Dynamical traps lead to the slowing down of intramolecular vibrational energy flow

Dynamical Tunneling in More than Two Degrees of Freedom

Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose-Einstein condensates trapped in optical lattices.

Classical Drift in the Arnold Web Induces Quantum Delocalization Transition

We demonstrate that quantum dynamical localization in the Arnold web of higher-dimensional Hamiltonian systems is destroyed by an intrinsic classical drift. Thus quantum wave packets and eigenstates may explore more of the intricate Arnold web than previously expected. Such a drift typically occurs, as resonance channels widen toward a large chaotic region or toward a junction with other resonance channels. If this drift is strong enough, we find that dynamical localization is destroyed. We establish that this drift-induced delocalization transition is universal and is described by a single transition parameter. Numerical verification is given using a time-periodically kicked Hamiltonian with a four-dimensional phase space.

Collision Induced Dissociation of Deprotonated Isoxazole and 3-Methyl Isoxazole via Direct Chemical Dynamics Simulations

Isoxazoles are an important class of organic compounds widely employed in synthesis and drug design. Fragmentation chemistry of the parent isoxazole molecule and its substituents has been the subject of several experimental and theoretical investigations. Collision induced dissociation (CID) of isoxazole and its substituents has been studied experimentally under negative ion conditions. Based on the observed reaction products, dissociation patterns were proposed. In the present work, we studied the dissociation chemistry of deprotonated isoxazole and 3-methyl isoxazole using electronic structure theory calculations and direct chemical dynamics simulations. Various deprotonated isomers of these molecules were activated by collision with an Ar atom, and the ensuing fractionation patterns were studied using on-the-fly classical trajectory simulations at the density functional B3LYP/6-31+G* level of electronic structure theory. A variety of reaction products and pathways were observed, and it was found that a nonstatistical shattering mechanism dominates the CID dynamics of these molecules. Simulation results are compared with experiments, and detailed atomic level dissociation mechanisms are presented.

Vibrational Energy Redistribution and Polaritonic Fermi Resonances in the Strong Coupling Regime

Intramolecular vibrational energy redistribution (IVR) plays a significant role in cavity-modified chemical reaction rates. As such, understanding the fundamental mechanisms by which the cavity modifies the IVR pathways is a fundamental step toward engineering the effect of the confined electromagnetic modes on the outcome of chemical processes. Here we consider an ensemble of M two-mode molecules with intramolecular anharmonic couplings interacting with an infrared cavity mode and consider their quantum dynamics and infrared spectra. Polaritonic Fermi resonances involving fundamental and overtone states of the polaritonic subsystem mediate efficient energy transfer pathways between otherwise off-resonant molecular states. These pathways are of collective nature, yet enabled by the intramolecular anharmonic couplings. Hence, through polaritonic Fermi resonances, cavity excitation can efficiently spread toward low-frequency modes while becoming delocalized over several molecules.

E-Z Isomerization in Guanidine: Second-order Saddle Dynamics, Non-statisticality, and Time-frequency Analysis

Our recent work on the E-Z isomerization reaction of guanidine using ab initio chemical dynamics simulations [Rashmi et al., Regul. Chaotic Dyn. 2021, 26, 119] emphasized the role of second-order saddle (SOS) in the isomerization reaction; however, we could not unequivocally establish the non-statistical nature of the dynamics followed in the reaction. In the present study, we performed thousands of on-the-fly trajectories using forces computed at the MNDO level to investigate the influence of second-order saddle in the E-Z isomerization reaction of guanidine and the role of intramolecular vibrational energy redistribution (IVR) on the reaction dynamics. The simulations reveal that while majority of the trajectories follow the traditional transition state pathways, 15 % of the trajectories follow the SOS path. The dynamics was found to be highly non-statistical with the survival probabilities of the reactants showing large deviations from those obtained within the RRKM assumptions. In addition, a detailed analysis of the dynamics using time-dependent frequencies and the frequency ratio spaces reveal the existence of multiple resonance junctions that indicate the existence of regular dynamics and long-lived quasi-periodic trajectories in the phase space associated with non-RRKM behavior.

