Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.     

Vibrational and rotational energy transfer in Ar + HF

State-to-state energy transfer cross sections for Ar + HF (v = 2, 4, and 6; J = 4, 6, 8, and 10) were computed using quasiclassical trajectories. Rotational energy transfer is invariant with increasing v, but vibrational energy transfer is significantly enhanced by increasing J.     

Collinear collisions in a well potential

Collinear collisions on the H₃⁺ potential energy surface for different mass combinations m, M, m are investigated by means of classical trajectory computations. Both, the probability for reaction, P_t, and for complex formation, P_e, depend periodically on the mass parameter (1 + 2m/M)^{$\text{1}\text{2}$}. This can easily be understood in terms of vibrational excitation of the symmetric and asymmetric modes of the reaction complex. If the collinear constraint is lifted, none of these features survive.     

Energy transfer in reactive and nonreactive collisions of Na with Na2

Stimulated by the experimental finding of vibrationally and rotationally cold dimers in supersonic nozzle molecular beams of sodium, we have studied energy transfer in collisions of Na with Na₂ over a wide range of initial relative translation energies E and impact parameters b by a classical mechanical trajectory method. The vibrational and rotational energies were initialized using Boltzmann distributions characterized by temperatures T_vib = 150 K, T_rot = 50 K. We find that for large values of E the energy transfer in reactive collisions increases with b while it decreases with b for the nonreactive collisions. For low values of E, energy transfer is a decreasing function of b for both reactive and nonreactive encounters. Both the reactive and nonreactive mechanisms are very efficient in effecting transfer, between 40–70% of the initial relative translational energy is converted into internal energy of the diatom, leading to the conclusion that the reverse collisions would result in the rapid relaxation observed in experiment.     

Quasiclassical trajectory state-to-state cross sections for energy transfer in Ar+ OH(υ = 9,J = 0,4, and 8) collisions

State-to-state energy transfer cross sections have been computed for Ar + OH(υ₁ = 9; J_i = 0,4, and 8) at initial relative translational energy 0.2 eV using quasiclassical trajectories. The results show that a relatively small amount of initial rotational excitation has a significant effect on the energy transfer. The energy transfer for J_i = 8 is dominated by transitions for which the vibrational and rotational energy changes are such that the translational energy changes are minimized.     

Classical model for electronically non-adiabatic collision processes resonance effects in electronic-vibrational energy transfer

A classical model for electronically non-adiabatic collision processes is applied to E → V energy transfer in a collinear system, A + BC (v = 1) → A¹ + BC (v = 0), resembling Br-H₂.The model, which treats electronic as well as translational, rotational, and vibrational degrees of freedom by classical mechanics, describes the resonance features in this process reasonably well.     

Persistence of MJ following vibrational and rotational energy transfer in molecular iodine excited by a single mode tunable dye laser

Excitation of iodine fluorescence with a single mode tunable dye laser allows extensive observation of features from vibrationally and rotationally transferred states populated through collisions. We have measured the circular polarisation of these features and observe a very high degree of polarisation following both vibrational and rotational energy transfer: thus transitions from states following ΔJ′ = 60 and Δν′ = 1, ΔJ′ = 60 are still highly polarized. This implies strong conservation of M_J throughout energetic inelastic collisions.     

Vibrational deactivation of DF

Rate constants for deactivation of DF in vibrational states n = 1 to 7 in collisions with DF (0) are calculated semiclassically in the temperature range from 300 K to 3000 K. The variation with the temperature agrees quite well with experiments for n = 1, although the theoretical rates are 30% lower than the experimental values for temperatures above 1200 K and 75% lower at 300 K. This difference is discussed. Single quantum transitions dominate. At 300 K the mechanism is predominantly a V—V transfer for n = 2 and a V-T/R transfer for n = 7, while both mechanisms contribute for n = 3–6. Collision complexes are important for both V—V and V-T/R energy transfer. Rotational relaxation times are calculated for HF and DF.     

Vibrational relaxation of compressed nD2 fluid

Experimental observations of the vibrational population relaxation time of ⁿD₂ fluid under pressures of up to 500 atm in the 25–85 K range are presented and described in terms of a semi-classical model for energy transfer in liquids. For comparison with the parameters of this model, a classical equivalent potential for quantum systems is derived from the “real” intermolecular potential.     

Vibrational relaxation of HF(υ = 3,4)

The vibrational relaxation of pure HF(υ = 3 and υ = 4) has been studied by pumping HF directly from υ = 0 to υ = 4. The relaxation rates of υ = 3 and υ = 4 were determined to be k³_T = (2.8 ± 0.4) × 10^?11 cm³ molecule^?1 s^?1 and k⁴_T = (7.2. ± 0.5) × 10^?11 cm³ molecule^?1 s^?1 at 293 K. It is shown that sigle quantum energy transfer can account for all the vibrational relaxation.     

