A protocol for the investigation of the intramolecular vibrational energy redistribution problem: the isomerization of nitrous acid as a case of study

The conformational isomerization of nitrous acid (HONO) promoted by excitation of the νOH or νNO stretching normal coordinates is the first observed case of an infrared-induced photochemical reaction. The energy captured by the excited normal modes is redistributed into a highly excited vibrational level of the τOH torsion normal coordinate, which is the isomerization reaction coordinate. Herein, we present simple numerical methods to qualitatively investigate the coupling between the normal coordinates and the possible gateways for vibrational energy redistribution leading to the isomerization process. Our methodology involves the generation of the relevant 2D potential energy surface (PES), by spanning the reaction coordinate and one of the 3N - 7 projected normal coordinates along the intrinsic reaction coordinate (IRC). Once the PES has been obtained, the time-independent wavefunctions are calculated using the standard discrete variable representation (DVR) approach. The reaction barrier is investigated using the interacting quantum atoms (IQA) decomposition scheme, evidencing an important contribution from the exchange-correlation energy to the isomerization. Coupling between normal coordinates indicates preferential normal modes to redistribute the vibrational energy. 1D deep tunneling rates were found to be negligible.

Don't forget the trans: double bond isomerism radical-acetylene growth reactions affect the primary stages of PAH and soot formation

In combustion, acetylene is a key species in molecular-weight growth reactions that form polycyclic aromatic hydrocarbons (PAHs) and ultimately soot particles. Radical addition to acetylene generates a vinyl radical intermediate, which has both trans and cis isomers. This isomerism can lead to profound changes in product distributions that are as yet insufficiently investigated. Herein, we explore acetylene addition to substituted trans-vinyl radicals, including potential rearrangement to cis structures, for eight combustion-related hydrocarbon radicals calculated using a composite method (G3X-K). Of these eight systems, the phenyl trans- and cis-Bittner-Howard HACA (hydrogen abstraction, C2H2 Addition) process, where acetylene successively adds to a phenyl radical via a β-styryl intermediate, is simulated using a unified Master Equation model. Including the trans-Bittner-Howard pathway changes the products significantly at all simulated temperatures (550-1800 K) and pressures (5.33 × 102-107 Pa), relative to a cis-only model. Typically, naphthalene remains the dominant product, but its abundance decreases at higher temperatures and pressures. For example, at 1200 K and 105 Pa, its branching ratio decreases from 78.5% to 62.9% when the trans pathway is included. At higher temperatures this decrease corresponds to the formation of alternative C10H8 isomers, including the cis product benzofulvene with 8% maximum abundance at 1200 K and 5.33 × 102 Pa, and E-2-ethynyl-1-phenylethylene, a trans product with 26% maximum abundance at 1800 K, with little pressure dependence. At higher pressures, our model predicts a range of C10H9 radicals, including resonance-stabilised radicals (RSRs). The impact of trans-vinyl radical chemistry in reactive environments means that they are essential to accurately describe combustion reactions and inhibit soot formation.

Cavity induced modulation of intramolecular vibrational energy flow pathways

Recent experiments in polariton chemistry indicate that reaction rates can be significantly enhanced or suppressed inside an optical cavity. One possible explanation for the rate modulation involves the cavity mode altering the intramolecular vibrational energy redistribution (IVR) pathways by coupling to specific molecular vibrations in the vibrational strong coupling (VSC) regime. However, the mechanism for such a cavity-mediated modulation of IVR is yet to be understood. In a recent study, Ahn et al. [Science 380, 1165 (2023)] observed that the rate of alcoholysis of phenyl isocyanate (PHI) is considerably suppressed when the cavity mode is tuned to be resonant with the isocyanate (NCO) stretching mode of PHI. Here, we analyze the quantum and classical IVR dynamics of a model effective Hamiltonian for PHI involving the high-frequency NCO-stretch mode and two of the key low-frequency phenyl ring modes. We compute various indicators of the extent of IVR in the cavity-molecule system and show that tuning the cavity frequency to the NCO-stretching mode strongly perturbs the cavity-free IVR pathways. Subsequent IVR dynamics involving the cavity and the molecular anharmonic resonances lead to efficient scrambling of an initial NCO-stretching overtone state over the molecular quantum number space. We also show that the hybrid light-matter states of the effective Hamiltonian undergo a localization-delocalization transition in the VSC regime.

A Strategy for Modeling Nonstatistical Reactivity Effects: Combining Chemical Activation Estimates with a Vibrational Relaxation Model

The kinetics of many chemical reactions can be readily explained with a statistical approach, for example, using a form of transition state theory and comparing calculated Gibbs energies along the reaction coordinate(s). However, there are cases where this approach fails, notably when the vibrational relaxation of the molecule to its statistical equilibrium occurs on the same time scale as the reaction dynamics, whether it is caused by slow relaxation, a fast reaction, or both. These nonstatistical phenomena are then often explored computationally using (quasi)classical ab initio molecular dynamics by calculating a large number of trajectories while being prone to issues such as zero-point energy leakage. On the other side of the field, we see resource-intensive quantum dynamics simulations, which significantly limit the size of explorable systems. We find that using a Fermi's golden rule type of model for vibrational relaxation, based on anharmonic coupling constants, we can extract the same qualitative information while giving insights into how to enhance (or destroy) the bottlenecks causing the phenomena. We present this model as a middle ground for exploring complex nonstatistical behavior, capable of treating medium-sized organic molecules or biologically relevant fragments. We also cover the challenges involved, in particular quantifying the excess energy in terms of vibrational modes. Relying on readily available electronic structure methods and providing results in a simple master equation form, this model shows promise as a screening tool for opportunities in mode-selective chemistry without external control.

