Disagreement between theory and experiment in the simplest chemical reaction: collision energy dependent rotational distributions for H + D2 --> HD(nu' = 3,j') + D

We present experimental rotational distributions for the reaction H + D2 --> HD(nu' = 3,j') + D at eight different collision energies between 1.49 and 1.85 eV. We combine a previous measurement of the state-resolved excitation function for this reaction [Ayers et al., J. Chem. Phys. 119, 4662 (2003)] with the current data to produce a map of the relative reactive cross section as a function of both collision energy and rotational quantum number (an E-j' plot). To compare with the experimental data, we also present E-j' plots resulting from both time-dependent and time-independent quantum mechanical calculations carried out on the BKMP2 surface. The two calculations agree well with each other, but they produce rotational distributions significantly colder than the experiment, with the difference being more pronounced at higher collision energies. Disagreement between theory and experiment might be regarded as surprising considering the simplicity of this system; potential causes of this discrepancy are discussed.     

Collision energy dependence of the HD(nu' = 2) product rotational distribution of the H + D2 reaction in the range 1.30-1.89 eV

An experimental and theoretical investigation of the collision energy dependence of the HD(nu' = 2,j') rotational product state distribution for the H + D2 reaction in the collision energy range of Ecol = 1.30-1.89 eV has been carried out. Theoretical results based on time-dependent and time-independent quantum mechanical methods agree nearly perfectly with each other, and the agreement with the experiment is good at low collision energies and very good at high collision energies. This behavior is in marked contrast to a previous report on the HD(nu' = 3,j') product state rotational distribution [Pomerantz et al., J. Chem. Phys. 120, 3244 (2004)] where a systematic difference between experiment and theory was observed, especially at the highest collision energies. The reason for this different behavior is not yet understood. In addition, this study employs Doppler-free spectroscopy to resolve an ambiguity in the E, F-X resonantly enhanced multiphoton ionization transition originating from the HD(nu' = 2,j' = 1) state, which is found to be caused by an accidental blending with the transition coming from the HD(nu' = 1,j' = 14) state.     

Corroboration of theory for H + D2 --> D + HD (v' = 3, j' = 0) reactive scattering dynamics

The differential cross section (DCS) for the reaction H + D2 --> D + HD (v' = 3, j' = 0) exhibits particularly rich dynamics; in addition to the expected direct recoil backscattering feature, a surprising time-delayed forward scattering feature appears that has been attributed to glory scattering arising from nearside and farside interference. This fact leads to a complex DCS that depends strongly on the collision energy. Its accurate calculation requires a fully quantum mechanical (QM) treatment. We report improved measurements of this DCS over the collision energy range 1.55 < or = E(coll) < or = 1.82 eV. Previous measurements using the core extraction method, while generally in agreement with theory, lacked sufficient resolution to capture all of the noteworthy behavior of the system; in the present work, we use ion imaging to observe many previously unresolved features of the DCS, particularly in the forward-scattered region. Agreement with QM calculations is found at all collision energies, reconciling an earlier discrepancy between experiment and theory near E(coll) = 1.54 eV.     

Molecular beam scattering studies of the reaction D + H2 (v = 0) and D + H2 (v = 1) → HD + H

The reaction D + H₂ → HD + H has been investigated in two molecular beam scattering experiments. Angular and time-of-flight distributions have been measured for the initial vibrational ground state (v = 0) at a most probable collision energy of E_cm = 1.5 eV and for the first vibrational excited state (v = 1) at E_cm = 0.28 eV with the same apparatus. Results for the ground-state experiment are compared with quasiclassical trajectory calculations(QCT) on the LSTH-hypersurface transformed into the laboratory system and averaged over the apparatus distributions. The agreement isquite satisfactory. At this high collision energy the HD products are no longer scattered in a backward direction but in a wide angular region concentrated about θ = 90° in the center-of-mass system. The absolute reactive cross section has been determined and the agreement with the theoretical value from QCT calculations is within the experimental error. The high sensitivity of the experiment to different properties of the doubly differential cross section has also been demonstrated. A preliminary evaluation of the experiment with initial vibrational excitation (v = 1) shows that the HD-product molecules are preferably backward scattered and the change of internal energy is small supporting the concept of a reaction which is adiabatic with respect to the internal degrees of freedom.     

