Reactive Scattering Cross Sections Research Articles

Fifty years of nucleophilic substitution in the gas phase.

Bimolecular nucleophilic substitution (SN2) reactions have become a model system for the investigation of structure–reactivity relationships, stereochemistry, solvent influences, and detailed atomistic dynamics. In this review, the progress during five decades of experimental and theoretical research on gas phase SN2 reactions is discussed. Many advancements of the employed methods have led to a tremendous increase in our understanding of the properties and the dynamics of these reactions. For reactions involving six atoms a quantitative agreement of the differential reactive scattering cross sections has already been achieved, in the future it is expected that even larger polyatomic reactions systems become tractable. Furthermore, studies with higher precision, improved reactant control, and a more accurate theoretical treatment of quantum effects are envisioned.

Reactive scattering and electron detachment for collisions of halogen negative ions with HCl, DCl, and HBr

Absolute total cross sections have been measured for collisions of Cl−, Br−, and I− with HCl, DCl, and HBr for projectile energies ranging from 5 to 300 eV. The processes investigated include reactive scattering and electron detachment. The reactive scattering cross sections exhibit considerable isotope effects and the collisional dynamics are discussed within the framework of a spectator-stripping model which involves proton or deuteron abstraction. The results for the I− projectile are substantially different from those for Cl− and Br−; this difference is suggested to be related to the relative stability of the molecular anion, HI−.

Approximate Quantum Mechanical Calculation of Reactive Scattering Cross Sections - The Fixed Angle Reactor Model (FARM)

An approximate three-dimensional quantum mechanical method for the calculation of atom-diatom reactive scattering cross sections and rate constants is described. The method is known as the Fixed Angle Reactor Model (FARM). Its key features are that it uses information from both classical trajectory and simplified quantum mechanical calculations to compute vibrational state-to-state reactive scattering cross sections. The classical trajectory calculations are used to estimate the degree to which torques acting during the approach of the collision partners are able to successfully reorient them into the most favorable geometry for subsequent reaction. This information is then used, together with fixed angle quantum reactive scattering calculations to approximate a full three-dimensional quantum reactive scattering calculation. Test results are presented for the reactions: H + H2(ν = 0) → H2(ν' = 0) + H and D + H2(ν = 1) → HD + H and comparison is made with other methods.

The approximate quantum mechanical calculation of reactive scattering cross sections: The fixed angle reactor model (FARM)

An approximate three-dimensional quantum mechanical method for the calculation of atom–diatom reactive scattering cross sections is described and tested by application to the H+H2→H2+H problem. The method, known as the fixed angle reactor model (FARM), combines reactive quantum mechanical calculations performed at fixed angles to yield differential and integral cross sections. It encompasses the best features of the bending corrected rotating linear model (BCRLM) and the reactive infinite order sudden (RIOS) methods, while correcting shortcomings of both. The FARM method is shown to yield reliable reactive cross sections at both low energies in the threshold region and at high energies.

An approximate three-dimensional quantum mechanical calculation of reactive scattering cross sections for the atomic hydrogen + molecular chlorine(v) .fwdarw. hydrogen chloride(v') + atomic chlorine reaction

An approximate three-dimensional quantum mechanical calculation of reactive scattering cross sections for the atomic hydrogen + molecular chlorine(v) .fwdarw. hydrogen chloride(v') + atomic chlorine reaction

An improved quasiclassical trajectory method for state to state reactive scattering cross sections and rate constants

A systematic scheme is developed for the incorporation into quasiclassical trajectory (QCT) methodology of recent advances in the understanding of vibrationally adiabatic barriers in collinear atom + diatom reactions. The resulting hybrid QCT method centers on a definite set of rules for optimally combining the results of forward and reverse trajectory calculations. It is argued, and demonstrated by practical examples, that the hybrid method will give a more consistently reliable account of the threshold behavior of collinear reaction cross sections than the conventional QCT method. Extension of the method to the three dimensional F+H2 reaction gives similarly encouraging results, both for state to state reaction cross sections and for rate constants.

Coupled channel distorted wave method of atom–molecule reactive scattering: Application to p a r a to o r t h o hydrogen molecule conversion

