Robert A. Harris

Pi‐Electron Hamiltonian

A new pi‐electron Hamiltonian is derived for planar conjugated molecules. The Hamiltonian includes the effect of dynamic screening of the pi electrons from one another by the sigma electrons, as well as the screening of the core. The method used in Van Vlecks method of unitary transformations.

Discretized propagators, Hartree, and Hartree–Fock equations, and the Hohenberg–Kohn theorem

The question of how electron exchange can be realistically included in discretized propagator treatments of simple quantum mechanical systems is investigated by showing how the many‐body Hartree and Hartree–Fock approximations can be formulated in terms of discretized propagators. The Hartree approximation takes a surprisingly simple form suggestive of Thomas–Fermi theories in high dimensional spaces. For the Hartree–Fock approximation, the effect of nonlocal potential energy operators on the short‐time propagators must be addressed. These nonlocal operators make the Hartree–Fock results considerably more complicated. However, in each case we indicate how the universal energy functional of the density implied by the Hohenberg–Kohn theorem may be obtained.

An electron gas treatment of the potential curve and polarizability tensor of the lowest 3Σ+u state of H2

A modification of the electron gas model of Gordon and Kim which is applicable to an electronic system with all of its spins parallel is used to determine the internuclear potential and the polarizability tensor of the 3Σ+u state of H2. The electron gas model together with the usual assumption of additive electron density gives results which compare favorably with the configuration interaction results in the region of intermediate internuclear separation.

On the kinetic theory of dense fluids. VIII. some comments on the formal computation of the non-equilibrium distribution function of a fluid

Abstract In this paper we consider two problems: 1. (a) The formal cluster expansion of the integro-differential equation determining the non-equilibrium n body distribution function, and 2. (b) Methods of computing the phase space transformation function. Two formal solutions for the phase space transformation function are presented, one exact for the case of weak interactions, and one approximate and connected closely with the concepts of local equilibrium and Brownian motion. The cluster expansion leads to collision kernels corresponding to multiple body encounters. The operators are so defined that at least one interaction must occur between a group of m molecules and a separate group of n molecules for there to be a non-vanishing contribution to the transport equation for the mth order distribution function. Interactions wholly within the group m or the group n make no contribution. To mitigate the difficulties in computing multiple body trajectories it is suggested that the approximate solutions for the transformation functions be used in the theory of dense fluids.

Kinetic Theory of the Moderately Dense Rigid‐Sphere Fluid. V. Relaxation in Momentum Space

We consider the problem of a dense rigid‐sphere fluid at equilibrium in configuration space but perturbed in momentum space. The relaxation time for the return to equilibrium is computed analytically and shown to correspond to very few collisions—about four at gas densities and about one at liquid densities. This result is in good agreement with machine computations by Alder and Wainwright and shock‐tube measurements by Greene, Cowan, and Hornig. The results indicated that correlated successive binary collisions need not be considered to first order in the finite dense rigid‐sphere fluid.

Kinetic Theory of Moderately Dense Rigid Sphere Fluids. III. The Formulation and Solution of the Transport Equation for Binary Mixtures

The theory of the moderately dense rigid sphere fluid is extended to mixtures. The modified Boltzmann equation is derived from the Liouville equation using the technique of time smoothing. The solution of the Boltzmann equation is given in terms of bracket integrals and the entropy production formulated in terms of the perturbation to the distribution function. The bracket integrals are not explicitly evaluated in this paper but a first order result valid for a mixture of spheres of equal diameters gives for the leading term of the diffusion coefficient D=D0/g0(2)(σ) with D0 the dilute gas diffusion coefficient, and g0(2)(σ) the pair correlation function evaluated at contact. This leading term is in agreement with the corresponding leading terms for the thermal conductivity and shear viscosity of a one component hard sphere fluid, which also differ from the dilute gas coefficients by the factor [g0(2)(σ)]—1. The results quoted in this abstract are the leading terms and do not include all contributions of ...

A consequence of the motional Stark effect in two photon spectroscopy

The effect of the presence of an external magnetic field on the two photon spectroscopy of an ideal gas of atoms or molecules is examined. It is then shown that the resulting ’’motional Stark effect’’, gives rise to a line shape which is not a delta function when the two photons have equal and opposite wave vectors. (AIP)

Kinetic Theory of the Moderately Dense Rigid‐Sphere Fluid. IV. Fluxes of Matter, Momentum, and Energy in a Mixture

The perturbation solution of the modified Boltzmann equation is used to obtain the fluxes of matter, momentum, and energy. The fluxes are evaluated to first order in the gradients of density, flow velocity, and temperature, and are left in terms of the Sonine polynomial expansion coefficients. As an example, the calculation of the isothermal diffusion coefficient is carried out for the general case of unequal masses and radii. In the limit of identical particles, D is proportional to (2kT/m)12(N/vσ2) {[1/g(σ)]+(const/v)+···} .