Quantum Dynamics of Open Systems

SOME OBSERVATIONS ON THE DYNAMICS OF REACTIVE COLLISIONS AND TRANSITION TIMES

There are a number of aspects of reactive collisions and rate theory which have eluded researchers. The first to be addressed is an ħ2 expansion of the thermal rate. Ninety years ago, Wigner derived the leading order term for symmetric reactions. The full expression valid for asymmetric reactions has been derived only very recently [1]. The resulting expression will be presented and discussed, especially in the view of challenging existing approximate theories which reduce to the parabolic barrier expression but do not account correctly for anharmonic effects.
The same result will then be used within the context of a recently formulated coherent state phase space representation of operators used to derive an exact expression for the symmetrized version of thermal correlation functions and especially the flux side correlation function which is used to obtain reaction rates. The coherent state representation necessitates the use of a smeared Gaussian flux operator, whose coherent state phase space representation is identical to the classical flux expression. This lead to a route of analytic semiclassical approximations for the thermal rate, as exemplified by a computation of the transmission factor through a symmetric and an asymmetric Eckart barrier using a thawed Gaussian approximation for both imaginary and real‐time propagation. As a byproduct, this example shows that one may obtain "good" tunneling rates using only above barrier classical trajectories even in the deep tunneling regime [2].
Recent experimental measurements of the transition path time distributions of proteins moving from the folded to the unfolded state and vice versa, presented theory with challenges. Early analysis suggested barrier heights that are much lower than the free energies of activation of the observed transitions, what are these barrier heights? Secondly, beyond the mere feat of following a protein as it folds or unfolds, is there anything really useful that we can actually learn from such experiments? These questions led to a few insights. One is the paradigm of a transition path barrier height which should be smaller than the activation energy, resolving partially the low barrier height puzzle [3]. A second one is the observation that when analyzed correctly, the measured distributions reveal long time tails which may be identified with a long lived
intermediate, between the folded and unfolded states [4].
Finally we will consider transition path times for quantum nonadiabatic transitions, showing that theories which do not account for phases associated with nuclear motion do not give good agreement with exact quantum transition times [5]. This result accentuates the need to test the quality of approximate theories not only using transition probabilities as criteria but also transition path times. We will also show that nonadiabatic coupling speeds up tunneling times [6].

References
[1] E. Pollak and J. Cao. J. Chem. Phys. 157, 074109 (2022)
[2] E. Pollak. S. Upadhyayula and J. Liu, J. Chem. Phys. 156, 244101 (2022).
[3] E. Pollak, Phys. Chem. Chem. Phys. 18, 28872 – 28882 (2016). DOI: 10.1039/C6CP05052B
[4] R. Dutta and E. Pollak, Phys. Chem. Chem. Phys. 23, 23787‐23795 (2021). DOI: 10.1039/D1CP03296H
[5] X. He, B. Wu, T. Rivlin, J. Liu, and E. Pollak, J. Phys. Chem. Lett. 13, 6966‐6974 (2022).
[6] T. Rivlin and E. Pollak, preprint, submitted to J. Chem. Phys. Lett..