Vibrational Energy Relaxation Research Articles

Unraveling the excited-state vibrational cooling dynamics of chlorophyll-a using femtosecond broadband fluorescence spectroscopy.

Understanding the dynamics of excited-state vibrational energy relaxation in photosynthetic pigments is crucial for elucidating the mechanisms underlying energy transfer processes in light-harvesting complexes. Utilizing advanced femtosecond broadband transient fluorescence (TF) spectroscopy, we explored the excited-state vibrational dynamics of Chlorophyll-a (Chl-a) both in solution and within the light-harvesting complex II (LHCII). We discovered a vibrational cooling (VC) process occurring over ∼6ps in Chl-a in ethanol solution following Soret band excitation, marked by a notable ultrafast TF blueshift and spectral narrowing. This VC process, crucial for regulating the vibronic lifetimes, was further elucidated through the direct observation of the population dynamics of higher vibrational states within the Qy electronic state. Notably, Chl-a within LHCII demonstrated significantly faster VC dynamics, unfolding within a few hundred femtoseconds and aligning with the ultrafast energy transfer processes observed within the complex. Our findings shed light on the complex interaction between electronic and vibrational states in photosynthetic pigments, underscoring the pivotal role of vibrational dynamics in enabling efficient energy transfer within light-harvesting complexes.

Numerical investigation of thermochemical non-equilibrium effects in Mach 10 scramjet nozzle

Abstract High-temperature non-equilibrium effects are prominent in scramjet nozzle flows at high Mach numbers. Hence, the thermochemical non-equilibrium gas model incorporating the vibrational relaxation process of molecules in the hydrocarbon-air reaction is developed to numerically simulate the flow of a hydrocarbon fuel scramjet nozzle at Mach 10. Besides, the results computed by the models of the thermally perfect gas, chemically non-equilibrium gas, and thermally non-equilibrium chemically frozen gas are applied for comparative studies. Results indicate that chemical non-equilibrium effects are more significant for the flow-field structure and parameters compared to thermal non-equilibrium effects. Meanwhile, vibrational relaxation and chemical reactions interact in the flow-field. The heat released from the chemical reactions in the flow-field of the thermochemical non-equilibrium gas model makes the thermal non-equilibrium effects weaker compared to the thermally non-equilibrium chemically frozen gas model; the chemical reactions in the thermochemical non-equilibrium gas model are more intense than in the chemically non-equilibrium gas model. Due to the slow relaxation of vibrational energy, the thermal non-equilibrium models predicted nozzle thrust lower than the thermal equilibrium models by approximately 1.11% to 1.33%; when considering the chemical reactions, the chemical non-equilibrium models predicted nozzle thrust higher than the chemical frozen models by approximately 7.30% to 7.54%. Hence, the structural design and performance study of the high Mach numbers scramjet nozzle must consider thermochemical non-equilibrium effects.

Can classical mechanics sense conical intersection?

Conical intersection (CI) leads to fast electronic energy transfer. However, Hamm and Stock [Phys. Rev. Lett. 109, 173201 (2012)] showed the existence of a vibrational CI and its role in vibrational energy relaxation. In this paper, we further investigate the vibrational energy relaxation using an isolated model Hamiltonian system of four vibrational modes with two distinctively different timescales (two fast modes and two slow modes). We show that the excitation of the slow modes plays a crucial role in the energy relaxation mechanism. We also analyze the system from a mixed quantum-classical (surface hopping method) and a completely classical point of view. Notably, surface hopping and even classical simulations also capture fast energy relaxation, which is a signature of CI's existence.

On the Statistical Regime, Coherence versus Incoherence and Ergodicity of Quantum Vibrational Trajectories in Soft Condensed Molecular Systems.

A theoretical-computational procedure, recently proposed for modelling Vibrational Energy Relaxation (VER) processes of a molecule (Quantum Center, QC) embedded in a complex atomic-molecular system, is extended and applied for analyzing in detail the features of the QC density matrix (DM) temporal evolution. The results, obtained using aqueous azide ion as a case study, show the total lack of coherence in the DM, when the system is prepared to be initially in a pure vibrational eigenstate. This finding is fully in line with the statistical interpretation of the process typically adopted also in the experimental studies where the relaxation processes are all described within the typical schemes of chemical kinetics. Consistently, when the initial vibrational state corresponds to an eigenstate mixture, although initially coherent, the DM relaxes to a fully incoherent condition with a mean lifetime related to the one of the diagonal elements relaxation. These specific DM features turn out to be essentially governed by the thermal equilibrium condition of the atomic-molecular classical coordinates which drive the ensemble of the quantum-trajectories toward the observed statistical regime. Finally, from the analysis of a single long timescale quantum vibrational trajectory it also clearly emerges its ergodic behaviour.

