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Competitive Reaction Rates of Hydrogen Atoms with HCl and Cl2
The Journal of Chemical Physics
Abstract
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A quasiclassical trajectory study of the electronically adiabatic exothermic reaction H + Br2 --> HBr + Br using 13 different semiempirical and empirical potential energy surfaces has been conducted. Detailed results are reported for 8035 reactive trajectories using Monte Carlo selection of initial conditions drawn from six different sets of distributions. For all the surfaces examined, the reaction is dominated by sideways collisions. The differential cross section for unit plane angle is sideways peaked but the differential cross section per unit solid angle peaks for molecular scattering angles (measured relative to the direction of the incident atom) in the range 156°-180°, i.e., backward scattering. There is a good correlation of scattering angle and initial orientation of the intermolecular axis, but it was not possible to use this correlation to guess a potential energy surface which yields a differential cross section in quantitative agreement with experimental results. The trajectory results, however, do indicate that a surface which has a low barrier or no barrier for collinear collisions yields too much forward scattering as compared to experiment. We find the computed angular distribution is not a strong function of atomic temperature in the range 300° to 5600°K or molecular temperature in the range 100° to 900°K. Under 300°K conditions the final state internal energy distributions are in good agreement with chemiluminescence results and at an atomic temperature of 2800°K the final translational energy distribution is in good agreement with molecular beam results. The reaction cross section is calculated to be a decreasing function of translational energy, in agrement with White and Su's interpretation of the hot atom studies; and the room temperature energy of activation is calculated to be only 0.2 kcal/mole which agrees with experiment within experimental error. The absolute values of the cross section and the room temperature rate constant are about a factor of 3 larger than experimental values. Many other details of the results are given and these may serve as a model study for the important mass combination where a light atom reacts with a heavy homonuclear diatomic molecule.
The importance of hot deuterium atoms in photolyses of DCl☒lCl2 mixtures at 1849 Å has been demonstrated, and the kinetics of this system have been described. Photodecomposition of DCl was followed by mass‐spectrometric analysis of the D2 formed after successive intervals of time. The observed decreases in the initial rate of D2 formation upon addition of CO2, and inert gases CO2, Xe, and CF4 may be readily interpreted in terms of a hot‐atom mechanism but cannot be made compatible with a completely thermal mechanism. Rate coefficient ratios for the hot‐atom reactions, were found to be k6 / k2 ≈ 6.5,k3DCl / k2 = 0.65,k3CO2 / k2 = 1.15,k3CF4 / k2 ≈ 1.15,andk3Xe / k2 < 0.1. The ratio k6 / k2 increased from 6.5 in the absence of inert gas to 9.2 when [CO2]/[DCl] = 1.87. This ratio increases to ≈ 300 for a thermal atom distribution at 300°K. Comparisons of thermalizing efficiencies for several molecules suggest that inelastic collisions are important in thermalizing hot atoms produced photochemically at 2.1 eV.
Potential energy surfaces (PES) for the reactions X + HD -2 ⇌ 2 HX + D -3 ⇌ 3 DX + H, where X is a halogen, are reviewed. Reactions involving two or three halogen atoms are also discussed. Many calculations have been performed using semiempirical variations of the London PES equation (LEPS methods) which was originally developed for treating the H + H2 reactions. There are many problems in extending this treatment to the halogen reactions and some of these, including excited electronic states, p Orbitals, relativistic effects, and possibilities for nonlinear transition states, are mentioned. Furthermore, the London equation and its variations are found to be pathologically sensitive to the input coulomb ratios, both when these are semiempirical and when they are theoretical. The use of transition state theory to relate postulated potential energy surfaces to experimental data causes further errors, especially for reaction 2 when X = Br or I. More importantly, rate data in thermal bulk-gas systems are insufficient to determine most PES features. Experiments which measure scattering angles and internal energies of the products combined with single-collision scattering theory interpretations will provide more critical conditions on trial PES topography. A priori calculations of potential energy surfaces will also be useful in some cases. For some cases, features such as reaction barrier height and location and width of the barrier can presently be assigned satisfactory qualitative values. However, the depth and even the existence of potential wells in many of the systems is uncertain. In cases where wells are known to exist, it is found that the semiempirical LEPS methods fail to reproduce observed force constants. The transferability of the Sato parameters in the LEPS methods from system to system is not promising, but it is possible that a single set of Sato parameters will serve well for both reactions 2 and 3 for a single X. New transition state isotope effects for reaction -2 with X = Br are presented. Although they give results closer to experimental values than do previous calculations, it is shown why little confidence can be placed in the absolute accuracy of the PES leading to these predictions.
