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.     

Exploring the accuracy level of new potential energy surfaces for the F + HD reactions: from exact quantum rate constants to the state-to-state reaction dynamics

Exact quantum reactive scattering calculations in the collision energy range 1-250 meV have been carried out for both the isotopic product channels of the title system. The dynamical studies compares an ab initio potential energy surface (PES) recently appeared in the literature (J. Chem. Phys., 2008, 129, 011103) with other phenomenological PESs. Vibrational branching ratios, cross sections and rate constants are presented and compared with molecular beam scattering experiments as well as with chemical kinetics data. In particular, the agreement of the vibrational branching ratios with experimental measurements is improved with respect to previous studies on other PESs, mainly because of the presence of a broad peak in the HF(v' = 3) integral cross section completely absent in the previous simulations. This feature, observed by molecular beam experiments, is the fingerprint of a new reaction mechanism operative in the dynamics described by the new PES. A conjecture for its origin, able to explain many of its characteristic aspects, is analyzed and discussed.     

On the origin of the forward peak and backward oscillations in the F + H(2)(v = 0) --> HF(v' = 2) + H reaction

We present a semiclassical complex angular momentum (CAM) analysis of the forward scattering peak which occurs at a translational collision energy around 32 meV in the quantum mechanical calculations for the F + H(2)(v = 0, j = 0) --> HF(v' = 2, j' = 0) + H reaction on the Stark-Werner potential energy surface. The semiclassical CAM theory is modified to cover the forward and backward scattering angles. The peak is shown to result from constructive/destructive interference of the two Regge states associated with two resonances, one in the transition state region and the other in the exit channel van der Waals well. In addition, we demonstrate that the oscillations in the energy dependence of the backward differential cross section are caused by the interference between the direct backward scattering and the decay of the two resonance complexes returning to the backward direction after one full rotation.     

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.     

Imaging the pair-correlated excitation function: The F+CH4-->HF(v')+CH3(nu=0) reaction

The velocity map ion imaging technique was applied to measure the reaction excitation function for the first time. It was found that the "raw" excitation function was significantly distorted by the density-to-flux transformation of the title reaction. Through a systematic investigation, possible reasons for such a dramatic effect are outlined. In addition, the state-resolved, pair-correlated excitation functions and branching ratios are presented. Effects of imperfect time slicing in the time-sliced velocity imaging technique in general are also discussed.     

Renner-Teller quantum dynamics of the N(2D) + H2-->NH + H reaction

We present the Born-Oppenheimer (BO) and Renner-Teller (RT) quantum dynamics of the reaction (14)N((2)D)+(1)H(2)(X (1)Sigma(g) (+))-->NH(X (3)Sigma(-))+H((2)S), considering the NH(2) electronic states X (2)B(1) and A (2)A(1). These states correlate to the same (2)Pi(u) linear species, are coupled by RT nonadiabatic effects, and give NH(X (3)Sigma(-))+H and NH(a (1)Delta)+H, respectively. We develop the Hamiltonian matrix elements in the R embedding of the Jacobi coordinates and in the adiabatic electronic representation, using the permutation-inversion symmetry, and taking into account the nuclear-spin statistics. Collision observables are calculated via the real wave-packet (WP) and flux methods, using the potential-energy surfaces of Santoro et al. [J. Phys. Chem. A 106, 8276 (2002)]. WP snapshots show that the reaction proceeds via an insertion mechanism, and that the RT-WP avoids the A (2)A(1) potential barrier, jumping from the excited to the ground surface and giving mainly the NH(X (3)Sigma(-)) products. X (2)B(1) BO probabilities and cross sections show large tunnel effects and are approximately four to ten times larger than the A (2)A(1) ones. This implies a BO rate-constant ratio k(X (2)B(1))k(A (2)A(1)) approximately 10(5) at 300 K, i.e., a negligible BO formation of NH(a (1)Delta). When H(2) is rotationally excited, RT couplings reduce slightly the X (2)B(1) reaction observables, but enhance strongly the A (2)A(1) reactivity. These couplings are important at all collision energies, reduce the collision threshold, and increase remarkably reaction probabilities and cross sections. The RT k(A (2)A(1)) is thus approximately 3.3 order of magnitude larger than the BO value, and degeneracy-averaged, initial-state-resolved rate constants increase by approximately 13% and by approximately 47% at 300 and 500 K, respectively. Owing to an overestimation of the X (2)B(1) potential barrier, the calculated thermal rate is too low with respect to that observed, but we obtain a good agreement by shifting down the calculated cross section.     

