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Published in *The journal of Chemical Physics*, 2021

Intramolecular energy flow (also known as intramolecular vibrational redistribution or IVR) is often assumed in Rice–Ramsperger–Kassel–Marcus, transition state, collisional energy transfer, and other rate calculations not to be an impediment to reaction. In contrast, experimental spectroscopy, computational results, and models based on Anderson localization have shown that ergodicity is achieved rather slowly during molecular energy flow. The statistical assumption in rate theories might easily fail due to quantum localization. Here, we develop a simple model for the interplay of IVR and energy transfer and simulate the model with near-exact quantum dynamics for a 10-degree of freedom system composed of two five-mode molecular fragments. The calculations are facilitated by applying the van Vleck transformation to local random matrix models of the vibrational Hamiltonian. We find that there is a rather sharp “phase transition” as a function of molecular anharmonicity “a” between a region of facile energy transfer and a region limited by IVR and incomplete accessibility of the state space (classically, the phase space). The very narrow transition range of the order parameter a happens to lie right in the middle of the range expected for molecular torsion, bending, and stretching vibrations, thus demonstrating that reactive energy transfer dynamics several kBT above the thermal energy occurs not far from the localization boundary, with implications for controllability of reactions.

Recommended citation: Chenghao Zhang, Edwin L. Sibert III, and Martin Gruebele , "A phase diagram for energy flow-limited reactivity", J. Chem. Phys. 154, 104301 (2021) https://doi.org/10.1063/5.0043665

Published in *Physical Review A*, 2022

Out-of-time-order correlators (OTOCs) can be used to probe how quickly a quantum system scrambles information when the initial conditions of the dynamics are changed. In sufficiently large quantum systems, one can extract from the OTOC the quantum analog of the Lyapunov coefficient that describes the timescale on which a classical chaotic system becomes scrambled. OTOCs have been applied only to a very limited number of toy models, such as the Sachdev-Ye-Kitaev model connected with black hole information scrambling, but they could find much wider applicability for information scrambling in quantum systems that allow comparison with experiments. The vibrations of polyatomic molecules are known to undergo a transition from regular dynamics at low energy to facile energy flow at sufficiently high energy. Molecules therefore represent ideal quantum systems to study scrambling in many-body systems of moderate size (here 6 to 36 degrees of freedoms). By computing quantum OTOCs and their classical counterparts we quantify how information becomes “scrambled” quantum mechanically in molecular systems. Between early “ballistic” dynamics, and late “saturation” of the OTOC when the full density of states is explored, there is indeed a regime where a quantum Lyapunov coefficient can be defined for all molecules in this study. Comparison with experimental rate data shows that slow scrambling as measured by the OTOC can reach the timescale of molecular reaction dynamics. Even for the smallest molecules we discuss, the Maldacena bound remains satisfied by regularized OTOCs, but not by unregularized OTOCs, highlighting that the former are more useful for discussing information scrambling in this type of moderate-size quantum system.

Recommended citation: C. Zhang, P. G. Wolynes, and M. Gruebele, Quantum Information Scrambling in Molecules,Phys. Rev. A 105, 033322 (2022)

Published in *The Proceedings of the National Academy of Sciences*, 2023

Energy flow in molecules, like the dynamics of other many-dimensional finite systems, involves quantum transport across a dense network of near-resonant states. For molecules in their electronic ground state, the network is ordinarily provided by anharmonic vibrational Fermi resonances. Surface crossing between different electronic states provides another route to chaotic motion and energy redistribution. We show that nonadiabatic coupling between electronic energy surfaces facilitates vibrational energy flow and, conversely, anharmonic vibrational couplings facilitate nonadiabatic electronic state mixing. A generalization of the Logan–Wolynes theory of quantum energy flow in many-dimensional Fermi resonance systems to the two-surface case gives a phase diagram describing the boundary between localized quantum dynamics and global energy flow. We explore these predictions and test them using a model inspired by the problem of electronic excitation energy transfer in the photosynthetic reaction center. Using an explicit numerical solution of the time-dependent Schrödinger equation for this ten-dimensional model, we find quite good agreement with the expectations from the approximate analytical theory.

Recommended citation: C. Zhang, M. Gruebele, D. E. Logan, and P. G. Wolynes , "Surface Crossing and Energy Flow in Many-Dimensional Quantum Systems", Proc. Natl. Acad. Sci. U.S.A. 120, e2221690120 (2023) https://doi.org/10.1073/pnas.222169012

** Published:**

In quantum systems, out of time order correlators (OTOCs) can be used to probe the sensitivity of the dynamics to perturbing the Hamiltonian or changing the initial conditions ordinarily associated with classical chaos or its quantum analog. The vibrations of polyatomic molecules are known to undergo a transition from regular dynamics at low energy to facile energy flow at sufficiently high energy. Molecules therefore represent ideal quantum systems to study the transition to chaos in many-body systems of moderate size (here 6 to 36 degrees of freedom). By computing quantum OTOCs and their classical counterparts we quantify how information becomes ‘scrambled’ quantum mechanically in molecular systems.

** Published:**

Intramolecular vibrational redistributionis often assumed in Rice–Ramsperger–Kassel–Marcus and other rate calculations. In contrast, experimental spectroscopy, computational results, and models based on Anderson localization have shown that ergodicity is achieved rather slowly during molecular energy flow and the statistical assumption might easily fail due to quantum localization.

** Published:**

Vibrational energy flow in molecules, like the dynamics of other many dimensional finite systems, involves quantum transport across a dense network of near resonant states. For molecules in their electronic ground state, the network is ordinarily provided by anharmonic vibrational Fermi resonances. Surface crossing between different electronic states provides another route to chaotic motion and energy redistribution. We show that nonadiabatic coupling between electronic energy surfaces facilitates vibrational energy flow, and conversely, anharmonic vibrational couplings facilitate nonadiabatic electronic state mixing. A generalization of the LoganWolynes theory of quantum energy flow in many-dimensional Fermi resonance systems to the two-surface case gives a phase diagram describing the boundary between localized quantum dynamics and global energy flow. We explore these predictions and test them using a model inspired by the problem of electronic excitation energy transfer in the photosynthetic reaction center. Using an explicit numerical solution of the time dependent Schrodinger equation for this ten-dimensional ¨ model, we find quite good agreement with the expectations from the approximate analytical theory.

Undergraduate course, *University 1, Department*, 2014

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Workshop, *University 1, Department*, 2015

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