Edward A. Mason

The Intermolecular Potentials for Some Simple Nonpolar Molecules

Experimental data on the crystal properties, second virial coefficients, and viscosity coefficients of Ne, A, Kr, Xe, CH4, N2, CO, O2, and CO2 were analyzed for the purpose of obtaining values of the parameters in the exp‐six intermolecular potential, [open phi](r)=e1−6/α[6αeα(1−r/rm)−(rmr)6]. For gases whose molecules are spherical, it was possible to reproduce, with a single set of potential parameters, not only the crystal, second virial, and viscosity data, but also data on other transport properties with fair accuracy. For gases whose molecules deviate appreciably from spherical symmetry it was necessary to choose at least two different sets of potential parameters in order to reproduce different types of properties. Such behavior was taken to indicate the inadequacy of the assumptions, made in the fundamental gas theories, that intermolecular forces are central and that intermolecular collisions are elastic.

The Intermolecular Potentials of Helium and Hydrogen

The parameters for helium and hydrogen of the ``exp‐six potential, [open phi](r)=e1−6/α[6αeα(1−r/rm)−(rmr)6], have been calculated by use of experimental values of the second virial coefficients and viscosity coefficients. Because of the uncertainty of the quantum corrections, no low temperature data were used in determining the parameters. The exp‐six potential is able to reproduce both the second virial and the viscosity coefficients within experimental error, and is thus an improvement over the simpler Lennard‐Jones (12‐6) potential. In addition, other transport properties are accurately predicted. A combination rule is suggested for calculation of the exp‐six potential between two unlike molecules from the potentials between two pairs of like molecules, and is used to calculate a number of properties of helium‐hydrogen mixtures with satisfactory results.

Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential

A large number of the Chapman and Cowling collision integrals have been calculated for gases obeying a modified Buckingham potential, [open phi](r)=e1−6/α[6αeα(1−r/rm)−(rmr)6]. The results are tabulated over a large temperature range, kT / e from 0 to 200, and for four values of the parameter α, 12, 13, 14, and 15. The treatment was entirely classical, and no corrections for quantum effects were made. The results should be applicable to most simple, nonpolar gases, and may be used to obtain information about intermolecular forces from the observed temperature dependence of gaseous transport properties.The second approximation to the thermal diffusion ratio and the third approximation to the coefficient of ordinary diffusion have been derived according to the method of Chapman and Cowling.Evaluation of the potential parameters for specific substances and applications of the results will be published later.

Interaction Energies for the H–H2 and H2–H2 System

Interaction energies for the H–H2 and H2–H2 systems have been obtained by a semiempirical perfectpairing procedure used previously. The results have been compared with interaction energies obtained from other sources and the agreement among the different curves is reasonably good. A brief discussion of the previous applications of this semiempirical scheme to other systems is included.

Short‐Range Intermolecular Forces. I

A method is given for accurately approximating most of the integrals which occur in calculations of intermolecular forces. Two types of integrals arise; those between orbital pairs which are separated by a considerable distance from each other, and those where the orbital pairs overlap. In the first case the orbital pairs are considered to be electrostatic charge distributions and their energy of interaction is given by a multipole expansion. From a practical standpoint it is necessary to consider only the first few terms (through quadrupoles) of such an expansion. When the orbital pairs overlap, the integral can be approximated by the Mulliken formula in terms of Coulombic type integrals which are then further approximated by the multipole expansion. The problem of calculating intermolecular forces is thereby reduced to the calculation of a number of classical electrostatic multipole interactions. The procedure can be applied to Coulombic as well as exchange forces. Examples are given for the interaction...

Energies of Various Interactions Between Hydrogen and Helium Atoms and Ions

A compilation is made of those interactions between hydrogen and helium atoms and ions whose potential curves are well established by virtue of being based on experimental data or on essentially exact quantum-mechanical calculations. These potential curves have been fitted with well-known empirical forms which should be useful in calculations of transport properties involving these interactions.