Partial barriers to chaotic transport in 4D symplectic maps

Chaotic transport in Hamiltonian systems is often restricted due to the presence of partial barriers, leading to a limited flux between different regions in phase space. Typically, the most restrictive partial barrier in a 2D symplectic map is based on a cantorus, the Cantor set remnants of a broken 1D torus. For a 4D symplectic map, we establish a partial barrier based on what we call a cantorus-NHIM-a normally hyperbolic invariant manifold with the structure of a cantorus. Using a flux formula, we determine the global 4D flux across a partial barrier based on a cantorus-NHIM by approximating it with high-order periodic NHIMs. In addition, we introduce a local 3D flux depending on the position along a resonance channel, which is relevant in the presence of slow Arnold diffusion. Moreover, for a partial barrier composed of stable and unstable manifolds of a NHIM, we utilize periodic NHIMs to quantify the corresponding flux.

Dissociation dynamics of a diatomic molecule in an optical cavity

We study the dissociation dynamics of a diatomic molecule, modeled as a Morse oscillator, coupled to an optical cavity. A marked suppression of the dissociation probability, both classical and quantum, is observed for cavity frequencies significantly below the fundamental transition frequency of the molecule. We show that the suppression in the probability is due to the nonlinearity of the dipole function. The effect can be rationalized entirely in terms of the structures in the classical phase space of the model system.

Theoretical Investigation of Dissociation versus Intramolecular Rearrangements in Aminohydroxymethylene

Aminohydroxymethylene (H₂N-C̈-OH) is the simplest aminooxycarbene which is a heteroatom stabilized carbene. This highly reactive molecule was prepared in an Ar matrix in a recent experimental work. Unimolecular reactivity of this astrochemically important molecule was investigated and only fragmentations were identified contrary to the observations of both fragmentations and intramolecular rearrangements in other hydroxycarbenes. These rearrangement reactions form the corresponding imine and carbonyl compounds. In the present work, direct chemical dynamics simulations of unimolecular chemistry of aminohydroxymethylene were performed in the gas phase to study atomic level dissociation mechanisms. Classical trajectories were generated on-the-fly using potentials and gradients computed at the density functional B3LYP/6-31+G* level of electronic structure theory. Simulation results showed that intramolecular rearrangements accompany fragmentations during the unimolecular decay process of aminohydroxymethylene. However, the average lifetime of the intermediate isomers were found to be only few picoseconds which might not have been long enough for detection in the experiments.

Dynamically induced conformation depending on excited normal modes of fast oscillation

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also by fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.

Phase space geometry of isolated to condensed chemical reactions

The complexity of gas and condensed phase chemical reactions has generally been uncovered either approximately through transition state theories or exactly through (analytic or computational) integration of trajectories. These approaches can be improved by recognizing that the dynamics and associated geometric structures exist in phase space, ensuring that the propagator is symplectic as in velocity-Verlet integrators and by extending the space of dividing surfaces to optimize the rate variationally, respectively. The dividing surface can be analytically or variationally optimized in phase space, not just over configuration space, to obtain more accurate rates. Thus, a phase space perspective is of primary importance in creating a deeper understanding of the geometric structure of chemical reactions. A key contribution from dynamical systems theory is the generalization of the transition state (TS) in terms of the normally hyperbolic invariant manifold (NHIM) whose geometric phase-space structure persists under perturbation. The NHIM can be regarded as an anchor of a dividing surface in phase space and it gives rise to an exact non-recrossing TS theory rate in reactions that are dominated by a single bottleneck. Here, we review recent advances of phase space geometrical structures of particular relevance to chemical reactions in the condensed phase. We also provide conjectures on the promise of these techniques toward the design and control of chemical reactions.

