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The topics to be discussed at this meeting are surveyed and an attempt is made to provide a context in which they might be placed.

When we speak of molecules in an environment we are sometimes thinking about an isolated molecule in an environment provided by an electromagnetic field and sometimes we are thinking about the molecule in a material environment, for example in a dilute gas of other molecules or as a part of a liquid or as a solute molecule in a bulk solvent or as part of a molecular crystal. We hope to be able to understand molecular properties in an environment in terms of the interactions between molecules and, if relevant, the electromagnetic field. It is from this perspective that intermolecular interactions will be considered in what follows.

Authors suggest using a three-line demonstration rather than an involved computation of the tetrahedral angle.

A theoretical model is described which is based on the assumption that the temperature dependence of hyperfine coupling constants (h.c.c.s) in the E.S.R. spectra of organic free radicals is due to nuclear vibrations. The model is tested on the α-proton h.c.c.s of the methyl and hydroxymethyl radicals and in each case it shows that, although only the lowest vibrational mode contributes to the temperature dependence of the h.c.c.s, other modes do contribute to the vibrationally averaged coupling constant.

The results of some highly accurate non-empirical ro-vibrational calculations on H 2 D + are reported including some for J = 30 which are the first calculations to describe such a highly rotationally excited state. These results are obtained using an improved version of our algorithm. The method used is a variational one and is well adapted to execution on supercomputers. The computational characteristics of the performance the method on the CRAY 1s and the CRAY XMP 48 are given.

The state-of-the-art in non-empirical calculations of potential energy surfaces for small molecules is discussed, as is the present position with respect to the analytic fitting of such surfaces. The results of some nonempirical vibration-rotation calculations performed on such analytic surfaces are presented and compared with experimental results. An attempt is made to assess the extent to which present methods of electronic structure calculation and present analytic fitting methods are adequate to produce surfaces for the interpretation of high-resolution spectral data.

It is shown that in the LCAO-MO-SCF problem, if the molecular orbital orthonormality constraints are introduced in the manner first suggested by Fletcher, then the Hessian of the problem is singular. It is suggested that this singularity may well account for the slow convergence observed using direct energy minimization methods to solve the SCF problem. Ways of avoiding the consequences of this singularity are discussed.

In this paper we obtain formulae useful in methods for the direct minimization of the energy functional in the LCAO-MO-MC-SCF approach. The formulae are appropriate for dealing with variations in both the linear and nonlinear parameters. We include formulae for the usual closed- and open-shell problems as special cases.

The theory of generalized product functions is extended to non-orthogonal group functions in the case of two groups. Calculations on beryllium and on some four-electron ions are based on such group functions, and are compared with similar calculations using orthogonal group functions. I t is shown that, in the case of the systems examined, the strong orthogonality restriction is not severe.

The problem that interested us (and by “us” is meant the author and his co-workers, Dr. D. Martin and Dr. R. Bartholomae), was if it was possible, starting from the full Hamiltonian for a triatomic molecule, to develop eigen functions of this full problem which, in some sensible way, represented a molecule that could be said to have a structure.

The basic approximation in CI theory is the linear combination of configurations $${{\Psi }_{\kappa }} = _{{\mathop{\Sigma }\limits_{{i = 1}} }}^{{\text{M}}}{{c}_{{\kappa j}}}{{\phi }_{j}}$$ (1.1)

To put the specialist part of this contribution into context it is perhaps appropriate on this occasion to try to explain, quite briefly, why it is difficult to intepret in theoretical terms the vibration-rotation spectra of non-rigid molecules. It will also be necessary to say a little about the way in which the vibration-rotation problem came to be formulated for normal (semi-rigid) molecules, if the difficulties of non-rigid molecules are to be properly understood. The summary that is offered here makes no pretence at explaining the complexities of the historical development of ideas about molecular vibration-rotation spectra but it is hoped that it will be self-contained and clear.

For molecules, other than diatomics, the whole notion of molecular structure rests, at present, upon the Eckart Hamiltonian, in the sense that the domain of validity of the Eckart Hamiltonian consists of that collection of molecular wave functions to which the notions of structure can be applied in a widely agreed and unambiguous way. The notion of structure in the Eckart Hamiltonian arises from the peculiar position that the framework co-ordinates occupy in the formalism. It is traditional to interpret these framework co-ordinates as being the equilibrium nuclear positions as expressed in a carefully defined reference frame, which can be called the Eckart frame.

Introduction to the Electron Theory or Small Molecules. By A. C. Hurley. Pp. 329. £12; $26.25. Electron Correlation in Small Molecules. By A. C. Hurley. Pp. 276. £10.50; $23. (Academic: London and New York, 1977.)

Charlotte Froese Fischer Chichester: J Wiley 1977 pp xi + 308 price £17.20 In the last 20 years selfconsistent field calculations on atoms, once the prerogative of a few painstaking researchers, have become readily available to experimenters and nonspecialists. Sophisticated computational packages have their dangers, and so Charlotte Froese Fischer's authoritative account of Hartree–Fock methods is to be welcomed both by the expert and the amateur user.

This part of the series presents the results obtained by open shell SCF computations on the G, N, O, and F Atoms.