Vibrational and translational enhancement of endothermic reactions: K + HCl(υ = 0,1) and K + HF(υ = 0,1)

The relative integral cross section for the two endothermic reactions K + HCl(υ = 0 and 1) → KCl + H and K + HF(υ = 0 and 1) → KF + H has been measured as a function of the collision energy E using the crossed molecular beam technique. The vibrationally excited state (υ = 1) has been populated thermally by heating the beam source to temperatures around 2000 K. The variation of the collision energy from thermal up to around 2.1 eV was achieved by seeding the K-beam with various carrier gases. The molecular reaction product was detected by surface ionization in connection with a time-of-flight method. The total energy threshold of the reactions has been found to be equal to or only slightly above the corresponding endothermicities. This suggests a vanishing or very low barrier crest on the potential energy hypersurfaces which is contradictory to recent theoretical results. The inclusion of tunneling in case of K + HF leads to a negligible rise of the barrier heights. The efficacy of translational and vibrational energy in promoting the reactive process has been directly compared over a wide range of collision energies. For K + HCl the vibrational enhancement of the reactivity descends with increasing E from approximately a factor of 10 at E = 0.08 eV to around unity for E ? 0.5 eV. The good agreement of this experimental result with phase space calculations suggests that the marked enhancements are predominantly caused by the long-range attraction between reagents in connection with an “early” barrier on the potential energy surface. In case of K + HF vibrational energy is by a factor of up to 380 more favourable in promoting the reaction than the same amount of translational energy. Again, with rising collision energy its efficacy decreases but promotes the reaction still by a factor of 70 at E = 1.7 eV. Since phase space theory fails here the reaction is certainly non-statistical and we conclude that the observed large efficacy of vibrational energy is due to a “late” barrier. The proposed barrier positions for the two systems are in accordance with theoretical results.     

A classical trajectory study of the effect of reaction barrier height on the vibrational energy transfer efficiency in the Cl + HCl system

The effects of reaction barrier height and initial rotational excitation of the reactants on the overall rate of H atom exchange between atomic chlorine and HCl (v = 0) and on the 0 → 1 vibrational excitation of HCl via reactive and nonreactive collisions have been investigated using quasiclassical trajectory techniques. Two empirical LEPS potential energy surfaces were employed in the calculations having reaction barrier heights of 9.84 and 7.05 kcal mol^?1. Trajectory studies of planar collisions were carried out on each surface over a range of relative translational energies with the ground-state HCI collision partner given initial rotational excitation corresponding J = 0, 3, and 7. Initial molecular rotation was found to be relatively inefficient in promoting the H atom exchange; the computed rate coefficient for H atom exchange between Cl + HCl (v = 0, J = 7) was only 4 times larger than that for CI + HCI (v = 0, J = 0). The vibrational excitation rate coefficient exhibited a stronger dependence on initial molecular rotational excitation. The observed increase in the vibrational excitation rate coefficient with increasing initial molecular rotational excitation was due primarily to nonreactive intermolecular R → V energy transfer. The vibrational excitation rate coefficients increase with decreasing reaction barrier height.     

The born approximation as a simple diagnostic method for direct molecular collisions with applications to Cl + HI and F + H2 reactions

Born approximation computations are presented and discussed for the Cl + HI → I + HCl and F + H₂ → H + HF reactions and their isotopic analogues. Most aspects of the role of reagent energy or the energy disposal in the products previously deduced from experiment or trajectory computations can be accounted for the Born approximation. The procedure used here neglects the interaction between non-bonded atoms. It does thereby provide a very simple computational scheme which requires as input only the spectroscopic constants of the reactants and products. In addition it offers simple qualitative interpretations of the trends in the results. The overall satisfactory agreement between the present results and past studies lends credibility to the basic propensity rule provided by the Born approximation: The most probable transitions are those that minimize the momentum transfer to the nuclei. The principle is discussed with special reference to exothermic (E′_T ? E_T) and endothermic transitions.The computations for Cl + HI indicate a decline of the reaction cross section with increasing kinetic energy and a strong enhancement by HI rotational energy. The surprisal analysis confirms the absence of vibrational population inversion for endothermic transitions. For the F + H₂ (and isotopic variants) reactions, the product-rotational state distribution extends nearly to the energy cut-off. The vibrational state distribution is somewhat different for para- and normal H₂ and, in general, the collision outcome is very sensitive to the initial rotational state of H₂ particularly at low translational energies. The HF/DF branching ratio is F + HD collisions is increasing with increase of the HD rotational state. The vibrational surprisal is essentially isotopically invariant.     

