Vibrational Relaxation Rate Research Articles

Photo-physical characteristics of color N3-center in diamond studied via UV femtosecond-laser pumped luminescence.

Micro-joule UV-range (350-415 nm) femtosecond-laser pulses generated via frequency-doubled parametric conversion of 525-nm 150-fs pulses of Yb-glass laser were used for "hot" photoluminescence excitation in a diamond plate enriched by blue-emitting N3-centers (zero-phonon line, ZPL, at 415 nm). Photoluminescence spectra acquired in the range of 400-500 nm exhibited wavelength-independent well-resolved ZPL and phonon progression bands, where the involved phonons possessed the only energies of 0.09 eV (LA-phonons) and 0.15 eV (softened LO/TO-phonons), potentially, as a result of a Clemens decay mechanism. Photoluminescence yield in the ZPL and other phonon bands exhibited the power slope of 1.8 at lower energies and ≈1 at higher energies. The transition zone at fluence ∼1014-15 photons/cm2 was related to the saturation of the pumped resonance transition and the slower non-radiative vibrational relaxation to the ZPL-related excited electronic state and the nanosecond spontaneous photoluminescence transition to the ground state. As a result, the absorption cross section σ(370-390 nm) ≈1·10-15 cm2 and concentration [N3] ≈6·1014 cm-3 were determined along with the ZPL absorption cross section σ(415 nm) ≈2.5·10-15 cm2, and the non-radiative vibrational relaxation rate was estimated, providing altogether the crucial information on lasing possibilities in N3-doped diamonds.

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.

Anti-Kasha emissions of single molecules in a plasmonic nanocavity.

Kasha's rule generally holds true for solid-state molecular systems, where the rates of internal conversion and vibrational relaxation are sufficiently higher than the luminescence rate. In contrast, in systems where plasmons and matter interact strongly, the luminescence rate is significantly enhanced, leading to the emergence of luminescence that does not obey Kasha's rule. In this work, we investigate the anti-Kasha emissions of single molecules, free-base and magnesium naphthalocyanine (H2Nc and MgNc), in a plasmonic nanocavity formed between the tip of a scanning tunneling microscope (STM) and metal substrate. A narrow-line tunable laser was employed to precisely reveal the excited-state levels of a single molecule located under the tip and to selectively excite it into a specific excited state, followed by obtaining a STM-photoluminescence (STM-PL) spectrum to reveal the energy relaxation from the state. The excitation to higher-lying states of H2Nc caused various changes in the emission spectrum, such as broadening and the appearance of new peaks, implying the breakdown of Kasha's rule. These observations indicate emissions from the vibrationally excited states in the first singlet excited state (S1) and second singlet excited state (S2), as well as internal conversion from S2 to S1. Moreover, we obtained direct evidence of electronic and vibronic transitions from the vibrationally excited states, from the STM-PL measurements of MgNc. The results obtained herein shed light on the energy dynamics of molecular systems under a plasmonic field and highlight the possibility of obtaining various energy-converting functions using anti-Kasha processes.

Time-resolved CO2, CO, and N2 vibrational population measurements in Ns pulse discharge plasmas

Time-resolved CO2 and N2 vibrational populations and translational-rotational temperature are measured in a CO2–N2 plasma sustained by a ns pulse discharge burst in plane-to-plane geometry. Time-resolved, absolute number density of CO generated in the plasma is also inferred from the experimental data. CO2 and CO vibrational populations are measured by mid-IR, tunable quantum cascade laser absorption spectroscopy, and N2 vibrational populations are measured by the ns broadband vibrational CARS. Transient excitation of N2 and CO2 asymmetric stretch vibrational energy modes is detected during the discharge burst. The time-resolved rate of CO generation does not correlate with N2 or CO2(ν 3) vibrational temperatures, indicating that CO2 dissociation via the vibrational excitation is insignificant at the present conditions. The rate of CO generation decreases gradually during the discharge burst. The estimated specific energy cost of the CO product is close to that of N atoms in pure nitrogen, measured previously at similar operating conditions. Comparison of the experimental data with the kinetic modeling analysis indicates that CO2 dissociation in collisions with electronically excited N2 molecules is the dominant channel of CO generation at the present conditions, although the inferred CO yield in these processes is significantly lower than 1. The effect of vibrational energy transfer between N2 and CO2 on the plasma chemical processes is insignificant. The kinetic model underpredicts a rapid reduction of the N2 and CO2(ν 3) vibrational temperatures during the later half of the discharge burst and in the afterglow. V–T relaxation of N2 by N and O atoms generated in the ns pulse discharge plasma does not affect the vibrational relaxation rate in a significant way. However, rapid V–T relaxation of CO2 by O atoms has a significant effect on the relaxation rate. The difference between the experimental data and the modeling predictions may be due to the unknown scaling of the CO2–O V–T rates with the vibrational quantum number.

