A time-dependent wave packet study of the H4 four-center reaction

A quantum model based on the time-dependent initial state selected wave packet approach was developed to study the four-center (4C) reaction, A₂ + B₂ → 2AB, and the competing collision induced dissociation (CID), A₂ + B₂ → A + B₂ + A, as applied to the H₂(v₁) + H₂(v₂) system important in combustion. A reduced three-dimensional model of the reaction with the atoms constrained to an isosceles trapezium and a realistic global potential energy surface of Aguado et al. [J. Chem. Phys. 101 (1994) 2742], following Hernández and Clary [J. Chem. Phys. 104 (1996) 8413], was used. A method to analyse the reaction flux for 4C and CID reaction probabilities is presented. The initial A₂ vibrational excitation is not only more efficient than translational energy in facilitating the 4C and CID processes, it also reduces the threshold energy. Both the 4C and CID processes exhibit similar threshold energy behavior. For low vibrational excitation in the A₂ diatom, the 4C process is dominant; as the A₂ diatom becomes highly excited the CID process becomes more important at low collision energies with B₂, but as the collision energy increases the 4C process is favored again.     

Rates of vibrational and dissociative excitation of diatomic molecules in atom-molecule collisions in a hot gas

Vibrational relaxation and dissociation in O₂-Ar at low O₂ contents are considered. The populations of the vibrational levels are found as functions of time. The vibrational relaxation time and the dissociation rate constant at 3000 to 20 000 K are calculated. The relaxation equation for the vibrational energy per unit volume in the presence of dissociation is considered.     

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.     

Vibrational energy disposal in reactions of fluorine atoms with hydrides of groups III,IV and V

The HF infrared chemiluminescence from the reactions of F atoms with B₂H₆, CH₄, CH₃F, CH₂F₂, CH₂Cl₂, CH₃ONO. CH₃NO₂, NH₃ (and ND₃). PH₃ and HNCO has been observed from a 300 K flowing-afterglow reactor. Experiments were done for a range of CH₄ and F atom concentrations to identify conditions which were free of vibrational relaxation and secondary reactions, and these conditions were used to assign initial HF(v) vibrational distributions for each reaction. The emission intensity from each reaction also was compared to that from CH₄ in order to obtain the relative HF formation rate constants at 300 K. Since the absolute rate constant for F + CH₄ is well established, the combination of all of these data provides absolute rate constants for HF(v) formation at 300 K. The ND₃ reaction was studied to obtain information on more vibrational levels in order to better estimate the HF(v = 0) and DF(v = 0) components of the ammonia distributions. With NH₃ and ND₃ there is no significant isotope effect on the energy disposal. Except for NHCO, for which an addition-elimination channel is possible, the HF(v) distributions are inverted and <f_v > = 0.60. Differences between the HF(v) distributions reported here and some other reports in the literature are noted: the present data are discussed as representative of direct H atom abstraction for 300 K Boltzmann conditions. The HCl infrared chemiluminescence from the F + CHCl₂ secondary reaction also was observed; the HCl(v) distribution was v₁: v₂: v₃: v₄: v₅ - 0.47: 0.23: 0.18: 0.08: 0.04.     

Competition between dissociation and exchange processes in a collinear A + BC collision. I. Exact quantum results

Exact quantum results for collision-induced dissociation on a reactive surface are presented. A modified LEPS potential-energy surface modeling the H + HD → H₂ + D system has been used. HD and H₂ bearing respectively 7 and 6 bound states. This system has been chosen because it displays significant reactive scattering for total energies above the dissociation threshold. Calculations have been performed using the time-dependent wavepacket method for two initial vibrational quantum numbers of the HD molecule (v = 0, 2). For each vibrational quantum number, two wavepackets with overlapping energy distributions have been run, covering a total energy range up to more than three times the dissociation energy. Comparison with previous collision-induced dissociation calculations shows that the dissociation is greatly enhanced by the presence of concomitant reactive scattering. A vibrational enhancement effect is also observed above the dissociation threshold; for higher energies the system exhibits a pronounced vibrational inhibition effect.     

