The case for a reactive resonance in F+H2

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H2 → FH + H reaction at Etrans = 62.09 meV

The aim of the present paper is to bring clarity, through simplicity, to the important and long-standing problem: does a resonance contribute to the forward-angle scattering of the F + H2 reaction? We reduce the problem to its essentials and present a well-defined, yet rigorous and unambiguous, investigation of structure in the differential cross sections (DCSs) of the following three state-to-state reactions at a translational energy of 62.09 meV: F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 0, 1, 2, mf = 0) + H, where vi, ji, mi and vf, jf, mf are the initial and final vibrational, rotational and helicity quantum numbers respectively. Firstly, we carry out quantum-scattering calculations for the Fu-Xu-Zhang potential energy surface, obtaining accurate numerical scattering matrix elements for indistinguishable H2. The calculations use a time-independent method, with hyperspherical coordinates and an enhanced Numerov method. Secondly, the following theoretical techniques are employed to analyse structures in the DCSs: (a) full and Nearside-Farside (NF) partial wave series (PWS) and local angular momentum theory, including resummations of the full PWS up to second order. (b) The recently introduced "CoroGlo" test, which lets us distinguish between glory and corona scattering at forward angles for a Legendre PWS. (c) Six asymptotic (semiclassical) forward-angle glory theories and three asymptotic farside rainbow theories, valid for rainbows at sideward-scattering angles. (d) Complex angular momentum (CAM) theories of forward and backward scattering, with the Regge pole positions and residues computed by Thiele rational interpolation. Thirdly, our conclusions for the three PWS DCSs are: (a) the forward-angle peaks arise from glory scattering. (b) A broad (hidden) farside rainbow is present at sideward angles. (c) A single Regge pole contributes to the DCS across the whole angular range, being most prominent at forward angles. This proves that a resonance contributes to the DCSs for the three transitions. (d) The diffraction oscillations in the DCSs arise from NF interference, in particular, interference between the Regge pole and direct subamplitudes.

Dynamical resonances in chemical reactions

The transition state is a key concept in the field of chemistry and is important in the study of chemical kinetics and reaction dynamics.

A review of dynamical resonances in A + BC chemical reactions

The concept of the transition state has played an important role in the field of chemical kinetics and reaction dynamics. Reactive resonances in the transition-state region can dramatically enhance the reaction probability; thus investigation of the reactive resonances has attracted great attention from chemical physicists for many decades. In this review, we mainly focus on the recent progress made in probing the elusive resonance phenomenon in the simple A  +  BC reaction and understanding its nature, especially in the benchmark F/Cl  +  H₂ and their isotopic variants. The signatures of reactive resonances in the integral cross section, differential cross section (DCS), forward- and backward-scattered DCS, and anion photodetachment spectroscopy are comprehensively presented in individual prototype reactions. The dynamical origins of reactive resonances are also discussed in this review, based on information on the wave function in the transition-state region obtained by time-dependent quantum wave-packet calculations.

INVESTIGATION OF THE CONTRIBUTION FOR THE NONCOLLINEAR CHANNEL OF THE F(2P3/2,2P1/2) + H2/D2 REACTIONS ON FOUR DIABATIC POTENTIAL ENERGY SURFACES

We performed the nonadiabatic time-dependent wave packet calculation on the four diabatic potential energy surfaces, which have the different barrier height, to investigate the contribution of the noncollinear channel for the F (2P) + H2/D2 (v = j = 0) reactions. The reaction probabilities, integral cross-sections, and rate constants are presented. The results indicate that the probabilities as the function of the collision energy have an obvious translation. The reactive activity of the reactions comes from the noncollinear reactive channel. The bent barrier height would decrease the reactive activity. The integral cross-sections are in the order of AWS < LWA-5 < LWA-78 ≈ MASW, which is opposite to that of the bent barrier height. At the lower temperature, the difference of the rate constants is unambiguous. As the temperature increases, the difference reduces. At the higher temperature, the rate constants computed on the four potential energy surfaces are close.