DWBA predicted relative product rotational state distribution for H + D2 → HD + D

Relative product rotational state distributions for H + D₂ → HD + D are reported based on the DWBA of Suck Salk, and are shown to agree reasonably well with observations. The rotational peak positions are found to have good correlation with computed “semiclassical” angular momentum.     

On the dynamics of the H+ +D2(v=0,j=0)-->HD+D + reaction: a comparison between theory and experiment

The H+ +D2(v=0,j=0)-->HD+D + reaction has been theoretically investigated by means of a time independent exact quantum mechanical approach, a quantum wave packet calculation within an adiabatic centrifugal sudden approximation, a statistical quantum model, and a quasiclassical trajectory calculation. Besides reaction probabilities as a function of collision energy at different values of the total angular momentum, J, special emphasis has been made at two specific collision energies, 0.1 and 0.524 eV. The occurrence of distinctive dynamical behavior at these two energies is analyzed in some detail. An extensive comparison with previous experimental measurements on the Rydberg H atom with D2 molecules has been carried out at the higher collision energy. In particular, the present theoretical results have been employed to perform simulations of the experimental kinetic energy spectra.     

Nearside-farside and local angular momentum analyses of time-independent scattering amplitudes for the H + D2 (vi = 0, ji = 0) --> HD (vf = 3, jf = 0) + D reaction

The scattering dynamics of the state-to-state reaction H + D2 (v(i) = 0, j(i) = 0, m(i) = 0) --> HD (v(f) = 3, j(f) = 0, m(f) = 0) + D is investigated, where vi, ji, mi and vf, jf, mf are initial and final vibrational, rotational, and helicity quantum numbers, respectively. We use accurate quantum scattering matrix elements for total energies in the range 1.52-2.50 eV (calculated stepwise in 0.01 eV increments). The theoretical tools used are a nearside-farside (NF) analysis of the partial wave series (PWS) for the scattering amplitude, together with NF local angular momentum (LAM) theory. We find that the backward scattering, which is the energy-domain analog of the time-direct reaction mechanism, is N dominated, whereas the forward scattering (time-delayed analog) is a result of NF interference between the more slowly varying N and F subamplitudes. The LAM analysis reveals the existence of a "trench-ridge" structure. We also resum the PWS up to three times prior to making the NF decomposition. We show that such resummations usually provide an improved physical interpretation of the NF differential cross sections (DCSs) and NF LAMs. We analyze two resummed scattering amplitudes in more detail, where particular values of the resummation parameters give rise to unexpected unphysical behavior in the N and F DCSs over a small angular range. We analyze the cause of this unphysical behavior and describe viable workarounds to the problem. The energy-domain calculations in this paper complement the time-domain results reported earlier by Monks, P. D. D.; Connor, J. N. L.; Althorpe, S. C. J. Phys. Chem. A 2006, 110, 741.     

Experimental study of the D + H2 (v = 1) reaction by CARS spectroscopy

The reactions D + H₂ (v = 0, 1) → HD (v = 0, 1) + H have been studiedin a discharge flow reactor by CARS-spectroscopy. For H₂(v = 0) molecules a rate constant of (4, 0 ± 1, 0) 10^?16 cm³ s^?1 is obtained at 310 K from measured HD (v = 0, 1) product yields. Keeping the degree of vibrational excitation of H₂in the microwave discharge in the range of 1% from the increase of the HD (v = 0, 1) CARS signals a rate of k_{2a, b} = (1, 0 ± 0, 4) 10^?13cm³ s^?1 is derived. The total consumption of H₂ (v = 1) in the presence of D atoms gives a rate k₂ = (1, 9 ± 0, 2) 10^?13 cm³ s^?1 at 310 K. The resultsare discussed in regard to previous measurements and theoretical treatments.     