Product rotational distribution in the photodissociation of CH3CF2Cl

In the laser-induced unimolecular dissociation CH₃CF₂Cl an exceedingly narrow rotational distribution of the HCl product has been observed. The experimental evidence suggests that a few rotations around J = 16 are unusually open channels to either the vibrational relaxation of HCl or the dissociation.The dissociation is investigated in steady state as well as in a thermal beam by far-infrared emission.     

On the vibrational dependence of electron impact ionization of diatomic molecules

The dependence of the Na₂ electron impact ionization rate is measured as a function of vibrational excitation in a crossed molecule-electron beamm arrangement at collision energiesE _coll ≤ 3 eV above the ionization threshold. Specific vibrational distributions in theX ¹∑ _g ⁺ state with average vibrational energies of 0.17 eV, 0.276 eV, and 0.349 eV, are prepared via Franck-Condon pumping using a narrow-band cw laser. Enhancement of the ionization rate is observed only at impact energies near the ionization threshold where the ionization rate increases linearly as a function of vibrational excitation. Analysis of the experimental data is based on three model calculations. The first of these calculations equates vibrational energy with kinetic energy and agrees well with the experimental data. A second, more refined model allows for differences in state-to-state ionization rates and uses Franck-Condon factors to estimate transition probabilities, but leads to a less favorable agreement. The third one employs a semi-classical formulation of the Franck-Condon principle. It provides the best agreement with the experimental data. In contrast with an earlier study of electron impact ionization of diatomic molecules [20], we find no evidence of dynamical modification of the ionization rate, due to vibrational motion of the nuclei, at the present level of accuracy of our data and analysis.     

Hydrogen-bonded and van der Waals complexes studied by a Gaussian density functional method. The case of (HF)2, ArHCl and Ar2HCl systems

Summary Linear combination of Gaussian-type orbitals local spin density calculations (LCGTO-LSD) have been performed to further test the applicability to the method of hydrogen-bonded and van der Waals systems. The calculated minimum energy structures and binding energies for the (HF)₂, ArHCl and Ar₂HCl complexes are presented. In addition, the harmonic vibrational frequencies are reported for (HF)₂. The results show that by using nonlocal corrections and increasing the number of radial points in the grid, the calculated parameters are close to experimental ones and provide some encouraging evidence for the reliable use of density functional theory for these complex systems.     

Rates of processes initiated by pulsed laser production of F atoms in the presence of HCl,CH4, and CF3H

Time-resolved vibrational chemiluminescence from HF has been recorded following the production of F atoms by the pulsed laser photolysis (λ = 266 nm) of F₂ in the presence of HCl, CH₄, and CF₃H. In the first two cases, experiments have been conducted by observing emission from HF(ν = 3) at four temperatures from 295 to 139 K. Rate constants have been determined over this range of temperature for the reactions of F atoms with HCl and CH₄ and of CH₃ radicals with F₂, and for the relaxation of HF(ν = 3) by HCl and CH₄. The reaction of F atoms with CF₃H is slower than those with HCl and CH₄ and measurements on the emission from HF(ν = 2) have been used to infer rate constants for reaction and relaxation only at 295 K. © 1994 John Wiley & Sons, Inc.     

Isomerisation of CF2ClCH2Cl and CFCl2CH2F by Interchange of Cl and F Atoms with Analysis of the Unimolecular Reactions of Both Molecules

