A.T. Amos

Intermolecular forces between large molecules

The long-range interaction between large molecules with localized electrons is written as the sum of individual interactions between localized charge distributions. Using minimal basis set ab initio Hartree-Fock wavefunctions the parameters needed to compute these interactions are obtained for water, methane and ethane. Interactions between pairs of these molecules are computed for various orientations to demonstrate the complex orientational dependence and the relative magnitudes of the various terms.

The calculation of chemical shifts in conjugated molecules

Within the context of pi-electron theory an expression for the proton chemical shifts in conjugated molecules is derived via a current density approach. Using London integral approximations the method is applied to benzene and naphthalene. Provided a particular form of the London Approximation is used, theoretical values in good agreement with experiment are obtained.

Dispersion interactions and solvent-shift effects

The problem of relating solvent-shift effects to excited-state polarizabilities is discussed. It is found that the chief difficulty is that of estimating the dispersion term in the interaction energy between a solvent molecule and a solute molecule, and it is shown that the differences in the values of excited-state polarizabilities which have been deduced from solvent-shift data are due to widely differing estimates of this dispersion term. In order to obtain meaningful results it is found necessary to assume that the change in the dispersion term is related to the change in the polarizability of a solute molecule on excitation. On the basis of this assumption, the use of a semi-empirical formula which connects solvent-shifts with these changes in the polarizability is discussed and it is found that the accuracy is such that very little useful information can be obtained.ZusammenfassungDas Problem, Lösungsmittelverschiebungen mit der Polarisierbarkeit angeregter Zustände in Verbindung zu bringen, wird diskutiert. Dabei zeigt sich, daß die Hauptschwierigkeit im Abschätzen des Dispersionsterms der Wechselwirkung Solvent-Solut-Molekül liegt und daß die Unterschiede in den Polarisierbarkeiten, die sich aus Daten für Lösungsmittelverschiebungen ergeben, auf die sehr unterschiedliche Abschätzung dieses Dispersionsterms zurückgehen. Um sinnvolle Resultate zu erhalten, muß angenommen werden, daß die Änderung des Dispersionsterms mit der Änderung der Polarisierbarkeit eines angeregten Solutmoleküls zusammenhängt. Auf dieser Grundlage wird eine entsprechende semiempirische Formel diskutiert; jedoch deren mangelnde Genauigkeit läßt keine eindeutigen Aussagen mehr zu.

Bond contributions to molecular refractive indices and Verdet constants

The frequency-dependent polarizability of a molecule whose Hartree-Fock wavefunction can be written in terms of localized orbitals is shown to be the sum of bond and inner-shell orbital contributions. A variational procedure is used to find these contributions for the molecules methane, ethane, ethylene, acetylene, water and ammonia. Theoretical values of the refractive indices and Verdet constants for these molecules are obtained.

The calculation of chemical shifts in conjugated molecules: II. A semi-rigorous calculation of the pi-electron contribution to the magnetic properties of benzene

Calculations are presented of the non-local pi-electron (ring current) contribution to the magnetic anisotropy of benzene and to the chemical shift experienced by an attached proton. The usual London Approximation (to simplify the integral evaluation) is not made, and the method thereby permits of a more detailed analysis of this approximation than has hitherto been possible.

A variational principle for the Heitler-London intermolecular interaction energy

An extension of the Delves variational principle is used to find an expression for the Heitler-London (exchange) interaction energy which differs from the exact results by second order terms. The auxiliary functions so introduced are found by relating the variational principle to Symmetry-Adapted Double Perturbation theory and, with neglect of a term likely to be small, this expression is the same as that usually used. From these considerations two criteria for the optimization of wavefunctions can be found. The criteria are applied to the Helium-Helium and Neon-Neon interactions using minimal basis wavefunctions and, by allowing the parameter values to vary with internuclear distance, significant improvements in the interaction energies are obtained, in particular those for Helium-Helium agreeing with accurate SCF results.

Extended Hückel calculations of the ionization potentials of some conjugated hydrocarbons

The prediction of ionization potentials of conjugated hydrocarbons using extended Hückel theory is reevaluated. Consequently, two major modifications to the theory are proposed and then tested on five sample molecules. Allowance for distinct sigma and pi orbital parameters as well as for diagonal and off-diagonal parameters constitute the changes examined and are shown to arise naturally from the theory. Subsequent testing of the reproduction of photoelectron spectra indicates significant improvements over previous usage of extended Hückel theory.

Frequency-dependent properties of the hydrogen atom: A generalized eigenvalue equation approach

The time-independent first-order perturbation equations which arise on considering the response of a system to a harmonic time-dependent perturbation are solved by using an expansion in terms of a complete discrete set of solutions of a generalized eigenvalue equation. Explicit formulae are obtained for several frequency-dependent properties of the hydrogen atom.