Role of van der Waals resonances in the vibrational relaxation of HF by collisions with H atoms

Vibrational relaxation of HF(v) in collisions with H atoms can occur by three pathways: inelastic scattering with and without H atom exchange, and, for v>or=3, the HF+H-->F+H2 reaction. Fully quantum, reactive scattering calculations on the Stark-Werner FH2 potential energy surface reveal narrow peaks in the energy dependence of the integral cross sections for each of these processes. By means of an adiabatic-bender analysis, we show that each of these peaks corresponds to the position of quasibound HF-H vibrational states trapped in the weak van der Waals well. The width of these resonances indicates that the lifetime of the quasibound states is up to 30 periods of the HF-H van der Waals vibration.

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.

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.

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.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.

A crossed-beam study of the F+HD→HF+D reaction: The resonance-mediated channel

This is the last report of our extensive studies on the title reaction. Presented here are the state-to-state differential cross section determinations at 11 collision energies, ranging from 1.30 to 4.53 kcal/mol. Together with previously reported results at six lower energies (0.4-1.18 kcal/mol), this perhaps represents one of the most comprehensive set of data from a single investigation for any chemical reaction. The information contents of this set of data are examined in detail, from which the dynamical consequences of reactive resonances are elucidated. Qualitative interpretations of some of the major findings are proposed. Observations that need further theoretical investigations for better physical understanding are pointed out.

Multireference configuration interaction calculations for the F(P2)+HCl→HF+Cl(P2) reaction: A correlation scaled ground state (1A′2) potential energy surface

This paper presents a new ground state (1 (2)A(')) electronic potential energy surface for the F((2)P)+HCl-->HF+Cl((2)P) reaction. The ab initio calculations are done at the multireference configuration interaction+Davidson correction (MRCI+Q) level of theory by complete basis set extrapolation of the aug-cc-pVnZ (n=2,3,4) energies. Due to low-lying charge transfer states in the transition state region, the molecular orbitals are obtained by six-state dynamically weighted multichannel self-consistent field methods. Additional perturbative refinement of the energies is achieved by implementing simple one-parameter correlation energy scaling to reproduce the experimental exothermicity (DeltaE=-33.06 kcalmol) for the reaction. Ab initio points are fitted to an analytical function based on sum of two- and three-body contributions, yielding a rms deviation of <0.3 kcalmol for all geometries below 10 kcalmol above the barrier. Of particular relevance to nonadiabatic dynamics, the calculations show significant multireference character in the transition state region, which is located 3.8 kcalmol with respect to F+HCl reactants and features a strongly bent F-H-Cl transition state geometry (theta approximately 123.5 degrees ). Finally, the surface also exhibits two conical intersection seams that are energetically accessible at low collision energies. These seams arise naturally from allowed crossings in the C(infinityv) linear configuration that become avoided in C(s) bent configurations of both the reactant and product, and should be a hallmark of all X-H-Y atom transfer reaction dynamics between ((2)P) halogen atoms.

Observation of Feshbach resonances in the F + H2 --> HF + H reaction

Reaction resonances, or transiently stabilized transition-state structures, have proven highly challenging to capture experimentally. Here, we used the highly sensitive H atom Rydberg tagging time-of-flight method to conduct a crossed molecular beam scattering study of the F + H2 --> HF + H reaction with full quantum-state resolution. Pronounced forward-scattered HF products in the v' = 2 vibrational state were clearly observed at a collision energy of 0.52 kcal/mol; this was attributed to both the ground and the first excited Feshbach resonances trapped in the peculiar HF(v' = 3)-H' vibrationally adiabatic potential, with substantial enhancement by constructive interference between the two resonances.

Direct evaluation of the lifetime matrix by the hyperquantization algorithm: Narrow resonances in the F+H2 reaction dynamics and their splitting for nonzero angular momentum

We propose a new method for the direct and efficient evaluation of the Felix Smith's lifetime Q matrix for reactive scattering problems. Simultaneous propagation of the solution to a set of close-coupled equations together with its energy derivative allows one to avoid common problems pertinent to the finite-difference approach. The procedure is implemented on a reactive scattering code which employs the hyperquantization algorithm and the Johnson-Manolopoulos [J. Comput. Phys. 13, 455 (1973); J. Chem. Phys 85, 6425 (1986)] propagation to obtain the complete S matrix and scattering observables. As an application of the developed formalism, we focus on the total angular momentum dependence of narrow under-barrier resonances supported by van der Waals wells of the title reaction. Using our method, we fully characterize these metastable states obtaining their positions and lifetimes from Lorentzian fits to the largest eigenvalue of the lifetime matrix. Remarkable splittings of the resonances observed at J>0 are rationalized in terms of a hyperspherical model. In order to provide an insight on the decay mechanism, the Q-matrix eigenvectors are analyzed and the dominant channels populated during the decomposition of metastable states are determined. Possible relevance of the present results to reactive scattering experiments is discussed.

