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1. Bath-induced stabilization of classical non-linear response in two-dimensional infrared spectroscopy

   https://doi.org/10.1063/5.0323828  

   Dutta, Rajesh; Reppert, Mike (March 2026, The Journal of Chemical Physics)

   A characteristic feature of the nonlinear response of integrable classical systems is divergence at long times, a consequence of the continuous spectrum of oscillation frequencies possible in anharmonic classical systems. Although bath-induced dissipation and dephasing can eliminate such instabilities, little is known about the specific conditions on system–bath interactions needed to stabilize classical nonlinear response functions. Here, we address this gap by incorporating system–bath interactions into a diagrammatic expansion for classical nonlinear response recently developed for weakly anharmonic systems. The resulting expression for the weakly anharmonic response function is remarkably simple and exhibits a one-to-one correspondence with the quantum counterpart in the ℏ → 0 limit, offering potential computational advantages in extending the approach to large, multi-oscillator systems. We find that, to lowest order in anharmonicity, the bath-induced stabilization of both linear and nonlinear classical response functions depends sensitively on the nature of spectral density, particularly on the balance between low-frequency and high-frequency components. Application of this classical diagrammatic approach to 2D IR spectroscopy of the amide I band captures the characteristic population-time-dependent dynamics associated with spectral diffusion, suggesting that the approach may prove useful in describing real experimental systems at ambient temperatures. 

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2. Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

   https://doi.org/10.1063/5.0053735  

   Provazza, Justin; Tempelaar, Roel; Coker, David F. (July 2021, The Journal of Chemical Physics)

   The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles. 

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3. Directed Evolution’s Selective Use of Quantum Tunneling in Designed Enzymes─A Combined Theoretical and Experimental Study

   https://doi.org/10.1021/acs.jpcb.4c08169  

   Korchagina, Kseniia; Balasubramani, Sree Ganesh; Berreur, Jordan; Gerard, Emilie F; Johannissen, Linus O; Green, Anthony P; Hay, Sam; Schwartz, Steven D (February 2025, The Journal of Physical Chemistry B)

   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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4. Quantum eigenstates from classical Gibbs distributions

   https://doi.org/10.21468/SciPostPhys.10.1.014  

   Claeys, Pieter W.; Polkovnikov, Anatoli (January 2021, SciPost Physics)

   null (Ed.)

   We discuss how the language of wave functions (state vectors) andassociated non-commuting Hermitian operators naturally emerges fromclassical mechanics by applying the inverse Wigner-Weyl transform to thephase space probability distribution and observables. In this language,the Schr"odinger equation follows from the Liouville equation, with \hbar ℏ now a free parameter. Classical stationary distributions can berepresented as sums over stationary states with discrete (quantized)energies, where these states directly correspond to quantum eigenstates.Interestingly, it is now classical mechanics which allows for apparentnegative probabilities to occupy eigenstates, dual to the negativeprobabilities in Wigner’s quasiprobability distribution. These negativeprobabilities are shown to disappear when allowing sufficientuncertainty in the classical distributions. We show that thiscorrespondence is particularly pronounced for canonical Gibbs ensembles,where classical eigenstates satisfy an integral eigenvalue equation thatreduces to the Schr"odinger equation in a saddle-pointapproximation controlled by the inverse temperature. We illustrate thiscorrespondence by showing that some paradigmatic examples such astunneling, band structures, Berry phases, Landau levels, levelstatistics and quantum eigenstates in chaotic potentials can bereproduced to a surprising precision from a classical Gibbs ensemble,without any reference to quantum mechanics and with all parameters(including \hbar ℏ )on the order of unity. 

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5. Quantum information scrambling and chemical reactions

   https://doi.org/10.1073/pnas.2321668121  

   Zhang, Chenghao; Kundu, Sohang; Makri, Nancy; Gruebele, Martin; Wolynes, Peter G (April 2024, Proceedings of the National Academy of Sciences)

   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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