State-to-state reaction probabilities for the H+O2(v,j)-->O+OH(v',j') reaction on three potential energy surfaces

We report state-to-state and total reaction probabilities for J=0 and total reaction probabilities for J=2 and 4 for the title reaction, both for ground-state and initially rovibrationally excited reactants. The results for three different potential energy surfaces are compared and contrasted. The potential energy surfaces employed are the DMBE IV surface by Pastrana et al. [J. Phys. Chem. 94, 8073 (1990)], the surface by Troe and Ushakov (TU) [J. Chem. Phys. 115, 3621 (2001)], and the new XXZLG ab initio surface by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. Our results show that the total reaction probabilities from both the TU and XXZLG surfaces are much smaller in magnitude for collision energies above 1.2 eV compared to the DMBE IV surface. The three surfaces also show different behavior with regards to the effect of initial state excitation. The reactivity is increased on the XXZLG and the TU surfaces and decreased on the DMBE IV surface. Vibrational and rotational product state distributions for the XXZLG and the DMBE IV surface show different behaviors for both types of distributions. Our results show that for energies above 1.25 eV the dynamics on the DMBE IV surface are not statistical. However, there is also evidence that the dynamics on the XXZLG surface are not purely statistical for energies above the onset of the first excited product vibrational state v'=1. The magnitude of the total reaction probability is decreased for J>0 for the DMBE IV and the XXZLG surfaces for ground-state reactants. However, for initially rovibrationally excited reactants, the total reaction probability does not decrease as expected for both surfaces. As a result the total cross section averaged over all Boltzmann accessible rotational states may well be larger than the cross section reported in the literature for j=1.     

Significant nonadiabatic effects in the S(1D) + HD reaction

A nonadiabatic quantum dynamics calculation involving four coupled potential energy surfaces (two degenerate 3A' ', one 3A', and one 1A') and the spin-orbit coupling matrix for these states is reported for the title reaction. The results show that the important discrepancy between theoretically calculated and experimentally measured intramolecular isotope effects can at least in part be attributed to significant nonadiabatic effects.     

The dependence of the branching ratio in the F+HD reaction on the initial rotational state of HD

Both classical trajectory and quantal scattering calculations indicate that the branching ratio in the F+HD reaction varies considerably with the initial rotational state of HD. Information theory argues that this variation must be reflected in the distribution of the reaction products. Hence, given the (normalized) product distribution for each reaction path one should be able to predict the dependence of the branching ratio on the state of the reagents. The trajectory computations of Muckerman are used to illustrate the procedure. First the dynamic constraint is identified and then the reaction probability matrix is constructed. The determination (“synthesis”) of the matrix, in terms of the given constraint invokes information theory and, in particular, the procedure of maximising the entropy. The branching ratio is readily computed from the elements of the probability matrix. Very good agreement is obtained between the trajectory-computed and the synthetic branching ratio for all initial rotational states of HD.The F+HD reaction has three possible final arrangement channels (one nonreactive and two reactive ones) and is used to illustrate the structure of the reaction probability matrix and the associated entropy measures.     

A quantum reaction dynamics study of the translational, vibrational, and rotational motion effects on the HD + H3+ reaction

Time-dependent, quantum reaction dynamics wavepacket approach is employed to investigate the impacts of the translational, vibrational, and rotational motion on the HD+H(3)(+) → H(2)D(+) + H(2) reaction using the Xie-Braams-Bowman potential energy surface [Z. Xie, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 122, 224307 (2005)]. We treat this five atom reaction with a seven-degree-of-freedom model by fixing one Jacobi and one torsion angle related to H(3) (+) at the lowest saddle point geometry of the potential energy surface. The initial state selected reaction probabilities show that the rotational excitations of H(+)-H(2) greatly enhance the reactivity with the reaction probabilities increased double at high rotational states compared to the ground state. However, the vibrational excitations of H(3) (+) hinder the reactivity. The ground state reaction probability shows no reaction threshold for this exoergic reaction, and as the translational energy increases, the reaction probability decreases. Furthermore, reactive resonances and zero point energy play very important roles on the reaction dynamics. The obtained integral cross section has the character of an exoergic reaction without a threshold: it decreases with the translational energy increasing. The calculated thermal rate constants using this seven-degree-of-freedom model are in agreement with a later experiment measurement.     