Vibrational deactivation in O(3P) + N2 collisions: from an old problem towards its solution

In a recent communication [2021 Phys. Chem. Chem. Phys. 23 15475–79] we showed that the correct modelling of vibrational quenching events in O + N2(v) collisions, a fundamental process in air plasmas, requires the detailed representation of intermediate and asymptotic regions of the interaction and the inclusion of several types of processes as vibration to translation (V–T) and vibro-electronic (V–E) energy transfer. For the first time from the publication of experimental results in the 70’s, we obtained theoretical results in agreement with experiments, even at room temperature. In the present work we extend the approach to better describe non-adiabatic V–E deactivation and include the evaluation of the role of the higher excited singlet N2O surface, characterized by new high quality ab initio calculations, to that of the triplet Π and Σ ones. Within this framework, we calculate V–T, V–E and the corresponding total vibrational relaxation rate coefficients for initial vibrational N2(v) quantum numbers up to v = 10 in a wide temperature range (200–10 000 K). These data are of uttermost importance for the modelling of air plasmas, of earth’s and planetary atmospheres and for the design and construction of aircrafts and air-breathing propulsion systems for very low earth orbit (VLEO) satellites.

Semi-empirical quantum optics for mid-infrared molecular nanophotonics.

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geometries have emerged as new platforms for implementing cavity quantum electrodynamics at room temperature. The use of IR nanoantennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer spatial and femtosecond temporal resolution. In order to advance the development of molecule-based quantum nanophotonics in the mid-IR, we propose a generally applicable semi-empirical methodology based on quantum optics to describe light-matter interaction in systems driven by mid-IR femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures. It also provides physical insights on the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the experimental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime to implement intensity-dependent phase shifts of the coupled system response with strong pulses and develop a vibrational chirping model to understand the effect. The semi-empirical quantum theory is equivalent to first-principles techniques based on Maxwell's equations, but its lower computational cost suggests its use as a rapid design tool for the development of strongly coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing.

Modeling vibrational relaxation rate using machine learning methods

The aim of the present study is to develop an efficient algorithm for simulating nonequilibrium gas-dynamic problems using the detailed state-to-state approach for vibrationalchemical kinetics. Optimization of the vibrational relaxation rate computation using machine learning algorithms is discussed. Since traditional calculation methods require a large number of operations, time and memory, it is proposed to predict the relaxation rates instead of explicit calculations. K-nearest neighbour and histogram based gradient boosting algorithms are applied. The algorithms were trained on datasets obtained using two classical models for the rate coefficients: the forced harmonic oscillator model and that of Schwartz-Slawsky-Herzfeld. Trained algorithms were used to solve the problem of spatially homogeneous relaxation of the O2-O mixture. Comparison of accuracy and calculation time by different methods is carried out. It is shown that the proposed algorithms allow one to predict the relaxation rates with good accuracy and to solve approximately the set of governing equations for the fluid-dynamic variables. Thus, we can recommend the use of machine learning methods in nonequilibrium gas dynamics coupled with detailed vibrational-chemical kinetics. The ways of further optimization of the considered methods are discussed.