Ballistic Energy Transport via Long Alkyl Chains: A New Initiation Mechanism

In an effort to increase the speed and efficiency of ballistic energy transport via oligomeric chains, we performed measurements of the transport in compounds featuring long alkyl chains of up to 37 methylene units. Compounds of the N3-(CH2)n-COOMe type (denoted as aznME) were synthesized with n = 5, 10, 15, 19, 28, 37 and studied using relaxation-assisted two-dimensional infrared spectroscopy. The speed of the ballistic transport, initiated by the N3 tag excitation, increased ca. 3-fold for the longer chains (n = 19-37) compared to the shorter chains, from 14.7 to 48 Å/ps, in line with an earlier prediction (Nawagamuwage et al. 2021, J. Phys. Chem. B, 125, 7546). Modeling, based on solving numerically the Liouville equation, was capable of reproducing the experimental data only if three wavepackets are included, involving CH2 twisting (Tw), wagging (W), and rocking (Ro) chain bands. The approaches for designing molecular systems featuring a higher speed and efficiency of energy transport are discussed.

Two stage decoherence of optical phonons in long oligomers

Molecular vibrations are generally responsible for chemical energy transport and dissipation in molecular systems. This transport is fast and efficient if energy is transferred by optical phonons in periodic oligomers, but its efficiency is limited by decoherence emerging due to anharmonic interactions with acoustic phonons. Using a general theoretical model, we show that in the most common case of the optical phonon band being narrower than the acoustic bands, decoherence takes place in two stages. The faster stage involves optical phonon multiple forward scattering due to absorption and emission of transverse acoustic phonons, i.e., collective bending modes with a quadratic spectrum; the transport remains ballistic and the speed can be altered. The subsequent slower stage involves phonon backscattering in multiphonon processes involving two or more acoustic phonons resulting in a switch to diffusive transport. If the initially excited optical phonon possesses a relatively small group velocity, then it is accelerated in the first stage due to its transitions to states propagating faster. This theoretical expectation is consistent with the recent measurements of optical phonon transport velocity in alkane chains, increasing with increasing the chain length.

More than just smoke and mirrors: Gas-phase polaritons for optical control of chemistry

Gas-phase molecules are a promising platform to elucidate the mechanisms of action and scope of polaritons for optical control of chemistry. Polaritons arise from the strong coupling of a dipole-allowed molecular transition with the photonic mode of an optical cavity. There is mounting evidence of modified reactivity under polaritonic conditions; however, the complex condensed-phase environment of most experimental demonstrations impedes mechanistic understanding of this phenomenon. While the gas phase was the playground of early efforts in atomic cavity quantum electrodynamics, we have only recently demonstrated the formation of molecular polaritons under these conditions. Studying the reactivity of isolated gas-phase molecules under strong coupling would eliminate solvent interactions and enable quantum state resolution of reaction progress. In this Perspective, we contextualize recent gas-phase efforts in the field of polariton chemistry and offer a practical guide for experimental design moving forward.

Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models

We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in the site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states, and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal-time connected density-density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry-André model. This work gives an affirmative answer to the question of whether it is possible to measure features of single-particle survival and transition probabilities by the dynamics of observables in many-body states.

Trajectory-Based Time-Resolved Mechanism for Benzene Reductive Elimination from Cyclopentadienyl Mo/W Phenyl Hydride Complexes

Calculated potential energy structures and landscapes are very often used to define the sequence of reaction steps in an organometallic reaction mechanism and interpret kinetic isotope effect (KIE) measurements. Underlying most of this structure-to-mechanism translation is the use of statistical rate theories without consideration of atomic/molecular motion. Here we report direct dynamics simulations for an organometallic benzene reductive elimination reaction, where nonstatistical intermediates and dynamic-controlled pathways were identified. Specifically, we report single spin state as well as mixed spin state quasiclassical direct dynamics trajectories in the gas phase and explicit solvent for benzene reductive elimination from Mo and W bridged cyclopentadienyl phenyl hydride complexes ([Me2Si(C5Me4)2]M(H)(Ph), M = Mo and W). Different from the energy landscape mechanistic sequence, the dynamics trajectories revealed that after the benzene C-H bond forming transition state (often called reductive coupling), σ-coordination and π-coordination intermediates are either skipped or circumvented and that there is a direct pathway to forming a spin flipped solvent caged intermediate, which occurs in just a few hundred femtoseconds. Classical molecular dynamics simulations were then used to estimate the lifetime of the caged intermediate, which is between 200 and 400 picoseconds. This indicates that when the η2-π-coordination intermediate is formed, it occurs only after the first formation of the solvent-caged intermediate. This dynamic mechanism intriguingly suggests the possibility that the solvent-caged intermediate rather than a coordination intermediate is responsible (or partially responsible) for the inverse KIE value experimentally measured for W. Additionally, this dynamic mechanism prompted us to calculate the kH/kD KIE value for the C-H bonding forming transition states of Mo and W. Surprisingly, Mo gave a normal value, while W gave an inverse value, albeit small, due to a much later transition state position.

