Energy Transfer Rate Coefficients Research Articles

Inelastic N_2+H_2 collisions and quantum-classical rate coefficients: large datasets and machine learning predictions

Rate coefficients for vibrational energy transfer are calculated for collisions between molecular nitrogen and hydrogen in a wide range of temperature and of initial vibrational states (vle 40 for N_2 and wle 10 for H_2). These data are needed for the modelling of discharges in N_2/H_2 plasma or of atmospheric and interstellar medium chemistry in different temperature ranges. The calculations were performed by a mixed quantum-classical method, to recover quantum effects associated with the vibrational motion, on a refined potential energy surface. The obtained rates present striking discrepancies with those evaluated by first-order perturbation theories, like the SSH (Schwartz, Slavsky, Herzfeld) theory, which are often adopted in kinetic modelling. In addition, we present a detailed, though preliminary, analysis on the performance of different Machine Learning models based on the Gaussian Process or Neural Network techniques to produce complete datasets of inelastic scattering rate coefficients. Eventually, by using the selected models, we give the complete dataset (i.e., covering the whole vibrational ladder) of rate coefficients for the textrm{N}_2(v)+textrm{H}_2(0) longrightarrow textrm{N}_2(v-Delta v)+textrm{H}_2(0), Delta v=1,2,3 processes.Graphical abstract

Absolute measurements of state-to-state rotational energy transfer between CO and H2 at interstellar temperatures

The authors measure experimentally and calculate the state-to-state rate coefficients for rotational energy transfer of CO in collision with H${}_{2}$ at the interstellar temperatures in the range of 5--20 K. Good agreements were found between the experiments performed in cold supersonic flows and close-coupling quantum scattering calculations for collisions between the two most abundant molecules in the interstellar medium.

Vibrational Energy Transfer in CO+N2 Collisions: A Database for V-V and V-T/R Quantum-Classical Rate Coefficients.

Knowledge of energy exchange rate constants in inelastic collisions is critically required for accurate characterization and simulation of several processes in gaseous environments, including planetary atmospheres, plasma, combustion, etc. Determination of these rate constants requires accurate potential energy surfaces (PESs) that describe in detail the full interaction region space and the use of collision dynamics methods capable of including the most relevant quantum effects. In this work, we produce an extensive collection of vibration-to-vibration (V–V) and vibration-to-translation/rotation (V–T/R) energy transfer rate coefficients for collisions between CO and N molecules using a mixed quantum-classical method and a recently introduced (A. Lombardi, F. Pirani, M. Bartolomei, C. Coletti, and A. Laganà, Frontiers in chemistry, 7, 309 (2019)) analytical PES, critically revised to improve its performance against ab initio and experimental data of different sources. The present database gives a good agreement with available experimental values of V–V rate coefficients and covers an unprecedented number of transitions and a wide range of temperatures. Furthermore, this is the first database of V–T/R rate coefficients for the title collisions. These processes are shown to often be the most probable ones at high temperatures and/or for highly excited molecules, such conditions being relevant in the modeling of hypersonic flows, plasma, and aerospace applications.

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)].

Energy exchange rate coefficients from vibrational inelastic O2(Σg-3) + O2(Σg-3) collisions on a new spin-averaged potential energy surface.

A new spin-averaged potential energy surface (PES) for non-reactive O2(Σg-3) + O2(Σg-3) collisions is presented. The potential is formulated analytically according to the nature of the principal interaction components, with the main van der Waals contribution described through the improved Lennard-Jones model. All the parameters involved in the formulation, having a physical meaning, have been modulated in restricted variation ranges, exploiting a combined analysis of experimental and ab initio reference data. The new PES is shown to be able to reproduce a wealth of different physical properties, ranging from the second virial coefficients to transport properties (shear viscosity and thermal conductivity) and rate coefficients for inelastic scattering collisions. Rate coefficients for the vibrational inelastic processes of O2, including both vibration-to-vibration (V-V) and vibration-to-translation/rotation (V-T/R) energy exchanges, were then calculated on this PES using a mixed quantum-classical method. The effective formulation of the potential and its combination with an efficient, yet accurate, nuclear dynamics treatment allowed for the determination of a large database of V-V and V-T/R energy transfer rate coefficients in a wide temperature range.

Rotational Energy Transfer in Highly Excited States of Lithium Dimer: Experiment and Modeling.