Neural network approach in modelling vibrational kinetics of carbon dioxide

The study is devoted to modeling nonequilibrium vibrational kinetics of carbon dioxide taking into account complex mechanisms of relaxation and intermode energy exchanges. The possibilities of using machine learning methods to improve the performance of numerical simulation of non-equilibrium carbon dioxide flows are studied. Various strategies for increasing the efficiency of the hybrid four-temperature model of CO2 kinetics are considered. The neural network approach proposed by the authors to calculate the rate of vibrational relaxation in each mode turned out to be the most promising. For the problem of spatially homogeneous relaxation, estimates of the error and computational costs of the developed algorithm are carried out, and its high accuracy and efficiency are demonstrated. For the first time, the carbon dioxide flow behind a plane shock wave was simulated in a full state-to-state approximation. A comparison with the results obtained in the framework of the hybrid four-temperature approach is carried out, and the equivalence of the approaches is shown. This makes it possible to recommend developed multitemperature approxima tions as the main tool for solving problems of nonequilibrium kinetics and gas dynamics. The hybrid four-temperature approach using the neural network method for calculating relaxation terms showed the acceleration of numerical simulation in time by more than an order of magnitude, while maintaining accuracy. This technique can be recommended for solving complex multidimensional problems of nonequilibrium gas dynamics, including state-to-state chemical reactions.

Pressure Effects on the Relaxation of an Excited Ethane Molecule in High-Pressure Bath Gases.

We use molecular dynamics to calculate the rotational and vibrational energy relaxation of C2H6 in Ar, Kr, and Xe bath gases over a pressure range of 10-400 atm and at temperatures of 300 and 800 K. The C2H6 is instantaneously excited by 80 kcal/mol randomly distributed into both vibrational and rotational modes. The computed relaxation rates show little sensitivity to the identity of the noble gas in the bath. Vibrational relaxation rates show a nonlinear pressure dependence at 300 K. At 800 K the reduced range of bath gas densities covered by the range of pressures does not yet show any nonlinearity in the pressure dependence. Rotational relaxation is characterized with two relaxation rates. The slower rate is comparable to the vibrational relaxation rate. The faster rate has a linear pressure dependence at 300 K but an irregular, nonlinear pressure dependence at 800 K. To understand this, a model was developed based on approximating the periodic box used in the molecular dynamics simulations by an equal-volume collection of cubes where each cube is sized to allow only single occupancy by the noble gas or the molecule. Combinatorial statistics then leads to a pressure- and temperature-dependent analytic distribution of the bath gas species the molecule encounters in a collision. This distribution, the dissociation energy of molecule/bath gas complexes and bath gas clusters, and the computed energy release per collision combine to show that only at 300 K is the energy release sufficient to dissociate likely complexes and clusters. This suggests that persistent and pressure-dependent clusters and complexes at 800 K may be responsible for the nonlinear pressure dependence of rotational relaxation.

An Experimental Study of Thermochemical Nonequilibrium

An experimental study of flows subjected to expanding conditions relevant to Mars entry is presented. A condition with a nominal velocity of was generated in the X2 expansion tunnel. Midwavelength infrared emission measurements of the 4.3 and bands were made over both a two-dimensional wedge model and for the freestream. Consistent results in the characterization of the freestream were obtained from pressure and spectroscopic measurements. The rotational and vibrational temperatures estimated in the wedge flow using the band were consistent with those estimated from the band. The difference between the translational–rotational temperature and the vibrational temperature was shown to be small in the freestream and expanding flow over the wedge model: less than 10%. Using vibrational relaxation rates tuned for postshock conditions, computational fluid dynamics simulations significantly overestimated the thermal nonequilibrium in the expanding flow, but not in the postshock (compressive) flow. This observation is consistent with past results for and CO, as well as at lower temperatures.

Computational study on the reaction collisions for the state-to-state process of N(4 S)+NO(2Π)→O(3 P)+N2(X 1Σ+ g)

Quasi-classical trajectory method has been employed in the theoretical calculations for the state-to-state processes of the reaction N(4 S)+NO(2Π)→O(3 P)+N2(X 1Σ+ g) over a temperature range of 300 K ≤ T ≤ 10,000 K on Global triplet potential energy surface (PES) for N2O system. The thermal rates calculated for the N + NO→O + N2 reaction show a great agreement with the previous theoretical and experimental results. The results obtained herein fill the gaps in the existing data for the state-to-state processes in the N2O system and could be applied to large temperature ranges relevant to the model of hypersonic gas flows. In addition, the vibrational relaxation rate coefficients of the non-reactive collision between N atom and NO molecule in the low vibrational excited state were calculated and reported.

