George G. Hall

The approximation of electron densities

This paper discusses the approximate representation of the electron density produced by an ab initio calculation. A linear combination of Gaussians is fitted to the density by minimizing a functional which is the consequent error in field-energy. The practical implementation of the procedure, following a Gaussian 80 calculation, is described and some of the complications are analysed.

The evaluation of moments for polycyclic hydrocarbons

The evaluation of some moments of the energy in the Hückel theory of conjugated molecules is considered. It is shown that, for molecules consisting entirely of hexagons, the moments μ4 and μ6 can be expressed in terms of four graphical invariants. Partial results are given for other molecules. Since the total energy can be expressed as a series of moments the implications for the energy are discussed. In this discussion two other invariants play a major role. The conclusion is suggested that an analysis of moments in terms of graphical invariants should be of prime importance in understanding these molecules.

The molecular electrostatic potential of some simple molecules

The calculation of the molecular electrostatic potential from simplified models of the electron density is considered. Results are shown for water, hydrogen fluoride and ammonia. Little loss of accuracy is evident when the density is represented by a linear sum of well-chosen Gaussians. When these are further simplified into sets of point charges the inner parts of the molecule are poorly represented. More elaborate point moments make the representation worse. On the other hand a mixed representation with point charges and one diffuse Gaussian gives all the essential features of the potential of these molecules.

Molecules with holes

The bual and laub operations are defined and shown to be a useful means of analysing and coordinating previous descriptions of polyhexes. Some implications of a polyhex having a hole are explored. The position of such molecules in the Dias periodic table is argued. Formulae for moments of the Hückel energy in terms of graphical invariants are derived. The change in π-electron energy when a hole is formed is calculated for some molecules.

Electric fields around molecules

Abstract The molecular cavity surface proposed by Hermann has been used to define electrical indices for each atom in a molecule. A method of calculating these is proposed which appeals to fractal ideas. To illustrate the utility of these indices an approximate calculation of their values integrated over the surface of the molecule has been made for a variety of molecules and the results correlated with experimental solubility data. The resulting calculated solubilities are in good agreement with the observations. The value of these indices in discussions of molecular recognition is argued.

A new method of calculating the spin density of trapped muonium in diamond

Abstract We propose a new method of calculating the spin density of trapped normal muonium in diamond by using the molecular electrostatic potential inside the diamond cluster as an external potential acting on the muonium. The exact wavefunctions of muonium are used in the perturbation calculation to ensure accuracy at the nucleus. For the enhancement factor ƒ, which measures the hyperfine coupling as compared to that of free muonium, we have obtained 0.716 and this is in better agreement with the experimental result, 0.831, than previous calculations have achieved.

Enumeration of Kekulé structures by matrix methods

Abstract A recent combinatorial method of enumerating the Kekule structures of polyhex is shown to be equivalent to a matrix method which leads to more rapid enumerations.

A simple model for a reaction surface

An analytical expression, which has some claim to be the simplest possible, is proposed for the potential governing a collinear reaction. It shows the desired qualitative features but, with only one available parameter, cannot fit a given surface accurately everywhere. The quality of fitting attainable is shown using the surface for the O + H2 reaction.Because of the simple form of this expression, it is possible to make broad generalizations about such reactions. From a plausible assumption about the parameter value the energy barrier and the transition state geometry can be predicted. These barriers agree well with those suggested by Johnston and Parr for hydrogen transfer reactions.

The electron density of the water molecule

The electron density of the water molecule, as calculated by a standard program, is approximated by linear combinations of spherical Gaussians. The accuracy of the result is studied as a function of the numbers and positions of the Gaussians. Since this shows where the charge is located in the molecule it has immediate physical significance. The building-up of the density can be followed in more and more detail. From these expansions, point charge models of water are readily deduced. These are compared with models of similar kinds used by other authors. Some of the calculations have been repeated with a wavefunction of higher accuracy to investigate the stability of the results. Results show that the more accurate density requires more Gaussians to represent its greater complexity.

The exponential map and the representation of reaction surfaces

Abstract It is shown that an exponential map of a reaction surface produces a result which is easier to interpret and use than the conventional graph. The important asymptotic limits, corresponding to the diatomics, are transformed into the axes and the map of the physically allowed configurations is of finite extent. Because of this finiteness the surface can be conveniently represented by polynomials. The fitting procedure for these is discussed and illustrated using the collinear reaction surface and the three-dimensional potential for H + H 2 . An eighth degree polynomial fits the first with an RMS error of less than 0.5 kcal mol −1 but higher terms are needed to obtain this accuracy for the nonlinear surface.