We report level-resolved rate coefficients for collision-induced rotational energy transfer in the 7Li2*-Ne system, with 7Li2* in the highly electronically excited E(3)1Σg+(vi = 4, ji = 31) and F(4)1Σg+(vi = 10, ji = 31) states. The distributions of rate coefficients are strikingly different from those previously measured for the A(1)1Σu+(vi = 2-24, ji = 30) state of the same molecule, falling off much more rapidly with increasing rotational quantum number change |Δj|. The reason for the difference was explored by means of an inverse Monte Carlo approach employing classical trajectories and a model potential, which was adjusted to give agreement with experiment. The modeling strongly suggests that the E and F state interaction potentials are much more nearly isotropic than that of the A state. The resulting dramatic reduction in rate coefficient, especially for large |Δj|, may be relevant in the relaxation of gases at high temperatures.

Vibrational relaxation of S2(a1Δg) by collisions with SF6 and CF4

Irradiation of the pulsed laser light at 248nm to the gaseous mixture of OCS and He generated vibrationally excited S2(a1Δg,v=2-4) by the S(1D)+OCS reaction. A single vibrational level of S2(a1Δg) was detected with laser-induced fluorescence (LIF) via the f1Δu-a1Δg transition. The rate coefficients for energy transfer from vibrational levels v=2 and 3 of S2(a1Δg) to SF6 and CF4 have been determined from the time-resolved LIF intensities recorded at varying pressures of SF6 and CF4. The reduced probability of energy transfer per collision derived from the rate coefficients enabled us to identify the ν4 mode of SF6 and CF4 as the energy-accepting vibration.

On the Relation between Population Kinetics and State-to-State Rate Coefficients for Vibrational Energy Transfer

Abstract The relation between time-dependent population of vibrational state and collision-induced state-to-state rate coefficients is discussed within the Landau–Teller kinetic equations for the relaxation of harmonic oscillators in a heat bath. In particular, the increase of the populations in the first and the second vibrational state of an initially cold oscillator shows a considerable variety of its relation to a single Landau–Teller state-to-state rate coefficient. It is suggested that this variety should be kept in mind when experimental studies of the relaxation of specific level are analyzed.

The effect of the intermolecular potential formulation on the state‐selected energy exchange rate coefficients in N2–N2 collisions

The rate coefficients for N2-N2 collision-induced vibrational energy exchange (important for the enhancement of several modern innovative technologies) have been computed over a wide range of temperature. Potential energy surfaces based on different formulations of the intramolecular and intermolecular components of the interaction have been used to compute quasiclassically and semiclassically some vibrational to vibrational energy transfer rate coefficients. Related outcomes have been rationalized in terms of state-to-state probabilities and cross sections for quasi-resonant transitions and deexcitations from the first excited vibrational level (for which experimental information are available). On this ground, it has been possible to spot critical differences on the vibrational energy exchange mechanisms supported by the different surfaces (mainly by their intermolecular components) in the low collision energy regime, though still effective for temperatures as high as 10,000 K. It was found, in particular, that the most recently proposed intermolecular potential becomes the most effective in promoting vibrational energy exchange near threshold temperatures and has a behavior opposite to the previously proposed one when varying the coupling of vibration with the other degrees of freedom.

Vibrational relaxation and vibration-rotation energy transfer between highly vibrationally excited KH(X1Σ+, v=14–21) and CO2

The vibrational levels of KH(X1Σ+, v″=0–3) were generated in the reaction of K (5P) and H2. Vibrational state total relaxation rate coefficientskv″(CO2) for KH (v″=14–21) are measured in an overtone pump-probe configuration. The rate coefficient kv″(CO2) is strongly dependent on vibrational quantum number. Scattered CO2 (0000, 32≤J≤48) molecules were excited to CO2 (1005, J+1) states. The rotational temperatures of CO2 (0000, J=32–48) states populated by collisions with highly vibrationally excited KH (v″=14–21) are obtained. The average rotational energy of the scattered CO2 molecules is increased by a factor of 2.33 when KH level v″=14 increases to v″=21. The average translational energy of the scattered CO2 molecules is increased roughly linearly as a function of CO2J state. Under single collision conditions, state-specific energy transfer rate coefficients for collisions of highly excited KH with CO2 are obtained. For v″=19, the integrated rate coefficients kint increases by a factor of 4.5 to v″=14.