Generalised Landau–Teller fitting of the vibrational relaxation rates in atom–diatom collisions: O2–Ar system as a case study

The common trajectory effective mass (CTEM) approach is applied to the calculation of the temperature dependence of the vibrational relaxation rate coefficient k 10 in collisions of a diatomic molecule with chemically inert atom on an anisotropic PES. As a case study, we consider the O2–Ar system for which experimental data across the wide temperature range and ab initio results for the PES are available. It is shown that temperature dependence of the vibrational relaxation rate coefficient k 10 is described by the CTEM approach with non-empirical value of the effective Landau–Teller characteristic temperature that indicates the contribution of O2 rotation in inducing vibrational transition.

Complex Formation and Dissociation Dynamics on Amorphous Silica Surfaces.

Benzene complex formation and dissociation dynamics with silanols on the amorphous silica surfaces of nanoporous SiO2, from a benzene/carbon tetrachloride solution, were measured by the growth of off-diagonal peaks in the two-dimensional infrared (2D IR) chemical exchange spectrum of the isolated Si-OD stretch. The presence of two types of isolated silanols, termed type I and II, was revealed, with dissociation time constants of 82 and 4.0 ps, respectively. The type I silanols are associated with the main IR absorption feature in the Si-OD stretching region, while the type II silanols give rise to a broader shoulder to lower frequency. Polarization selective pump-probe (PSPP) measurements provided the vibrational lifetimes and orientational relaxation rates of the two silanols in the CCl4 (free) and benzene (complex) environments. The type II silanols constitute roughly 30% of the isolated silanol population and exhibit a substantially faster rate of vibrational relaxation, making the type I dynamics the dominant contribution to the PSPP and 2D IR signals. From the measured dissociation times, the enthalpies of formation for the two surface complexes were obtained, with the formation of the type I complex being significantly more exothermic. As the type II site is preferentially removed from the amorphous silica surface with increasing activation temperature, the results provide a reasonable explanation for the increased exothermicity of benzene adsorption on silica with increasing activation temperature in previous calorimetry experiments.

An ultrafast vibrational study of dynamical heterogeneity in the protic ionic liquid ethyl-ammonium nitrate. I. Room temperature dynamics.

Using ultrafast two-dimensional infrared spectroscopy (2D-IR), a vibrational probe (thiocyanate, SCN-) was used to investigate the hydrogen bonding network of the protic ionic liquid ethyl-ammonium nitrate (EAN) in comparison to H2O. The 2D-IR experiments were performed in both parallel (⟨ZZZZ⟩) and perpendicular (⟨ZZXX⟩) polarizations at room temperature. In EAN, the non-Gaussian lineshape in the FTIR spectrum of SCN- suggests two sub-ensembles. Vibrational relaxation rates extracted from the 2D-IR spectra provide evidence of the dynamical differences between the two sub-ensembles. We support the interpretation of two sub-ensembles with response function simulations of two overlapping bands with different vibrational relaxation rates and, otherwise, similar dynamics. The measured rates for spectral diffusion depend on polarization, indicating reorientation-induced spectral diffusion (RISD). A model of restricted molecular rotation (wobbling in a cone) fully describes the observed spectral diffusion in EAN. In H2O, both RISD and structural spectral diffusion contribute with similar timescales. This complete characterization of the dynamics at room temperature provides the basis for the temperature-dependent measurements in Paper II of this series.

An exact solution in the theory of fluorescence resonance energy transfer with vibrational relaxation

The elegant expression of Förster that predicts the well-known 1/R6 distance (R) dependence of the rate of energy transfer, although widely used, was derived using several approximations. Notable among them is the neglect of the vibrational relaxation in the reactant (donor) and product (acceptor) manifolds. Vibrational relaxation can play an important role when the energy transfer rate is faster than the vibrational relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibrational states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we develop a Green's function-based generalized formalism and obtain an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibrational relaxation. We find that the application of the well-known Förster's expression might lead to overestimation of R.

Quantum dynamics of the energy transfer for vibrationally excited HF (v = 7) colliding with D2 (v = 0): Theory assessing experiment.