Energy dependence of rotational and vibrational distributions of N2(C) for the Ar*(3P0,2) + N2(X) excitation transfer reaction

The Ar* + N₂(X) → N₂(C, v′, N′) + Ar excitation transfer reaction has been investigated experimentally in two different atomic beam experiments. The inelastic cross sections Q_{v′ = 0}(E) and Q_{v′ = 1}(E) to the v′ vibrational level have been measured in the energy range 0.06 ⩽ E(eV) ⩽ 6, using a crossed beam machine. Both cross sections show a behaviour typical for a curve crossing mechanism, with maximum values Q₀ = 8.0 Ų and Q₁ = 1.2 Ų at E = 0.16 eV and E = 0.13 eV, respectively. The oscillatory behaviour of the ratio Q₁(E)/Q₀(E), as first observed by Cutshall and Muschlitz, is also present in our data. Within the model of Gislason et al. the results indicate a decreasing bond stretching with increasing energy. As an alternative we discuss the possibility that the oscillation is due to a different energy dependence of the cross sections for the Ar*(³P₀) and Ar*(³P₂) fine structure states in the mixed beam of metastable Ar*. The vibrational and rotational distributions have also been measured at E = 0.065 eV in a small scale atomic beam-scattering cell experiment, which can be considered as an intermediate between a bulk experiment and a crossed beam experiment. The relative vibrational populations are n_v′ = 100, 16.0, 3.03 and 0.31 for v′ = 0 through 3, with rotational “temperatures” of T_rot,v′ = 1960, 1010, 370 and 130 K. Pronounced deviations (“hump”) of the Boltzmann rotational distributions occur at N′ ≈ 27 for v′ = 0, 1 and 2, with a fractional population of 1, 3 and 11%. For v′ = 0 the “hump” is largely obscured by overlap with the v′ = 1 bandhead. These bimodal distributions are in qualitative agreement with the results of Nguyen and Sadeghi for v′ = 0. The results are discussed within the framework of a curve crossing mechanism with the Ar⁺-N⁻₂ diabatic potential as an intermediate. By assuming equal charges on both N atoms the Coulomb potential of the collinear orientation lies lower (0.45 eV at R = 2.5 Å) than the perpendicular orientation, with the consequence of different transfer probabilities for both orientations. Within a classical model or rotational excitation the final N′ values can be calculated for both orientations, resulting in much higher N′ values for the perpendicular orientation. This mechanism supplies a qualitative explanation for the observed bimodal rotational distributions.     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

The exchange reaction H2 (ν = 1) + H = H + H2

The classical trajectory method is applied to calculate the total cross section for the exchange reaction H₂(ν = 1) + H = H + H₂. The vibrational excitation is shown to influence efficiently the threshold value. Partial reaction rate-constants calculated on the basis of the cross sections obtained are in good agreement with those measured in H-maser experiments.     

Vibrational and rotational distributions of the CH(A2Delta) product of the C(2)H + O(3P) reaction studied by fourier transform visible (FTVIS) emission spectroscopy

The C(2)H + O((3)P) --> CH(A) + CO reaction is investigated using Fourier transform visible emission spectroscopy. The O((3)P) and C(2)H radicals are produced by simultaneous 193 nm photolysis of SO(2) and C(2)H(2) precursors, respectively. The nascent vibrational and rotational distributions of the CH(A) product are obtained under time-resolved, but quasi-steady-state, conditions facilitated by the short lifetime of the CH(A) emission. The vibrational temperature of the CH(A) product is found to be appreciably hotter (2800 +/- 100 K) than the rotational distributions in the v' = 0 (1400 +/- 100 K) and v' = 1 (1250 +/- 250 K) levels. The results suggest that the reaction may proceed through an electronically excited HCCO() intermediate; moreover, the vibrational excitation compared to rotational excitation is higher than expected based on a statistical distribution of energy and may be the result of geometrical changes in the transition state. The CH(A) emission is also observed in a C(2)H(2)/O/H reaction mixture using a microwave discharge apparatus to form O atoms, with subsequent H atom production. The nascent rotational and vibrational distributions of the CH(A) determined by the microwave discharge apparatus are very similar to the CH(A) distributions obtained in the photodissociation experiment. The results support the idea that the C(2)H + O((3)P) reaction may play a role in low-pressure C(2)H(2)/O/H flames, as previously concluded.     

