Molecular Beam Scattering Research Articles

Determination of Intermolecular Potentials by the Inversion of Molecular Beam Scattering Data. I. The Inversion Procedure

A practical solution of the inversion problem within the realms of the WKB approximation is reported. The basic input information is only the measured relative differential cross section, from which the WKB phase function or the classical deflection function is constructed. The absolute potential curve is then determined by the application of a modified Firsov method. The problem of which part of the differential cross section is readily measurable and also suitable for the inversion procedure is studied. A practical procedure is proposed and tested by using a simulated example.

He–H2 Potential Parameters from Molecular Beam Scattering Experiments

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Long-Lived Collision Complexes in Molecular Beam Scattering Experiments

Evidence is reported for long-lived complexes formed in nonreactive collisions in crossed molecular beams of alkali metals and a number of compounds, most of them containing oxygen atoms. Experimental details and a description of the reduction of data into center-of-mass quantities are given. Differential scattering cross sections and distributions of final relative kinetic energy are deduced. A calculation using a statistical theory for one of the systems studied, K + SO2, is compared with the experimental results.

Determination of Intermolecular Potentials by Inversion of Molecular Beam Scattering Data

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Expansion Coefficients for Analysis of Molecular Beam Scattering Data via the Buckingham–Corner Intermolecular Potential

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Determination of the Li–Hg Intermolecular Potential from Molecular-Beam Scattering Measurements

The experimental differential-cross-section extrema data of Groblicki and Bernstein have been analyzed and yield a family of potential parameters. These results were combined with the inferences obtainable from the glory extrema in the total cross sections of Rothe and Veneklasen to deduce a potential compatible with both experiments. The resulting potential is found to have a well depth ε = 1.70 × 10−13erg ± 3% with a size parameter rm = 3.02 Å ± 3%. The long-range coefficient is C6 = 4.4 × 10−58erg·cm6 ± 60%.

Experiments on the Scattering of Molecular Beams for the Study of Reactions of Potassium with Methyl Iodide, Hydrogen Bromide, and Bromine

Experiments on the Scattering of Molecular Beams for the Study of Reactions of Potassium with Methyl Iodide, Hydrogen Bromide, and Bromine

Dipole—Dipole Scattering in Molecular Beams. Variation of Total Cross Section with Velocity and Rotational Overlap

Total cross sections were measured for scattering of velocity-selected beams of alkali halide molecules KCl, CsCl, and CsBr by HBr and CH3I and, for comparison, for Kr and Xe. The pressure in the scattering chamber was monitored by a second crossed beam of alkali atoms, which allowed direct measurement of the ratios of cross sections for different molecules interacting with the same scattering gas. As expected from the first-order selection rules, the results indicate that the contribution of rotationally inelastic transitions produced by the angle-dependent dipole—dipole force depends strongly on the extent to which the rotational spectra of the two molecules overlap. Inelastic scattering appears to be dominant for the CH3I systems, where the overlap is very good. The cross sections are ∼5000 Å2 (compared with ∼1400 Å2 for elastic van der Waals scattering; both corrected for angular resolution) and the velocity dependence is much weaker than for elastic scattering. In the Appendix simple approximate formulas are derived from which the first-order inelastic dipole—dipole cross section can be calculated without numerical integrations over impact parameters and rotational distributions.

Iterative Mapping of Phase-Shift Space to Potential Space in Molecular-Beam Scattering

An iterative mapping procedure has been developed which correlates variations in the scattering phase shifts to intermolecular potential changes. Although a point-by-point potential is generated, a six-parameter potential form has been assumed for convenience in the generation of the phase shifts via the JWKB approximation. The method has been texted using standard phase shifts to ascertain the inaccuracies to be expected with potential variations. From the calculations, the accuracy of the potential points generated in the mapping is limited only to the technique used to fit them and is found independent of the bowl shape.

Molecular-Beam Scattering from the (111) Plane of Silver

The spatial distributions of molecular beams of CH4, NH3, He, Ne, Ar, and Xe scattered from the (111) plane of an epitaxially grown Ag single crystal have been examined both during growth of the Ag crystal and immediately afterward, and no distinction between these modes was observable. The scattering of Ne, CH4, and NH3 has been compared to illustrate the important role of the gas—metal interaction energy; NH3, the most strongly interacting gas, gives rise to nearly diffuse scattering, while Ne is nearly specularly directed. Although the scattering of He is essentially specularly directed at all incident angles and temperatures, the heavier gases (Ar and Xe) exhibit scattering maxima lying between the specular direction and the tangent to the surface (supraspecular scattering), with the location of the maxima depending in a complex manner on the angle of incidence of the beam and the beam energy. Since a necessary condition for supraspecularity is that the beam temperature be greater than the surface temperature, an energy-transfer step seems to be involved in determining the particle trajectory. Similar complexities in the intensity of the scattered-beam maxima are observed; however, no simple explanation seems to suffice in this case.

