Vibrational Time Scale Research Articles

Time-resolved THz Stark spectroscopy of molecules in solution

For decades, it was considered all but impossible to perform Stark spectroscopy on molecules in a liquid solution, because their concomitant orientation to the applied electric field results in overwhelming background signals. A way out was to immobilize the solute molecules by freezing the solvent. While mitigating solute orientation, freezing removes the possibility to study molecules in liquid environments at ambient conditions. Here we demonstrate time-resolved THz Stark spectroscopy, utilizing intense single-cycle terahertz pulses as electric field source. At THz frequencies, solute molecules have no time to orient their dipole moments. Hence, dynamic Stark spectroscopy on the time scales of molecular vibrations or rotations in both non-polar and polar solvents at arbitrary temperatures is now possible. We verify THz Stark spectroscopy for two judiciously selected molecular systems and compare the results to conventional Stark spectroscopy and first principle calculations.

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting.

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

Exploring solute-defect interactions in nanosized palladium hydrides across multiple time scales

We employ two different atomistic methods to investigate solute-defect interactions in nanosized palladium–hydrogen (Pd–H) systems across multiple time scales. The first method, referred to as Diffusive Molecular Dynamics (DMD), focuses on capturing hydride phase transformation and the evolution of solute-induced lattice defects over a diffusive time scale. The second method, Molecular Dynamics (MD), provides more detailed insights into atomic movements and lattice relaxation over the time scale of thermal vibrations. These two methods are connected with MD simulations initialized using statistical measures of microscopic variables obtained from DMD at different H/Pd ratios. Our study demonstrates that DMD effectively captures the propagation of an atomistically sharp hydride phase boundary as well as the dynamics of solute-induced misfit dislocations and stacking faults. While the H-concentrated phase leads to a reduction in the vibrational energy, the presence of stacking faults locally increases the vibrational energy of both Pd and H atoms. Furthermore, the MD simulation results align with DMD in terms of equilibrium potential energy, the preservation of hydride phase boundary, and the spatial distribution of stacking faults. We thoroughly characterize the lattice crystalline structures in four key regions of the particle. We observe a preference for H atoms to occupy tetrahedral interstitial sites near stacking faults due to the lower stacking fault energies provided by these sites within the H-concentrated phase.

Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids.

We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle's response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic response only correlates with the dynamics on the vibrational timescale.

Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water.

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

Monitoring of an engineering structure in the process of its operation in a corrosive environment

The functioning of engineering structures that perform critical technological operations isimpossible without monitoring its deformation state. The fundamental engineering problem of thisstudy is the development of an automated system for monitoring deformation processes in a structuresubject to severe corrosion, as well as the adaptation of this system to the aggressive effects of theexternal environment (exposure to salt brines and aerosols, operation at low temperatures). Theengineering structure is a large-scale metal construction for lifting and unloading potash ore from amine shaft. A mathematical model has been created for this structure, considering the main weight,size and stiffness characteristics. Installation locations and sensors parameters were determined onthe basis of numerical experiments. The systems of sensors adapted to the conditions of a corrosiveenvironment have been developed to control quasi-static, vibrational and dynamic processes ondifferent time scales. Examples of readings of various types of sensors are given to illustrate theresponse of the structure to natural, man-made and technological processes.

Linear stability analysis of one-dimensional detonation coupled with vibrational relaxation

The linear stability of one-dimensional detonations with one-reaction chemistry coupled with molecular vibration nonequilibrium is investigated using the normal mode approach. The chemical kinetics in the Arrhenius form depend on an averaged temperature model that consists of translational–rotational mode and vibrational mode. The Landau–Teller model is applied to specify the vibrational relaxation. A time ratio is introduced to denote the ratio between the chemical time scale and the vibrational time scale in this study, which governs the vibrational relaxation rate in this coupling kinetics. The stability spectrum of disturbance eigenmodes is obtained by varying the bifurcation parameters independently at a different time ratio. These parameters include the activation energy, the degree of overdrive, the characteristic vibrational temperature, and the heat release. The results indicate that the neutral stability limit shifts to higher activation energy on the vibrational nonequilibrium side with a smaller time ratio, implying that the detonation is stabilized. A similar observation is seen at a lower degree of overdrive. Compared with the above two parameters, the characteristic vibrational temperature plays a minor role in the stabilization of detonation, and no change in the number of eigenmodes is identified throughout the selected range. By plotting the neutral stability curves relating the heat release to the above parameters, the decreases in instability ranges are obviously seen under vibrational nonequilibrium. The thermal nonequilibrium effect on detonation stability is clearly demonstrated. The analysis presented in this paper is ultimately justified by comparing the results with numerical simulation.