A detailed kinetic model of the HCl chemical laser produced by the flash photolytically initiated H2Cl2 explosion is described, and the results of computer calculations on such a system are discussed. It is shown that currently accepted values of the various rate constants, supplemented in a few cases by reasonable estimates of previously unmeasured rate constants, are adequate to approximate the observed laser behavior of this system. It is also shown that the chemistry of such a system is extremely complex, and exhibits a high degree of coupling between one reaction and another; therefore, great care is required to extract kinetic data from the optical behavior of such laser systems. It is further argued that different hydrogen halide lasers may behave quite differently from each other, depending on the relative magnitudes of the various rate constants involved.
The effects of reaction barrier height and initial rotational excitation of the reactants on the overall rate of H atom exchange between atomic chlorine and HCl (v = 0) and on the 0 → 1 vibrational excitation of HCl via reactive and nonreactive collisions have been investigated using quasiclassical trajectory techniques. Two empirical LEPS potential energy surfaces were employed in the calculations having reaction barrier heights of 9.84 and 7.05 kcal mol−1. Trajectory studies of planar collisions were carried out on each surface over a range of relative translational energies with the ground-state HCI collision partner given initial rotational excitation corresponding J = 0, 3, and 7. Initial molecular rotation was found to be relatively inefficient in promoting the H atom exchange; the computed rate coefficient for H atom exchange between Cl + HCl (v = 0, J = 7) was only 4 times larger than that for CI + HCI (v = 0, J = 0). The vibrational excitation rate coefficient exhibited a stronger dependence on initial molecular rotational excitation. The observed increase in the vibrational excitation rate coefficient with increasing initial molecular rotational excitation was due primarily to nonreactive intermolecular R → V energy transfer. The vibrational excitation rate coefficients increase with decreasing reaction barrier height.
A potential barrier of the kind studied by Fowler and others may be represented by the analytic function V (Eq. (1)). The Schrödinger equation associated to this potential is soluble in terms of hypergeometric functions, and the coefficient of reflection for electrons approaching the barrier with energy W is calculable (Eq. (15)). The approximate formula, 1-ρ=exp{-∫4πh(2m(V-W))12dx} is shown to agree very well with the exact formula when the width of the barrier is great compared to the de Broglie wave-length of the incident electron, and W<Vmax.
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The relative rates of the reactions H+HCl↠k3H2+Cl and H+Cl2↠k6HCl+Cl, were determined in the temperature range of 0° to 62°C and found to be given by k3∕k6=(0.143±0.033) exp−(1540±130∕RT). The temperature-independent factor in the above expression is interpreted in terms of the structure and the vibrational frequencies of the HCl2 transition state. The doubly degenerate bending frequency of this transition state is found to have a value of about 105 cm−1.
A new method of drawing the potential energy surface has been devised and compared with Eyring’s semi-empirical method. The points different from the latter method are that an appropriate function for the anti-bonding state of a diatomic molecule is assumed and the overlap integral is not ignored. The so-called Coulomb fraction in Eyring’s method is not used and the London equation has been slightly modified.
As an example the activation energy of hydrogen atom-molecule reaction has been calculated. So far as this reaction is concerned, the present method gives more reasonable value than Eyring’s method.
In terms of certain lengths near the saddlepoint of an activated complex relative to the de Broglie wave length of the atom being transferred, the reaction coördinate of bimolecular atom-transfer reactions is profitably classified as: (1) essentially classical, (2) essentially separable or (3) non-separable. In terms of the location of the saddlepoint and energy-distance curvatures through the saddlepoint, simple general rate expressions for case 1 and case 2 are given, including a small degree of tunnelling, utilizing the recent general method (ref. 6) of evaluating the configuration integral of any molecule. Hydrogen atom transfer reactions below several hundred degrees centigrade are in the region of non-separable reaction coordinates. For these cases more information about the potential energy surface is needed than the saddlepoint geometry and curvatures. Sample calculations using the Sato-potential energy surface for H 3, as evaluated by Weston, illustrate an approximate method for treating non-separable reactions, including large degrees of non-separable tunnelling. The hydrogen-deuterium isotope effect in reactions of methyl radicals with hydrocarbons is worked out in detail, and this method of handling large degrees of tunnelling appears to agree with the experimental data over a wide temperature range (although there is large experimental error).