Differential cross sections for H + D2 → HD(v' = 2, j' = 0,3,6,9) + D at center-of-mass collision energies of 1.25, 1.61, and 1.97 eV

We have measured differential cross sections (DCSs) for the reaction H + D(2) → HD(v' = 2,j' = 0,3,6,9) + D at center-of-mass collision energies E(coll) of 1.25, 1.61, and 1.97 eV using the photoloc technique. The DCSs show a strong dependence on the product rotational quantum number. For the HD(v' = 2,j' = 0) product, the DCS is bimodal but becomes oscillatory as the collision energy is increased. For the other product states, they are dominated by a single peak, which shifts from back to sideward scattering as j' increases, and they are in general less sensitive to changes in the collision energy. The experimental results are compared to quantum mechanical calculations and show good, but not fully quantitative agreement.     

Computation of cross sections for the F+H2(v=0,j=0) → FH(v′j)+H reaction by the hyperspherical method

Summary A quantum mechanical calculation of cross sections for the reaction F+H₂(v=0,j=0) FH(vj)+H has been performed on the T5A semiempirical potential surface using hyperspherical coordinates. State-to-state integral and differential cross sections converge rapidly with the number of components of the total angular momentum projection onto the axis of least inertia. Thev=3 differential cross section has a forward peak whose magnitude increases with energy whereas thev=2 differential cross section has a backward maximum, in qualitative agreement with cross-beam experiments. Thev=2 andv=3 rotational distributions are in rather good agreement with experiment, but not the vibrational branching ratios.     

Mean potential statistical theory of the H+ + D2 → HD + D+ reaction

The reactive collision process H(+) + D(2)(ν = 0, j = 0) → HD + D(+) is theoretically analyzed for collision energies ranging from threshold up to 1.3 eV. It is assumed that the reaction takes place via formation of a collision complex. In calculations, a statistical theory is used, based on a mean isotropic potential deduced from a full potential energy surface. Calculated integral cross sections, opacity functions, and rotational distributions of the HD products are compared with recent statistical and quantum mechanical calculations performed using a full potential energy surface. Satisfactory agreement between the results obtained using the two statistical methods is found, both of which however overestimate the existing quantum mechanical predictions. The effects due to the presence of identical particles are also discussed.     

Infinite order sudden approximation treatment of the H + D2 → HD + D reaction

Results of a study of the H + D₂ → HD + D reaction within the quantum infinite order sudden approximation (RIOS) are reported here for the total energy range 1.0317 ⩽ E_t ⩽ 2.1417 eV. We present the vibrationally selected integral and total integral cross sections, and the latter are compared with both classical and experimental results. The RIOS results are in excellent agreement with the experimental results at 1.0317 eV and in reasonable agreement (≈ 20% high) at 2.1417 eV.     

Semiclassical glory analyses in the time domain for the H + D2(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction

We make the first application of semiclassical (SC) techniques to the plane-wavepacket formulation of time-domain (T-domain) scattering. The angular scattering of the state-to-state reaction, H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D, is analysed, where v and j are vibrational and rotational quantum numbers, respectively. It is proved that the forward-angle scattering in the T-domain, which arises from a delayed mechanism, is an example of a glory. The SC techniques used in the T-domain are: An integral transitional approximation, a semiclassical transitional approximation, a uniform semiclassical approximation (USA), a primitive semiclassical approximation and a classical semiclassical approximation. Nearside-farside (NF) scattering theory is also employed, both partial wave and SC, since a NF analysis provides valuable insights into oscillatory structures present in the full scattering pattern. In addition, we incorporate techniques into the SC theory called "one linear fit" and "two linear fits", which allow the derivative of the quantum deflection function, Θ?(')(J), to be estimated when Θ?J exhibits undulations as a function of J, the total angular momentum variable. The input to our SC analyses is numerical scattering (S) matrix data, calculated from accurate quantum collisional calculations for the Boothroyd-Keogh-Martin-Peterson potential energy surface No. 2, in the energy domain (E-domain), from which accurate S matrix elements in the T-domain are generated. In the E-domain, we introduce a new technique, called "T-to-E domain SC analysis." It half-Fourier transforms the E-domain accurate quantum scattering amplitude to the T-domain, where we carry out a SC analysis; this is followed by an inverse half-Fourier transform of the T-domain SC scattering amplitude back to the E-domain. We demonstrate that T-to-E USA differential cross sections (DCSs) agree well with exact quantum DCSs at forward angles, for energies where a direct USA analysis in the E-domain fails.     