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.     

Anatomy of the S(1D) + H2 reaction: the dynamics on two new potential energy surfaces from quantum dynamics calculations

We present exact quantum integral and differential cross sections for the title reaction from a time-dependent wavepacket method which takes account of all Coriolis couplings. We employ two new potential energy surfaces fitted using the double many-body expansion (DMBE) method. The difference between the two surfaces is that for the first the data was extrapolated to the complete basis set limit (CBS) and for the second the data was corrected semi-empirically (SEC). While the DMBE/CBS surface is, on first impressions, regarded as the most accurate, our results show that this surface gives consistent smaller cross section when compared to previous results employing an earlier surface, named Ho after its first author. We also find that the DMBE/CBS surface features an unphysical barrier for contracted H(2) distances which explains the smaller results. The DMBE/SEC surface, which is based on the same data, does not show the same barrier and the results compare much better to previous theoretical results as well as those from experiment. While we find that overall the differential cross sections from the DMBE/SEC surface are forward scattered, which is in line with experiment, the cross sections do not rise steeply enough with decreasing energy showing that this surface is not sufficiently attractive at low energies. We find this is due to a shallow van der Waals well present for the Ho surface but not on the DMBE surfaces.     

A quantum scattering study of collinear state-testate reaction probabilities for the F + H2(v) → HF(v') + H system

A new quantum scattering approach (linear combination of arrangement channels-scattering wavefunction, LCAC-SW) proposed by Deng and his co-workers is used to calculate collinear state-to-state reaction probabilities for the F + H₂(v) → HF(v') + H system. Several interesting problems such M threshold energy, compound states and enhance by translational energy of the reactants and the vibration excitation of products are discussed and they are compared with other theoretical investigations reported in the literature. It is shown that the LCAC-SW approach is the successful one of quantum scattering methods.     

Exact quantum dynamics of N(2D) + H2 --> NH + H reaction: cross-sections, rate constants, and dependence on reactant rotation

Using an exact Chebyshev wave packet method, initial state-specified (upsilon(i)=0, j(i)=0,2) integral cross-sections and rate constants are obtained for the title reaction on the latest ab initio potential energy surface. Reaction probabilities up to J=29 are dependent on the reactant rotation and show mild oscillations superimposed on a broad background. Due to a barrier in the entrance channel, the cross sections increase with energy with clear thresholds and the rate constants vary with temperature in the Arrhenius form. The calculated canonical rate constant is in good agreement with the experimental measurements. Our results also indicate that the quasiclassical trajectory method underestimates the rate due to the neglect of tunneling, while the quantum statistical approach overestimates because of the short lifetime of the reaction intermediate.     

Mixed quantum-classical reaction path dynamics of C2H5F --> C2H4 + HF

A mixed quantum-classical method for calculating product energy partitioning based on a reaction path Hamiltonian is presented and applied to HF elimination from fluoroethane. The goal is to describe the effect of the potential energy release on the product energies using a simple model of quantized transverse vibrational modes coupled to a classical reaction path via the path curvature. Calculations of the minimum energy path were done at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G** levels of theory, followed by energy-partitioning dynamics calculations. The results for the final HF vibrational state distribution were found to be in good qualitative agreement with both experimental studies and quasiclassical trajectory simulations.     

New results for the OH (nu = 0,j = 0) + CO (nu = 0,j = 0) --> H + CO2 reaction: Five- and full-dimensional quantum dynamical study on several potential energy surfaces