Vibrational relaxation of ethylene oxide and ethylene oxide-rare-gas mixtures

The collision-induced vibrational energy relaxation of ethylene oxide (C₂H₄O) was studied by means of laser-induced fluorescence. The time-dependent population of the vibrational modes v₃ and v₅/v₁₂ was measured after excitation of CH-stretching vibrations near 3000 cm^?1. Rate constants for the vibrational energy transfer by collisions with C₂H₄O and the rare gases are deduced, and a simplified model for the vibrational relaxation of C₂H₄O is discussed.     

Vibrational relaxation in atom exchange reactions: A classical trajectory study of H + H2(ν) and D + D2(ν) collisions using an accurate potential

A quasiclassical trajectory study has been carried out to investigate the dynamics of collisions between H + H₂(1 ? ν ? 4) and D + D₂(1 ? ν ? 4), using the accurate Yates-Lester potential. Reaction is selectively enhanced by the vibrational excitation of the diatomic reagent, as judged by information theory, but the degree of selectivity falls as the vibrational energy is successively increased. The calculated results are in fair agreement with experimental measurements on the removal of H₂(ν = 1) by H but not with those for D₂(ν = 1) by D.     

Theoretical unimolecular kinetics for CH4 + M ⇄ CH3 + H + M in eight baths, M = He, Ne, Ar, Kr, H2, N2, CO, and CH4

Ensembles of classical trajectories are used to study collisional energy transfer in highly vibrationally excited CH(4) for eight bath gases. Several simplifying assumptions for the CH(4) + M interaction potential energy surface are tested against full dimensional direct dynamics trajectory calculations for M = He, Ne, and H(2). The calculated energy transfer averages are confirmed to be sensitive to the shape of the repulsive wall of the intermolecular potential, with an exponential repulsive wall required for quantitative predictions. For the diatomic baths, the usual "separable pairwise" approximation for the interaction potential is unable to describe the orientation dependence of the interaction potential accurately, and the ambiguity in the resulting parametrizations contributes an additional uncertainty to the predicted energy transfer averages of 20-40%. On the other hand, the energy transfer averages are shown to be insensitive to the level of theory used to describe the intramolecular CH(4) potential, with a computationally efficient semiempirical tight binding potential for hydrocarbons performing equally well as an MP2 potential. The relative collisional energy transfer efficiencies of the eight bath gases are discussed and shown to be a function of temperature. The ensemble-averaged energy transferred in deactivating collisions <ΔE(d)> for each bath is used to parametrize a single-exponential-down model for collisional energy transfer in master equation calculations. The predicted decomposition rate coefficients for CH(4) agree well with available experimental rate coefficients for M = He, Ar, Kr, and CH(4). The effect of vibrational anharmonicity on the predicted rate coefficients is considered briefly.     

Vibrational energy transfer according to the morse potential: Application to self-relaxation of methane

The perturbation integral in the semiclassical theory of vibrational energy transfer is derived in closed form for a Morse potential. The temperature dependence of VT tranfer in CH₄CH₄ collisions is investigated, using a recently published numerical CH₄ potential to determine the parameters of the Morse potential.     

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. © 2014 Wiley Periodicals, Inc.     

Semi-classical study of the molecular dissociation: H2 + He

Accurate vibrational wave functions and a state-dependent model interaction potential were used in the study, within the framework of a semi-classical theory, of the vibrational excitation and dissociation of the hydrogen molecule in collinear collisions with the helium atom. A molecule initially in the excited state is shown to be very efficient in energy transfer and twice more likely to be further excited than to be de-excited. The change in the population distribution among the vibrational states at the first few collisions was analyzed. It is shown that the population of the first vibrational excited state ψ₁ reaches its maximum after the very first collision and that of ψ₂ after the second. It is also found that at a sufficiently high collision energy, ψ₅ is the most efficient state in dissociation at the second collision while ψ₆ contributes most at the third collision.     

Vibrational relaxation of HF(v = 1) by F atoms

The rate of vibrational relaxation of HF(v = 1) by F atoms has been calculated using quasi-classical trajectory techniques. An attempt has been made to account for the effects of multiple potential energy surfaces on the vibrational relaxation efficiency within the electronically adiabatic assumption. Toward this end two potential energy surfaces were investigated. The LEPS equation was used to construct a reactive surface for F + HF′ → FH + F′ having a reaction barrier height of 5.4 kcal/mole, which is in agreement with a bond energy-bond order prediction. A nonreactive interaction potential consisting of atom-atom Morse functions was calibrated to Noble and Kortzeborn's [J. Chem. Phys. 52, 5375 (1970)] LCAO-MO-SCF results for FHF(²II). The results are in qualitative agreement with experiment. However, the nonreactive surface appears to be too repulsive, and consequently, the contribution of collisions on the nonreactive surface to the total vibrational relaxation rate coefficient are overestimated.