A DWBA study of angular distributions for the state-to-state reactive scattering process of F + H2 → HF + H

Based on our earlier three-dimensional DWBA theory, we discuss angular distributions and the roles of various angular momenta. The theory predicts a relatively small number of partial waves, backward scattering, and broadening of angular distributions with increased energy, for the reaction F+ H₂ (v_a = 0, j_a = 0) → HF (v_b = 2 j_b = 0) + H     

Overlapping resonances and Regge oscillations in the state-to-state integral cross sections of the F+H2 reaction

A Regge pole analysis is employed to explain the oscillatory patterns observed in numerical simulations of integral cross section for the F+H(2)(v=0,j=0)-->HF(v(')=2,j(')=0)+H reaction in the translational collision energy range 25-50 meV. In this range the integral cross section for the transition, affected by two overlapping resonances, shows nearly sinusoidal oscillations below 38 meV and a more structured oscillatory pattern at larger energies. The two types of oscillations are related to the two Regge trajectories which (pseudo) cross near the energy where the resonances are aligned. Simple estimates are given for the periods of the oscillations.     

Lifetime of reactive scattering resonances: Q-matrix analysis and angular momentum dependence for the F+H2 reaction by the hyperquantization algorithm

We report a study on the behavior with total angular momentum J of several resonances occurring at collision energies below or slightly above the reaction barrier in the F+H2-->HF+H reaction. Resonance positions and widths are extracted from exact time-independent quantum mechanical calculations using the hyperquantization algorithm and Smith's Q-matrix formalism which exploits complete S-matrix information. The results confirm previous work but provide much greater insight. Identification of quasi-bound states responsible for the resonances based on adiabatic models for the long-range atom-molecule interactions both in the entrance and exit channels, is successful except for the feature occurring at the lowest energy, which is found to overlap with an exit-channel resonance for J approximately 7. The two features are analyzed as overlapping resonances and their excellent Lorentzian fits, with well-behaved J-dependences of positions and widths, support the interpretation of the low-energy feature as a resonance to be associated to the triatomic transition state of the reaction. Resonance role on the reactive observables (integral cross sections and angular distributions) is investigated. The mechanism leading to forward scattering in the reactive differential cross section is commented, while the effects on rate constants, as well as the sensitivity of the resonance pattern to modification of the potential energy surface, are fully discussed elsewhere.     

Interacting resonances in the F+H2 reaction revisited: complex terms, Riemann surfaces, and angular distributions

We study the effect of overlapping resonances on the angular distributions of the reaction F+H2(v=0,j=0)-->HF(v=2,j=0)+H in the collision energy range from 5 to 65 meV, i.e., under the reaction barrier. Reactive scattering calculations were performed using the hyperquantization algorithm on the potential energy surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. The positions of the Regge and complex energy poles are obtained by Pade reconstruction of the scattering matrix element. The Sturmian theory is invoked to relate the Regge and complex energy terms. For two interacting resonances, a two-sheet Riemann surface is contracted and inverted. The semiclassical complex angular momentum analysis is used to decompose the scattering amplitude into the direct and resonance contributions.     

A state-to-state dynamical study of the Br + H(2) reaction: comparison of quantum and classical trajectory results

We present a detailed theoretical investigation of the dynamics corresponding to the strongly endothermic Br + H(2) (v = 0-1, j = 0) → H + HBr reaction in the 0.85 to 1.9 eV total energy range. State-averaged and state-to-state results obtained through time-independent wave packet (TIWP) and time-independent quantum mechanical (TIQM) calculations and quasiclassical trajectories (QCT) are compared and analyzed. The agreement in the results obtained with both quantum mechanical results is very good overall. However, although QCT calculations reproduce the general features, their agreement with the QM results is sometimes only qualitative. The analysis of the mechanism based on state-averaged results turns out to be deceptive and conveys an oversimplified picture of the reaction consistent with a direct-rebound mechanism. Consideration of state-to-state processes, in contrast, unveils the existence of multiple mechanisms that give rise to a succession of maxima in the differential cross section (DCS). Such mechanisms correlate with different sets of partial waves and display similar collision times when analyzed through the time-dependent DCS.     

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction

The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation.     

