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

Reactant-Product Decoupling Technique Using the Intermediate Coordinate Method

Although the reactant-product decoupling (RPD) technique was proposed over two decades ago, it remains an efficient approach for calculating product state-resolved information on some simple direct reactions using the quantum wave packet method. In the past, usually the RPD technique employed the collocation method to transform the wave function between reactant and product arrangements, which requires quite large computational efforts. In this work, the intermediate coordinate (IC) method is employed to realize the RPD technique. Numerical examples demonstrate that this new IC RPD (IRPD) technique has superior computational efficiency compared with the original method employing the collocation method. Especially, the new IRPD technique significantly saves disk space and computer memory. To illustrate the features of our new method, the total reaction probabilities of the H + H2, H + Br2, and F + H2 reactions with J = 0 and the differential cross sections of the H + H2 and F + H2 reactions at a series of collision energy are calculated and presented. With this efficient and effective new RPD technique, the Li + HF reaction, which involves sharp resonances with long-range wave functions in the van der Waals wells in both the reactant and product arrangements, is also calculated with several J at the product state-resolved level to reveal the ability of the RPD technique for describing resonance wave functions. With these numerical examples, it is found that, for the reaction with resonances, the RPD approach should be applied carefully. Otherwise, it is very possible that the resonances could disappear with the application of the RPD technique.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially in the neighborhood of a reactive threshold.

THEORETICAL STUDY ON PARTIAL POTENTIAL SURFACE AND SCATTERING RESONANCE STATE OF THE ASYMMETRICAL H EXCHANGING X + H2O → XH + OH (X = Cl, F, H) REACTIVE SYSTEM

In the course of an extensive investigation aimed at understanding the detailed mechanism of a prototypical polyatomic reaction, several remarkable observations were uncovered. To interpret these findings, we surmise the existence of a reactive resonance in this polyatomic reaction. The system of concern is X + H 2 O → XH + OH ( X = Cl, F, H ), and it belongs to a type of asymmetrical H exchanging reaction. Because the concerned electronic number is quite small, it is usually regarded as a template constructed the model of theory or experiment. In this paper, compared with the symmetrical systems, we constructed the partial potential surfaces of asymmetrical systems in order to research their resonance states. All results are in good agreement with previous theoretical and experimental works.

Breakdown of the Born-Oppenheimer Approximation in the F+ o -D 2 → DF + D Reaction

The reaction of F with H2 and its isotopomers is the paradigm for an exothermic triatomic abstraction reaction. In a crossed-beam scattering experiment, we determined relative integral and differential cross sections for reaction of the ground F(2P(3/2)) and excited F*(2P(1/2)) spin-orbit states with D2 for collision energies of 0.25 to 1.2 kilocalorie/mole. At the lowest collision energy, F* is approximately 1.6 times more reactive than F, although reaction of F* is forbidden within the Born-Oppenheimer (BO) approximation. As the collision energy increases, the BO-allowed reaction rapidly dominates. We found excellent agreement between multistate, quantum reactive scattering calculations and both the measured energy dependence of the F*/F reactivity ratio and the differential cross sections. This agreement confirms the fundamental understanding of the factors controlling electronic nonadiabaticity in abstraction reactions.

Exact quantum calculations of the kinetic isotope effect: cross sections and rate constants for the F+HD reaction and role of tunneling

In this paper we present integral cross sections (in the 5-220 meV collision energy range) and rate constants (in the 100-300 K range of temperature) for the F+HD reaction leading to HF+D and DF+H. The exact quantum reactive scattering calculations were carried out using the hyperquantization algorithm on an improved potential energy surface which incorporates the effects of open shell and fine structure of the fluorine atom in the entrance channel. The results reproduce satisfactorily molecular beam scattering experiments as well as chemical kinetics data for both the HF and DF channels. In particular, the agreement of the rate coefficients and the vibrational branching ratios with experimental measurements is improved with respect to previous studies. At thermal and subthermal energies, the rates are greatly influenced by tunneling through the reaction barrier. Therefore exchange of deuterium is shown to be penalized with respect to exchange of hydrogen, and the isotopic branching exhibits a strong dependence on translational energy. Also, it is found that rotational excitation of the reactant HD molecule enhances the production of HF and decreases the reactivity at the D end, obtaining insight on the reaction stereodynamics.