Electron Energy Transfer Rate Coefficients of Carbon Dioxide

An extensive set of integral cross sections (ICSs) for electron impact vibrational excitation of the CO(2) molecule has been used to calculate electron energy transfer rate coefficients. The ICSs for electron impact symmetric stretch vibrational excitation are measured by using a high resolution double trochoidal electron spectrometer, while ICSs for the bending and asymmetric vibrations have been adopted from previous publications. Calculations of the energy transfer rate coefficients are performed for the equilibrium conditions in the mean electron energy range from 0 to 11 eV. By use of extended Monte Carlo simulations, electron energy distribution functions (EEDFs) and electron energy transfer rate coefficients are determined in the nonequilibrium conditions, for low and moderate values of the electric field over gas number density ratios, E/N, up to 150 Td. Contributions of higher vibrational levels are emphasized. The results are compared with the data available in the literature.

Rate coefficients for reaction and for rotational energy transfer in collisions between CN in selected rotational levels (XΣ+2, v=2, N=, 1, 6, 10, 15, and 20) and C2H2

Rate coefficients (ktot,Ni) are reported (a) for total removal (reactive+inelastic) of CN(X2Sigma+,v=2,Ni) radicals from selected rotational levels (Ni=0, 1, 6, 10, 15, and 20) and (b) for state-to-state rotational energy transfer (ki-->f) between levels Ni and other rotational levels Nf in collisions with C2H2. CN radicals were generated by pulsed laser photolysis of NCNO at 573 nm. A fraction of the radicals was then promoted to a selected rotational level in v=2 using a tunable infrared "pump" laser operating at approximately 2.45 microm, and the subsequent fate of this subset of radicals was monitored using pulsed laser-induced fluorescence (PLIF). Values of ktot,Ni were determined by observing the decay of the PLIF signals as the delay between pump and probe laser pulses was systematically varied. In a second series of experiments, double resonance spectra were recorded at a short delay between the pump and probe laser pulses. Analysis of these spectra yielded state-to-state rate coefficients for rotational energy transfer, ki-->f. The difference between the sum of these rate coefficients, Sigmafki-->f, and the value of ktot,Ni for the same level Ni is attributed to the occurrence of chemical reaction, yielding values of the rotationally selected rate coefficients (kreac,Ni) for reaction of CN from specified rotational levels. These rate coefficients decrease from (7.9+/-2.2)x10(-10) cm3molecule-1 s-1 for Ni=0 to (0.8+/-1.3)x10(-10) cm3 molecule-1 s-1 for Ni=20. The results are briefly discussed in the context of microcanonical transition state theory and the statistical adiabatic channel model.

Rotational energy transfer in NO (A 2Sigma+,v'=0) by N2 and O2 at room temperature.

State-to-state rotational energy transfer (RET) rate coefficients for NO (A 2Sigma+, v'=0, J=5.5, 11.5, 17.5) were measured for N2 and O2 at room temperature using a pump-probe method. The NO A 2Sigma+ state is prepared by 226 nm light and the RET is monitored by fluorescence from the D 2Sigma+ v'=0 state, following excitation by a time-delayed laser at approximately 1.1 microm. Additionally, total collisional removal and final state distributions were measured exciting in the Q1+P21 band head, to simulate an NO laser-induced fluorescence atmospheric monitoring scheme. Time-resolved modeling is used to understand relaxation mechanisms and predict relaxation times in ambient air. H2O at atmospherically relevant concentrations does not affect the degree of RET in ambient air.

Determination of nitrogen V–V transfer rates by stimulated Raman pumping

Abstract Stimulated Raman scattering is used to vibrationally excite pure N2 in the pressure range 300–760 Torr at room temperature. The subsequent temporal evolution of the populations of vibrational levels as high as v=6 is probed by spontaneous Raman scattering. The experimental results are compared to predictions from a Master Equation kinetics modeling code, incorporating V–V energy transfer rate coefficients derived from several published theoretical models. Predictions using the rate coefficients given by the three-dimensional Forced Harmonic Oscillator Free Rotator (FHO-FR) model are found to give the best overall agreement with the experimental data, although agreement with the three-dimensional models of Billing and Fisher, and Bogdanov et al. is also found to be quite good.