Communication: non-adiabatic coupling and resonances in the F + H2 reaction at low energies

Quantum reactive scattering calculations on accurate potential energy surfaces predict that at energies below ～5 meV, the reaction of F atoms with H(2) is dominated by the Born-Oppenheimer (BO) forbidden reaction of the spin-orbit excited F((2)P(1∕2)) atom. This non-BO dominance is amplified by low-energy resonances corresponding to quasi-bound states of the HF(v = 3, j = 3) + H product channel. Neglect of non-adiabatic coupling between the electronic states of the F atom leads to a qualitatively incorrect picture of the reaction dynamics at low energy.     

Mechanism and control of the F+H2 reaction at low and ultralow collision energies

This article uses theoretical methods to study the dependence on stereodynamical factors of the mechanism and reactivity of the F+H2 reaction at low and ultralow collision energies. The impact of polarization of the H2 reactant on total and state-to-state integral and differential cross sections is analyzed. This leads to detailed pictures of the reaction mechanism in the cold and ultracold regimes, accounting, in particular, for distinctions associated with the various product states and scattering angles. The extent to which selection of reactant polarization allows for external control of the reactivity and reaction mechanism is assessed. This reveals that even the simplest of reactant polarization schemes allows for fine, product state-selective control of differential and (for reactions involving more than a single, zero orbital angular momentum partial wave) integral cross sections.     

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.     

Quantum scattering LCAC-SW theory studies on reaction probabilities of three-dimensional H + H2 (v, j) → H2 (v′, j′) + H reaction

Upon the Liu, Siegbahn, Truhlar, Horowitz (LSTH) potential energy surface, the reaction probabilities of the three-dimensional (3-D) state-to-state H + H₂ (v, j) →H ₂(v′, j′) + H reaction are calculated with the linear combination of arrangement channels-scattering wavefunction (LCAC-SW) method. In the calculation, the vibration function of H₂ and the radial propagating wave functions are expanded by the real Gauss functions. The calculated threshold energy and the resonating structure are consistent with the results of the accurate quantum scattering calculations, which shows the accuration, simplicity and practicability of the LCAC-SW method. Project supported by the National Natural Science Fondation of China and the Doctoral Foundation of the State Education Commission of China.     

Exact state-to-state quantum dynamics of the F + HD --> HF(v' = 2) + D reaction on model potential energy surfaces

In this paper, we present the results of a theoretical investigation on the dynamics of the title reaction at collision energies below 1.2 kcal/mol using rigorous quantum reactive scattering calculations. Vibrationally resolved integral and differential cross sections, as well as product rotational distributions, have been calculated using two electronically adiabatic potential energy surfaces, developed by us on the basis of semiempirical modifications of the entrance channel. In particular, we focus our attention on the role of the exothermicity and of the exit channel region of the interaction on the experimental observables. From the comparison between the theoretical results, insight about the main mechanisms governing the reaction is extracted, especially regarding the bimodal structure of the HF(v = 2) nascent rotational state distributions. A good overall agreement with molecular beam scattering experiments has been obtained.     

A crossed-beam study of the F+HD-->DF+H reaction: the direct scattering channel

State-to-state differential cross sections of the title reaction are presented at four collision energies, ranging from 1.18 to 4.0 kcal /mol. Product angular distributions are predominantly backscattered at low energies and shift toward sideways (peaking near 150 degrees ) at higher energies. Experimental evidence for contributions from migratory trajectories was found in the more detailed angle-specific internal state distributions. The dynamics of this reaction is mostly governed by classical mechanics, and several major findings can qualitatively be rationalized. These "classical" behaviors serve as "references" and are to be contrasted to the attributes observed for the other isotopic product channel, HF+D, in a forthcoming paper.     

Theoretical evidence for nonadiabatic vibrational deexcitation in H2(D2) state-to-state scattering from Cu(100)

Dynamical calculations are presented for electronically nonadiabatic vibrational deexcitation of H2 and D2 in scattering from Cu(111). Both the potential energy surface and the nonadiabatic coupling strength were obtained from density functional calculations. The theoretically predicted magnitude of the deexcitation and its dependence on incident energy and isotope are all in agreement with state-to-state scattering experiments [on Cu(100)], and this gives indirect evidence for a nonadiabatic mechanism of the observed deexcitation. Direct evidence could be obtained by measuring the chemicurrent associated with the deexcitation, and its properties have been predicted.     