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.

A resonance-mediated non-adiabatic reaction: F*(2P1/2) + HD --> HF(v' = 3) + D

The reaction of F(2P3/2,1/2) + HD --> HF(v' = 3) + D was investigated in a rotating-source, crossed-beam machine. The high translational energy resolution afforded by the Doppler-selected time-of-flight technique enabled us to distinguish the differential attributes of the HF(v' = 3) + D products of the ground state (2P3/2) reaction from those due to the spin-orbit excited (2P1/2) one. It was found that the F*(2P1/2) reactivity is significantly smaller than that for F(2P3/2), and the two state-to-state angular distributions exhibit remarkable similarities, though some differences were noted. Comparing the results with those concluded previously, we assert that both the adiabatic (F(2P3/2) + HD) and, in particular, the non-adiabatic (F*(2P1/2) + HD) reactions are predominantly mediated by a resonance mechanism for the formation of the HF(v' = 3) + D channel.

Angular distributions for the F+H2→HF+H reaction: The role of the F spin-orbit excited state and comparison with molecular beam experiments

We report quantum mechanical calculations of center-of-mass differential cross sections (DCS) for the F+H(2)-->HF+H reaction performed on the multistate [Alexander-Stark-Werner (ASW)] potential energy surfaces (PES) that describe the open-shell character of this reaction. For comparison, we repeat single-state calculations with the Stark-Werner (SW) and Hartke-Stark-Werner (HSW) PESs. The ASW DCSs differ from those predicted for the SW and HSW PES in the backward direction. These differences arise from nonadiabatic coupling between several electronic states. The DCSs are then used in forward simulations of the laboratory-frame angular distributions (ADs) measured by Lee, Neumark, and co-workers [J. Chem. Phys. 82, 3045 (1985)]. The simulations are scaled to match experiment over the range 12 degrees <Theta(lab)<80 degrees. As a natural consequence of the reduced backward scattering, the ASW ADs are more forward and sideways scattered than predicted by the HSW PES. At the two higher collision energies (2.74 and 3.42 kcal/mol) the enhanced sideways scattering of HF v(')=2 products bring the ASW ADs in very good agreement with the experiment. At the lowest collision energy (1.84 kcal/mol), the simulations, for all three sets of PESs consistently underestimate the sideways scattering. The residual disagreements, particularly at the lowest collision energy, may be due to the known deficiencies in the PESs.

Quantum scattering calculations on chemical reactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.

Scattering resonances in the simplest chemical reaction

Recent studies of state-resolved angular distributions show the participation of reactive scattering resonances in the simplest chemical reaction. This review is intended for those who wish to learn about the state-of-the-art in the study of the H + H2 reaction family that has made this breakthrough possible. This review is also intended for those who wish to gain insight into the nature of reactive scattering resonances. Following a tour across several fields of physics and chemistry where the concept of resonance has been crucial for the understanding of new phenomena, we offer an operational definition and taxonomy of reactive scattering resonances. We introduce simple intuitive models to illustrate each resonance type. We focus next on the last decade of H + H2 reaction dynamics. Emphasis is placed on the various experimental approaches that have been applied to the search for resonance behavior in the H + H2 reaction family. We conclude by sketching the road ahead in the study of H + H2 reactive scattering resonances.

Crossed-beam studies of neutral reactions: state-specific differential cross sections

Crossed-molecular-beam and laser techniques have enabled experimentalists to measure the state-resolved differential cross sections of elementary chemical reactions. This article reviews recent progress in this area. Particular emphasis is placed on some intriguing physical phenomena associated with a few benchmark reactions and how these measurements help in answering fundamental questions about reaction dynamics. We examine specifically the geometric phase effects in the reaction H + D2, the dynamical resonance phenomenon in F + HD, the unusually large spin-orbit reactivity in Cl((2)P) + H2, the insertion reaction O((1)D) + H2, and the mode-specific reactivity in Cl + CH4(nu). The give-and-take between experiment and theory in unraveling the physical picture of the dynamics is illustrated throughout this review.