Sheldon Green

Rotational excitation in H2-H2 collisions - Close-coupling calculations

Rotational excitation in molecule−molecule collisions has been treated for the first time by accurate quantum close−coupling scattering calculations, employing an expansion basis set of two to three rotational levels for each molecule and correctly accounting for exchange of identical particles. Elastic and inelastic cross sections have been computed for collisions of para−para, ortho−ortho, and para−ortho hydrogen molecules assuming an intermolecular potential suggested previously. The accuracy of recent ’’effective potential’’ calculations is demonstrated by comparison with the exact quantum results.

On the factorization and fitting of molecular scattering information

The factorization of cross sections of various kinds resulting from the infinite order sudden approximation is considered in detail. Unlike the earlier study of Goldflam, Green, and Kouri, we base the present analysis on the factored IOS T‐matrix rather than on the S‐matrix. This enables us to obtain somewhat simpler expressions. For example, we show that the factored IOS approximation to the Arthurs–Dalgarno T‐matrix involves products of dynamical coefficients TLl and Percival–Seaton coefficients fL(jl‖j0l0‖J). It is shown that an optical theorem exists for the TlL dynamical coefficients of the T‐matrix. The differential scattering amplitudes are shown to factor into dynamical coefficients qL(χ) times spectroscopic factors that are independent of the dynamics (potential). Then a generalized form of the Parker–Pack result for Σj(dσ/d?)(j0→j) is derived. It is also shown that the IOS approximation for (dσ/d?)(j0→j) factors into sums of spectroscopic coefficients times the differential cross sections out of...

Rotational excitation of symmetric top molecules by collisions with atoms. II. Infinite order sudden approximation

The infinite order sudden approximation is extended to rotational excitation of symmetric tops by collisions with atoms. The formalism is developed first for ’’primitive’’ or ’’one‐ended’’ tops. The proper parity adapted linear combinations which describe real rotors are then considered. Modifications needed for asymmetric rigid rotors are noted briefly. For all of these cases generalized spectroscopic relaxation cross sections are discussed; these include degeneracy averaged state‐to‐state integral cross sections and pressure broadening cross sections as special cases. In the IOS formalism these cross sections factor into dynamical terms which contain all the system dependent collision information and spectroscopic coefficients which contain the dependence on rotational levels and angular momentum coupling. This factorization is similar to that obtained for linear rotors, but differs insofar as the dynamical factors cannot all be expressed in terms of single state‐to‐state cross sections and insofar as t...

Energy transfer in NH3-He collisions

The electron gas intermolecular potential for NH3–He developed previously is shown to be inadequate for a quantitative description of energy transfer in this system by comparing with available experimental data—pressure broadening, double resonance, and beam scattering. A new potential is constructed by combining the Hartree–Fock results of Davis, Boggs, and Mehrotra with semiempirical long‐range induction and dispersion terms. The resulting potential is shown to be in harmony with beam scattering and pressure broadening measurements. It is found that the quadrupole‐induced–dipole interaction, which has been invoked previously to account for pressure broadening in this system, is not, in fact, as effective as the short‐range anisotropy. Although results are in general accord with double resonance data, a few unresolved discrepancies remain. It is suggested that these are due to improper consideration of the dependence of cross sections on degenerate magnetic quantum levels in the experimental analysis. Us...

Validity of approximate methods in molecular scattering: Thermal HCl–He collisions

Accurate close coupling scattering calculations are presented for thermal energy HCl–He collisions. The interaction potential is obtained from the Gordon–Kim electron gas model, adjusted to have the correct long‐range multipole form. A variety of phenomenological cross sections are computed from the close coupling S matrix, and these are compared with results from several commonly employed approximate methods. In particular, it is found that the total integral, total differential, and gas kinetic cross sections are accurately predicted by the central field approximation which retains just the spherical average of the interaction. Integral inelastic cross sections are represented quite accurately by the coupled states approximation of McGuire and Kouri, but only qualitatively by the effective potential method of Rabitz. Pressure broadening cross sections from the close coupling calculation are in much better agreement with experiment than either Anderson theory calculations or the classical trajectory stud...

Computational tests of angular momentum decoupling approximations for pressure broadening cross sections

The utility of several approximate scattering methods for predicting collision induced spectral pressure broadening has been tested by comparison with accurate close coupling results. In particular, broadening of the pure rotational spectra of HD, HCl, CO, and HCN—all perturbed by low energy collisions with He atoms—has been computed using the effective potential formalism of Rabitz, the decoupled l‐dominant approximation of DePristo and Alexander, and the jz‐conserving coupled states method of McGuire and Kouri. For this last method, pressure broadening cross sections have been obtained with the new, correct expression recently derived by Goldflam and Kouri as well as with an earlier formalism based on an incorrect labeling of the scattering matrices. These methods were found to be generally disappointing for predicting pressure broadening with the exception of the new, correctly formulated jz‐conserving coupled states method which was found to agree quantitatively (better than 5%) with close coupling va...

On the use of pressure broadening data to assess the accuracy of CO–He interaction potentials

LBL-11 075 Preprint NATIONAL RESOURCE FOR COMPUTATION IN CHEMISTRY Submitted to The Journal of Chemical Physics ON THE USE OF PRESSURE BROADENING DATA TO ASSESS THE ACCURACY OF CO-He INTERACTION POTENTIALS Sheldon Green and Lowell D. Thomas June 1980 TWO-WEEK LOAN COPY is a Library which may Copy borrowed for two weeks. a personal retention copy; call fo. Divisiony Ext. 6782. Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48 and for the National Science Foundation under Interagency Agreement CHE-7721305

Vibrational dependence of pressure induced spectral linewidths and line shifts: Application of the infinite order sudden scattering approximation

The infinite order sudden (IOS) approximation to molecular rotation is applied to simplify the theory of linewidths and shifts in vibration–rotation spectra. This approximation is expected to be most accurate for hard, short‐range collisions and is therefore complementary to Anderson theory which is best for weak, glancing collisions. The IOS approximation predicts identical linewidths and shifts for P‐ and R‐branch transitions with the same line number. It also predicts zero line shifts for pure rotational spectra. The dependence of linewidths and shifts on vibrational band is seen to be due mainly to variation in diagonal vibrational matrix elements of the intermolecular potential. Calculations are performed for the 0–0, 0–1, and 0–2 bands of CO perturbed by He, using a theoretical interaction potential with no semiempirical or adjustable parameters; results are in satisfactory accord with experimental data.

Calculated properties for no X2Π and A2Σ

Abstract Restricted Hartree—Fock functions for NO X 2 Π and A 2 Σ + have been calculated using a large, Slater-type basis set. Several molecular properties, including hyperfine constants, have been computed and are found to agree rather well with experimental values.

Comment on determination of the interaction potential between Ar and HCl

To test the accuracy of the Gordon‐Kim theory of intermolecular forces, predicted and experimental values are compared for Ar–HCl. The method appears to accurately predict the short‐range repulsive forces and also the position (but possibly not the depth) of the potential well.