Frederick R. W. McCourt

A new determination of the ground state interatomic potential for He2

A simple accurate potential of the HFD-B form, which appears to be the best characterization of the He-He interaction constructed to date, is presented. It has been fitted to low temperature second virial coefficient data and recent accurate room temperature viscosity data, while at the same time pinning the repulsive wall to the value calculated by Ceperley and Partridge at 1 Bohr. It possesses a well depth of 10·948 K, considerably deeper than many of the recent empirical or ab initio potentials. It reproduces, within experimental error, such dilute gas properties as second virial coefficients, viscosities and thermal conductivities over a wide temperature range. It also predicts, within experimental error, such microscopic properties as differential cross sections, high energy integral cross sections and backward glory oscillations in the integral cross sections. Finally, it accounts for nuclear magnetic relaxation in 3He and supports a weakly bound state in the 4He interaction.

Multiproperty determination of a new N2–Ar intermolecular interaction potential energy surface

A new multiproperty potential energy surface for the N2–Ar intermolecular interaction is reported. The present determination is based upon molecular beam total differential and integral scattering data, taken together with the temperature dependence of the interaction second virial coefficient, transport properties, transport property field effects, and relaxation phenomena, such as pressure broadening of the depolarized Rayleigh line and longitudinal nuclear spin relaxation. The primary fit has been made to the beam scattering and virial data, and refinements to the potential parameters thus determined have been made by employing the data available for the gas phase transport and relaxation phenomena. The potential energy surface employed is an empirical Morse–Morse–spline–van der Waals form, in which the potential parameters depend upon the angle between the N2 figure axis and the line joining the centers of mass of N2 and Ar. No N2 stretching dependence has been included in the present determination. C...

An essentially exact evaluation of transport cross-sections for a model of the helium-nitrogen interaction

Essentially exact calculations of the transport collision integrals for a realistic model of the intermolecular pair potential of helium and nitrogen are reported. The collision dynamics for the interaction of the atom and molecule have been treated within the framework of the Arthurs and Dalgarno closecoupled formalism and the calculations are free from all approximation except inevitable numerical round-off. The direct calculation of collision integrals covers the temperature range 70 K to 300 K. The range has been extended upwards to 500 K with the aid of complementary classical calculations without loss of accuracy. The results serve as the first set of ‘benchmark’ calculations of transport collision integrals for a heavy molecular system with a realistic anisotropic pair potential. They are used to assess the accuracy of various approximate schemes for the evaluation of the same quantities. It is found that classical trajectory methods are in good agreement with the close-coupled calculations above 2...

New anisotropic potential energy surfaces for N2-Ne and N2-Ar

New anisotropic potential energy surfaces of the Hartree-Fock plus damped dispersion (HFD) type have been obtained for the N2-Ne and N2-Ar interactions. The SCF energies utilized in constructing the short-range part of the interactions were computed at 20 points on each surface by using basis sets of double zeta plus polarization quality. Anisotropic C 6 and C 8 dispersion coefficients, utilized in constructing the long-range part of the interaction, have been calculated with a recently obtained combining rule. Several procedures are introduced for estimating the anisotropic damping factors used in the description of the correlation energy contributions in the HFD model. The essential differences amongst the surfaces reported here arise from these estimates. Comparisons are made with other available anisotropic N2-Ne and N2-Ar surfaces. The predictive ability of all surfaces with respect to the temperature dependence of the interaction second virial coefficient, B 12(T), has also been tested. For the N2-N...

Production and relaxation cross sections for the shear viscosity Senftleben–Beenakker effect. I. Formal expressions and their coupled‐states and infinite‐order–sudden approximations for atom–diatom systems

Starting from kinetic theory collision integrals obtained from a generalized Boltzmann equation for a linear molecule in a bath of atomic perturbers and using Liouville (vector) space algebra, general expressions are derived for the three cross sections determining the shear viscosity Senftleben–Beenakker effects. These expressions are presented in terms of S‐matrix elements in the total‐J representation since this representation is especially useful for dynamical calculation and approximation procedures. Coupled‐states and infinite‐order–sudden dynamical approximations are then introduced and expressions obtained for the three cross sections in initial‐l, final‐l, and average‐l labeling schemes. All cross sections simplify greatly when initial or final‐l labeling is employed but little or not at all when average‐l labeling is used. Nonetheless, even when the latter choice is made, less work will be involved than would be required for the corresponding full close‐coupled or coupled‐states calculation.

