Kubo-transformed time correlation function (TCF), being the most classical-like quantum TCF. Here we discuss whether the choice of the Kubo-transformed TCF as a starting point for simulating vibronic spectra is as unambiguous as it is for vibrational ones. A generalized quantum TCF is proposed that contains many of the well-established TCFs as particular cases. It provides a framework to develop numerical protocols for simulating vibronic spectra via quasi-classical trajectory-based methods that allow for dynamics on many potential energy surfaces and nuclear quantum effects. The performance of the methods based on the well-known TCFs is investigated on 1D anharmonic model systems at finite temperatures. The flexibility inherent to the formulation of the generalized TCF provides a route to construct new TCFs that may lead to better numerical protocols as is shown on the same models.