Excitation energy transfer and vibronic relaxation through light-harvesting dendrimer building blocks: A nonadiabatic perspective.

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like π-conjugated macromolecules) involve a directional cascade of local excitation energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally excited electronic states via conical intersections. The smallest PPE building block that is able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (hence, 2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From linear-response time-dependent density functional theory electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1 + 2)-state-8-dimensional vibronic-coupling Hamiltonian model for running subsequent multiconfiguration time-dependent Hartree wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted herein through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity.

A Linearized Semiclassical Dynamics Study of the Multiquantum Vibrational Relaxation of NO Scattering from a Au(111) Surface.

The vibrational relaxation of NO molecules scattering from a Au(111) surface has served as the focus of efforts to understand nonadiabatic energy transfer at metal-molecule interfaces. Experimental measurements and previous theoretical efforts suggest that multiquantal NO vibrational energy relaxation occurs via electron-hole pair excitations in the metal. Here, using a linearized semiclassical approach, we accurately predict the vibrational relaxation of NO from the νi = 3 state for different incident translational energies. We also accurately capture the central role of transient electron transfer from the metal to the molecule in mediating the vibrational relaxation process but fall short of quantitatively predicting the full extent of multiquantum relaxation for high incident vibrational excitations (νi = 16).

Vibrational Anharmonicity and Energy Relaxation in Nanoscale Acoustic Resonators.

The fundamental and n = 3 overtones of Au nanoplate thickness vibrations have been studied by transient absorption microscopy. The frequencies of the n = 3 overtone are less than 3× the frequency of the fundamental. This anharmonicity is explained through a continuum mechanics model that includes organic layers on top of the nanoplate and between the nanoplate and the glass substrate. In this model, anharmonicity arises from coupling between the vibrations of the nanoplate and the organic layers, which creates avoided crossings that reduce the overtone frequencies compared to the fundamental. Comparison of the experimental and calculated quality factors shows that coupling occurs to the top organic layer. Good agreement between the measured and calculated quality factors is obtained by introducing internal damping for the nanoplate. These results show that engineering layers of soft material around metal nanostructures can be used to control the vibrational lifetimes.

Energy relaxation pathways and their isotope effects of water bending mode in liquid phase: A nonequilibrium ab initio molecular dynamics simulation study

Vibrational energy relaxation pathways and the rates of excited bending mode of water molecules (H2O) in bulk liquid water (H2O), and the rates of the excited bending mode of HOD molecules in D2O (isotopically diluted water) were examined via non-equilibrium ab initio molecular dynamics (NE-AIMD) simulation. The NE-AIMD simulation showed a significantly fast relaxation of the bend vibration, at the timescale of 127 fs in pure water and 144 fs in isotopically diluted water. The main relaxation pathway for pure and isotopically diluted water was found to be driven by intramolecular bend–libration coupling (84% in pure water and 96% in isotopically diluted water). In the case of pure water, intermolecular coupling between bend–bend vibrations was small but non-negligible (11%), whereas such intermolecular coupling was negligible in isotopically diluted water owing to a large frequency mismatch between the excited bend vibration and the surrounding bend vibrations.

Stochastic model of collisional energy transfer based on the diffusion equation

Collisional energy transfer from highly excited polyatomic molecules in a heat reservoir is considered as a diffusion process in energy space. It is taken into account that the density of the vibrational states of polyatomic molecules is very high and presented by a continuous energy function. Both the average energy transfer moments per collision and these moments averaged over an ensemble of molecules have been calculated to obtain an exact analytical solution to the diffusion equation. At long times, the solution to the diffusion equation converges to the equilibrium Boltzmann distribution. The conditional probability density decays at long times with a vibrational energy relaxation time. The ensemble averages tend to equilibrium with the same characteristic time.

Combinational Vibration Modes in H2O/HDO/D2O Mixtures Detected Thanks to the Superior Sensitivity of Femtosecond Stimulated Raman Scattering.

Overtones and combinational modes frequently play essential roles in ultrafast vibrational energy relaxation in liquid water. However, these modes are very weak and often overlap with fundamental modes, particularly in isotopologues mixtures. We measured VV and HV Raman spectra of H2O and D2O mixtures with femtosecond stimulated Raman scattering (FSRS) and compared the results with calculated spectra. Specifically, we observed the mode at around 1850 cm-1 and assigned it to H-O-D bend + rocking libration. Second, we found that the H-O-D bend overtone band and the OD stretch + rocking libration combination band contribute to the band located between 2850 and 3050 cm-1. Furthermore, we assigned the broad band located between 4000 and 4200 cm-1 to be composed of combinational modes of high-frequency OH stretching modes with predominantly twisting and rocking librations. These results should help in a proper interpretation of Raman spectra of aqueous systems as well as in the identification of vibrational relaxation pathways in isotopically diluted water.