The recombination of CF₂Cl with CH₂Cl and CFCl₂ with CH₂F were employed to generate CF₂ClCH₂Cl* and CFCl₂CH₂F* molecules with 381 and 368 kJ mol^?1, respectively, of vibrational energy in a room‐temperature bath gas. The unimolecular reactions of these molecules, which include HCl elimination, HF elimination, and isomerisation by interchange of chlorine and fluorine atoms, were characterized. The three rate constants for CFCl₂CH₂F were 2.9×10⁷, 0.87×10⁷ and 0.04×10⁷ s^?1 for HCl elimination, isomerisation and HF elimination, respectively. The isomerisation reaction must be included to have a complete characterization of the unimolecular kinetics of CFCl₂CH₂F. The rate constants for HCl elimination and HF elimination from CF₂ClCH₂Cl were 14×10⁷and 0.37×10⁷ s^?1, respectively. Isomerisation that has a rate constant less than 0.08×10⁷ s^?1 is not important. These experimental rate constants were matched to calculated statistical rate constants to assign threshold energies, which are 264, 268, and 297 kJ mol^?1, respectively, for isomerisation, HCl elimination, and HF elimination for CFCl₂CH₂F and 314, 251, and 289 kJ mol^?1 in the same order for CF₂ClCH₂Cl. Density functional theory was used to evaluate the models that were needed for the statistical rate constants; the computational method was B3PW91/6‐31G(d′,p′). Threshold energies for the unimolecular reactions of CF₂ClCH₂Cl and CFCl₂CH₂F are compared to those for CF₂ClCH₃ and CFCl₂CH₃ to illustrate the elevation of threshold energies by F‐ or Cl‐atom substitution at the beta carbon atom (identified by C_H). The DFT calculations systematically underestimate the threshold energy for HCl elimination.     

Stability of molecular form of HCl in water vapor: A computer simulation

The free energy and entropy of the dissociation of HCl molecule into ions in water vapor, HCl(H₂O) _n + mH₂O → H₃O + (H₂O) _n+m -1Cl^?, were calculated. The dependences of various parameters on the interionic distance at 273 K and various vapor pressures were obtained. A detailed model taking into account unpaired covalent-type interactions, polarization interactions, charge transfer effect, and hydrogen bonds was applied. The numerical values of the parameters were reconstructed from the experimental data on the free energy and enthalpy of the first reactions of addition of vapor molecules to ions, and also from the results of quantum-chemical calculations of the energy and geometry of locally stable configurations of clusters HCl(H₂O) _n . Despite lower internal energy of the dissociated state, the molecular form is absolutely stable in clusters of water molecules. The dissociated state is relatively stable. Accumulation of unrecombined ion pairs in clusters is possible with a decrease in the temperature to 200 K.     

Triatom-triatom collisions: Fixed angle close-coupling study of vibrational excitation in the 12CO2+13CO2 system

A close-coupling approach to the calculation of quantal vibrational transition probabilities for the fixed angle scattering of a linear triatomic molecule with another linear triatomic molecule is described. The method is applied to the ¹²CO₂+¹³C0₂ collisional system. For a calculated inelastic transition probability to have an appreciable magnitude, it is found that the amount of energy transferred in a transition must be very small and just one quantum of energy must be exchanged between either the symmetric stretch or the asymmetric stretch vibrational modes of ¹²C0₂ and ¹³CO₂. For collisional energies away from threshold, the probabilities for transitions involving the symmetric stretch ¹²CO₂ and ¹³CO₂ modes are insensitive to long range multipole terms in the potential energy surface, while the probabilities for energy exchange between the asymmetric stretch modes are considerably diminished when the long range terms are removed from the potential energy surface. A brief discussion is presented on the possibilities of extending the technique to the calculation of vibrational excitation cross sections for three-dimensional triato—triatom collisions.     

Proton affinity of SO3

Collision-induced dissociation (CID) of the radical cation H₂SO₄⁺ gives the product pairs H₂O⁺+SO₃ and HO+HSO₃⁺ with a 1:3 ratio that is essentially independent of collision energy. Statistical analysis of the two channels indicates that the proton affinity of HO is 3±4 kJ/mol lower than that of SO₃. This can be used to derive PA(SO₃)=591±4 kJ/mol at 0 K and 596±4 kJ/mol at 298 K. Previously, Munson and Smith bracketed the proton affinity as PA(HBr)=584 kJ/mol<PA(SO₃)<PA(CO)=594 kJ/mol. The threshold of 152±16 kJ/mol for formation of H₂O⁺+SO₃ indicates that the barrier to CID is small or nonexistent, in contrast to the substantial barriers to decomposition for H₃SO₄⁺ and H₂SO₄.     