Probing the anharmonicity of vibrational polaritons with double-quantum two-dimensional infrared spectroscopy

Strong coupling between the molecular vibrations and electromagnetic fields of light confined to an infrared cavity leads to the formation of vibro-polaritons - quasi-particles thought to provide the means to control the rates of chemical reactions inside a dark cavity. Despite the mechanisms indicating how vibrational coupling to the vacuum fields can affect the reaction rates are still not well understood, it has been recently demonstrated that the formation of the polariton states alters the ultrafast relaxation dynamics of the strongly coupled system. The relaxation dynamics in molecules, which is known to be important for the chemical reactivity, is directed by anharmonic couplings involving multiple intra- and inter-molecular vibrational degrees of freedom. However, the impact of the molecular anharmonicity on the polariton states remains elusive. Some theoretical models, employed to interpret the experimental observations, assume that vibrational polaritons are harmonic. Others assume a certain anharmonicity of vibro-polaritons; however, to date, it has not been experimentally determined. Herein, we performed double-quantum two-dimensional third-order nonlinear infrared spectroscopy of the carbonyl stretching (C=O) vibrational modes in a thin film of polymethyl methacrylate polymer (PMMA) strongly coupled to the surface lattice resonances of the periodic arrays of half-wavelength infrared disk antennas. We found that, indeed, the mechanical anharmonicity of polaritons is very small. Quantitatively, our results place an upper bound on a polariton mechanical anharmonicity of 2 cm-1, compared with that of the C=O mode in a PMMA film of 15 cm-1. Thus, our results support previous assumptions regarding the harmonic character of vibro-polaritons.

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.

On the intramolecular vibrational energy redistribution dynamics of aromatic complexes: A comparative study on C6H6-C6H5Cl, C6H6-C6H3Cl3, C6H6-C6Cl6 and C6H6-C6H5F, C6H6-C6H3F3, C6H6-C6F6

Chemical dynamics Simulation studies on benzene dimer (Bz2) and benzene-hexachlorobenzene (Bz-HCB) as performed in the past suggest that the coupling between the monomeric (intramolecular) vibrational modes and modes generated due to the association of two monomers (intermolecular) has to be neither strong nor weak for a fast dissociation of the complex. To find the optimum coupling, four complexes are taken into consideration in this work, namely, benzene-monofluorobenzene, benzene-monochlorobenzene, benzene-trifluorobenzene (Bz-TFB), and benzene-trichlorobenzene. Bz-TFB has the highest rate of dissociation among all seven complexes, including Bz2, Bz-HCB, and Bz-HFB (HFB stands for hexafluorobenzene). The set of vibrational frequencies of Bz-TFB is mainly the reason for this fast dissociation. The mass of chlorine in Bz-HCB is optimized to match its vibrational frequencies similar to those of Bz-TFB, and the dissociation of Bz-HCB becomes faster. The power spectrum of Bz-TFB, Bz-HCB, and Bz-HCB with the modified mass of chlorine is also computed to understand the extent of the said coupling in these complexes.

Electronic-state chaos, intramolecular electronic energy redistribution, and chemical bonding in persisting multidimensional nonadiabatic systems

We study the chaotic, huge fluctuation of electronic state, resultant intramolecular energy redistribution, and strong chemical bonding surviving the fluctuation with exceedingly long lifetimes of highly excited boron clusters. Those excited states constitute densely quasi-degenerate state manifolds. The huge fluctuation is induced by persisting multidimensional nonadiabatic transitions among the states in the manifold. We clarify the mechanism of their coexistence and its physical significance. In doing so, we concentrate on two theoretical aspects. One is quantum chaos and energy randomization, which are to be directly extracted from the properties of the total electronic wavefunctions. The present dynamical chaos takes place through frequent transitions from adiabatic states to others, thereby making it very rare for the system to find dissociation channels. This phenomenon leads to the concept of what we call intramolecular nonadiabatic electronic-energy redistribution, which is an electronic-state generaliztion of the notion of intramolecular vibrational energy redistribution. The other aspect is about the peculiar chemical bonding. We investigate it with the energy natural orbitals (ENOs) to see what kind of theoretical structures lie behind the huge fluctuation. The ENO energy levels representing the highly excited states under study appear to have four robust layers. We show that the energy layers responsible for chaotic dynamics and those for chemical bonding are widely separated from each other, and only when an event of what we call "inter-layer crossing" happens to burst can the destruction of these robust energy layers occur, resulting in molecular dissociation. This crossing event happens only rarely because of the large energy gaps between the ENO layers. It is shown that the layers of high energy composed of complex-valued ENOs induce the turbulent flow of electrons and electronic-energy in the cluster. In addition, the random and fast time-oscillations of those high energy ENOs serve as a random force on the nuclear dynamics, which can work to prevent a concentration of high nuclear kinetic energy in the dissociation channels.