High energy vibrational excitations of nitromethane in liquid water.

The pathways and timescales of vibrational energy flow in nitromethane are investigated in both gas and condensed phases using classical molecular mechanics, with a particular focus on relaxation in liquid water. We monitor the flow of excess energy deposited in vibrational modes of nitromethane into the surrounding solvent. A marked energy flux anisotropy is found when nitromethane is immersed in liquid water, with a preferential flow to those water molecules in contact to the nitro group. The factors that permit such anisotropic energy relaxation are discussed, along with the potential implications on the molecule's non-equilibrium dynamics. In addition, the energy flux analysis allows us to identify the solvent motions responsible for the uptake of solute energy, confirming the crucial role of water librations. Finally, we also show that no anisotropic vibrational energy relaxation occurs when nitromethane is surrounded by argon gas.

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.

A phenomenological model for plasma-assisted combustion with NRP discharges in methane-air mixtures: PACMIND

The recent advances in plasma-assisted combustion must now be strengthened through high-fidelity numerical simulations. However, detailed plasma-combustion coupled simulations in complex geometry and turbulent flow involving hundreds of discharges are still unaffordable due to prohibitive computational costs. In this work, a Plasma-Assisted Combustion phenoMenological modelIng for Non-equilibrium Discharges (PACMIND) is proposed. The model aims to avoid computing in detail the plasma phase and consists of incorporating the leading order plasma effects on the reactive compressible Navier–Stokes equations. It consists of two ultra-fast effects with radical productions and gas heating, as well as a slower gas heating due to vibrational energy relaxation. Based on detailed kinetic simulations, the model has been applied to air and methane-air mixtures and contains respectively 5 species, 3 reactions and 12 species, 7 reactions. The model has been validated against experiments in air and detailed plasma-assisted combustion ignition simulations in methane-air at various equivalence ratios and reduced electric fields. Significant improvements regarding ignition delay times have been observed by comparison with an existing model. In addition, the model accounts for NOx production by plasma discharge and covers the full range of conditions encountered in a premixed flame. Hence, it opens the way to the simulation of realistic 3D turbulent configurations with minimal over-costs.

Metal-Induced Fast Vibrational Energy Relaxation: Quantum Nuclear Effects Captured in Diabatic Independent Electron Surface Hopping (IESH-D) Method.

In this paper, we propose a simple approach to include quantum nuclear effects in the weak electronic coupling regime within the independent electron surface hopping (IESH) method for simulating nonadiabatic dynamics near metal surfaces. Our method uses electronic states in a diabatic basis, and electronic transitions between metal and molecular states are included using Landau-Zener theory. We benchmark our novel approach using a two-state model system for which exact results (obtained from Fermi's golden rule) are available. We further investigate the effect of metallic electrons on the rate and the pathway of vibrational energy relaxation.

Peak heat flux prediction of hypersonic flow over compression ramp under vibrationally excited free-stream condition

In hypersonic shock tunnel experiments, the high-temperature reservoir gas expands and accelerates so rapidly that there is not enough time for vibrational energy relaxation. As a result, thermal nonequilibrium gas flow is frequently encountered in the test section, and this significantly affects the measured heat flux. In this paper, hypersonic compression-ramp flows are studied numerically to investigate the effect of incomplete vibrational energy accommodation on the separation flow structure and peak heat flux in the reattachment region under low-to-medium Reynolds number and high Mach number conditions. Numerical results and theoretical analysis suggest that the vibrational energy accommodation has no noticeable impact on the length scale of the separation zone, but strongly influences the peak heat flux of the separated ramp flows. Decomposing the peak heat flux into translational–rotational energy and vibrational energy components, qtr and qv, respectively, we find that qv/qtr characterizes the nonequilibrium degree of the vibrational energy accommodation. A formula for predicting the peak heat flux is then proposed, taking the effect of incomplete vibrational energy accommodation into consideration. Finally, surface heat flux measurements in a hypersonic shock tunnel indicate that a deviation of up to 13% in total peak heat flux could arise if vibrational energy accommodation is not considered under the vibrationally excited free-stream condition.