Angular scattering using parameterized S matrix elements for the H + D2(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction: an example of Heisenberg's S matrix programme

A neglected topic in the theory of reactive scattering is the use of parameterized scattering (S) matrix elements to calculate differential cross sections (DCSs). We construct four simple parameterizations, whose moduli are smooth step-functions and whose phases are quadratic functions of the total angular momentum quantum number. Application is made to forward glory scattering in the DCS of the H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction at a translational energy of 1.81 eV, where v and j are vibrational and rotational quantum numbers respectively. The parameterized S matrix elements can reproduce the forward scattering for centre-of-mass reactive scattering angles up to 30° and can identify the total angular momenta (equivalently, impact parameters) that contribute to the glory. The theoretical techniques employed to analyze structure in the DCS include: nearside-farside theory, local angular momentum theory--in both cases incorporating resummations of the partial wave series representation of the scattering amplitude--and the uniform semiclassical theory of forward glory scattering. Our approach is an example of Heisenberg's S matrix programme, in which no potential energy surface is used. Our calculations for the DCS using the four parameterized S matrix elements are counterexamples to the following universal statements often found in the chemical physics literature: "every molecular scattering investigation needs detailed information about the interaction potential," and "an accurate potential energy surface is an essential element in carrying out simulations of a chemical reaction". Both these statements are false.     

On the fine-structure dependence of the Cs(7p, 2P12,320)+H2→ CsH+H reaction cross section

The experimentally observed effect of the Cs¹ fine-structure level on the title reaction is reproduced by a rough (collinear, one dimensional) dynamical treatment using accurate long-distance entrance channel potentials, as obtained from an effective Hamiltonian method, and hemiquantal dynamics in the collision energy range 0.03 to 0.13 eV. The system is shown to behave adiabatically at large distances, to undergo a transition from adiabatic to diabatic behaviour with respect to spin-orbit coupling in the 11–8.5 au Cs-H distance range, and to transfer adiabatically the whole ²Σ⁺ weight of the electronic wavefunction into theionic channel in the harpooning region.     

Dynamic aspects of the reaction O(1D) + H2S → OH + SH

The energy distribution of nascent OH(²Π, υ, J) produced in the reaction of O(¹D) with H₂S has been measured by laser-induced fluorescence. The rotational distributions in υ″ = 0 and υ″ = 1 are Boltzmannian with temperature parameters T_r″-0 = 2300 ± 100 K and T_r⁻-1 = 2650 ± 150 K. A population ratio N(υ″ = 1)/N(υ″ = 0) = 0.17 is observed. The product-state distribution over the different spin and A components is statistically within the experimental uncertainty of 20%. A comparison of the OH product populations from the title reaction with the well known OH yield from the O(¹D)+H₂O reaction shows that 25% of the reactive encounters follow the reaction channel which produces OH in υ″ = 0 and υ″ = 1.     

Capture and dissociation in the complex-forming CH(v = 0,1) + D2 → CHD + D, CD2 + H, CD + HD reactions and comparison with CH(v = 0,1) + H2

Rate coefficients for the CH(v = 0,1) + D(2) reaction have been determined for all possible channels (T: 200-1200 K), using the quasiclassical trajectory method and a suitable treatment of the zero point energy. Calculations have also been performed on the CH(v = 1) + H(2) reaction and the CH(v = 1) + D(2) → CH(v = 0) + D(2) process. Most of the results can be understood considering the key role played by the deep minimum of the potential energy surface (PES), the barrierless character of the PES, the energy of the reaction channels, and the kinematics. The good agreement found between theory and experiment for the rate coefficients of the capture process of CH(v = 0) + D(2), the total reactivity of CH(v = 1) + D(2), H(2), as well as the good agreement observed for the related CH(v = 0) + H(2) system (capture and abstraction), gives confidence on the theoretical rate coefficients obtained for the capture processes of CH(v = 1) + D(2), H(2), the individual reactive processes of CH(v = 1) + D(2), H(2), the abstraction and abstraction-exchange reactions for CH(v = 0) + D(2), and the inelastic process mentioned above, for which there are no experimental data available, and that can be useful in combustion chemistry and astrochemistry.     

