Light Atom Transfer Reactions Research Articles

Cumulative reaction probability and reaction eigenprobabilities from time-independent quantum scattering theory

The cumulative reaction probability (CRP) is a gross characteristic of rearrangement collision processes defining the reaction rate constant. This paper presents a complete development of the approach to the theory of CRP that we have recently proposed [Phys. Rev. Lett. 80, 41 (1998)]. In the core of this approach lies an alternative expression for CRP in terms of the outgoing wave Green's function which is formally equivalent to the Miller's definition of this quantity in terms of the scattering matrix [J. Chem. Phys. 62, 1899 (1975)] and to the Miller-Schwartz-Tromp formula [J. Chem. Phys. 79, 4889 (1983)], but is direct, in contrast to the former, and more suitable for practical calculations than the latter. Furthermore, our approach rests on solid grounds of time-independent quantum scattering theory and provides an appealing competitive alternative to the absorbing potential formulation given by Seideman and Miller [J. Chem. Phys. 96, 4412 (1992); 97, 2499 (1992)]. Ideologically, it is close to the approach considered earlier for a one-dimensional model by Manolopoulos and Light [Chem. Phys. Lett. 216, 18 (1993)], but is formulated from scratch for realistic systems with many degrees of freedom. The strongest point of our approach is that its final working formulas are expressed in terms of the Wigner-Eisenbud $\mathcal{R}$ matrix, so they can be easily implemented on the basis of many existing quantum scattering codes. All these features are discussed and illustrated by calculations of the CRP and reaction eigenprobabilities for two prototypical light atom transfer reactions in heavy-light-heavy triatomic systems in three dimensions for zero total angular momentum.

Hyperspherical elliptic coordinates for the theory of light atom transfer reactions in atom-diatom collisions

We formulate and demonstrate a new method for quantum 3D calculations of light atom transfer reactions in atom-diatom collisions. The method follows a general scheme of the hyperspherical method, in common with other hyperspherical formulations in the field. The main novelty consists in the hyperspherical elliptic coordinates (ξ,η) used to parametrize the hypersphere. These coordinates have been introduced recently for studying three-body Coulomb systems, and here we apply them to study a system of three atoms. The coordinates are defined and their relation with the Smith-Whitten and Delves coordinates is explored. On account of a big difference between vibrational and rotational excitation energies in molecules, the hyperspherical adiabatic Hamiltonian allows adiabatic separation between ξ and η. This not only greatly facilitates solution of the hyperspherical adiabatic eigenvalue problem, but also provides an approximate classification of the states by a pair of indices (nξ,nη) representing vibrational and rotational quantum numbers simultaneously for a reagent and a product. Another novel technology exploited here is the Slow/Smooth Variable Discretization (SVD) method. The SVD is used for treating nonadiabatic couplings between the ξ and η motions, as well as between the motions with respect to the hyperradius and the hyperangular variables. The whole scheme is illustrated by calculations for the reaction O(3P)+HCl→OH+Cl for zero total angular momentum. It is shown to be very efficient, accurate, and providing a framework of choice for elucidating light atom transfer reaction mechanisms.

Effect of reagent rotation on product energy disposal in the light atom transfer reaction O(3P)+HCl(v=2,J=1,6,9)→OH(v′,N′)+Cl(2P)

A rovibronic-state-to-rovibronic-state experiment has been performed on the reaction O(3P)+HCl(v=2,J=1,6,9)→OH(v′,N′)+Cl(2P). The O(3P) atoms are produced with a known energy by photolysis of NO2. The HCl(v=2,J) molecules are prepared by IR excitation of thermal HCl using an optical parametric oscillator. All energetically accessible OH rovibrational product levels are probed by laser-induced fluorescence for each prepared HCl rotational level. The OH(v′=0,N′) rotational distribution shows a dip at N′=11, the depth of which decreases with increasing HCl rotational excitation. The available energy of reaction is partitioned so that 40% appears as OH vibration (V′), 32% as OH rotation (R′), and 28% as product translation (T′). This energy partitioning does not change with HCl rotation, in contrast to the general expectation for light atom transfer reactions of approximate conservation of internal angular momentum (R→R′). A substantial vibrational inversion is observed, in agreement with the vibrational adiabaticity (V→V′) expected for such reactions.