A combined experimental and theoretical study of rotational energy transfer in collisions between NO(X 2Π1/2, v=3,J) and He, Ar and N2 at temperatures down to 7 K

Infrared-ultraviolet double resonance (IRUVDR) experiments have been implemented in the ultra-cold environment provided by a CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) apparatus. With this technique rate coefficients of two kinds have been measured for rotational energy transfer in collisions between NO and He, Ar and N2: (a) rate coefficients for total removal from specific states of NO(X 2Π1/2; v=3; J=0.5, 3.5 or 6.5) and (b) state-to-state rate coefficients for rotational energy transfer from these levels to specific final states. Using different Laval nozzles, results have been obtained at several different temperatures: for He as collision partner, 295, 149, 63, 27, 15 and 7 K; for Ar, 139, 53, 44 and 27 K; and for N2, 86 and 47 K. The thermally averaged cross-sections for total removal show remarkably little variation, either with temperature or with initial rotational state. The variation of state-to-state rate coefficients with ΔJ shows three general features: (i) a decrease with increasing ΔJ; (ii) a propensity to favor even ΔJ transitions over odd ΔJ changes; and (iii) at lower temperatures, decreases in J are increasingly favored over increases in J and the distribution of rate coefficients against ΔJ becomes narrower. The experimental rate coefficients for collisions with He and Ar are compared with those from both close coupled and coupled states calculations based on potential energy surfaces determined within the coupled electron pair approximation (CEPA) with a large atomic orbital basis set. The agreement between theory and experiment of both the total and the state-to-state rate coefficients is excellent over the complete range of temperatures covered in the experiments.

Total and state-to-state rate coefficients for rotational energy transfer in collisions between NO(X 2Π) and He at temperatures down to 15 K

Infrared-ultraviolet double resonance (IRUVDR) experiments have been implemented in the ultra-cold environment provided by a CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) apparatus. This has enabled us to measure rate coefficients for rotational energy transfer in collisions between NO and He of two kinds: those relating to total removal from a specific rovibrational state of NO( X 2Π; Ω = 1 2 ; ν = 3; J = 0.5, 3.5 or 6.5 ) and also state-to-state rate coefficients for transfer from these levels. Using different Laval nozzles, results have been obtained at four different temperatures: 149, 63, 27 and 15 K, and are also reported for 295 K.

Intramolecular energy transfer rates for vinyl bromide and deuterium-substituted vinyl bromides from power spectrum line splittings

Continuous frequency modulated (CFM) line splittings are used to determine the energy transfer rate coefficients for the local C–Br and C=C vibrational modes in vinyl bromide and the C–H stretching modes in doubly deuterium-substituted vinyl bromides. The global potential developed by Abrash et al. is employed in all calculations. Energy transfer rate coefficients are extracted from the fine structure spacing of the numerically computed power spectrum of the bond coordinates. The consistency of the averaged individual rate coefficients is evaluated by comparison with results obtained from local mode energy decay curves. It is found that the total intramolecular vibrational relaxation (IVR) rate coefficients for all modes investigated are large relative to the unimolecular decomposition rate. However, previous studies show that IVR is not globally rapid so statistical behavior of the unimolecular reaction is not expected. It is shown that near overlapping resonances in the power spectrum make it difficult to accurately extract CFM line splittings. This limitation effectively precludes the use of power spectra to investigate IVR rates for some modes. For the specific case of vinyl bromide, it is demonstrated that the C–Br and C=C stretching modes have sufficiently isolated bands that IVR rates out of these modes can be determined from the line splittings. However, the superposition of the three C–H stretching fundamentals makes it essentially impossible to investigate these modes in vinyl bromide. For the case of doubly deuterium-substituted vinyl bromides, the C–H stretching fundamental is well isolated so that IVR relaxation rates can be easily obtained from the power spectrum line splittings. The consistency of the IVR rate coefficients obtained from line splittings is investigated by calculation of these coefficients from the envelopes of bond energy decay curves. The differences between the two results varies from 15% for the C=C stretch to 43% for one of the C–H stretching modes. The average deviation is 30% which is in accord with the accuracy of the method (±25%) previously estimated by Agrawal et al. The effect of initial local excitation energy on the line splittings and associated rate coefficients is investigated for the C–Br stretching mode. The results show that the line splitting and rate coefficients are nearly independent of excitation energy below 0.8 eV. Above this energy, both the line splittings and the IVR rate coefficients increase rapidly. This is interpreted as being due to increased intermode coupling at higher energies produced by the greater vibrational anharmonicity. It is concluded that CFM line splittings can be effectively used as a probe of energy transfer rates in six-atom molecules provided the modes under examination have reasonably isolated bands in the power spectrum.