Numerical analysis of the vibration-chemistry coupling effect on one-dimensional detonation stability

A one-dimensional numerical simulation of detonation propagation is performed with an introduction of the vibrational relaxation mechanism in a single-step chemical model for the first time. This coupling mechanism is constructed based on the energy transfer between the translational-rotational mode and the vibrational mode, together with an averaged two-temperature model in chemical kinetics. A time ratio τα between the characteristic chemical time scale and the characteristic vibrational time scale is introduced to illustrate whether this coupling effect is crucial in stabilizing the detonation. The simulation is initialized first with an extended steady-state profile and the inclusion of the vibrational energy in the equations. For the particular case considered in this study with a nondimensional heat release Q=50, a ratio of specific heat γ=1.2, and a nondimensional characteristic vibrational temperature ϑ=20, the stability boundary is indicated at an activation energy Ea=26.47 under thermal equilibrium. Two mildly unstable cases for a Chapman-Jouguet (CJ) detonation and an overdriven detonation are then studied with the variation of τα. The results reveal that the detonation is stabilized by the vibrational nonequilibrium effect with a smaller pulsation amplitude and a longer oscillation period in the shock pressure history, and the neutral stability is shifted. For the CJ detonation case, the critical τα below which the coupling effect is significant is 7.2. The stabilization of detonation can be attributed to the reduction of the overall chemical reaction rate by vibrational relaxation and thus a shift of the stability limit towards higher activation energy. For an overdriven detonation, the critical τα is approximately 21 for the studied cases. Since the changes in both overdriven factors f and τα contributed to the stabilization of detonation, a reduction of the neutral stability limit of f is foreseen when the coupling effect is significant. Lastly, the effect of different ϑ on the stability limit is demonstrated at equilibrium state with vibrational energy included and it is suggested that the shift of stability limit would reach the maximum at around ϑ=15. This inaugural work provides a reference on the importance of considering thermal nonequilibrium flow in detonation stability and the implication to the related engine design.

Real-Time Path Integral Simulation of Exciton-Vibration Dynamics in Light-Harvesting Bacteriochlorophyll Aggregates.

The mechanism of excitation energy transfer in photoexcited bacteriochlorophyll (BChl) aggregates poses intriguing questions, which have important implications for the observed efficiency of photosynthesis. We investigate this process through fully quantum mechanical calculations of exciton-vibration dynamics in chains and rings of BChl a molecules, with parameters characterizing the B850 ring of the LH2 complex of photosynthetic bacteria. The calculations are performed using the modular path integral methodology, which allows the exact treatment of 50 intramolecular vibrations on each pigment using parameters obtained from spectroscopic Huang-Rhys factors with computational effort that scales linearly with aggregate length. Our results indicate that the interplay between electronic and vibrational time scales leads to the rapid suppression but not the overdamping of electronic coherence, which facilitates the spreading of excitation energy throughout the aggregate.

Chemical reaction mechanism related vibrational nonequilibrium effect on the Zel'dovich−von Neumann−Döring (ZND) detonation model