Oscillations in product state distributions in the light-atom transfer reactions Cl+HCl→ClH+Cl and O+HCl→OH+Cl

Three-dimensional quasiclassical trajectory studies of the reactions Cl+HCl→ClH+Cl and O+HCl→OH+Cl, which belong to the class heavy+light-heavy→heavy-light+heavy, reveal the novel phenomenon of oscillations in product state distributions as a function of collision energy. The conditions for obtaining such oscillations are the same as those found in earlier studies for obtaining oscillations in partial cross sections.

Correlations between dynamical properties and features of potential energy surfaces for the light atom transfer reactions O+HCl→OH+Cl AND Cl+HCl→ClH+Cl

A three-dimensional quasiclassical trajectory study of the dynamics of the light atom transfer reaction O(3P) + HCl(ν=0)→ OH + Cl was carried out employing two LEPS potential energy surfaces (I and II). Attention was focused mainly on three-dynamical properties; the oscillatory behavior of partial cross sections as a function of collision energy; the rotational excitation of the products; and the influence of reagent rotation on reactivity. Distinct differences were found between surfaces I and II with respect to these properties. The examination of individual trajectories indicated that there is a significant difference in the nature of these surfaces. While surface I is governed by weak repulsive forces, surface II is governed by strong attractive forces which tend to direct the reactants toward a collinear geometry. The present results confirm conclusions reached from an earlier study of the reaction Cl+HCl→ClH+Cl concerning correlations between dynamical properties and features of potential energy surfaces. For surfaces of the type that we termed HREP, since they are of repulsive nature and they lead to highly rotationally excited products, no significant oscillations of partial cross sections are obtained and reagent rotation promotes the reaction. On the other hand, for surfaces of the type that we termed COLD (collinearly directing), since they tend to direct the reactants toward a collinear geometry and form rotationally “cold” products, significant oscillations of partial cross sections are obtained and reagent rotation causes a decline in reactivity.

Approximate quantum mechanical treatment of light-atom transfer reactions

The use of collinear-type hyperspherical coordinates to investigate three-dimensional light-atom transfer reactions within the framework of the adiabatic approximation (with respect to rotational motion) originally devised by Bowman is proposed. In the cases of (1) symmetric light-atom transfer and (2) near-resonant asymmetric light-atom transfer reactions, explicit approximate analytical expressions available for collinear reaction probabilities are suggested to estimate directly the three-dimensional reaction cross sections and rate constants. It is also demonstrated that the Rosen-Zener formula is applicable to collinear asymmetric light-atom transfer reactions without introducing any diabatic representation of potentials.

Quantum dynamical calculations of linear exchange reactions in combined coordinates

A new method of quantum dynamical calculations for light-atom transfer reactions in linear triatomic systems is proposed. The method is based on the use of a special translational—vibrational coordinate system where the potential surface cuts at a fixed translational coordinate represent a double-well potential. A double set of harmonic oscillator functions localized in the reagent and product valleys are used as an analytical vibrational basis. The two-dimensional Schrödinger equation is reduced to a one-dimensional matrix differential equation by averaging over the vibrational coordinate. The equation is solved by the propagation Wigner R -matrix technique ensuring an accurate conservation of the probability flux at any size of the vibrational basis. The dynamics of the hydrogen and deuterium atoms transfer in the reactions of the methyl radical with methane and toluene was calculated. The total probabilities of these reactions in the tunnelling energy region were shown to depend only slightly on the resonance misfit. The Arrhenius activation energy is ≈ 3 kcal mol −1 lower than the quantum barrier height.