Full- [six-dimensional (6-D)] and reduced-dimensional [five-dimensional (5-D)] quantum wave packet calculations have been performed for the title reaction to obtain reaction probabilities deriving from the ground rovibrational states of OH and CO with total angular momentum J = 0. Three potential energy surfaces (PES) are studied, namely, those of Bradley and Schatz (BS), Yu, Muckerman, and Sears (YMS), and Lakin, Troya, Schatz, and Harding (LTSH). 6-D calculations are performed only for the BS PES, while 5-D results are reported for all three PES'. The 6-D results obtained in the present work improve on those previously reported, since a larger vibrational basis and a better representation of the OH and CO bonds has been introduced. In particular, we now employ a generalized Lanczos-Morse discrete variable representation for both the OH and CO vibrations. In a further improvement, the generalized discrete variable representation of the CO vibration is based on different CO intramolecular potentials for the asymptotic and product grids employed in our projection formalism. This new treatment of the vibrational bases allows for a large reduction in computation time with respect to our previous implementation of the wave packet method, for a given level of accuracy. As a result, we have been able to extend the range of collision energies for which we can obtain converged 6-D results to a higher energy (0.8 eV) than was possible before (0.5 eV). The comparison of the new 6-D and previous 5-D results for the BS PES shows good agreement of the general trend in the reaction probabilities over all collision energies considered (0.1-0.8 eV), while our previous 6-D calculation showed reaction probabilities that differed from the 5-D results by up to 10% between 0.5 and 0.8 eV. The 5-D reaction probabilities reveal interesting trends for the different PES'. In particular, at low energies (< 0.2 eV) the LTSH PES gives rise to much larger reactivity than the other PES', while at high energies (> 0.3 eV) its reaction probability decreases with respect to the BS and YMS PES', being more than a factor of 2 smaller at 0.8 eV. A 5-D calculation on a modified version of the LTSH surface shows that the van der Waals interaction in the entrance channel, which is not correctly described in the other PES' is largely responsible for its larger reactivity at low energies. The large difference between the 5-D reaction probabilities for the YMS and LTSH PES' serves to emphasize the importance of the van der Waals interaction for the reactivity at low energies, because most of the stationary point energies on the YMS and LTSH PES are rather similar, being in line with high-level ab initio information.     

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.     

Probing Feshbach resonances in F+H2(j=1)-->HF+H: dynamical effect of single quantum H2-rotation

Full quantum state resolved scattering of the F atom reaction with H(2)(j=0) and H(2)(j=1) was investigated at the collision energies of 0.19 and 0.56 kcalmol. Dramatic difference between the dynamics for the F+H(2)(j=0,1) reactions at both collision energies have been observed. Forward scattering HF(v(')=2) products have been observed unambiguously for the F+H(2)(j=1) reaction at low collision energies, which was attributed to the Feshbach resonances. This study provides a unique case of reaction resonances involving a rotationally excited reagent.     

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.     

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.     

Reduced dimensionality quantum scattering calculations on the F + CH(4) --> FH + CH(3) reaction

The existence of recently observed scattering resonances in the hydrogen abstraction reaction F + CH4 --> FH + CH3 was investigated using the reduced dimensionality rotating line umbrella (RLU) quantum scattering model and employing an analytical potential energy surface, PES-2006, recently developed by our group. The calculations were performed in hyperspherical coordinates. The wells found in the hyperspherical adiabats, the oscillatory pattern in the cumulative and state-to-state reaction probabilities, the forward/backward predominance in the differential cross section at a collision energy of 1.8 kcal mol(-1), and the dramatic change of the scattering angle with energy are related to scattering resonances, and they are assigned to a quasi-bound complex on the vibrationally adiabatic ground-state potential.     

Quantum dynamics study of the K+HF(v=0-2,j=0)-->KF+H reaction and comparison with quasiclassical trajectory results

Extensive quantum real wave packet calculations within the helicity decoupling approximation are used to analyze the influence of the HF vibrational excitation on the K+HF(v=0-2,j=0)-->KF+H reaction. Quantum reaction probabilities P and reaction cross sections sigma are compared with corresponding quasiclassical trajectory (QCT) results. Disregarding threshold regions for v=0 and 1 (v=2 has no threshold), both approaches lead to remarkably similar results, particularly for sigma, validating the use of the QCT method for this system. When moving from v=0 to v=1 there is a large increase in P and sigma, as expected for a late barrier system. For v=2 the reaction becomes exoergic and P approximately 0.95 (with the exception of large total angular momenta where centrifugal barriers play a role). While substantial vibrational enhancement of the reactivity is thus seen, it is still quite less than that inferred from experimental data in the intermediate and high collision energy ranges. The origin of this discrepancy is unclear.     

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.