Scale-Invariant Survival Probability at Eigenstate Transitions

Understanding quantum phase transitions in highly excited Hamiltonian eigenstates is currently far from being complete. It is particularly important to establish tools for their characterization in time domain. Here, we argue that a scaled survival probability, where time is measured in units of a typical Heisenberg time, exhibits a scale-invariant behavior at eigenstate transitions. We first demonstrate this property in two paradigmatic quadratic models, the one-dimensional Aubry-Andre model and three-dimensional Anderson model. Surprisingly, we then show that similar phenomenology emerges in the interacting avalanche model of ergodicity breaking phase transitions. This establishes an intriguing similarity between localization transition in quadratic systems and ergodicity breaking phase transition in interacting systems.

Antenna-coupled infrared nanospectroscopy of intramolecular vibrational interaction

Many photonic and electronic molecular properties, as well as chemical and biochemical reactivities are controlled by fast intramolecular vibrational energy redistribution (IVR). This fundamental ultrafast process limits coherence time in applications from photochemistry to single quantum level control. While time-resolved multidimensional IR-spectroscopy can resolve the underlying vibrational interaction dynamics, as a nonlinear optical technique it has been challenging to extend its sensitivity to probe small molecular ensembles, achieve nanoscale spatial resolution, and control intramolecular dynamics. Here, we demonstrate a concept how mode-selective coupling of vibrational resonances to IR nanoantennas can reveal intramolecular vibrational energy transfer. In time-resolved infrared vibrational nanospectroscopy, we measure the Purcell-enhanced decrease of vibrational lifetimes of molecular vibrations while tuning the IR nanoantenna across coupled vibrations. At the example of a Re-carbonyl complex monolayer, we derive an IVR rate of (25±8) cm-1 corresponding to (450±150) fs, as is typical for the fast initial equilibration between symmetric and antisymmetric carbonyl vibrations. We model the enhancement of the cross-vibrational relaxation based on intrinsic intramolecular coupling and extrinsic antenna-enhanced vibrational energy relaxation. The model further suggests an anti-Purcell effect based on antenna and laser-field-driven vibrational mode interference which can counteract IVR-induced relaxation. Nanooptical spectroscopy of antenna-coupled vibrational dynamics thus provides for an approach to probe intramolecular vibrational dynamics with a perspective for vibrational coherent control of small molecular ensembles.

Wavepacket dynamical study of H-atom tunneling in catecholate monoanion: the role of intermode couplings and energy flow

We present a study of H-atom tunneling in catecholate monoanion through wavepacket dynamical simulations. In our earlier study of this symmetrical double-well system [Phys. Chem. Chem. Phys., 2022, 24, 10887], a limited number of transition state modes were identified as being important for the tunneling process. These include the imaginary frequency mode Q₁, the CO scissor mode Q₁₀, and the OHO bending mode Q₂₉. In this work, starting from non-stationary initial states prepared with excitations in these modes, we have carried out wavepacket dynamics in two and three dimensional spaces. We analyse the dynamical effects of the intermode couplings, in particular the role of energy flow between the studied modes on H-atom tunneling. We find that while Q₁₀ strongly modulates the donor-acceptor distance, it does not exchange energy with Q₁. However, excitation in Q₂₉ or Q₁ does lead to rapid energy exchange between these modes, which modifies the tunneling rate at early times.

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.

Influence of a Methyl Group on the Unidirectional Flow of Vibrational Energy in an Adenine-Thymine Base Pair

The role of a methyl group in intramolecular vibrational energy redistribution (IVR) of the hydrogen-bonded adenine-thymine base pair has been studied using classical dynamics procedures. Energy transferred to the doorway bond thymine-NH from the vibrationally excited H₂O(v) efficiently redistributes among various bonds of the base pair through vibration-to-vibration coupling, depositing a large fraction of the available energy in the terminal bond adenine-NH. On the other hand, the extent of energy flow in the reverse direction from the excited adenine-NH to thymine-NH is insignificant, indicating IVR in adenine-thymine resulting from the intermolecular interaction with a vibrationally excited H₂O molecule, is direction-specific. The unidirectional flow is due to the coupling of stretch-torsion vibrations of a methyl group with conjugated bonds on the thymine ring, when the methyl rotor is present and is adjacent to the vibrationally excited thymine-NH. The insignificance of energy flow from the terminal-to-terminal bond in the reverse direction is attributed to the absence of a methyl group on the adenine moiety, even though the molecule has many CC and CN bonds coupled to their neighbors.

Quantum Chaos in the Dynamics of Molecules

Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule.

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.