Absolute rate coefficients for methyl radical reactions by laser photolysis/time-resolved infrared chemiluminescence: methyl-d3 + HX .fwdarw. methane-d3 + X (X = Br, I)

Absolute rate coefficients are reported for the room temperature reactions of deuterated methyl radicals with HI and HBr, CD/sub 3/ + HI (HBr) ..-->.. CD/sub 3/H + I(Br). Excimer laser photolysis of CD/sub 3/I is used to generate methyl radicals, and time-resolved infrared chemiluminescence from the CH stretch of the CD/sub 3/H products is detected to follow the time evolution of the reaction. The rate constants obtained in this manner are (7.7 +/- 0.7) x 10/sup -12/ cm/sup 3/ molecule/sup -1/ s/sup -1/ for CD/sub 3/ + HI and (4.7 +/- 0.4) x 10/sup -12/ cm/sup 3/ molecule/sup -1/ s/sup -1/ for CD/sub 3/ + HBr. These rate constants are considerably greater than earlier, indirectly measured values and indicate that the activation energy for these light-atom transfer reactions is lower than previously believed. 53 references, 3 figures, 2 tables.

A model study of symmetric light atom transfer reactions

Abstract A collinear model for symmetric light atom transfer reactions is constructed and generalized analytically to 3D scattering via a sudden and an adiabatic approach. The model predicts oscillations in the energy dependence of the full 3D integral cross section in the threshold region. The conditions for oscillatory behaviour are a light atom transfer reaction which occurs on a collinearly dominated, low-barrier potential energy surface. At higher energies there is a switch from a loose to a tight transition state which prevents further oscillations in the cross section. For reactions with large activation energy, such as the Cl + HCl exchange reaction, already at threshold the transition state is tight so that one does not find an oscillatory integral cross section. For the Cl+HCl reaction on the Last-Baer potential energy surface, the model rate constants are in good agreement with experiment. Implications of our study for future 3D quantal and classical computations are discussed in detail.

Dynamics of collinear asymmetric light atom transfer reactions

The Rosen–Zener formula in its sophisticated form is shown to be applicable to asymmetric collinear light atom transfer reactions with near degeneracy of asymptotic vibrational levels. The formula is applied to simple model systems and is demonstrated to work well over a wide range of energy for both systems with and without reaction barrier. It is also discussed that effects of surface topology and masses on reaction dynamics are effectively investigated by hyperspherical coordinates.

Reaction surface Hamiltonian for the dynamics of reactions in polyatomic systems

The reaction path description of chemical reactions has difficulty if there are regions where the reaction path is sharply curved, as is typically the case, e.g., in light atom (e.g., H,D) transfer reactions. It is shown here how this can be overcome by introducing two reaction coordinate-like degrees of freedom, i.e., two coordinates, r1 and r2, that are allowed to undergo arbitrarily large amplitude motion (LAM). Rather than a reaction path and a reaction coordinate measuring distance along it, the picture is now that of a reaction surface with two reaction-like coordinates (r1,r2) which specify position on the surface. The reaction surface is defined by minimizing the potential energy of the polyatomic system for fixed values of r1 and r2, and an algorithm for using ab initio quantum chemistry methods to do this is described. The remaining (3N−8) internal degrees of freedom are characterized as local harmonic motion orthogonal to the reaction surface; these local normal modes are defined by diagonalizing an appropriately projected force constant matrix. The classical (and quantum) reaction surface Hamiltonian is then derived, i.e., the Hamiltonian for which the dynamical variables are the two reaction-like coordinates (r1,r2) and the (3N−8) local normal mode coordinates (plus the usual three Euler angles for overall rotation), and their conjugate momenta. A zeroth order dynamical model is also described which has the form of a collinear-like atom–diatom reaction, i.e., a system with two degrees of freedom—in an effective 2D potential. This effective potential consists of the actual potential energy on the 2D reaction surface, the vibrationally adiabatic energy of the (3N−8) local normal modes, and the rotational energy of the complete polyatomic system, the latter two quantities being functions of the coordinates (r1,r2) on the reaction surface.

Classical analysis of collinear light atom transfer reactions

A classical direct reaction theory is formulated and shown to account for the recently observed quantal oscillations in the reaction probability of light atom transfer reactions. Quasiperiodic orbits and irregular orbits are found for the systems although the potential energy surfaces used have only saddle points in the interaction region. These orbits imply the existence of a new type of bound species—an adiabatic molecule.