Quasi-classical approaches to vibronic spectra revisited

Abstract

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.

Modeling the absorption lineshape of embedded systems from molecular dynamics: A tutorial review

“…In principle, the fast dynamics of the nuclear DOFs should be treated quantum mechanically, for example, in a time‐domain framework, by evaluating the evolution on the nuclear wavepacket on the excited‐state PES . However, classical or semiclassical dynamics can be used to obtain vibronic spectra from the evolution of the excitation energy governed by the ground‐state PES by defining appropriate (semi)classical time correlation functions …”

Theoretical X‐ray spectroscopy of transition metal compounds

“…However, the spectra could be equivalently expressed in as Fourier transforms of multitime dipole correlation functions . For instance for XAS, these are two‐point and for RIXS four‐point dipole correlation functions . Beyond this perturbational regime, that is, for strong‐field excitation, or in cases of (shaped) ultrashort laser pulses, one has to resort to explicit solution of the time‐dependent Schrödinger equation including the field‐matter interaction.…”

“…45 For instance for XAS, these are two-point and for RIXS four-point dipole correlation functions. [62][63][64][65] Beyond this perturbational regime, that is, for strong-field excitation, or in cases of (shaped) ultrashort laser pulses, one has to resort to explicit solution of the time-dependent Schrödinger equation including the field-matter interaction. Compared to the QC methods, real-time (RT) propagation approaches have received less attention so far.…”

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

“…From previous work, it has been found that the Wigner averaged classical limit (WACL), which evolves the nuclear degrees of freedom on the arithmetic mean surface of the ground and excited state, generally gives rise to the most accurate results. 20,22,23 The forward-backward initial-value representation (FB-IVR), 24 which is related to the Herman-Kluk propagator, 25 can additionally exactly reproduce spectra for systems that involve a frequency change under photoexcitation, but this approach cannot easily be converged for high-dimensional condensed-phase problems and the Herman-Kluk prefactor becomes unstable when applied to anharmonic models. 26 While WACL has been relatively successful in accurately obtaining Frank-Condon spectra for certain condensed-phase systems, it cannot describe nonadiabatic transitions between coupled exciton states and so is not an appropriate method for photosynthetic lightharvesting systems.…”