Intramolecular Vibrational Energy Redistribution Research Articles

Nitrile Vibrational Lifetimes as Probes of Local Electric Fields.

Optical measurements of electric fields have wide-ranging applications in the fields of chemistry and biology. Previously, such measurements focused on shifts in intensity or frequency. Here, we show that nitrile vibrational lifetimes can report local electric fields through ultrasensitive picosecond mid-infrared-near-infrared double-resonance fluorescence spectro-microscopy on Rhodamine 800. Using a robust convolution fitting approach, we observe that the nitrile vibrational lifetimes are strongly linearly correlated (R2 = 0.841) with solvent reaction fields. Supported by density functional theory, we rationalize this trend through a doorway model of intramolecular vibrational energy redistribution. This work provides new fundamental insights into the nature of vibrational energy flow in large polyatomic molecular systems and establishes a theoretical basis for electric field sensing with vibrational lifetimes, offering a new experimental dimension for probing intracellular electrostatics.

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.

Photodissociation dynamics of m- and p-cresol in the S1 state: Interplay between the mode-randomization and H atom tunneling reaction.

The H atom tunneling dissociation dynamics of the S1 state of meta- or para-cresol has been investigated by using the picosecond time-resolved pump-probe spectroscopy in a state-specific manner. The S1 state lifetime (mainly due to the H atom tunneling reaction) is found to be mode-dependent whereas it quickly converges and remains constant as the rapid intramolecular vibrational energy redistribution (IVR) starts to participate in the S1 state relaxation with the increase of the S1 internal energy (Eint). The IVR rate and its change with increasing Eint have been reflected in the parent ion transients taken by tuning the total energy (hνpump + hνprobe) just above the adiabatic ionization threshold (so that the dissipation of the initial mode-character could be monitored as a function of the reaction time), indicating that the mode randomization rate into the S1 isoenergetic manifolds exceeds the tunneling rate quite early in terms of Eint for m-cresol (≤∼1200cm-1) or p-cresol (≤∼800cm-1) compared to the case of phenol (≤∼1800cm-1). Though the H atom tunneling dynamics of phenol (S1) seems to be little influenced by the methyl substitution on the either m- or p-position, the IVR rate has been found to be strongly accelerated due to the sharply-increasing (S1) density of states with increasing Eint due to the pivotal role of the low-frequency CH3 torsional mode.

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.

Inhibition of vibrational energy flow within an aromatic scaffold via heavy atom effect.

The regulation of intramolecular vibrational energy redistribution (IVR) to influence energy flow within molecular scaffolds provides a way to steer fundamental processes of chemistry, such as chemical reactivity in proteins and design of molecular diodes. Using two-dimensional infrared (2D IR) spectroscopy, changes in the intensity of vibrational cross-peaks are often used to evaluate different energy transfer pathways present in small molecules. Previous 2D IR studies of para-azidobenzonitrile (PAB) demonstrated that several possible energy pathways from the N3 to the cyano-vibrational reporters were modulated by Fermi resonance, followed by energy relaxation into the solvent [Schmitz et al., J. Phys. Chem. A 123, 10571 (2019)]. In this work, the mechanisms of IVR were hindered via the introduction of a heavy atom, selenium, into the molecular scaffold. This effectively eliminated the energy transfer pathway and resulted in the dissipation of the energy into the bath and direct dipole-dipole coupling between the two vibrational reporters. Several structural variations of the aforementioned molecular scaffold were employed to assess how each interrupted the energy transfer pathways, and the evolution of 2D IR cross-peaks was measured to assess the changes in the energy flow. By eliminating the energy transfer pathways through isolation of specific vibrational transitions, through-space vibrational coupling between an azido (N3) and a selenocyanato (SeCN) probe is facilitated and observed for the first time. Thus, the rectification of this molecular circuitry is accomplished through the inhibition of energy flow using heavy atoms to suppress the anharmonic coupling and, instead, favor a vibrational coupling pathway.