Energy transfer as a function of collision energy. I Collision partners: Hydrogen halides + inert gases,hydrogen halides,H2S and propane

Infrared emission has been recorded from a heated seeded supersonic primary beam of HCl or HF (1) prior to collision with a target beam, and (2) subsequent to that collision. Mean collision energy and collision partner were varied systematically. After correction for elastic scattering, the net population change due to inelastic scattering in a translation—rotation (T ? R) energy-transfer encounter was obtained for specific J states ranging from J = 0–16 of vibrational level υ = 1 of the primary-beam molecule. The broad picture is that a net transfer into low-J states out of higher-J states takes place at low collision energies, and the converse at high collision energies. These observations are interpreted in terms of the “exponential model” for the relative cross sections of T ? R inelastic collisions, S^R (J_i → J_f), proposed earlier [J.C. Polanyi and K.B. Woodall, J. Chem. Phys. 56 (1972) 1563], modified here to satisfy microscopic reversibility. The constant C in the model, which governs the exponential decrease in S^R with increasing energy difference ΔE_J between J_f and J_i, can be derived, as a function of collision energy T, from the present experimental data; C decreases as T increases, i.e. larger ΔJ become more probable. In order to check the validity of the model, it was compared with 3D trajectory results; according to this criterion it was found to give a very good representation of S^R(J_i → J_f) with a single value for C, within a limited range of J_i. The collision partners HCl + HF exhibit anomalously efficient rotational deactivation; evidence is presented which indicates that at low collision energies this is due to resonant R → R transfer. Very efficient deactivation of HCl by HCl, at low collision energy, is likely to be due to V — V transfer.     

A full dimensional time-dependent wave packet study for the H4 four-center, collision induced dissociation, and single exchange reactions: reaction probabilities for J=0

A time-dependent initial state selected wave packet method has been developed to study the H2(v(1)=10-11,j1=0)+H2'(v2=0,j2=0)-->HH'+HH' four-center (4C) reaction, and two other competing reactions: the H2+H2'-->H+H+H2' collision induced dissociation (CID) and the H2+H2'-->H+HH'+H' single exchange (SE) reaction, in full six dimensions. Initial state-specific total reaction probabilities for these three competing reactions are presented for total angular momentum J=0 and the effects of reagent vibration on reactions are examined. It is found that (a) the CID process is the dominant process over the whole energy range considered in this study, but the 4C and SE processes also have non-negligible probabilities; (b) the SE process has a lower threshold energy than the 4C process, but the SE probability increases slower than the 4C probability as collision energy increases; (c) the vibrational excitation of H2(v1) is much more efficient than translational motion for promoting these processes, in particular to the CID process.     

Collision induced dissociation in a flowing afterglow-tandem mass spectrometer for the selective detection of C5 unsaturated alcohols and isoprene

A flowing afterglow-tandem mass spectrometer (FA-TMS) was used to study a series of C₅ unsaturated alcohols and isoprene. The analytical procedure was validated through collision induced dissociation (CID) experiments on proton hydrates. In the FA, reagent H₃O⁺ ions were used to chemically ionize the alcohols under study and isoprene. Chemical ionization (CI) by H₃O⁺ is widely used, especially in PTR-MS instruments, and produces a main peak at m/z 69 for all studied compounds, implying the impossibility to distinguish them by a simple quadrupole mass filter. The CID of these ions at m/z 69 resulted in daughter ions with the same masses but with different intensities depending on the organic compound, the collision energy and the Ar target gas pressure in the collision cell. From these observations, pentenols were easily distinguished from methylbutenols and 3-methyl-3-buten-1-ol from the other compounds. CID experiments were also performed on the protonated alcohol, which is only a stable ion for 1-penten-3-ol, 2-methyl-3-buten-2-ol and 3-methyl-3-buten-1-ol, showing different CID patterns as a function of the collision energy. The coupling between a FA reactor and a TMS has proven to be a valuable approach to identify C₅ unsaturated alcohols and isoprene.     

