Atom Exchange Reaction Research Articles

Transition states, trapped trajectories, and classical bound states embedded in the continuum

We show that the best choice of transition state, for the atom exchange reaction in a classical collinear collision of an atom with a diatomic, is a classical bound state embedded in the continuum: a periodic vibration of the triatomic system across the interaction region of the potential surface. These unstable bound states also serve as limit sets of the trapped trajectories that form the boundary of reactivity bands in molecular collisions, and we comment on the implications of this result for calculation of product state distributions. Numerical calculations of transition states are presented for the collinear H+H2 and F+H2 reactions.

Information theory analysis of angular momentum disposal in chemical reactions

Several vector properties of single collisions between gas-phase molecules can now be measured by molecular beam techniques. Such properties consist of correlations among the directions of relative velocity vectors and angular momentum vectors of the reactant and product molecules. Here we examine the utility of information theory for analysis of these multidimensional correlations. Vector distributions generated from impulsive and statistical models for an A+BC→AB+C atom exchange reaction are analyzed, with particular emphasis on the triple angle correlation relating the initial and final velocity vectors to the product rotational momentum. For the impulsive model, the entropy deficiencies for the angular degrees of freedom are found to be larger than those for the energy distributions and the largest contribution comes from the triple angle correlation. However, it is argued that information theory cannot assess the comparative value of different kinds of data. Also discussed are the effects of approximate dynamical constraints on multidimensional entropy deficiencies.

Molecular beam scattering experiments on the abstraction and exchange reactions of deuterium atoms with the hydrogen halides HCl, HBr, and HI

Molecular beam scattering experiments have been carried out on the abstraction and exchange reactions of deuterium atoms (T=2600 K) with the hydrogen halides HX(T=300 K) in the range of scattering angles: 0°⩽ϑcm⩽70° (ϑcm=0° is the direction of the incident D-atom beam). The apparatus employed a very sensitive electron bombardment detector with a sufficiently low H2 background to make possible the measurement of differential cross sections of about 0.1 Å2/sr for reactively scattered HD and H and nonreactively scattered D-atoms. The measured HD signal can be largely attributed to various background sources and only serves to establish a rough upper limit on the abstraction cross section in the angular range investigated. The H-atom signal was more intense. The observed angular distribution was forward peaked, and is attributed to the exchange reaction. The nonreactively scattered D-atom signal was used in conjunction with a recently reported effective spherically symmetric potential to provide an absolute calibration of the detector sensitivity. The measured integral cross sections for the exchange reactions are 2.3 Å2 (D+HCl), 1.3 Å2 (D+HBr) and 1.6 Å2 (D+HI) with an estimated error of about ±30%. The absolute cross sections and the H-atom angular distributions are consistent with the DX distributions measured by McDonald and Herschbach. Both experimental angular distributions are considerably narrower than those predicted by the recent classical trajectory calculations of Raff, Suzukawa, and Thompson. The implications of the new data for the activation energies for the exchange reactions are discussed.

On the rate and activation energy of the Br + Br 2 ataom-exchange reaction

The Br + Br 2 atom-exchange reaction has been studied using quasiclassical trajectories and a semi-empirical potential-energy surface with shallow, long-range wells. The computed reaction rate coefficient is in good agreement with experiment. The computed reaction activation energy is ≲ 1 kcal/mole.

ChemInform Abstract: REACTIONS OF ENERGETIC HYDROGEN ATOMS WITH BROMINE AND HYDROGEN BROMIDE

AbstractEin Vergleich der Anregungsfunktionen für die Reaktionen von Br2 mit energiereichen H‐, D‐ und T‐Atomen zeigt das "Vorhandensein eines Isotopeneffekts, durch den die schwereren Atome begünstigt werden.

Dynamics of the oxygen exchange reaction

The classical trajectory technique has been used to analyse the thermoneutral oxygen atom exchange reaction at a microscopic level. The calculations show that a direct exchange mechanism makes the major contribution to the reactive cross section, and that very few reactions proceed via long-lived complexes. The calculated macroscopic rate constants at 300 and 500 K are in good agreement with the experimental results.

A PNO–CEPA calculation of the barrier height for the collinear atom exchange reaction H′+BrH→H′Br+H

A PNO–CEPA calculation of the barrier height for the collinear atom exchange reaction H′+BrH→H′Br+H

Vibrational relaxation in atom exchange reactions: A classical trajectory study of H + H 2(ν) and D + D 2(ν) collisions using an accurate potential

A quasiclassical trajectory study has been carried out to investigate the dynamics of collisions between H + H 2(1 ⩽ ν ⩽ 4) and D + D 2(1 ⩽ ν ⩽ 4), using the accurate Yates-Lester potential. Reaction is selectively enhanced by the vibrational excitation of the diatomic reagent, as judged by information theory, but the degree of selectivity falls as the vibrational energy is successively increased. The calculated results are in fair agreement with experimental measurements on the removal of H 2(ν = 1) by H but not with those for D 2(ν = 1) by D.