Discrepancies in detonation cell size are always found between experiments and numerical simulations. The recent numerical simulation by Shi et al. (2016) included the vibrational relaxation effect in molecules and revealed that the vibrational nonequilibrium effect may be one of the reasons for the above discrepancy. In this study, a steady one-dimensional Zel'dovich–von Neumann–Döring (ZND) model is modified to account for the vibrational nonequilibrium effect in gaseous detonation. By introducing a new parameter α, which is defined as the ratio of translational-rotational mode of the specific heat at constant volume to the overall specific heat at constant volume, the translational-rotational energy and the vibrational energy are treated separately in the energy conservation equation. Both the single step and the two step Arrhenius models are used to describe the chemical reaction progress, and the Landau–Teller model and Park's two-temperature model are applied to describe the vibrational energy relaxation and the coupling between the molecular vibration and the chemical reaction, respectively. The parametric study on the modified ZND model is conducted and compared with the conventional ZND one, including the activation energy in chemical model, the ratio of the chemical time scale to the vibrational relaxation time scale and the characteristic vibrational temperature. The results show that the half reaction length is relatively not sensitive to the variation of characteristic vibrational temperature applied in the model (compared with the activation energy and the time ratio), but is increased to a significant extent with the increase of the activation energy and the decrease of the time ratio, when considered the vibrational nonequilibrium. The simulated half reaction lengths in the modified model are in good agreement with those in the conventional model, if the chemical time scale is larger than the vibrational relaxation time scale above a critical ratio when the vibrational nonequilibrium effect is insignificant.

Influence of water and enzyme SpnF on the dynamics and energetics of the ambimodal [6+4]/[4+2] cycloaddition

SpnF is the first monofunctional Diels-Alder/[6+4]-ase that catalyzes a reaction leading to both Diels-Alder and [6+4] adducts through a single transition state. The environment-perturbed transition-state sampling method has been developed to calculate free energies, kinetic isotope effects, and quasi-classical reaction trajectories of enzyme-catalyzed reactions and the uncatalyzed reaction in water. Energetics calculated in this way reproduce the experiment and show that the normal Diels-Alder transition state is stabilized by H bonds with water molecules, while the ambimodal transition state is favored in the enzyme SpnF by both intramolecular hydrogen bonding and hydrophobic binding. Molecular dynamics simulations show that trajectories passing through the ambimodal transition state bifurcate to the [6+4] adduct and the Diels-Alder adduct with a ratio of 1:1 in the gas phase, 1:1.6 in water, and 1:11 in the enzyme. This example shows how an enzyme acts on a vibrational time scale to steer post-transition state trajectories toward the Diels-Alder adduct.

Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses

Computational studies of supercooled liquids often focus on various analyses of their "underlying inherent states"-the glassy configurations at zero temperature obtained by an infinitely fast (instantaneous) quench from equilibrium supercooled states. Similar protocols are also regularly employed in investigations of the unjamming transition at which the rigidity of decompressed soft-sphere packings is lost. Here we investigate the statistics and localization properties of low-frequency vibrational modes of glassy configurations obtained by such instantaneous quenches. We show that the density of vibrational modes grows as ω^{β} with β depending on the parent temperature T_{0} from which the glassy configurations were instantaneously quenched. For quenches from high temperature liquid states we find β≈3, whereas β appears to approach the previously observed value β=4 as T_{0} approaches the glass transition temperature. We discuss the consistency of our findings with the theoretical framework of the soft potential model, and contrast them with similar measurements performed on configurations obtained by continuous quenches at finite cooling rates. Our results suggest that any physical quench at rates sufficiently slower than the inverse vibrational time scale-including all physically realistic quenching rates of molecular or atomistic glasses-would result in a glass whose density of vibrational modes is universally characterized by β=4.

Theoretical study of photoinduced proton coupled electron transfer reaction using the non-perturbative hierarchical equations of motion method

Photoinduced proton coupled electron transfer (PCET) reactions, in which the charge transfer process is initiated by light absorption, are of special interest to both theoretical and experimental studies. In this work, by employing the non-perturbative hierarchical equation of motion method, we investigate several aspects of concerted photoinduced PCET based on an extended spin-boson model where the correlation between the electron and proton baths is considered explicitly. It is found that the vibrational relaxation on the donor state plays an important role in the initial stage of the non-equilibrium PCET dynamics after photon excitation, and the equilibrium rate dynamics is recovered at times longer than the vibrational relaxation time scale. The numerically exact results are compared with those obtained from the non-equilibrium Fermi’s golden rule, which is found to be less accurate for the non-equilibrium dynamics in the case of large electronic couplings. The isotope effect in photoinduced PCET is also investigated, where the non-equilibrium dynamics and equilibrium rate dynamics show very different isotope effects.