Full-dimensional time-dependent wave packet dynamics of H2 + D2 reaction

Collision induced dissociation (CID), four center reaction (4C), and single exchange reaction (SE) in H(2) (v(1) = high) + D(2) (v(2) = low) were studied by means of time-dependent wave packet approach within a full-dimensional model. Initial state-selected total reaction probabilities for the three competitive processes have been computed on two realistic global potential energy surfaces of Aguado-Suárez-Paniagua and Boothroyd-Martin-Keogh-Peterson (BMKP) with the total angular momentum J = 0. The role of both vibrationally excited and rotationally excited reagents was examined by varying the initial vibrational and rotational states. The vibrational excitation of the hot diatom gives an enhancement effect on the CID process, while the vibrational excitation of the cold diatom gives an inhibition effect. The rotational excitation of both reagents has a significant effect on the reaction process. The 4C and SE probabilities are at least one order of magnitude smaller than the CID probabilities over the energy range considered. Isotope substitution effects were also studied by substituting the collider D(2) by H(2) and HD on the BMKP potential energy surfaces. The CID process is most efficient for the H(2) + D(2) combination and least efficient for the H(2) + H(2) combination and is different for the 4C and SE processes.     

Double step-ladder model of activation in the processes of high-temperature dissociation of polyatomic molecules

A unified mechanism of the interaction of vibrational relaxation and dissociation of polyatomic molecules working in a wide temperature range (from 2000 to 10000 K) is proposed, which is described by a double step-ladder model. Relaxation due to collisions with the transfer of small and large portions of energy is taken into account. The transfer efficiency of the portions of thermal energy in the high-temperature decomposition upon the collisions of CO₂ molecules with atomic and molecular partners is determined. The reaction rate constant of high-temperature dissociation of carbon dioxide is calculated. The data presented in the article suggest a new method for elucidating the mechanism of energy exchange in the absence of vibrational and translational equilibrium and at ultrahigh temperatures when the dissociation takes place during the time of several collisions.     

Nonequilibrium vibrational populations and dissociation rates of oxygen in electrical discharges

Nonequilibrium vibrational distributions and dissociation rates of molecular oxygen in both electrical and thermal conditions have been calculated by solving a system of master equations including V-V (vibration-vibration), V-T (vibration-translation) and e-V (electron-vibration) energy exchanges. The dissociation constant under thermal conditions (i.e. without electrons) follows an Arrhenius law with an activation energy of 120 kcal/mole, while the corresponding rates under electrical conditions (5000 ? T_e ? 15000 K, 300 ? T_g ? 1000 K, 10¹¹ ? n_e ? 10¹² cm^?3,5 ? p ? 20 torr) increase with decreasing gas (T_g) and electron (T_e) temperatures and pressure (p) and with increasing electron density (n_e). These results are explained on the basis of the different interplay of V-V and V-T energy exchanges and are rationalized by means of simplified models proposed in the literature. The accuracy of the present results is discussed paying particular attention to the dependence of V-V and V-T rate coefficients on the vibrational quantum number. A comparison of the calculated dissociation rates with the corresponding ones obtained by the direct electron impact mechanism shows that the present mechanism prevails at low electron and gas temperatures. Finally a comparison is shown between theoretical and experimental dissociation rates under electrical and thermal conditions.     

Calculations of vibrational energy transfer using semi-classicals matrix theory

We utilize an extension of Miller's semi-classical S matrix theory to calculate resonant and non-resonant vibrational energy transfer probabilities. The collisions under study are collinear D₂D₂ interactions at energies below and above the classical dynamic transition threshold and collinear H₂D₂ interactions above the dynamic threshold. Below threshold we employ an initial angle representation. We find that the computed probabilities are in substantial agreement with exact quantum mechanical computations and represent a major improvement over quasi-classical results. At energies above threshold we apply the first order and the classical semi-classical versions of the theory. The results indicate fair agreement with quantum mechanical calculations, but no significant improvement over quasi-classical results.