Differential Tunneling-Driven and Vibrationally-Induced Reactivity in Isomeric Benzazirines

Quantum mechanical tunneling of heavy-atoms and vibrational excitation chemistry are unconventional and scarcely explored types of reactivity. Once fully understood, they might bring new avenues to conduct chemical transformations, providing access to a new world of molecules or ways of exquisite reaction control. In this context, we present here the discovery of two isomeric benzazirines exhibiting differential tunneling-driven and vibrationally-induced reactivity, which constitute exceptional results for probing into the nature of these phenomena. The isomeric 6-fluoro- and 2-fluoro-4-hydroxy-2H-benzazirines (3-a and 3'-s) were generated in cryogenic krypton matrices by visible-light irradiation of the corresponding triplet nitrene 3 2-a, which was produced by UV-light irradiation of its azide precursor. The 3'-s was found to be stable under matrix dark conditions, whereas 3-a spontaneously rearranges (τ1/2 ∼64 h at 10 and 20 K) by heavy-atom tunneling to 3 2-a. Near-IR-light irradiation at the first OH stretching overtone frequencies (remote vibrational antenna) of the benzazirines induces the 3'-s ring-expansion reaction to a seven-member cyclic ketenimine, but the 3-a undergoes 2H-azirine ring-opening reaction to triplet nitrene 3 2-a. Computations demonstrate that 3-a and 3'-s have distinct reaction energy profiles, which explain the different experimental results. The spectroscopic direct measurement of the tunneling of 3-a to 3 2-a constitutes a unique example of an observation of a species reacting only by nitrogen tunneling. Moreover, the vibrationally-induced sole activation of the most favorable bond-breaking/bond-forming pathway available for 3-a and 3'-s provides pioneer results regarding the selective nature of such processes.

Unified master equation for molecules in phonon and radiation baths

We have developed a unified quantum optical master equation that includes the dissipative mechanisms of an impurity molecule in crystals. Our theory applies generally to polyatomic molecules where several vibrational modes give rise to intramolecular vibrational redistributions. The usual assumption on identical shapes of the nuclear potentials in ground and excited electronic states and the rotating wave approximation have been relaxed, i.e. the vibrational coordinates are different in the ground and excited states, with counter-rotating terms included for generality. Linear vibrational coupling to the lattice phonons accounts for dissipations via non-radiative transitions. The interaction of a molecule with photons includes Herzberg–Teller coupling as the first order non-Condon interaction where the transition dipole matrix elements depend linearly on vibrational coordinates. We obtain new cross terms as the result of mixing the terms from the zeroth-order (Condon) and first-order (non-Condon) approximations. The corresponding Lamb shifts for all Liouvilleans are derived explicitly including the contributions of counter-rotating terms. The computed absorption and emission spectra for carbon monoxide is in good agreement with experimental data. We use our unified model to obtain the spectra for nitrogen dioxide, demonstrating the capability of our theory to incorporate all typical dissipative relaxation and decoherence mechanisms for polyatomic molecules. The molecular quantum master equation is a promising theory for studying molecular quantum memory.

Using mirrors to control molecular dynamics

An optical cavity mixes molecular vibrations with light and changes chemical reactivity

Dynamically Hidden Reaction Paths in the Reaction of CF3+ + CO

Reaction paths on a potential energy surface are widely used in quantum chemical studies of chemical reactions. The recently developed global reaction route mapping (GRRM) strategy automatically constructs a reaction route map, which provides a complete picture of the reaction. Here, we thoroughly investigate the correspondence between the reaction route map and the actual chemical reaction dynamics for the CF₃⁺ + CO reaction studied by guided ion beam tandem mass spectrometry (GIBMS). In our experiments, FCO⁺, CF₂⁺, and CF⁺ product ions were observed, whereas if the collision partner is N₂, only CF₂⁺ is observed. Interestingly, for reaction with CO, GRRM-predicted reaction paths leading to the CF⁺ + F₂CO product channel are found at a barrier height of about 2.5 eV, whereas the experimentally obtained threshold for CF⁺ formation was 7.48 ± 0.15 eV. In other words, the ion was not obviously observed in the GIBMS experiment, unless a much higher collision energy than the requisite energy threshold was provided. On-the-fly molecular dynamics simulations revealed a mechanism that hides these reaction paths, in which a non-statistical energy distribution at the first collisionally reached transition state prevents the reaction from proceeding along some reaction paths. Our results highlight the existence of dynamically hidden reaction paths that may be inaccessible in experiments at specific energies and hence the importance of reaction dynamics in controlling the destinations of chemical reactions.

Intramolecular vibrational energy redistribution in nucleobases: Excitation of NH stretching vibrations in adenine–uracil + H2O

Redistribution of vibrational energy in the adenine–uracil base pair is studied when the base pair undergoes an intermolecular interaction with an overtone-bending vibration excited H2O(2[Formula: see text]bend) molecule. Energy transfer is calculated using the structural information obtained from density functional theory in the solution of the equations of motion. Intermolecular vibrational energy transfer (VET) from H2O(2[Formula: see text]bend) to the uracil–NH stretching mode is efficient and rapidly followed by intramolecular vibrational energy redistribution (IVR) resulting from coupling between vibrational modes. An important pathway is IVR carrying energy to the NH-stretching mode of the adenine moiety in a subpicosecond scale, the energy build-up being sigmoidal, when H2O interacts with the uracil–NH bond. The majority of intermolecular hydrogen bonds between the base pair and H2O are weakened but unbroken during the ultrafast energy redistribution period. Lifetimes of intermolecular HB are on the order of 0.5 ps. The efficiency of IVR in the base pair is due to near-resonance between coupled CC and CN vibrations. The resonance also exists between the frequencies of H2O bend and NH stretch, thus facilitating VET. When H2O interacts with the NH bond at the adenine end of the base pair, energy flow in the reverse direction to the uracil–NH stretch is negligible, the unidirectionality discussed in terms of the effects of uracil CH stretches. The energy distributed in the CH bonds is found to be significant. The IVR process is found to be nearly temperature independent between 200 and 400 K.