Translational energy requirements and disposal in molecular collisions: II. Branching ratios and products state distributions for the exchange reactions of alkali atoms with alkali halides

Experimental reactive/non-reactive branching ratios in the complex forming M' + MX collisions are often found to deviate from those computed by statistical theories. Information theory, using the momentum transfer constraint, is employed to relate this deviance to the distribution of translational energy in the products. The experimental results for the branching ratios and mean product energies in K + CsF and K + RbF (obtained by Stolte, Proctor, and Bernstein) are found to be consistent and are used to predict the translational energy distribution in the products. The low branching ratio in K + CsF is shown to imply that the energy distribution for non-reactive scattering is nearly statistical while for reactive scattering the distribution is significantly narrower compared to the statistical results. Using the experimental results for K + CsF and K + RbF it was also found possible to predict the branching ratio and the energy disposal in the Cs + KF and the Rb + KT reactions. The experimental results for the mean product energies in M + M'X reactions. X = Cl or I (obtained by Miller, Safron, and Herschbach), are used to compute the branching ratios in good agreement with the experimental values. A relation between energy disposal and the geometrical structure of the collision complex is discussed as a possible dynamical model for the proposed connection between branching and products energy distribution in complex forming reactions.

A PNO—CEPA calculation of the barrier height for the collinear atom exchange reaction Cl′ + HCl → Cl′H + Cl

Abstract A barrier height of 16.6 kcal mol−1 has been calculated for the collinear atom exchange reaction Cl′ +_HCL → Cl′H + Cl by means of the coupled electron pair approximation CEPA. The long-range attraction between the chlorine atoms has a non-negligible influence on the barrier height. The remaining correlation errors are estimated to reduce the barrier height by 10 to 15 kcal mol−1 to 2 to 7 kcal mol−1.

Significance of limiting low pressure product yields from energetic atomic exchange reactions

The limiting low pressure yield behavior has been characterized for gas phase substitution reactions of energetic 3H and 18F atoms with aliphatic and alicyclic substances. The limiting yields correlate well with the respective critical energies for secondary unimolecular decomposition. The interpretation of this behavior leads to quantitative descriptions for the hydrogen-for-hydrogen and F-for-F primary product internal excitation energy distributions together with approximate descriptions of total energy disposal for the threshold hydrogen-for-hydrogen processes.

Molecular beam kinetics: Exchange reactions of deuterium atoms with hydrogen halides

A crossed-beam study finds the reactions of D atoms with HCl, HBr, and HI give large yields of DCl, DBr, and DI, corresponding to reaction cross sections of the order 1–10 Å2. This demonstrates that the exceptionally small steric factors or transmission coefficients previously inferred from analysis of chain reaction mechanisms are low by several orders of magnitude. The reactively scattered deuterium halides recoil predominantly into the backward hemisphere with respect to the incident D atoms. In each case, the reaction exoergicity is ∼1 kcal/mole and the mean initial collision energy is 9 kcal/mole (with the D beam at 2800 °K, the hydrogen halide at 250 °K). The most probable final relative translational energy of the products is ≳4 kcal/mole for the HCl and HBr reactions and 7 kcal/mole for the HI reaction. The magnitude of the reaction cross sections and the predominant backward recoil and translational energy of the products are consistent with recent classical trajectory calculations based on semiempirical potential surfaces.

On the thermal rate coefficient and activation energy of the I+I2 atom-exchange reaction

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Vibrational relaxation in atom-exchange reactions. Classical trajectory study of Cl + HCl and Cl + DCl collisions

A classical trajectory study has been carried out to investigate the dynamics of Cl + HCl (v= 1) and Cl + DCl (v= 1) collisions, where these are restricted to a single potential hypersurface. Calculations were performed on five LEPS potentials ranging from one with a moderately high barrier (+26.0 kJ mol–1) for H or D atom transfer to one with a moderately deep well (–25.9 kJ mol–1) with the three atoms in a linear, symmetric configuration. On all these surfaces, vibrational relaxation occurred predominantly in collisions where the trajectory passed at least once through the symmetric (rAB=rBC) configuration, and rate constants have been calculated both for transfer of molecules to v= 0 and for atom-exchange. Comparison with the observed rates of de-excitation of HCl (v= 1) and DCl (v= 1) by Cl atoms suggest that if energy transfer occurs principally in electronically adiabatic collisions then the barrier for H atom transfer must be lower than has been previously supposed.

ICR studies of some hydrogen atom abstraction reactions: X+ + H2 → XH+ + H

Ion cyclotron resonance methods are used to identify and to measure the rate constants for the abstraction of a hydrogen atom from H2 by CH+, CH2+, CH4+, N+, NH+, NH2+, NH3+, O+, OH+, H2O+, CO+, N2+, C2+, and C2H+ ions. Although in most cases hydrogen atom abstraction is the only available exothermic pathway for these reactions at thermal energies, the rate constants measured show that except for O+, CO+, and N2+, a large fraction of collisions between these ions and H2 are not reactive. The rate constants measured range from a low of (3±1) × 10−13 cm3/sec for the NH3+−H2 reaction to (1.73±0.04) × 10−9 cm3/sec for the N2+−H2 reaction. These values compare to the Langevin value of about 1.5 × 10−9 cm3/sec for collisions between these ions and H2. An examination was also made for possible thermoneutral hydrogen atom exchange reactions for those ions which do not react with H2 (CH5+, CH3+, NH4+, H3O+, H2S+, H3S+). The only exchange reaction observed was for collisions between CD3+ ions and H2, for which a rate constant of (5.1±0.5) × 10−10 cm3/sec was measured.