It is still challenging to accurately qualify the rate coefficients for vibrationally excited molecules in experiment. In particular, for the energy transfer between HF (v = 7) and D2 (v = 0), which is a prototype for near resonant collisional transfer of vibrational excitation from one molecule to the other, the two available experimental results of rate coefficients contradict each other by a factor of nearly 20. In order to benchmark these data, in this work, the rate coefficients of vibration-vibration energy transfer processes of this system at temperatures ranging from 100 to 1500 K were calculated by employing the coupled-states approximation based on our recently developed full-dimensional ab initio intermolecular potential energy surface. The state-to-state rate coefficients were found to follow the general energy gap law. The calculated total vibration-vibration energy transfer rate coefficients decrease with the increase in the angular momentum of HF at most temperatures. The vibrational relaxation rate coefficient decreases monotonously with the temperature, and the calculated result of 8.1 × 10-11 cm3 mol-1 s-1 at room temperature is in very good agreement with the experimental value reported by Dzelzkalns and Kaufman [J. Chem. Phys. 77, 3508 (1982)].

The C(3P) + O2(3Σg-) → CO2 ↔ CO(1Σ+) + O(1D)/O(3P) reaction: thermal and vibrational relaxation rates from 15 K to 20 000 K.

Thermal rates for the C(3P) + O2(3Σg−) ↔ CO(1Σ+)+ O(1D)/O(3P) reaction are investigated over a wide temperature range based on quasi classical trajectory (QCT) simulations on 3-dimensional, reactive potential energy surfaces (PESs) for the 1A′, (2)1A′, 1A′′, 3A′ and 3A′′ states. These five states are the energetically low-lying states of CO2 and their PESs are computed at the MRCISD+Q/aug-cc-pVTZ level of theory using a state-average CASSCF reference wave function. Analysis of the different electronic states for the CO2 → CO + O dissociation channel rationalizes the topography of this region of the PESs. The forward rates from QCT simulations match measurements between 15 K and 295 K whereas the equilibrium constant determined from the forward and reverse rates is consistent with that derived from statistical mechanics at high temperature. Vibrational relaxation, O + CO(ν = 1,2) → O + CO(ν = 0), is found to involve both, non-reactive and reactive processes. The contact time required for vibrational relaxation to take place is τ ≥ 150 fs for non-reacting and τ ≥ 330 fs for reacting (oxygen atom exchange) trajectories and the two processes are shown to probe different parts of the global potential energy surface. In agreement with experiments, low collision energy reactions for the C(3P) + O2(3Σg−, ν = 0) → CO(1Σ+) + O(1D) lead to CO(1Σ+, ν′ = 17) with an onset at Ec ∼ 0.15 eV, dominated by the 1A′ surface with contributions from the 3A′ surface. Finally, the barrier for the COA(1Σ+) + OB(3P) → COB(1Σ+) + OA(3P) atom exchange reaction on the 3A′ PES yields a barrier of ∼7 kcal mol−1 (0.300 eV), consistent with an experimentally reported value of 6.9 kcal mol−1 (0.299 eV).

Floquet engineering of molecular dynamics via infrared coupling.

We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infrared-active vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equation approach, we derive correlation functions and stationary quantities showing strongly modified optical response of the infrared-dressed molecule. The coherent excitation of molecular vibrational modes in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced vibronic coherence and control over vibrational sideband amplitudes. The additional coupling to an infrared cavity allows for the controlled suppression of undesired sidebands, an effect stemming from the Purcell enhancement of vibrational relaxation rates.

Quartz-enhanced photoacoustic spectroscopy exploiting low-frequency tuning forks as a tool to measure the vibrational relaxation rate in gas species

We demonstrated that quartz-enhanced photoacoustic spectroscopy (QEPAS) is an efficient tool to measure the vibrational relaxation rate of gas species, employing quartz tuning forks (QTFs) as sound detectors. Based on the dependence of the QTF resonance frequency on the resonator geometry, a wide range of acoustic frequencies with narrow detection bandwidth was probed. By measuring the QEPAS signal of the target analyte as well as the resonance properties of different QTFs as a function of the gas pressure, the relaxation time can be retrieved. This approach has been tested in the near infrared range by measuring the CH4 (nν4) vibrational relaxation rate in a mixture of 1% CH4, 0.15 % H2O in N2, and the H2O (ν1) relaxation rate in a mixture of 0.5 % H2O in N2. Relaxation times of 3.2 ms Torr and 0.25 ms Torr were estimated for CH4 and H2O, respectively, in excellent agreement with values reported in literature.

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.