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.

Nonadiabatic effects in the H+D2 reaction

The state-to-state dynamics of the H+D2 reaction is studied by the reactant-product decoupling method using the double many-body expansion potential energy surface. Two approaches are compared: one uses only the lowest adiabatic sheet while the other employs both coupled diabatic sheets. Rotational distributions for the reaction H+D2 (upsilon = 0, j = 0)-->HD(upsilon' = 3, j')+D are obtained at eight different collision energies between 1.49 and 1.85 eV; no significant difference are found between the two approaches. Initial state-selected total reaction probabilities and integral cross sections are also given for energies ranging from 0.25 up to 2.0 eV with extremely small differences being observed between the two sets of results, thus showing that the nonadiabatic effects in the title reaction are negligible at least for small energies below 2.0 eV.

Recent advances in crossed-beam studies of bimolecular reactions

A critical overview of the recent progress in crossed-beam reactive scattering is presented. This review is not intended to be an exhaustive nor a comprehensive one, but rather a critical assessment of what we have been learning about bimolecular reaction dynamics using crossed molecular beams since year 2000. Particular emphasis is placed on the information content encoded in the product angular distribution-the trait of a typical molecular beam scattering experiment-and how the information can help in answering fundamental questions about chemical reactivity. We will start with simple reactions by highlighting a few benchmark three-atom reactions, and then move on progressively to the more complex chemical systems and with more sophisticated types of measurements. Understanding what cause the experimental observations is more than computationally simulating the results. The give and take between experiment and theory in unraveling the physical picture of the underlying dynamics is illustrated throughout this review.

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.

Nonadiabatic reactant-product decoupling calculation for the F(P1∕22)+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.

Direct evidence for nonadiabatic dynamics in atom+polyatom reactions: Crossed-jet laser studies of F+D2O→DF+OD

Quantum-state-resolved reactive-scattering dynamics of F+D(2)O-->DF+OD have been studied at E(c.m.)=5(1) kcal/mol in low-density crossed supersonic jets, exploiting pulsed discharge sources of F atom and laser-induced fluorescence to detect the nascent OD product under single-collision conditions. The product OD is formed exclusively in the v(OD)=0 state with only modest rotational excitation (<E(rot)> =0.50(1) kcal/mol), consistent with the relatively weak coupling of the 18.1(1) kcal/mol reaction exothermicity into "spectator" bond degrees of freedom. The majority of OD products [68(1)%] are found in the ground ((2)Pi(32) (+/-)) spin-orbit state, which adiabatically correlates with reaction over the lowest and only energetically accessible barrier (DeltaE( not equal) approximately 4 kcal/mol). However, 32(1)% of molecules are produced in the excited spin-orbit state ((2)Pi(12) (+/-)), although from a purely adiabatic perspective, this requires passage over a DeltaE( not equal) approximately 25 kcal/mol barrier energetically inaccessible at these collision energies. This provides unambiguous evidence for nonadiabatic surface hopping in F+D(2)O atom abstraction reactions, indicating that reactive-scattering dynamics even in simple atom+polyatom systems is not always isolated on the ground electronic surface. Additionally, the nascent OD rotational states are well fitted by a two-temperature Boltzmann distribution, suggesting correlated branching of the reaction products into the DF(v=2,3) vibrational manifold.

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.

Quantum Wave Packet Study of the H+ + D2 Reaction on Diabatic Potential Energy Surfaces

The exact three-dimensional nonadiabatic quantum dynamics calculations were carried out for the title reaction by a time-dependent wave packet approach based on a newly constructed diabatic potential energy surface (Kamisaka et al. J. Chem. Phys. 2002, 116, 654). Three processes including those of reactive charge transfer, nonreactive charge transfer, and reactive noncharge transfer were investigated to determine the initial state-resolved probabilities and reactive cross sections. The results show that a large number of resonances can be observed in the calculated probabilities due to the deep well on adiabatic ground surface and the dominant process is the reactive noncharge-transfer process. Some interesting dynamical features such as v-dependent and j-dependent behaviors of the probabilities are also revealed. In addition, a good agreement has been achieved in the comparison between the calculated quantum cross sections from the ground rovibrational initial state and the experimental measurement data.