Monte Carlo classical dynamical study of the Cl + Cl2 and I + I2 systems: Vibrational relaxation and atom-exchange reactions

The Monte Carlo quasiclassical trajectory method is used to investigate the atom-exchange reactions and the vibrational relaxation in the systems Cl + Cl2 and I + I2. The Cl + Cl2 system is examined over the temperature range 500–1500°K and initial vibrational states ν = 0, 1, 3, 7, and 14, and the I + I2 system is examined over the temperature range 700–1500°K and initial vibrational levels ν = 0, 1, 7, 10, 12, and 14. London equation potential-energy surfaces are employed; the energy barrier to linear configuration atom exchange is zero for Cl + Cl2 and about 5.9 kcal/mole for I + I2. The rates of atom exchange for both Cl + Cl2 and I + I2 are calculated as a function of temperature and initial vibrational state. Vibrational relaxation rate coefficients are calculated for individual transitions ν→ν′ for both reactive and nonreactive collisions. It is found that both nonreactive collisions and atom-exchange reactions contribute to the vibrational relaxation.

Semiclassical theory for low-energy molecular collisions II. Atomic exchange reactions

A form of semiclassical theory of molecular collisions, previously formulated and applied to H+, H2 vibrational excitation in I, is applied to H, H2 atomic exchange. The formulation involves separation of the potential into two parts, a ``trajectory'' potential along which only elastic scattering can occur and ``coupling'' potential which can produce inelastic or reactive scattering. The first part is chosen such that the classical two-body central force formulas apply. This determines the coupling potential in the parameters, the classical trajectory R (t), and the classical deflection function θ(t). The time-dependent Schrödinger equation is then solved to produce the reactive probabilities. The problem is formulated in a coordinate system in which initial and final scattering coordinates are constrained to remain the same throughout the reaction. This procedure produces asymptotic momentum transfer or ``recoil'' factors of the form exp[(i/ℏ)μν · R] which multiply the vibrational-rotational wavefunctions, but it preserves orthogonality in the scattering wavefunctions and permits the coupled equations in the two-state approximation to be approximately decoupled in the symmetric process. Calculations are carried out to illustrate effect of trajectory on reaction probabilities.

Isotopic exchange reactions between nitrogen oxides and oxyhalides

The kinetics of atom exchange reactions among CINO, NO, and NO/sub 2/ were studied using a time-of-flight mass spectrometer in two reactors of different sunface-to-volume ratio, over a temperature range of 0 to 23 deg . The reactions proceed according to the equations Cl/sup 14/NO + /sup 15/NO/sub 2/ yields Cl/sup 15/NO/sub 2/ + /sup 14 /NO, Cl/sup 14/NO + /sup 15/NO/sub 2/ yields Cl/sup 15/NO + /sup 14/NO/sub 2/, Cl/sup 14/NO + /sup 15/NO yields Cl/ sup 15/NO + / sup 14/NO, with the secondorder rate constant, k = (1.78 plus or minus 0.04) x 10/sup 5/ expSTA-(3350 plus or minus 150)/T! M/sup -1/ sec/sup - 1/ for the first two reactions and k = (1.64 plus or minus 0.10) x 10/s up 6/ expSTA--(3145 plus or minus 150)/T! M/sip -1/ sec/sup -1/ for the last reaction. Bimolecular mechanisms for the reactions are proposed similar to those for the corresponding reactions in NO--NO/sub 2/ and NO/sub 2/-NO/sub 2/ systems. However, the rates of reactions in the present systems are slower by a factor of ~10/sup 6/ at 23 deg . (auth)

Vibrational excitation in atom exchange reactions

A simple, predictive, retreat coordinate model has been developed for the calculation of vibrational distributions in exothermic atom transfer reactions. Reaction is assumed to take place over a BEBO (bond energy–bond order) potential energy surface and the relative contributions made by attractive and repulsive release are assessed. The method has been applied to three types of reaction system, X + HY, H + XY and X + YZ.

Dynamical coupling in the differential equations approach to atom-diatom exchange reactions

The atomic exchange reaction A + BC → AB + C is investigated quantum mechanically employing a coupled differential equations approach. The relative motion in reactant and product channels is described in the common coordinate R 3 (the AC nuclear separation) and is developed in three-dimensional space. The total wave functions of the system are expressed as a superposition of valence bond electronic states of the initial (A, BC) and final (AB, C) configurations, with the coefficients describing the relative and internal (vibrational, rotational) nuclear motions. Choosing convenient trial functions with the appropriate boundary conditions and using the Kohn variational principle, a set of differential (rather than the usual integro-differential) equations is obtained for the relative motion wave functions in R 3. The potential matrix elements turn out to be dynamical in that they depend on the initial k 1 and final k 2 wave vectors. Two-state coupled channel calculations of the differential and integral cro...