Abstraction versus insertion in the reaction O(1D2)+H2→OH(υ″ = 2) + H

The product hydroxyl radical arising from the reaction O(¹D₂)+H₂→OH+H was detected by LIF following excitation of the off-diagonal transition OH(A²Σ⁺, υ′=1←X²Π, υ″=2) in the region 348–357 nm. The rotational population distribution in υ″=2 appears to be inverted and quite similar to that previously reported for υ″=0 and 1. Because rotationally cool OH was not observed, there is no evidence for the existence of an abstractive pathway in which the subject reaction occurs without the initial formation, via insertion, of a chemically activated HOH collision complex.     

The absorption cross section of the HCO radical at 614.59 nm and the rate constant for HCO+HCO → H2CO+CO

Using a combination of XeCl exciplex laser flash photolysis of gas-phase glyoxal and formaldehyde and time-resolved cw dye laser absorption at 614.59 nm, we have determined the ratio k₁/σ for the reaction HCO+HCO → H₂CO+CO (1) at 295 ±2 K. Similar studies involving the 308 nm photolysis of a variety of aldehydes combined with a determination of the absolute yields of the resulting hydrocarbon products have allowed us to deduce the initial yields of HCO radicals and hence the absorption cross section for HCO at the monitoring wavelength. We find σ=(2.3±0.6) × 10⁻¹⁸ cm², giving k₁=(7.5±2.9)× 10⁻¹¹cm³ molecule⁻¹ s⁻¹. Our values are compared with previous results.     

Quasi-classical trajectory-gaussian binning study of the OH + D2 → HOD(v1',v2',v3') + D angle-velocity and vibrational distributions at a collision energy of 0.28 eV

The angle-velocity and product vibrational state distributions for the OH + D(2) reaction at a collision energy of 0.28 eV have been calculated using the quasi-classical trajectory-gaussian binning (QCT-GB) method and the Wu-Schatz-Lendvay-Fang-Harding (WSLFH) analytical potential energy surface. Comparison with high resolution molecular beam experiments shows that, differing from what happens when using the standard QCT method (i.e., histogram binning), very good results are obtained for both distributions. Hence, the strong differences previously observed between QCT and experimental results mainly come from an inadequate pseudoquantization of HOD rather than from other quantum effects. This is probably the first time that such a high level of agreement between theory and high resolution experimental data has been found in polyatomic reaction dynamics.     

Time-dependent wave packet theory for state-to-state differential cross sections of four-atom reactions in full dimensions: application to the HD + OH → H2O + D reaction

Time-dependent wave packet method has been developed to calculate differential cross section for four-atom reactions in full dimension, utilizing an improved version of reactant-product-decoupling scheme. Differential cross sections for the title reaction were calculated for collision energy up to 0.4 eV. It is found that the differential cross sections for the reaction are all peaked in the backward direction. The majority of H(2)O is produced in the first stretch excited state, with a large fraction of available energy for the reaction going into H(2)O internal motion. As compared in a previous report by Xiao et al. [Science 333, 440 (2011)], the differential cross section at E(c) = 0.3 eV and the differential cross section at the backward direction as a function of collision energy agree with experiment very well, indicating it is possible now to calculate complete dynamical information for some simple four-atom reactions, as have been done for three-atom reactions in the past decades.     

The gas-phase and solution mechanism of the isotope exchange reaction OH- + D2 = OD- + HD: Beam study of the solvated-ion reaction OH-. H2O + D2 in the collision energy range 0–2 eV

In a tandem mass spectrometer we have measured the excitation functions (reaction cross section as a function of collision energy) for the following solvated-ion reactant pairs: OH^-.(H₂O) + H₂; OD^-.(D₂O) + D₂; and OH^-.(H₂O) + D₂—in the collision energy range 0–2 eV. Product channels include H₃O^--type production, collision-induced dissociation of reactants and products (OH^- and H^- types) and isotopic mixing. These solvated-ion reactions are used to correlate the reactivity of the isotope exchange reaction OH^- + D₂→OD^- + HD occuring in the gas phase and solution, identifying a proton-transfer mechanism occuring within an H₃O^- intermediate.     