Trajectory Calculations for Bergman Cyclization Predict H/D Kinetic Isotope Effects Due to Nonstatistical Dynamics in the Product

An unusual H/D kinetic isotope effect (KIE) is described, in which isotopic selectivity arises primarily from nonstatistical dynamics in the product. In DFT-based quasiclassical trajectories of Bergman cyclization of (Z)-3-hexen-1,5-diyne (1) at 470 K, the new CC bond retains its energy, and 28% of nascent p-benzyne recrosses back to the enediyne on a vibrational time scale. The competing process of intramolecular vibrational redistribution (IVR) in p-benzyne is too slow to prevent this. Deuteration increases the rate of IVR, which decreases the fraction of recrossing and increases the yield of statistical (trapable) p-benzyne, 2. Trapable yields for three isotopomers of 2 range from 72% to 86%. The resulting KIEs for Bergman cyclization differ substantially from KIEs predicted by transition state theory, which suggests that IVR in this reaction can be studied by conventional KIEs. Leakage of vibrational zero point energy (ZPE) into the reaction coordinate was probed by trajectories in which initial ZPE in the CH/CD stretching modes was reduced by 25%. This did not change the predicted KIEs.

Ligand-centred fluorescence and electronic relaxation cascade at vibrational time scales in transition-metal complexes.

Using femtosecond-resolved photoluminescence up-conversion, we report the observation of the fluorescence of the high-lying ligand-centered (LC) electronic state upon 266 nm excitation of an iridium complex, Ir(ppy)3, with a lifetime of 70 ± 10 fs. It is accompanied by a simultaneous emission of all lower-lying electronic states, except the lowest triplet metal-to-ligand charge-transfer ((3)MLCT) state that shows a rise on the same time scale. Thus, we observe the departure, the intermediate steps, and the arrival of the relaxation cascade spanning ∼1.6 eV from the (1)LC state to the lowest (3)MLCT state, which then yields the long-lived luminescence of the molecule. This represents the first measurement of the total relaxation time over an entire cascade of electronic states in a polyatomic molecule. We find that the relaxation cascade proceeds in ≤10 fs, which is faster than some of the highest-frequency modes of the system. We invoke the participation of the latter modes in conical intersections and their overdamping to low-frequency intramolecular modes. On the basis of literature, we also conclude that this behavior is not specific to transition-metal complexes but also applies to organic molecules.

Beating the amorphous limit in thermal conductivity by superlattices design.

The value measured in the amorphous structure with the same chemical composition is often considered as a lower bound for the thermal conductivity of any material: the heat carriers are strongly scattered by disorder, and their lifetimes reach the minimum time scale of thermal vibrations. An appropriate design at the nano-scale, however, may allow one to reduce the thermal conductivity even below the amorphous limit. In the present contribution, using molecular-dynamics simulation and the Green-Kubo formulation, we study systematically the thermal conductivity of layered phononic materials (superlattices), by tuning different parameters that can characterize such structures. We have discovered that the key to reach a lower-than-amorphous thermal conductivity is to block almost completely the propagation of the heat carriers, the superlattice phonons. We demonstrate that a large mass difference in the two intercalated layers, or weakened interactions across the interface between layers result in materials with very low thermal conductivity, below the values of the corresponding amorphous counterparts.

Ultrafast photophysics of transition metal complexes.