An analytical expression for temperature-dependent infrared intensities in fully coupled anharmonic molecular systems

We present the analytical expression for determining the temperature evolution of absolute integrated infrared (IR) intensities of fundamental bands in fully coupled anharmonic molecular systems. Only harmonic frequencies and integrated IR intensities (within the double harmonic approximation) are needed to predict the absolute temperature-dependent IR intensities of the fundamental bands. These quantities can be readily obtained from ab initio electronic structure calculations for relatively large molecules. In order to illustrate the accuracy of the expression we compare the results from this formula using harmonic frequencies and intensities from a tight-binding potential energy surface with the results from semiclassically prepared molecular dynamics (SCP-MD) simulations on the same potential energy surface for the naphthalene molecule. For a favorable comparison with experimental data we use the same analytical expression with the more accurate B3LYP/cc-pVDZ harmonic frequencies and intensities. We conclude that the IR intensity changes that our proposed formula predicts in the fundamental vibrational bands are mainly due to intramolecular vibrational energy redistribution (IVR).

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.

Investigation on the ultrafast relaxation dynamics of the S1 state of 3,4-difluoroaniline

The ultrafast dynamics of 3,4-difluoroaniline is studied by time-resolved velocity map imaging and mass spectroscopy. Following the excitation with 299.6 or 291.8 nm to the S1 state, relaxation process with three decay components is explored. The hundreds-of-picosecond decay is attributed to the intersystem crossing to triplet state and the nanosecond decay represents the following relaxation of the triplet state. However, the dynamics in hundreds-of-femtoseconds for two excitations are different. We intend to designate it as the molecules leaving the Franck-Condon region at 299.6 nm and as the intramolecular vibrational energy redistribution at 291.8 nm with highly vibrational excitation.

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.

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.

Cavity-enabled enhancement of ultrafast intramolecular vibrational redistribution over pseudorotation.

Vibrational strong coupling (VSC) between molecular vibrations and microcavity photons yields a few polaritons (light-matter modes) and many dark modes (with negligible photonic character). Although VSC is reported to alter thermally activated chemical reactions, its mechanisms remain opaque. To elucidate this problem, we followed ultrafast dynamics of a simple unimolecular vibrational energy exchange in iron pentacarbonyl [Fe(CO)₅] under VSC, which showed two competing channels: pseudorotation and intramolecular vibrational-energy redistribution (IVR). We found that under polariton excitation, energy exchange was overall accelerated, with IVR becoming faster and pseudorotation being slowed down. However, dark-mode excitation revealed unchanged dynamics compared with those outside of the cavity, with pseudorotation dominating. Thus, despite controversies around thermally activated VSC modified chemistry, our work shows that VSC can indeed alter chemistry through a nonequilibrium preparation of polaritons.

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.

Inefficient intramolecular vibrational energy redistribution for the H + HO2 reaction and negative internal energy dependence for its rate constant

Quasiclassical trajectories (QCT) and newly constructed global potential energy surfaces are used to compute thermal and nonthermal rate constants for the H + HO2 reaction. The thermal QCTs rate constants are up to 50% smaller than transition state theory (TST) rate constants based on the same level of electronic structure theory. This reduction is demonstrated to result from inefficient intramolecular vibrational energy redistribution (IVR) in the transient H2O2 well, with a significant fraction of trajectories that reach the H2O2 well promptly dissociating back to reactants instead of via the heavily statistically favored 2OH channel. The nonstatistical reduction factor, κIVR, that quantifies this effect is shown to increase in importance with temperature, with κIVR = 0.81 at 300 K and 0.47 at 2500 K. Finally, we show that inefficient IVR causes H + HO2 rate constants mediated by H2O2 to depend inversely on the initial vibrational excitation of HO2.

Infinitene: Computational Insights from Nonadiabatic Excited State Dynamics.

Progress in organic synthesis opens exploration of a rich diversity of molecules with interesting new structural topologies. This is the case of a recently synthesized helically twisted figure-eight molecule coined infinitene. The molecule belongs to a numerous family of looped polyarenes, where the degree of π-conjugation is controlled by high strain energies and steric hindrances. A particular balance of these ingredients leads to unusual optoelectronic properties potentially suitable for a range of applications in nanoelectronics and photonics. Due to its recent discovery, the photophysical properties of infinitene remain unexplored. In this Letter, atomistic nonadiabatic excited state molecular dynamics modeling unveils unique features of intramolecular electronic and vibrational energy relaxation and redistribution that take place after molecular photoexcitation. Our results detail relationships between optical and electronic properties providing useful knowledge for future molecular designs related to infinitene.

