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Discusses the development of a perturbation theory to treat rotationally inelastic scattering using an adiabatic basis set. Extension of the theory to include closed channels; Recasting of theory into the exact integration of a set of semiclassical couple equations.

We have calculated equilibrium constants for the reaction of noble gas atoms becoming trapped inside C60 molecules. Two models of the potential were used: a Lennard-Jones (12,6) potential between the noble gas atom and each carbon atom and the MM3 molecular mechanics program. We assume that the vibration of the noble gas atom is uncoupled to the cage vibrations and calculate the corresponding partition function classically. The results for the two potentials agree for helium and neon but disagree strongly for krypton and xenon, with the MM3 results being much smaller than the Lennard-Jones results. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A simple method is given for using a fast but not necessarily accurate scattering approximation to interpolate the results of an exact calculation. The goal is to minimize the number of points where the expensive, exact calculation must be done. The approximate theory is used to remove the rapidly varying parts of the exact S-matrix to obtain a slowly varying correction matrix which can then be interpolated over a large interval in energy or angular momentum. After the interpolation, the rapidly varying approximate parts are put back in to give an accurate S-matrix. The method preserves the phase of the S-matrix. It is demonstrated for the cases of symmetric molecular charge exchange and for rotationally inelastic scattering. [ABSTRACT FROM AUTHOR]

We have used a Monte Carlo trajectory calculation to model the chemiionization reaction, HI+B→I-+HB+. B is, in our experiments, a polyatomic amine, but the model treats it as a single atom. The reaction occurs on two potential energy surfaces, one covalent dissociating to the reactants, and one ionic corresponding to the products. Several restrictions were included in the model to account for the fact that B is really a molecule. Classical trajectories were then run at a range of energies and for several variations of potential parameters. The model showed that the reactive cross section rises rapidly as a function of translational energy and that the dynamic threshold energy is 0.38 eV higher than the minimum energy required to form the products. Product angular distributions at low energies show a peak in the forward direction but give a large amount of scattering at and behind the center of mass, in qualitative agreement with the experiments. As the energy increases, the distribution shifts to smaller angles. The Coulomb interaction in the ionic surface introduces some novel features not seen in most reactions. [ABSTRACT FROM AUTHOR]

We develop two semiclassical perturbation approximations to treat the charge exchange between a molecular ion and its neutral counterpart. In one case we use a diabatic vibrational basis set appropriate to the dissociated species. The scattering is then treated using an exponential first-order perturbation theory. In the second case a vibrationally adiabatic basis set is used. Comparisons with exact results for O+2+O2 show that the adiabatic theory is the more accurate at 8 eV, but the two have comparable accuracy at 36 eV. [ABSTRACT FROM AUTHOR]

The electronically inelastic two-state problem is solved by using a double perturbation theory. The wave function is expressed as a set of coupled differential equations in a diabatic representation, and the elastic wave functions are removed from the exact wave functions to give a set of coupled differential equations for the coefficients of the elastic functions. These are then linearized about the crossing point in the potential-energy curves and solved as in the Landau–Zener approximation. The approximate, Landau–Zener coefficients are then removed from the exact coefficients to give a set of differential equations for the resulting second-level coefficients. Having removed most of the problem in these two steps, the resulting second-level equations can usually be solved accurately by an exponential perturbation theory. The theory is designed as a prototype for more complicated inelastic and spectroscopic problems for which a computer solution of the Schrödinger equation is impractical. [ABSTRACT FROM AUTHOR]

We develop a method of successive approximations for molecular scattering theory. This consists of a recipe for removing from the Schrödinger equation, one by one, the wave functions of a set of approximate solutions. The radial wave function is expressed as a linear combination of the well-behaved and singular solutions of the first approximation, and a set of coupled differential equations is obtained for the coefficients of the approximate solutions. A similar set of coefficients is obtained for the next approximation, and the exact coefficients are expressed in terms of the approximate coefficients to yield a set of second-level coefficients. The process can be continued like pealing off the layers of an onion. At each stage the coupled differential equations for the coefficients is equivalent to the Schrödinger equation. Finally, one can either ignore the remaining coefficients or approximate the coupled equations by a simple perturbation theory. [ABSTRACT FROM AUTHOR]

Molecular dynamics has been used to examine the influence of the permanent dipole moment on the rotational diffusion of a diatomic molecule in liquid water. Several runs were made for various values of the dipole moment of the solute ranging from 0 to 20 D. The resultant rotational diffusion times compare favorably with dielectric friction theories up to about 17 D, but for dipole moments larger than this, the time constants are seen to increase much more rapidly than can be explained by dielectric friction theories. This deviation from dielectric friction theory is discussed in terms of a local change in solvation structure. [ABSTRACT FROM AUTHOR]

We have examined the classical limits to the orbital and energy sudden approximations. It is shown that at large orbital and rotational quantum numbers the transformations which diagonalize the coupling matrix in the sudden limit also diagonalize the coupling matrix in the classical limit. The eigenvalues are no longer a delta function fixed in position during the collision but become a narrow wave packet moving with the classical velocity. The result is a uniform approximation valid in both the sudden and classical limits. A key feature of the theory is the use of the discrete-variable representation which allows an accurate counting of quantum states in the sudden representation. The theory should improve the accuracy of the sudden approximation while requiring little additional computer time. [ABSTRACT FROM AUTHOR]

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N2 are very much more accurate than the IOS and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N2 show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory. [ABSTRACT FROM AUTHOR]

Using crossed seeded nozzle beams we have examined the energy dependence of the cross section for the reaction SbF5+RX→SbF5X-+R+, where X is a halogen and R an organic radical. By using a range of carrier gases in the two beams and by varying the nozzle temperature and the beam intersection angle, we can separately vary the relative translational energy and the vibrational temperatures of the beams. Near the threshold, vibrational energy seems to play a very important role. At energies well above threshold, the reactive cross section appears to depend largely on translational energy. We explain this by assuming that the reaction takes place on two potential energy surfaces. By choosing RX properly, the R+ product will decompose. In two cases we observe that, although vibrational energy in RX has a minor effect on the halide abstraction, it is very important in the subsequent decomposition of R+. [ABSTRACT FROM AUTHOR]

Using crossed molecular beams we have studied the dynamics of several electron transfer reactions, A+B→A++B-, where A is an organic base and B is SnCl4, SbF5, or TiCl4. We propose a simple, modified stripping model whereby the electron jumps at the point where the ionic and covalent surfaces cross to form a pair of ions produced by a vertical, Franck–Condon transition. All initial energy in excess of this vertical threshold appears in the translational energy of the products. This model is verified in one case where the vertical ionization potential and electron affinity are known and is then used to obtain a rough vertical electron affinity of SbF5. Except at the lowest energies all the reactions follow this modified stripping mechanism. [ABSTRACT FROM AUTHOR]