Spectral line shapes in systems undergoing continuous frequency modulation

The power spectrum line shapes for oscillators undergoing a continuous modulation of the vibrational frequency are investigated. It is shown that the single, sharp line normally characteristic of such systems broadens and exhibits a wealth of fine structure components. The characteristic fine structure pattern is one of decreasing amplitude and spacing. This continuous frequency modulation (CFM) effect has been examined for a series of model oscillators that includes harmonic systems with linear and exponential variation of the frequency without amplitude damping, a harmonic system with exponential damping of both the resonant frequency and the amplitude, and a Morse oscillator whose kinetic energy is being exponentially damped. An analytic expression for the power spectrum of a harmonic oscillator whose frequency is varying linearly with time is derived. This result demonstrates that the position of the fine structure extrema depends linearly upon the initial oscillator frequency and the square root of the absolute value of the modulation rate. The peak-to-peak spacing is shown to be proportional to the square root of the absolute value of the modulation rate. It is suggested that the CFM effect is the fundamental explanation of many previous empirical observations concerning power spectra. The CFM effect for a harmonic system with an exponentially modulated frequency is very similar to that observed for linear modulation. When amplitude depression is included, there is a significant intensity decrease of many of the spectral lines. Investigation of a Morse oscillator shows that energy transfer in an anharmonic system produces a CFM effect. By assuming that the analytic result for a harmonic oscillator with a linear modulation is transferable to the anharmonic case, an expression is obtained that relates the peak-to-peak fine structure spacing to the Morse potential parameters, the initial oscillator energy and the IVR rate coefficient. An experimental example of a CFM effect is presented by taking an NMR spectrum of H2O and HCCl3 in DCCl3 while the main B0 field is varying with time. The CFM effect is used to extract energy transfer rate coefficients for a diatomic molecule isolated in an argon matrix at 12 K and for total IVR rate coefficients for relaxation of the N=O and O–H local modes in cis-HONO. It is also shown that instantaneous energy transfer rates in small molecules can be determined by using local frequency analysis to compute the temporal variation of the CFM band spacings. It is concluded that line shape analysis can be effectively used as a probe of energy transfer rates.

Energy Transfer Rate Coefficients from Trajectory Calculations and Contributions of Supercollisions to Reactive Rate Coefficients

Quasiclassical trajectory calculations on the CS2−CO system were performed. Analytical biexponential functions were fit to the trajectory results, and energy-dependent energy transfer transition probability functions and rate coefficients were derived. They, in turn, were used in solutions of master equations. Unimolecular rate coefficients for cyclobutane fission and cyclobutene isomerization in Ar bath gas at various temperatures were obtained. Supercollisions, collisions which transfer more than 5 times the average energy transferred in a down collision, were found to contribute to the high-energy tail of the biexponential transition probability function. To assess their contribution to the unimolecular rate coefficients, their values which were obtained from trajectory-based double-exponential transition probabilities are compared with those obtained from single-exponential weak-collision transition probabilities. For cyclobutane fission an ∼5-fold increase in the value of the rate coefficient is foun...

Collisional Excitation of H 2 Molecules by H Atoms

view Abstract Citations (25) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Collisional Excitation of H 2 Molecules by H Atoms Lepp, S. ; Buch, V. ; Dalgarno, A. Abstract Semiclassical trajectory calculations of the rate coefficients for rotational and vibrational energy transfer were carried out for collisions of hydrogen atoms with hydrogen molecules at a temperature of 1000 K, using three potential energy surfaces. For one surface the calculations were carried down to 200 K. The rate coefficients for reactive collisions are similar for all three surfaces. For nonreactive collisions, rate coefficients for pure rotational transitions in which j changes from 0 to 2 and from 1 to 3 change significantly from one surface to another but for higher angular momenta transitions the differences tend to disappear. The validity of the semiclassical calculations is assessed. Publication: The Astrophysical Journal Supplement Series Pub Date: May 1995 DOI: 10.1086/192164 Bibcode: 1995ApJS...98..345L Keywords: ISM: MOLECULES; MOLECULAR PROCESSES full text sources ADS |