On the N2–He potential energy surface

A detailed comparison of the predictive powers of two recently determined empirical and two recently proposed theoretical potential energy surfaces for the N2–He interaction has been carried out. In particular, the following properties have been tested: at the microscopic level, total and state‐to‐state differential cross sections and absolute total integral cross sections, while at the macroscopic level, interaction second virial, diffusion, viscosity, and thermal conductivity coefficients, as well as the rotational relaxation time, depolarized Rayleigh spectral collision broadening, and shear viscosity and thermal conductivity field‐effect data in N2–He mixtures. Exact calculations have been employed, from the close‐coupling method for treating scattering data at low energies to the classical trajectory method with second‐order corrections to compute the effective cross sections that determine the bulk transport and relaxation phenomena.The empirical exponential‐spline–Morse‐spline–van der Waals surface...

Quantum mechanical calculations of effective collision cross-sections for He-N2 interaction

For the He-N2 system quantum mechanical calculations of the effective cross-sections that govern both the viscomagnetic effect and the collision broadening of the depolarized Rayleigh (DPR) line in mixtures have been performed. The results provide a set of ‘benchmark’ cross-sections for atom-heavy rigid rotor systems interacting through a realistic anisotropic intermolecular potential. In addition, comparisons have been made with equivalent calculations using the classical trajectory approach. The accuracy of the classical calculations has been tested, both at the macroscopic level in the temperature range from 70 K to 500 K and at an intermediate level as a function of the total energy. The results indicate that the classical trajectory calculations are in good agreement with the present quantal calculations. For all cross-sections the difference between classical and quantal results becomes progressively smaller with increase in total energy or temperature. This indicates that a hybrid scheme, which emp...

A comparison between classical trajectory and infinite-order sudden calculations of transport and relaxation cross sections for N2-Ne mixtures

Classical trajectory calculations of effective cross sections have been carried out for the N2-Ne system using the recent HFD3(N2-Ne) potential surface of McCourt et al. Forty-five such cross sections governing a wide variety of transport and relaxation phenomena in binary gaseous mixtures have been calculated at a number of temperatures ranging from 77K to 1100K. Wherever possible, we have made comparisons with much cheaper infinite-order sudden approximation (IOSA) calculations in order to assess their reliability. For cross sections relating to diffusion and viscosity, IOSA errors are less than 5·4 per cent, but, for cross sections which vanish for isotropic interactions, the IOSA is much less reliable, with possible errors of up to a factor of two. At the same time, we have compared our classical trajectory results for this surface with available experimental results. We find that the HFD3(N2-Ne) surface is too anisotropic, by as much as 20 per cent.

Close‐coupled and coupled‐states calculation of shear viscosity SBE cross sections for the H2–He system

Close‐coupled (CC) and coupled‐state (CS) calculations of kinetic theory relaxation and production cross sections are presented for the system H2 at infinite dilution in a bath of He. Performing these calculations for the same potential has allowed a test to be made of the efficacy of the CS procedure for use in calculating kinetic theory cross sections, especially those determining the Senftleben–Beenakker effects (SBE) in transport phenomena. The CS procedure is found to work extremely well (better than 1% agreement with CC results) for those cross sections that are predominantly elastic, to work rather well for relaxation cross sections determined either by reorientation of energetically inelastic collisonal events (about 10% agreement with CC results), and to work relatively poorly for production cross sections. In fact, the CS procedure for light molecules fares only marginally better than the IOS procedure for heavier molecules in the calculation of production cross sections. Finally, using only CC ...

A study of the ArCl2 Van der Waals complex: Ab initio-based potential energy surfaces, the relative stability of conformers, and the “hidden” microwave spectrum

Two new ground state potential energy surfaces have been obtained for the ArCl2 Van der Waals complex, one purely ab initio, the other constructed from empirical ArCl potentials modified in terms of ab initio data for the ArCl2 and ArCl moities. The ab initio surface has a well for the linear conformer that is slightly deeper than that for the T-shaped conformer, but inclusion of the zero-point energies reverses the relative binding in the two configurations. The microwave spectrum has been calculated using the new potential surfaces, and a series of lines that can be associated with the linear conformer have been predicted. Possible reasons for their nonobservability under the usual experimental conditions are discussed. A simple modification which employs empirical information on the ArCl potentials used in modelling the ArCl2 potential surface transforms the well for the T-shaped conformer into the global minimum, with a dissociation energy that lies within 0.5% of the experimental value, and microwave...