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(2νbend) 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(2νbend) 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 0.5ps. 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 400K.

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.

Strong Torsion-Vibration Interaction in N-Methylpyrrole Observed by Far-Infrared Spectroscopy.

An interaction between methyl torsion and the low-lying out-of-plane methyl wag vibration has been observed in toluene, p-fluorotoluene, and m-fluorotoluene, contravening the traditional assumption used when analyzing spectra that methyl torsion can be treated independently of the small-amplitude vibrations. When a methyl group is attached to a planar frame, out-of-plane methyl wag vibrations always occur, and hence this type of interaction between methyl torsion and vibration is potentially extensive. To probe whether this coupling occurs beyond toluene and its derivatives, we have studied the far-infrared absorption band for the out-of-plane methyl wagging mode in N-methylpyrrole. The torsional sequence structure reveals a particularly strong torsion-vibration interaction. Spectral simulations yield a torsion-vibration coupling matrix element of 34.0 cm-1, over twice the value for toluene. The large torsion-vibration coupling constant implies that there is a significant tilting of the methyl group out of plane. Quantum chemistry calculations reveal a much larger out-of-plane methyl tilt angle in N-methylpyrrole compared to toluene, qualitatively consistent with this expectation. This is the first nontoluene derivative for which this type of torsion-vibration interaction has been reported and shows that the effect extends beyond toluenes. When present, this interaction links small-amplitude vibrations to the methyl torsion, providing a mechanism to bring the increased density of states into play and accelerate the rate of intramolecular vibrational energy redistribution.

Manipulating the dynamics of a Fermi resonance with light. A direct optimal control theory approach

Direct optimal control theory for quantum dynamical problems presents itself as an interesting alternative to the traditional indirect optimal control. The method relies on the first discretize and then optimize paradigm, where a discretization of the dynamical equations leads to a nonlinear optimization problem. It has been applied successfully to the control of a bistable system where the wavepacket had been approximated by a parameterized Gaussian, leading to a semiclassical set of equations of motion (A. R. Ramos Ramos, O. K\"uhn, Front. Phys. 9 (2021) 615168). Motivated by these results, in the present paper we extend the application of the method to the case of exact wavepacket propagation using the example of a generic Fermi-resonance model. In particular we address the question how population of the involved overtone state can be avoided such as to reduce the effect of intramolecular vibrational energy redistribution. A methodological advantage is that direct optimal control theory offers flexibility when choosing the running cost, since there is no need to compute functional derivatives and coupling terms as in the case of indirect optimal control. We exploit this fact to include state populations in the running cost, which allows their optimization.

Dynamical Behavior of Aromatic Trimer Complexes in Unimolecular Dissociation Reaction at High Temperatures. Case Studies on C6H6-C6F6-C6H6 and C6H6 Trimer Complexes.

The intramolecular vibrational energy redistribution (IVR) dynamics during unimolecular dissociation of aromatic trimers at high temperatures is the primary interest of this study. Chemical dynamics simulations are performed for the unimolecular dissociation of benzene-hexafluorobenzene-benzene (Bz-HFB-Bz) and benzene trimer (Bz-trimer) complexes at a temperature range of 1000-2000 K. Partial dissociation of both the complexes is observed, which leads to a dimer and a monomer in the dynamics. However, the probability of such dissociation was found much lower in the case of the Bz-trimer, which further decreases with the increase of temperature. The rate of partial dissociation of Bz-HFB-Bz is faster at 1500, 1800, and 2000 K, whereas the rate of complete dissociation of the Bz-trimer is significantly faster than Bz-HFB-Bz at all temperatures. This is just the opposite of the corresponding dimer's dissociation, where benzene-hexafluorobenzene (Bz-HFB) dissociates at a faster rate than the benzene dimer (Bz-dimer). Thus, the dissociation dynamics of the trimer is different than that of the dimer. Simulations with excited intramolecular and intermolecular modes of the trimer complexes reveal that energy flows from intermolecular to intramolecular modes of Bz-HFB-Bz more freely than the Bz-trimer, and the dissociation process becomes slower for the former. Calculated activation energies for both types of dynamics are much lower than the corresponding binding energies, which may be due to the anharmonicity. The Arrhenius equation with an anharmonic correction factor is considered to recalculate the activation energy and pre-exponential factor.