A phase diagram for energy flow-limited reactivity

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 k_BT above the thermal energy occurs not far from the localization boundary, with implications for controllability of reactions.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Dynamics of a gas-phase SNAr reaction: non-concerted mechanism despite the Meisenheimer complex being a transition state

The commonly accepted mechanism of the nucleophilic aromatic substitution (SNAr) reaction has been found to be governed by the nature of the Meisenheimer structure on the potential energy surface. A stable Meisenheimer intermediate favors a stepwise mechanism, while a Meisenheimer transition state favors a concerted mechanism. Here, we show by using a detailed potential energy map (using the DFT and DLPNO-CCSD(T)/CBS methods) and ab initio classical trajectory simulations that the F- + C6H5NO2 SNAr reaction involves a Meisenheimer transition state and follows a stepwise mechanism in contrast to the expected concerted pathway. The stepwise mechanism observed in the trajectory simulations takes place by the formation of various ion-dipole and σ-complexes. While the majority of the trajectories follow the multi-step mechanism and avoid the minimum energy path, a considerable fraction exhibit a roaming atom mechanism where the F atom hovers around the phenyl ring before the formation of the products.

Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific assumptions about the extent of intramolecular vibrational energy flow in the system. However, the nature of the transition to the statistical regime as a function of the molecular parameters is far from being completely understood. Here, we use tools from nonlinear dynamics to study the transition to statisticality in a model unimolecular reaction by explicitly visualizing the high dimensional classical phase space. We identify generic features in the phase space involving the intersection of two or more independent anharmonic resonances and show that the presence of correlated, but chaotic, intramolecular dynamics near such junctions leads to nonstatisticality. Interestingly, akin to the stability of asteroids in the Solar System, molecules can stay protected from dissociation at the junctions for several picoseconds due to the phenomenon of stable chaos.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

Relevance of the Resonance Junctions on the Arnold Web to Dynamical Tunneling and Eigenstate Delocalization

We study the competition and correspondence between the classical and quantum routes to intramolecular vibrational energy redistribution (IVR) in a three degrees of freedom model effective Hamiltonian. Specifically, we focus on the classical and the quantum dynamics near the resonance junctions on the Arnold web that are formed by an intersection of independent resonances. The regime of interest models the IVR dynamics from highly excited initial states near dissociation thresholds of molecular systems wherein both classical and purely quantum, involving dynamical tunneling, routes to IVR coexist. In the vicinity of a resonance junction, classical chaos is inevitably present, and hence one expects the quantum IVR pathways to have a strong classical component as well. We show that with increasing resonant coupling strengths the classical component of IVR leads to a transition from coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we establish that the quantum IVR dynamics can be predicted based on the structures on the classical Arnold web. In addition, we investigate the nature of the highly excited eigenstates to identify the quantum signatures of the multiplicity-2 junctions. For the parameter regimes studies herein, by projecting the eigenstates onto the Arnold web, we find that eigenstates in the vicinity of the junctions are primarily delocalized due to dynamical tunneling.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Bifurcations of families of 1D-tori in 4D symplectic maps

The regular structures of a generic 4d symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1d-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations, no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example, we study two coupled standard maps by visualizing the elliptic and hyperbolic 1d-tori in a 3d phase-space slice, local 2d projections, and frequency space. The observed bifurcations are consistent with the analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.

Breaking of a bond: when is it statistical?

Unimolecular dissociation dynamics of a model three degree of freedom triatomic molecule is studied in order to understand the mechanisms for deviations from statisticality. Performing a wavelet based time–frequency analysis of the dynamics allows for the dynamics to be followed on the network of nonlinear resonances, also called as the Arnold web. The results indicate that the long lifetime trajectories spend a considerable amount of time trapped near junctions in the web. It is argued that characterizing the dynamics near such junctions might lead to deeper insights into the origins of nonstatistical dynamics.