The microscopic reaction dynamics and branching ratio in the F + HCOOH and F + H2CO reactions

Infrared chemiluminescence under conditions of arrested relaxation has been applied to the study of the hydrogen and deuterium abstraction reactions of HCOOH, DCOOH and H₂CO with F atoms. Two distinctly different modes of product excitation are observed, depending upon whether the reaction proceeds via the formyl or carboxyl hydrogen. Reaction at the formyl hydrogen (or deuterium) causes substantial inversion in the diatomic product internal energy distributions. The F + H₂CO and F + DCOOH reactions respectively channel 56% and 54% of the available energy into vibration in the product diatomic when they occur at the formyl site. In both cases the product energy distributions are qualitatively similar to those observed in direct reactions of triatomic systems on repulsive energy surfaces. In contrast to these, reaction at the carboxyl hydrogen of DCOOH gives an HF2 product vibrational distribution having a Boltzmann equilibrium shape at a temperature of 4300 K. The ratio of HF to DF product from the F + DCOOH study shows that reaction occurs at the carboxyl hydrogen approximately twice as often as at the formyl site. Comparison with triatomic reactions involving the same mass-combinations implies that abstraction of the formyl hydrogen occurs via single-collision, direct encounters, whereas reaction at the carboxyl site involves a long-lived complex in which extensive randomisation of the reaction exoergicity among all the product vibrational modes can occur.     

Glory and thresholds effects in H+D2 reactive angular scattering

We analyse H+D₂ reactive angular scattering using the S-matrix elements obtained by Aoiz et al. and Althorpe et al. Enhancement of small angle scattering in the v^′=3←v=0 H+D₂ delayed reaction is attributed to a glory effect caused by threshold resonances in the v=3 vibrationally adiabatic channel. The oscillatory structures in the reactive angular distributions are shown to be of nearside–farside (NP) origin and are likely to arise from capture in a number of relatively short-lived barrier Regge states at large angular momenta. Padé reconstruction of the reactive matrix element is discussed in detail.     

Nonadiabatic reactant-product decoupling calculation for the F(2P(1/2)) + H2 reaction

In this paper we present a theoretical study using time-dependent nonadiabatic reactant-product decoupling method for the state-to-state reactive scattering calculation of F((2)P(1/2))+H(2) (nu=j=0) reaction on the Alexander-Stark-Werner potential energy surface. In this nonadiabatic state-to-state calculation, the full wave function is partitioned into reactant component and a sum of all product components. The reactant and product components of the wave function are solved independently. For the excited state reaction, the state-to-state reaction probabilities for J=0.5 are calculated. Comparing the state-to-state reaction probabilities, it is found that the vibrational population of the HF product is dominated by vibrational levels nu=2 and 3. The rotation specific reaction probabilities of HF product in j=1 and 2 are larger than those in other rotational levels. As the rotation quantum number j increases, the positions of the peak in the rotational reaction probability of HF product in nu=3 shift to higher collision energy.     

The dynamics of the Cl+n-C4H10-->HCl (v',j') + C4H9 reaction at 0.32 eV

Rotational state resolved center-of-mass angular scattering and kinetic energy release distributions have been determined for the HCl (v' = 0, j' = 0-6) products of the reaction of chlorine with n-butane using the photon-initiated reaction technique, coupled with velocity-map ion imaging. The angular and kinetic energy release distributions derived from the ion images are very similar to those obtained previously for the Cl plus ethane reaction. The angular distributions are found to shift from forward scattering to more isotropic scattering with increasing HCl rotational excitation. The kinetic energy release distributions indicate that around 30% of the available energy is channeled into internal excitation of the butyl radical products. The data analysis also suggests that H-atom abstraction takes place from both primary and secondary carbon atom sites, with the primary site producing rotationally cold, forward scattered HCl (v' = 0) products, and the secondary site yielding more isotropically scattered HCl (v' = 0) possessing higher rotational excitation. The mechanisms leading to these two product channels are discussed in the light of the present findings, and in comparison with studies of other Cl plus alkane reactions.     

Quantum-mechanical differential reaction cross sections for the F + H2(ν = 0) - FH(ν′= 2.3) + H reaction

Velocity scatterring angle intensity maps for the F + H₂(ν = 0): j = 0) $\text{\$}\text{?}$FH(ν′ = 2, 3: j′) + 11 reaction are predicted from quantum-mechanical J conserving, calculations. The extent of the shift in the angular distribution from backscattering at 1.8 kcal/mole to sideways scattering (intensity peak at 100°) at 3.0 kcal/mole is in quantitative agreement with recent crossed molecular beans experiments.