We present a three dimensional coupled channel distorted wave approach of the atom–molecule reactive scattering. The full entrance channel wave functions are obtained from the inelastic vibrational and rotational close-coupling approximation, and reactive cross sections are evaluated with those wave functions employing the transition matrix (T matrix) method. Therefore, in contrast to the previous adiabatic distorted wave model of the reactive scattering, the present method allows for the target molecule to be dynamically distorted following the motion of the incident atom. The formulation of the approach and efficient computational procedures for obtaining the reactive T matrix elements are presented. The reactive scattering cross sections and the rate constants of the H+H2 para to ortho hydrogen molecule conversion have been evaluated to illustrate the computational aspects of the present method. The wave function obtained from the rotational close-coupling approximation yields better results on the reactive cross section than that from the pure vibrational coupling. The wave function computed from the simultaneous vibrational and rotational close-coupling approximation results in the most accurate cross section. This indicates that in order to obtain accurate results with the T matrix method, the simultaneous vibrational and rotational distortions of the target molecule should be considered when approximating the full entrance channel wave function. The differential cross section and the rotational distribution of the product molecule calculated from the present coupled channel distorted wave scheme are qualitatively similar to those obtained from the previous adiabatic distorted wave method; however, the magnitude of the cross sections from the present theory is larger than the previous ones. This might arise from the fact that the vibrational distortion of the target in the previous adiabatic distorted wave model is not sufficiently large. The present approach is shown to account for all major features of the reactive scattering in the H3 system.

Reactive cross section as a function of collision energy. I. H(D)+Br2→HBr(DBr)+Br

Reactive scattering cross sections are measured for H(D)+Br2→HBr(DBr)+Br by crossing a beam of hydrogen atoms with a beam of Br2.(AIP)

Model for H+2(v = 0)–He collisions above 2 eV

A classical model with no adjustable parameters employing Lennard-Jones type potentials is used to describe collision processes between H2+ (ν=0) ions and He atoms at relative energies above 2 eV. The assumptions that justify such an approach are discussed as well as the possibility of additional simplifications. Model predictions for collision-induced dissociation and reactive scattering cross sections compare favorably with data from four laboratories. Predicted angular distributions of product HeH+ and H2+ as well as vibrational and rotational energy partitioning for these products are also reported.

Atom-Molecule Reaction D+H2 → HD+H Studied by Molecular Beams

Collisions between deuterium atoms and hydrogen molecules have been studied in a modulated crossed beam experiment. The relative signal intensity and the signal phase for product HD from reactive collisions allowed determination of both the angular distribution and HD mean velocity as a function of angle. From these a relative differential reactive scattering cross section in center-of-mass coordinates was deduced. The experiment indicates that reactively formed HD having little or no internal excitation, departs from the collision anistropically, with maximum amplitude 180° from the direction of the incident D beam in c.m. coordinates, which shows that the D–H–H reacting configuration is short-lived compared to its rotation time. Nonreactive scattering of D by H2 was used to assign absolute values to the differential reactive scattering cross sections.

Quantum mechanical theory of three-body rearrangements: exact total cross-section calculations for a three-dimensional model

The quantum mechanical coupled channel τ operator formalism has been used to derive coupled integral equations for three-body reactions in three dimensions (neglecting dissociation). These integral equations differ significantly from the usual Lippmann-Schwinger integral equations in that they are already essentially Fredholm equations of the second kind. (That is, the ‘kernel’ for these equations does not involve the appearance of ‘lesser’ and ‘greater’ radial variables.) The formalism is used to calculate total reactive scattering cross sections for a three-dimensional model for a three-body system. Results are presented over a range of energies from about 0·2 eV to 1·2 eV.

Differential cross sections for chemically reactive systems

A quantum mechanical theory is developed for the differential and total elastic and reactive scattering cross sections for an electronically adiabatic bimolecular exchange reaction, with the restriction that the three atoms are constrained to move on a straight line, but with the whole system free to rotate in three dimensions. The introduction of a set of natural collision coordinates, together with a vibrationally adiabatic approximation, is used to reduce the scattering problem to the solution of one-dimensional Schrodinger equations. Semi-classical expressions for the elastic and reactive phase shifts are derived. The partial wave summations that occur in the theory are evaluated by semi-classical techniques and elastic and reactive differential cross sections are calculated for three different kinds of potential surface. A feature of the calculations is the appearance of a new kind of rainbow, which is named a ‘cubic’ rainbow since it arises when the deflection function varies cubically with impact p...

Perturbed Morse Oscillator Approximation in Reactive Collisions. II. A Repulsive Potential

The H+Br2→HBr+Br reaction has been considered to form a linear collision intermediate and detailed reactive scattering cross sections have been computed quantum mechanically using a perturbed Morse oscillator approximation. These computations employed a diatomics-in molecules potential-energy surface distorted to make it moderately repulsive, i.e., the potential energy of the collision intermediate was made to be closer to that of the reactants than to that of the products. The resulting cross sections are peaked about the lower allowed vibrational quantum numbers of product HBr for a wide range of initial conditions corresponding to temperatures from 300° to 1000°K. This appearance of the heat of reaction as relative translation rather than as internal excitation is in agreement with both experiment and semiclassical calculations. Specific rate coefficients and pre-exponential factors calculated from the computed cross sections are also in satisfactory agreement with experiment.