The H + D2 → HD + D reaction at 0.55, 0.98, 1.10 and 1.30 eV: A distorted-wave study using a new distortion potential

The static-static distorted-wave method has been applied to the H+D₂(v = 0, j = 0) → HD(v', j')+D reaction on the LSTH potential energy surface at four energies. A new static distortion potential has been used that is obtained from the preferred collinear configuration of the atoms together with an average over the unperturbed molecular wavefunction. The rotational distributions agree well with recent experimental data and with other theoretical information.     

Rovibrational state specific scattering distributions of the O((1)D) + CD(4)→ OD + CD3 (v1, v2, N) reaction

The rovibrational state distributions and state-resolved scattering distributions of CD(3) radicals produced by the reaction O((1)D) + CD(4) were investigated by crossed molecular beam ion imaging. The rotational structure of the resonance-enhanced multiphoton ionization spectrum of CD(3) in the ground vibrational state indicates that the low K rotational states of CD(3) radicals are preferentially populated. The state-resolved scattering distributions of CD(3) (v = 0) and those of the excited states of the out-of-plane bending (v(2)) mode exhibit a structureless forward-scattering component due to an insertion pathway and a structured backward-scattering component due to an abstraction path. The scattering distributions of CD(3) in the excited state of the C-D symmetric stretch (v(1)) do not exhibit the abstraction component. The scattering distribution of the abstraction component gradually extends in the forward direction with increasing intensity as the v(2) vibration becomes more strongly excited. This suggests that abstraction with a larger impact parameter results in stronger excitation of v(2).     

Comment on the possible role of the reaction H+H2O→H2+OH in the radiolysis of water at high temperatures

In a recent paper (Radiation Physics and Chemistry, 2005, vol. 74, pp. 210) it was suggested that the anomalous increase of molecular hydrogen radiolysis yields observed in high-temperature water is explained by a high activation energy for the reaction H+H₂O→H₂+OH. In this comment we present thermodynamic arguments to demonstrate that this reaction cannot be as fast as suggested. A best estimate for the rate constant is 2.2×10³ M⁻¹ s⁻¹ at 300 °C. Central to this argument is an estimate of the OH radical hydration free energy vs. temperature, ΔG_hyd(OH)=0.0278t−18.4 kJ/mole (t in °C, equidensity standard states), which is based on analogy with the hydration free energy of water and of hydrogen peroxide.     

Kinetic energy dependence of the total symmetric electron transfer cross section for the H2+(ν′o) + H2(ν″o = 0) system

We report the first experimental and theoretical observation of a broad peak in the kinetic energy dependence of the total cross sections for the title reaction with ν′_o = 0 and 1, in the laboratory collision energy range of 8–400 eV. A theoretical analysis reveals that the peak in the total cross section is due to the strong coupling among the many vibrational states of the reactants and products in the electron transfer process.     

Adiabatic and non-adiabatic quantum dynamics calculation of O(1D) + D2 → OD + D reaction

Adiabatic (1A' or 1A' state) and non-adiabatic (2A'/1A' states) quantum dynamics calculations have been carried out for the title reaction (O((1)D) + D(2) → OD + D) to obtain the initial state-specified (v(i) = 0, j(i) = 0) integral cross section and rate constant using the potential energy surfaces of Dobbyn and Knowles. A total of 50 partial wave contributions have been calculated using the Chebyshev wave packet method with full Coriolis coupling to achieve convergence up to the collision energy of 0.28 eV. The total integral cross section and rate constant are in excellent agreement with experimental as well as quasi-classical trajectory results. Contributions from the adiabatic pathway of the 1A' state and the non-adiabatic pathway of the 2A'/1A' states, increase significantly with the collision energy. Compared to the O((1)D) + H(2) system, the kinetic isotope effect (k(D)/k(H)) is found to be nearly temperature independent above 100 K and its value of 0.77 ± 0.01 shows excellent agreement with the experimental result of 0.81.     

Quantum dynamics calculation of reaction probability for H+Cl_2→HC1+Cl

We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + CI2 based on the GHNS potential energy surface with total angular momentum J= 0. The effects of the translational, vibrational and rotational excitation of CI2 on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.