Observing Intramolecular Vibrational Energy Redistribution via the Short-Time Fourier Transform

Intramolecular vibrational energy relaxation (IVR) is important in many problems in chemical physics. Here, we apply the short-time Fourier transform method for analyzing IVR with classical dynamics. Calculating time-dependent Fourier transforms to perform such an analysis requires extending the usual Fourier transform method, and we do that here. The guiding concept behind the generalization is that if there is a shift of vibrational energy from one frequency range to another, we see a difference between the spectrum before the shift and the spectrum after the shift. We use time-window functions to transform the power spectrum of a trajectory into a time-dependent density spectrum of the average kinetic energy. The time-dependent average kinetic energy for each interval of the spectrum becomes an indicator to monitor the extent and nature of the energy transfer into and out of the corresponding modes. We illustrate this method for the H₂O molecule. By analyzing cases with different initial conditions, we show that the short-time Fourier transform method can distinguish trends in IVR that depend on the initial distribution of energy and not just on the total energy.

Fundamental studies of vibrational resonance phenomena by multivalued resummation of the divergent Rayleigh-Schrödinger perturbation theory series: deciphering polyad structures of three H216O isotopologues

A fundamental quantitative study of the vibrational resonances of three H₂¹⁶O H,D-isotopologues with a quartic Watson Hamiltonian was carried out using the resummation of the high-order (∼λⁿ, n ≤ 203) divergent Rayleigh-Schrödinger perturbation theory (RSPT) series by quartic Padé-Hermite multivalued diagonal approximants PH^[m,m,m,m,m], m ≤ 40. The resonance condition between a pair of states is formulated as the existence of a common complex energy solution branch point inside the unit circle: |E(λ_j)|,  Re(λ_j)² + Im(λ_j)² ≤ 1. For the matrix formulation of the vibrational problem (VCI), the existence of common branch points is governed by the Katz theorem and they can be found as roots of discriminant polynomials. The main branches of the Padé-Hermite approximants typically reproduce VCI energies with high accuracy while alternative branches often fit nearby resonant states. The resummation of the RSPT series for H₂O and D₂O (up to the tenth polyad) revealed not only Fermi and Darling-Dennison resonances, but also unusual (0,2,-5) and (5,-2,0) resonance effects matching the (5,2,5) polyad structure, while the (3,2,1) structure was rigorously confirmed for HDO. It is demonstrated that the (5,2,5) polyad structure ensures good organization of high-energy resonating states and breaks down the classic (2,1,2) structure. The advocated methodology of quantitative description of resonance phenomena and revealing polyad structures is suitable for larger molecules and can be adapted to linear molecules and symmetric tops. Its application ensures rigorous classification of vibrational states and can be used in quantitative vibration-rotation spectroscopy.

Identification of the invariant manifolds of the LiCN molecule using Lagrangian descriptors

In this paper, we apply Lagrangian descriptors to study the invariant manifolds that emerge from the top of two barriers existing in the LiCN⇌LiNC isomerization reaction. We demonstrate that the integration times must be large enough compared with the characteristic stability exponents of the periodic orbit under study. The invariant manifolds manifest as singularities in the Lagrangian descriptors. Furthermore, we develop an equivalent potential energy surface with 2 degrees of freedom, which reproduces with a great accuracy previous results [F. Revuelta, R. M. Benito, and F. Borondo, Phys. Rev. E 99, 032221 (2019)2470-004510.1103/PhysRevE.99.032221]. This surface allows the use of an adiabatic approximation to develop a more simplified potential energy with solely 1 degree of freedom. The reduced dimensional model is still able to qualitatively describe the results observed with the original 2-degrees-of-freedom potential energy landscape. Likewise, it is also used to study in a more simple manner the influence on the Lagrangian descriptors of a bifurcation, where some of the previous invariant manifolds emerge, even before it takes place.

Ultrafast vibrational dynamics of a solute correlates with dynamics of the solvent

Two-dimensional infrared (2D-IR) spectroscopy is used to measure the spectral dynamics of the metal carbonyl complex cyclopentadienyl manganese tricarbonyl (CMT) in a series of linear alkyl nitriles. 2D-IR spectroscopy provides direct readout of solvation dynamics through spectral diffusion, probing the decay of frequency correlation induced by fluctuations of the solvent environment. 2D-IR simultaneously monitors intramolecular vibrational energy redistribution (IVR) among excited vibrations, which can also be influenced by the solvent through the spectral density rather than the dynamical friction underlying solvation. Here, we report that the CMT vibrational probe reveals solvent dependences in both the spectral diffusion and the IVR time scales, where each slows with increased alkyl chain length. In order to assess the degree to which solute-solvent interactions can be correlated with bulk solvent properties, we compared our results with low-frequency dynamics obtained from optical Kerr effect (OKE) spectroscopy-performed by others-on the same nitrile solvent series. We find excellent correlation between our spectral diffusion results and the orientational dynamics time scales from OKE. We also find a correlation between our IVR time scales and the amplitudes of the low-frequency spectral densities evaluated at the 90-cm^-1 energy difference, corresponding to the gap between the two strong vibrational modes of the carbonyl probe. 2D-IR and OKE provide complementary perspectives on condensed phase dynamics, and these findings provide experimental evidence that at least at the level of dynamical correlations, some aspects of a solute vibrational dynamics can be inferred from properties of the solvent.