Reactive Scattering in Molecular Beams: Velocity Analysis of KBr Formed in the K+Br2 Reaction

The velocity distributions of scattered K and KBr from collisions of crossed thermal beams of K+Br2 have been measured over the range 200–850 m/sec at four laboratory angles Θ=10°, 15°, 20°, 30°. The results confirm that most of the energy released in the reaction (∼45 kcal/mole) appears in internal excitation rather than in translational motion of the products, as inferred previously from qualitative kinematic analysis of angular-distribution measurements. An approximate transformation to the center-of-mass coordinate system is carried out to evaluate for each Θ the distribution of the final relative translational kinetic energy E′ of the products. These distributions have a roughly Maxwellian shape (broader by ∼20%). The position of the peak varies from E′=1 to 4 kcal/mole for Θ=30°→10° (as compared with E=1.2 kcal/mole for the most probable initial relative kinetic energy of the reactants); the integrated intensity of cumulative yield with E′≳5 kcal/mole is ∼25% at 10° and ∼50% at 30° and with E′≲15 kcal/mole it is ∼75% at 10° and ∼90% at 30°. The distribution of the vibrational excitation Wv′ of the KBr for Θ=30° is also estimated by combining these results with data from electric-deflection experiments which provide an estimate of the rotational excitation. The vibrational excitation peaks near Wv′ ∼43 kcal/mole and the cumulative yield with Wv′≳30 kcal/mole is ∼90%. The ``electron-jump'' mechanism suggested by previous results, K+Br2→K++Br2−→K+Br− +Br, again offers plausible qualitative interpretations (perhaps not unique) for the main features of the observed energy distributions.

Reactive Scattering in Molecular Beams: Electric-Deflection Analysis of Rotational Excitation of Products

Reactive Scattering in Molecular Beams: Electric-Deflection Analysis of Rotational Excitation of Products

Reactive Scattering in Molecular Beams: Evidence for a Stripping Mechanism in Reactions of Alkali Atoms with Halogens

Author(s): Wilson, K.R.; Kwei, G.H.; Norris, J.A.; Herm, R.R.; Birely, J.H.; Herschbach, D.R.

Molecular Beam Scattering at Thermal Energies

A review is presented on the interpretation of measured angular distributions in terms of differential scattering cross sections in molecular beam scattering at thermal energies. Special attention is given to velocity distributions in the beam and scattering gas. Conversion of data to the center- of-mass system, apparatus, scope of thermal molecular-beam-scattering studies, and recent advances in elastic scattering at thermal energies are discussed. 75 references are included. (P.C.H.)

WKB Analysis of Molecular Beam Scattering and the Lennard-Jones Potential

The WKB method was used in the interpretation of molecular beam scattering. Particular attention was given to small angle scattering where the sensitivity to the intermolecular potential is greatest. It was found that the Lennard-Jones potential does not fit the data and that, for the case investigated, the minimum in the potential probably needs to be broadened. Empirical relationships between the phase shifts and the intermolecular potential were found which should be of value in the inversion problem. A calculation of rainbow scattering was made.

Validity of the WKB Approximation in the Interpretation of Molecular Beam Scattering Data

The validity of several approximations pertinent to molecular scattering has been investigated. The WKB method was found to be reliable and was used to demonstrate the sensitivity of molecular scattering data to the intermolecular potential.

High-Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L-J(n, 6) and Exp-6(α) Potentials

Explicit expressions are derived for the total elastic scattering cross sections in the high-velocity region for molecules interacting according to L-J (n, 6) and exp-6(α) potentials. Cross sections are presented in tabular and graphical form.

Wide-Angle Scattering in Molecular Beams. The Rainbow Effect

Differential elastic scattering cross sections have been measured for collisions of potassium with krypton and hydrogen bromide at different energies in the thermal energy range. In all qualitative details the results can be explained assuming an interaction potential of type exp-6 (Buckingham). Rainbow scattering is observed and potential parameters are evaluated. Even though several hundred partial waves contribute to the scattering the experimental evidence appears to indicate the need for the semiclassical rather than the classical treatment of wide-angle scattering in the region of the rainbow maximum.

Semiclassical Equivalence Relationship Applied to the Calculation of Molecular-Beam Scattering Phase Shifts

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WKB Approximation and Molecular Beam Scattering

WKB Approximation and Molecular Beam Scattering