The properties of transition metal complexes are interesting not only for their potential applications in solar energy conversion, OLEDs, molecular electronics, biology, photochemistry, etc. but also for their fascinating photophysical properties that call for a rethinking of fundamental concepts. With the advent of ultrafast spectroscopy over 25 years ago and, more particularly, with improvements in the past 10-15 years, a new area of study was opened that has led to insightful observations of the intramolecular relaxation processes such as internal conversion (IC), intersystem crossing (ISC), and intramolecular vibrational redistribution (IVR). Indeed, ultrafast optical spectroscopic tools, such as fluorescence up-conversion, show that in many cases, intramolecular relaxation processes can be extremely fast and even shorter than time scales of vibrations. In addition, more and more examples are appearing showing that ultrafast ISC rates do not scale with the magnitude of the metal spin-orbit coupling constant, that is, that there is no heavy-atom effect on ultrafast time scales. It appears that the structural dynamics of the system and the density of states play a crucial role therein. While optical spectroscopy delivers an insightful picture of electronic relaxation processes involving valence orbitals, the photophysics of metal complexes involves excitations that may be centered on the metal (called metal-centered or MC) or the ligand (called ligand-centered or LC) or involve a transition from one to the other or vice versa (called MLCT or LMCT). These excitations call for an element-specific probe of the photophysics, which is achieved by X-ray absorption spectroscopy. In this case, transitions from core orbitals to valence orbitals or higher allow probing the electronic structure changes induced by the optical excitation of the valence orbitals, while also delivering information about the geometrical rearrangement of the neighbor atoms around the atom of interest. With the emergence of new instruments such as X-ray free electron lasers (XFELs), it is now possible to perform ultrafast laser pump/X-ray emission probe experiments. In this case, one probes the density of occupied states. These core-level spectroscopies and other emerging ones, such as photoelectron spectroscopy of solutions, are delivering a hitherto unseen degree of detail into the photophysics of metal-based molecular complexes. In this Account, we will give examples of applications of the various methods listed above to address specific photophysical processes.

Vibrational relaxation and energy migration of N-methylacetamide in water: the role of nonbonded interactions.

Nonequilibrium molecular dynamics (MD) simulations together with physics-based force fields are used to follow energy flow between vibrationally excited N-methylacetamide (NMA) and water. The simulations are carried out with a previously validated force field for NMA, based on a multipolar representation of the electrostatics, and with a new fluctuating point charge model. For the water solvent, a flexible and a rigid model was employed to distinguish between the role of inter- and intramolecular degrees of freedom. On a 10 ps time scale about 90% of the available energy goes into the solvent. The remaining energy resides within internal NMA-degrees of freedom from where energy flow takes place on longer time scales. The total amount of energy transferred to the solvent on the 10 ps time scale does not depend on whether the water molecules are rigid or flexible during the simulations. Vibrational energy relaxation time scales include two regimes: one on the several 100 fs time scale and a longer one, ranging from 6 to 10 ps. This longer time scale agrees with previous simulations but overestimates the experimentally determined relaxation time by a factor of 2, which can be explained by the classical treatment of the vibrations. Including a previously determined quantum correction factor brings the long time scale into quite favorable agreement with experiment. Coupling to the bending vibration of the water molecules in H-bonding contact with the excited C═O chromophore is substantial. The equilibrium and nonequilibrium distribution of the bending angles of the water molecules in contact with the local oscillator are non-Gaussian, and one approaches the other on the subpicosecond time scale. Analysis of the water velocity distribution suggests that the C═O vibrational energy relaxes into the solvent water shells in an impulsive fashion on a picosecond time scale.

Direct Test of the Equivalency of Dynamic IR and Dynamic Raman Spectroscopies As Techniques for Observing Ultrafast Molecular Dynamics

We report the temperature-dependent infrared (IR) and Raman spectra of Fe(CO)3(η(4)-norbornadiene). This molecule undergoes carbonyl ligand site exchange on the vibrational time scale, and the effect of this exchange is observable as coalescence of the carbonyl bands in both the IR and Raman spectra. We outline a theory that we used to account for these effects and report simulations of the experimental spectra. We used these simulations to extract the carbonyl ligand exchange rates at various temperatures from the IR and Raman data. This data was used to calculate the activation energy for carbonyl exchange, yielding activation energies of 1.2 ± 0.2 and 1.4 ± 0.1 kcal/mol from the IR and Raman data, respectively. These activation energies are statistically identical and are consistent with previously reported values. This constitutes the first direct comparison between dynamic IR and Raman spectroscopies, and we find them to give identical results.

Dynamic criticality at the jamming transition

We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, ϕ = ϕJ). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near ϕJ is divided in three different regimes separated by a characteristic temperature scale T(⋆)(ϕ) that vanishes quadratically with the distance to ϕJ. While two of them, (T < T(⋆)(ϕ), ϕ > ϕJ) and (T < T(⋆)(ϕ), ϕ < ϕJ), are described by harmonic theories developed in the zero temperature limit, the third one for T > T(⋆)(ϕ) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T(⋆)(ϕ) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specifically-dedicated experiments.