Revealing the effects of molecular orientations on the azo-coupling reaction of nitro compounds driven by surface plasmonic resonances

A recent report on the azo coupling of 4-nitrobenzo-15-crown-ether (4NB15C) and 4-nitrothiophenol (4NTP) indicated that the reaction barrier could be reduced greatly with surface plasmonic effects on silver dendritic nanostructures in aqueous solution. Accordingly, an azo coupling reaction mechanism was proposed based on one or two SERS peaks. Toward a profound understanding of this azo coupling reaction mechanism, it is crucial to scrutinize the origin of the full SERS spectrum. Here, we construct a molecular model consisting of 4NTP and 4NB15C on an Ag₇ cluster that simulates a silver dendritic nanostructure, and investigate the SERS spectra of the azo coupling of these two molecules. We propose five different adsorption sites and 13 different orientations of 4NTP on the Ag₇ cluster and optimize the geometries of the five configurations. With each optimized configuration of 4NTP adsorbed on Ag₇, we further consider the azo coupling product with a 4NB15C molecule and simulate the corresponding Raman spectra. Comparing the measured Raman spectra and model analysis, we conclude that the azo coupling reaction depends decisively on a parallel molecular orientation of the adsorbed 4NTP relative to the facets of Ag₇, the orientation of which further directs the subsequent reaction for the product of 4NB15C-4NTP.

Observation of a dipole-bound excited state in 4-ethynylphenoxide and comparison with the quadrupole-bound excited state in the isoelectronic 4-cyanophenoxide

Negative ions do not possess Rydberg states but can have Rydberg-like nonvalence excited states near the electron detachment threshold, including dipole-bound states (DBSs) and quadrupole-bound states (QBSs). While DBSs have been studied extensively, quadrupole-bound excited states have been more rarely observed. 4-cyanophenoxide (4CP^-) was the first anion observed to possess a quadrupole-bound exited state 20 cm^-1 below its detachment threshold. Here, we report the observation of a DBS in the isoelectronic 4-ethynylphenoxide anion (4EP^-), providing a rare opportunity to compare the behaviors of a dipole-bound and a quadrupole-bound excited state in a pair of very similar anions. Photodetachment spectroscopy (PDS) of cryogenically cooled 4EP^- reveals a DBS 76 cm^-1 below its detachment threshold. Photoelectron spectroscopy (PES) at 266 nm shows that the electronic structure of 4EP^- and 4CP^- is nearly identical. The observed vibrational features in both the PDS and PES, as well as autodetachment from the nonvalence excited states, are also found to be similar for both anions. However, resonant two-photon detachment (R2PD) from the bound vibrational ground state is observed to be very different for the DBS in 4EP^- and the QBS in 4CP^-. The R2PD spectra reveal that decays take place from both the DBS and QBS to the respective anion ground electronic states within the 5 ns detachment laser pulse due to internal conversion followed by intramolecular vibrational redistribution and relaxation, but the decay mechanisms appear to be very different. In the R2PD spectrum of 4EP^-, we observe strong threshold electron signals, which are due to detachment, by the second photon, of highly rotationally excited anions resulted from the decay of the DBS. On the other hand, in the R2PD spectrum of 4CP^-, we observe well-resolved vibrational peaks due to the three lowest-frequency vibrational modes of 4CP^-, which are populated from the decay of the QBS. The different behaviors of the R2PD spectra suggest unexpected differences between the relaxation mechanisms of the dipole-bound and quadrupole-bound excited states.

Machine learning classification of disrotatory IRC and conrotatory non-IRC trajectory motion for cyclopropyl radical ring opening

Quasiclassical trajectory analysis is now a standard tool to analyze non-minimum energy pathway motion of organic reactions. However, due to the large amount of information associated with trajectories, quantitative analysis of the dynamic origin of reaction selectivity is complex. For the electrocyclic ring opening of cyclopropyl radical, more than 4000 trajectories were run showing that allyl radicals are formed through a mixture of disrotatory intrinsic reaction coordinate (IRC) motion as well as conrotatory non-IRC motion. Geometric, vibrational mode, and atomic velocity transition-state features from these trajectories were used for supervised machine learning analysis with classification algorithms. Accuracy >80% with a random forest model enabled quantitative and qualitative assessment of transition-state trajectory features controlling disrotatory IRC versus conrotatory non-IRC motion. This analysis revealed that there are two key vibrational modes where their directional combination provides prediction of IRC versus non-IRC motion.