Time dependent quantum dynamics study of the O++H2(v=0,j=0)-->OH++H ion-molecule reaction and isotopic variants (D2,HD)

The time dependent real wave packet method using the helicity decoupling approximation was used to calculate the cross section evolution with collision energy (excitation function) of the O++H2(v=0,j=0)-->OH++H reaction and its isotopic variants with D2 and HD, using the best available ab initio analytical potential energy surface. The comparison of the calculated excitation functions with exact quantum results and experimental data showed that the present quantum dynamics approach is a very useful tool for the study of the selected and related systems, in a quite wide collision energy interval (approximately 0.0-1.1 eV), involving a much lower computational cost than the quantum exact methods and without a significant loss of accuracy in the cross sections.     

Electronic transitions in collinear H+ + D2 (ν = 0) → HD+ (ν = 0,1) + D via classical trajectories in complex time and complex phase space

A semiclassical treatment of electronic transitions in the collinear rearrangement H⁺ + D₂ (ν = 0) → HD⁺ (ν = 0,1) + D is presented. The treatment represents an extension of Stueckelberg's method for a single nuclear degree of freedom to collisions involving several nuclear degrees of freedom. The classical limit of scattering amplitudes (S-matrix elements) is calculated for the transition between the two adiabatic potential energy surfaces corresponding to the two lowest singlet states of HD⁺₂. S-matrix elements are constructed from trajectories propagating in complex time and complex phase space, which make localized transitions between the two surfaces by crossing their complex line of intersection. The action along each trajectory acquires an imaginary part, which contributes exponential damping to the corresponding amplitude for electronic transition.     

Stereodynamics of the F + HD(v = 0, j = 1) reaction: direct vs. resonant mechanisms

The stereodynamics and mechanism of the F + HD(v = 0, j = 1) → HF (DF) + D (H) reactions have been thoroughly analysed at collision energies in the 0-160 meV range. Specifically, this study is focused on (i) the comparison between the stereodynamics of the collisions leading to HF and DF formation, and (ii) the stereodynamical fingerprints of the resonance that occurs at low collision energies in the HF channel and whose manifestation in the total cross section is greatly diminished for initial j > 0. While previous studies were limited to the analysis of integral cross sections (ICS), differential cross sections (DCS) and reaction probabilities, in the present work we have included the analysis of vectorial quantities such as the direction of the initial rotational angular momentum and internuclear axis, and their effect on reactivity. In particular, polarisation parameters (PP) and polarisation dependent differential cross sections (PDDCS), quantities that describe how the intrinsic HD rotational angular momentum and molecular axis polarisations contribute to reaction, are calculated and examined. The evolution of the PPs with the collision energy differs markedly between the two reaction channels. For the DF channel, the PP values are small and change very little in the energy range in which DF formation is appreciable. In contrast, rapid fluctuations in the magnitude and sign of the PPs are observed in the HF channel at low collision energies in and around the resonance. As the collision energy increases, direct (non-resonant) scattering prevails, and the various quantities are reasonably well accounted for by the QCT calculations, as in the case of the DF channel. The intrinsic directional information has been used to access the extent of control that can be achieved through polarisation of the HD molecule prior to collision. It was found that the same extrinsic preparation leads to very different outcomes on the HF channel DCS when the collision energy is close to the resonance. It is also shown that polarisation of the HD internuclear axis along the initial relative velocity enhances the effect of the resonance and allows its clear identification. Finally, the effect of different extrinsic preparations on the angle-velocity DCS is found to be strong, thus allowing considerable control of product angular distributions.