William E. Palke

Quantum mechanical streamlines. I. Square potential barrier

Exact numerical calculations are made for the scattering of quantum mechanical particles from a square two‐dimensional potential barrier. This treatment is an exact analog of both frustrated total reflection of perpendicularly polarized light and the longitudinal Goos‐Hanchen shift. Quantum mechanical streamlines (which are analogous to either classical mechanical trajectories or optical rays) are plotted. These streamlines are smooth, continuous, and have continuous first derivatives even through the classically forbidden region. The streamlines form quantized vortices surrounding each of the nodal points (which result from interference between the incident and reflected waves). Similar vortices occur in reactive collisions of H + H2 (McCullough and Wyatt; Kuppermann, Adams, and Truhlar) and undoubtedly play an important role in molecular collision dynamics. The theory for these vortices is given in a companion paper. A comparison is given between our numerical calculations and the stationary phase appro...

Small chain approximation for the electronic structure of polyacetylene

Abstract It is demonstrated that many properties of interest for polyacetylene chains can be predicted on the basis of Hartree-Fock calculations on short model molecules. The equilibrium geometries, energies per C 2 H 2 unit, and isomerization energies converge by a chain length of six or eight carbons. The ionization potential, band gaps, and band widths converge more slowly, but their limiting values can be obtained readily by extrapolating results of calculations on chains up to a length of eight carbons.

Effect of vibrations on the internal rotation barrier in ethane

The effect on the ethane internal rotation barrier of (1) zero‐point vibrational averaging and (2) distortions in equilibrium geometry during internal rotation is determined. We find that the (previously ignored) averaging term is 374±90 cal/mole which is substantially larger, and opposite in sign, to the distortion correction of −161±20 cal/mole. The isotope shift, other experimental tests, and some important implications of our results are discussed.

ON THE STRUCTURE AND PHOTODISSOCIATION DYNAMICS OF AR+3

Abstract New ab initio calculations are reported that indicate Ar + 3 is a linear, asymmetric C ∞v molecule with equilibrium bond lengths R 1 = 2.47 A and R 2 = 2.73 A. The potential energy surface is very shallow along the asymmetric stretch coordinate indicating excursions of the least bound argon atom of 0.5 to 0.7 A in the vibrational ground state. These calculations indicate Ar + 3 is essentially an Ar + 2 . Ar cluster and support the interpretation of DeLuca and Johnson on the origin of the UV (300 nm) and visible (550 nm) photodissociation bands. New data are provided on the photodissociation dynamics as well, and implication of these data on the detailed dynamics discussed.

The photoluminescence properties of the copper(I) clusters Cu4I4A4 (A = aromatic amine) in solution

Abstract Solutions of the copper(I) tetranuclear clusters Cu 4 I 4 A 4 (A = pyridine or substituted pyridine) in room temperature toluene display two luminescence bands in the visible region of the spectrum. The higher energy emission has been assigned as a transition from a metal-to-pyridine charge transfer state on the basis of pyridine substituent effects, while the much more intense lower energy emission has been assigned as a cluster-centered transition owing to its presence even when A is a saturated amine. The two emission display relatively long, but different, lifetime and appear to originate from states which are essentially uncoupled. Calculations using effective relativistic core potential methods suggest that the cluster-centered emission is from an excited state which can be visualized as the result of electronic promotion from a HOMO which is largely iodide in character to a LUMO which is largely copper (4s and 4p) in character.

The infrared spectroscopy of chemisorbed molecules; a dynamical theory of the line shape

A one dimensional model is used to examine the infrared line shape for the vibration of an atom chemisorbed on a solid. The calculation assumes that the mechanism of broadening is the coupling between the vibration of the atom and those of the lattice. It is shown that this mechanism cannot explain the large linewidths observed experimentally in case the solid is a metal. We believe that in this situation the broadening of the line is caused by the coupling between the vibrational motion of the chemisorbed molecule and the electronic degrees of freedom of the metal.

Effects of exchange energy and orbital orthogonality on barriers to internal rotation

In order to determine the effect of the Pauli principle on internal rotation barriers, we have calculated exchange and orbital orthogonality contributions to barriers for a small group of molecules: ethane, methanol, acetaldehyde, and hydrogen peroxide. To evaluate exchange contributions it was necessary to formulate variation equations and to energy‐optimize simple product wavefunctions of orthogonal orbitals (Hartree‐product wavefunctions). The resulting orbitals resemble very closely the Edmiston–Ruedenberg localized Hartree–Fock orbitals. Our results indicate that exchange contributions to the barriers in ethane and acetaldehyde are quite small. For methanol and hydrogen peroxide, our calculated contributions are considerably larger and suggest that, at least in some molecules, exchange contributions cannot be ignored. For all of the molecules, however, the exchange contribution is greatly overshadowed by that of end‐to‐end orbital orthogonality.

Calculation of Hyperfine Coupling Constants in Inorganic Radicals

Hyperfine coupling constants have been calculated for the well‐known radicals HCO, NO2, NF2, ClO2, and CF3 as well as a large number of related species. An SCF Hartree‐Fock‐type approach was used with a minimum basis set of Slater‐type orbitals to obtain MO coefficients of the singly occupied orbital. Some of the coupling constants were obtained directly from the ab initio calculations; others were estimated by use of semiempirical relations. Comparison with experimental data shows fair agreement. In addition, the structures of NF2, O3+,O3−, O3, and CF3 were computed.

Computer simulation studies of the dependence on density of the orientational order in nematic liquid crystals

Abstract Simulations of the temperature dependence of the nematic orientational order parameter, [Pbar] 2, at different densities have been made using the Gay-Berne potential. The results are used to calculate Γ = −(∂In T/∂ IN V) [Pbar] 2, which is a measure of the relative sensitivity of [Pbar] 2 to temperature and density. Previous experimental measurements of Γ have obtained values in the range 2–6 for real nematogens, whilst the present simulations yield Γ = 8 ± 1. Changing the Gay-Berne potential by increasing the steepness of the repulsive term increases the calculated value of Γ, whilst changing the relative well depths for side-by-side compared to end-to-end arrangements of Gay-Berne particles leaves Γ virtually unchanged. These exploratory calculations suggest that Γ is a useful parameter for testing the parametrizations of model potentials.

The lowest energy structures of C+7, C7 and C−7. An ab initio study

Abstract Ab initio calculations have been carried out, indicating the ground state of C + 7 is cyclic (≈ 0.9 eV more stable than linear C + 7 ) but C 7 and C − 7 have linear ground states. Calculations also indicate that the ring opening transition state in C + 7 lies ≈ 2.3 eV above the ground state and is of near C 2v symmetry.