Geometry of complex instability and escape in four-dimensional symplectic maps

In 4D symplectic maps complex instability of periodic orbits is possible, which cannot occur in the 2D case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter variation. The change in the geometry of regular structures is visualized using 3D phase-space slices and in frequency space using the example of two coupled standard maps. The chaotic dynamics is studied using escape time plots and by computations of the 2D invariant manifolds associated with the complex unstable fixed point. Based on a normal-form description, we investigate the underlying transport mechanism by visualizing the escape paths and the long-time confinement in the surrounding of the complex unstable fixed point. We find that the slow escape is governed by the transport along the unstable manifold while going across the approximately invariant planes defined by the corresponding normal form.

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.

Vibrational Energy Relaxation of Deuterium Fluoride in d-Dichloromethane: Insights from Different Potentials

Vibrationally excited deuterium fluoride (DF) formed by fluorine atom reaction with a solvent was found (Science, 2015, 347, 530) to relax rapidly (less than 10 ps) in acetonitrile-d₃ (CD₃CN) and dichloromethane-d₂ (CD₂Cl₂). However, insights into how CD₂Cl₂ facilitates this energy relaxation have so far been lacking, given the weak interaction between DF and a single CD₂Cl₂. In this work, we report the results of reactive simulations with a two-state reactive empirical valence bond (EVB) potential to study the energy deposited into nascent DF after transition-state passage and of nonequilibrium molecular dynamics simulations using multiple different potential energy functions to model the relaxation dynamics. For these second simulations, we used the standard Merck molecular force field (MMFF) potential, an MMFF-based covalent-ionic empirical valence bond (EVB) potential (EVB^CI), a newly developed potential [referred to as MMFF(rDF)] which extends upon the MMFF potential by making the DF/CD₂Cl₂ interaction depend on the value of the D-F bond stretching coordinate and by taking the anisotropic charge distribution of the solvent molecules into account, the polarizable atomic multipole optimized energetics for biomolecular applications (AMOEBA) potential, and the quantum mechanics/molecular mechanics (QM/MM) potential. The relaxation is revealed to be highly sensitive to the potential used. Neither standard MMFF nor EVB^CI reproduces the experimentally observed rapid relaxation dynamics, and they also fail to provide a good description of the interaction potential between DF and CD₂Cl₂ as calculated using CCSD(T)-F12. This is attributed to the use of a point-charge model for the solute and to failing to model the anisotropic electrostatic properties of CD₂Cl₂. The MMFF(rDF), AMOEBA, and QM/MM potentials all reproduce the CCSD(T)-F12 two-body DF---CD₂Cl₂ interaction potential rather well but only with the QM/MM approach is fast vibrational relaxation obtained (lifetimes of ∼288, ∼186, and ∼8 ps, respectively), which we attribute to differences in the solute-solvent local structure. With QM/MM, a unique "many-body" interaction pattern in which DF is in close contact with two solvent Cl atoms and more than three solvent D atoms is found, but this structure is not seen with other potentials. The QM/MM dynamics also display enhanced solute-solvent interactions with vibrationally excited DF that induce a DF band redshift and hence a resonant overlap with solvent C-D modes, which facilitate the intermolecular energy transfer. Our work also suggests that potentials used to model energy relaxation need to capture the fine structure of solute-solvent interactions and not just the two-body part.

Bond-Breaking/Bond-Forming Reactions by Vibrational Excitation: Infrared-Induced Bidirectional Tautomerization of Matrix-Isolated Thiotropolone

Infrared vibrational excitation is a promising approach for gaining exceptional control of chemical reactions, in ways that cannot be attained via thermal or electronic excitation. Here, we report an unprecedented example of a bond-breaking/bond-forming reaction by vibrational excitation under matrix isolation conditions. Thiotropolone monomers were isolated in cryogenic argon matrices and characterized by infrared spectroscopy and vibrational computations (harmonic and anharmonic). Narrowband near-infrared irradiations tuned at frequencies of first CH stretching overtone (5940 cm^-1) or combination modes (5980 cm^-1) of the OH tautomer, the sole form of the compound that exists in the as-deposited matrices, led to its conversion into the SH tautomer. The tautomerization in the reverse direction was achieved by vibrational excitation of the SH tautomer with irradiation at 5947 or 5994 cm^-1, corresponding to the frequencies of its CH stretching combination and overtone modes. This pioneer demonstration of bidirectional hydroxyl ↔ thiol tautomerization controlled by vibrational excitation creates prospects for new advances in vibrationally induced chemistry.

Low-Temperature Vibrational Energy Transport via PEG Chains

We used relaxation-assisted two-dimensional infrared spectroscopy to study the temperature dependence (10-295 K) of end-to-end energy transport across end-decorated PEG oligomers of various chain lengths. The excess energy was introduced by exciting the azido end-group stretching mode at 2100 cm^-1 (tag); the transport was recorded by observing the asymmetric C═O stretching mode of the succinimide ester end group at 1740 cm^-1. The overall transport involves diffusive steps at the end groups and a ballistic step through the PEG chain. We found that at lower temperatures the through-chain energy transport became faster, while the end-group diffusive transport time and the tag lifetime increase. The modeling of the transport using a quantum Liouville equation linked the observations to the reduction of decoherence rate and an increase of the mean-free-path for the vibrational wavepacket. The energy transport at the end groups slowed down at low temperatures due to the decreased number and efficiency of the anharmonic energy redistribution pathways.