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The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.
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This content will become publicly available on February 6, 2026
Directed Evolution’s Selective Use of Quantum Tunneling in Designed Enzymes─A Combined Theoretical and Experimental Study
Natural enzymes are powerful catalysts, reducing the apparent activation energy for reaction, enabling chemistry to proceed as much as 1015 times faster than the corresponding solution reaction. It has been suggested for some time that in some cases quantum tunneling can contribute to this rate enhancement by offering pathways through a barrier inaccessible to activated events. A central question of interest to both physical chemists and biochemists is the extent to which evolution introduces below the barrier or tunneling mechanisms. In view of the rapidly expanding chemistries for which artificial enzymes have now been created, it is of interest to see how quantum tunneling has been used in these reactions. In this paper, we study the evolution of possible proton tunneling during C-H bond cleavage in enzymes that catalyze the Morita-Baylis-Hillman (MBH) reaction. The enzymes were generated by theoretical design followed by laboratory evolution. We employ classical and centroid molecular dynamics approaches in path sampling computations to determine if there is a quantum contribution to lowering the free energy of the proton transfer for various experimentally generated protein and substrate combinations. This data is compared to experiments reporting on the observed kinetic isotope effect (KIE) for the relevant reactions. Our results indicate modest involvement of tunneling when laboratory evolution has resulted in a system with a higher classical free energy barrier to chemistry (that is when optimization of processes other than chemistry result in a higher chemical barrier.)
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- Award ID(s):
- 2244981
- PAR ID:
- 10651528
- Publisher / Repository:
- ACS, J. Phys. Chem B
- Date Published:
- Journal Name:
- The Journal of Physical Chemistry B
- Volume:
- 129
- Issue:
- 5
- ISSN:
- 1520-6106
- Page Range / eLocation ID:
- 1555 to 1562
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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