Rapid vibrational relaxation dynamics and strong Solute-Solvent interactions of the nitrite anion

In this work, we have used steady-state and ultrafast vibrational spectroscopy to measure the absorption band centers and widths, as well as vibrational energy relaxation (VER) lifetimes for the antisymmetric ν3 stretching band of the nitrite (NO2–) anion in H2O, D2O, and DMSO. The nitrite IR absorption bands are very broad and the excited state has an extremely short VER lifetime in all three solvents, suggesting that NO2– interacts quite strongly with all of them. We also measured and analyzed reflection spectra for NaNO2 pressed pellets and determined that the damping is fast in the reststrahlen band.

Ultrafast 2DIR comparison of rotational energy transfer, isolated binary collision breakdown, and near critical fluctuations in Xe and SF6 solutions.

The density dependence of rotational and vibrational energy relaxation (RER and VER) of the N2O ν3 asymmetric stretch in dense gas and supercritical Xe and SF6 solutions for near critical isotherms is measured by ultrafast 2DIR and infrared pump-probe spectroscopy. 2DIR analysis provides precise measurements of RER at all gas and supercritical solvent densities. An isolated binary collision (IBC) model is sufficient to describe RER for solvent densities ≤ ∼4M where rotational equilibrium is re-established in ∼1.5-2.5 collisions. N2O RER is ∼30% more efficient in SF6 than in Xe due to additional relaxation pathways in SF6 and electronic factor differences. 2DIR analysis revealed that N2O RER exhibits a critical slowing effect in SF6 at near critical density (ρ* ∼ 0.8) where the IBC model breaks down. This is attributable to the coupling of critical long-range density fluctuations to the local N2O free rotor environment. No such RER critical slowing is observed in Xe because IBC break down occurs much further from the Xe critical point. Many body interactions effectively shield N2O from these near critical Xe density fluctuations. The N2O ν3 VER density dependence in SF6 is different than that seen for RER, indicating a different coupling to the near critical environment than RER. N2O ν3 VER is only about ∼7 times slower than RER in SF6. In contrast, almost no VER decay is observed in Xe over 200ps. This VER solvent difference is due to a vibrationally resonant energy transfer pathway in SF6 that is not possible for Xe.

Effects of molecular shape and flexibility on fast sound of organic liquids.

Inelastic x-ray scattering spectra of four organic liquids, n-hexane, cyclohexane, ethylene glycol dimethyl ether, and 1,4-dioxane, were measured, and the sound velocity in the nm-1 wavenumber and meV energy regimes was determined. Compared with the corresponding values in the hydrodynamic limit, the sound velocity in the nm-1 regime was faster, and the positive dispersion of the longitudinal modulus was stronger in liquids composed of ring structures (cyclohexane and 1,4-dioxane) than in those of linear chain structures (n-hexane and ethylene glycol dimethyl ether). Molecular dynamics simulation of n-hexane and cyclohexane was also performed. The difference in the positive dispersion of the longitudinal modulus was reproduced by simulation, and it was elucidated by the difference in the longitudinal modulus in the q = 0 limit and the THz frequency regime. The excess part of the longitudinal modulus from the hydrodynamic limit was further divided into various contributions, and the smaller excess modulus of n-hexane was mainly ascribed to two reasons. The first one is that the shear modulus of n-hexane is smaller in the THz regime, and the second one is that the positive dispersion of the bulk modulus due to the vibrational energy relaxation is weaker. The second mechanism was further interpreted in terms of the fast vibrational energy relaxation of intramolecular modes associated with the chain deformation of n-hexane.

Assessment of multi-temperature relaxation models for carbon dioxide vibrational kinetics

Several advanced models for multi-temperature vibrational energy relaxation rates are implemented to study adiabatic bath relaxation in carbon dioxide, among them a hybrid model based on state-to-state relaxation rates, the model based on the rigorous Chapman–Enskog theory, and modifications of the Landau–Teller (LT) models. Different sets of rate coefficients for vibrational energy transitions (Schwartz, Slawsky and Herzfeld (SSH) theory, forced harmonic oscillator (FHO) model) are used as well as various techniques for the relaxation time evaluation. Based on isothermal bath simulations it is found that the FHO model provides good agreement with experimentally measured relaxation times. Assessment of relaxation models shows that the three-temperature model based on the Chapman–Enskog theory yields excellent agreement with the detailed hybrid approach while being more computationally efficient; two-temperature models and modifications of the LT formulas cannot provide reliable description of intermode exchanges in polyatomic gases. The choice of the model for transition probabilities is crucial for identifying key relaxation mechanisms. When the FHO model is applied, strongly coupled relaxation in all CO2 modes is found whereas the model of SSH yields overpredicted relaxation rate in the symmetric-bending mode and almost uncoupled slow relaxation in the asymmetric mode. Possible ways for further model validation under glow discharge conditions are discussed.

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.