Electron Diffraction Determinations of Gas-phase Molecular Structures

1 Some Current Trends in Gas-phase Electron Diffraction Procedures

1977 marked the fiftieth anniversary of the first publication describing an electron diffraction experiment. To commemorate the event, the American Crystallographic Association called a special meeting. The historical factors leading to the discovery of this phenomenon were reviewed in a special paper.

To the critical observer of gas-phase electron diffraction (GED) as applied to structural chemistry, the record of this tool must appear somewhat mottled. The first successful structural studies of gaseous molecules by high-energy elastic electron scattering originally raised high hopes for a breakthrough in understanding the structure of matter. To some extent the technique has indeed contributed to such a development, but, like no other method of structural chemistry, GED combines quantitative precision with essential incompleteness because it gives only one-dimensional information. In addition to producing some very valuable and fundamental structural insight, interpretations of electron diffraction data have, therefore, sometimes engendered strikingly misleading structural models.

In view of these characteristic imperfections, it is important to take note of a striking metamorphosis of current GED techniques. Very recently gradual improvements of data analysis have produced a rather spectacular revolution of GED leading to a general enhancement of its versatility. It is now possible to supplement GED data with observables or their expectation values from other sources, by applying modes of analysis which were not known or not practical a decade or even a few years ago, The term 'electron diffraction' is, therefore, in a large number of current studies really the collective synonym for a matrix of complex and hybrid operations involving various consistently combined, different techniques. This development has had its main impact in two different areas, viz. in joint spectro-scopic–diffraction studies and, more recently, in hybrid theoretical–GED investigations.

In the former, rotational constants obtained from spectroscopy are incorporated into GED data analysis. Proper vibrational corrections are needed to make diffraction and spectroscopy compatible. As a result of this joint application of different observables, it was often possible to determine very accurately the structural parameters of molecules for which very little information could have been obtained by either GED or spectroscopy alone. It is only about ten years ago that the first consistent joint study appeared which made use of the proper vibrational corrections and a least-squares scheme.

In hybrid theoretical-GED investigations, calculated molecular parameters are incorporated into the data analysis in order to reduce the number of independent unknown variables. This has been done, for example, by optimizing the strain energies of model geometries employing molecular mechanics or quantum mechanical approximations. Thus in some cases, when several molecular models could be fitted to the same experimental diffraction pattern, their strain energies were used to discriminate against some of them. In other cases optimized molecular conformations were used as starting points for the least-squares analysis of the diffraction data. For relatively large molecules, the starting geometry can strongly bias the least-squares minimum, projecting in this manner the computational assumptions into the experimental results. With the continuing advancement of ab initio quantum mechanics, it seems now also possible to transfer calculated geometrical parameters (e.g. differences between nearly equal bond distances) directly, as constraints, into the least-squares scheme.

In other investigations, available force fields were used to derive mean amplitudes of vibration which are also, in principle, observables of the diffraction experiment. These theoretical amplitudes, or some of them, or amplitude differences calculated for a group of correlated distances, were then often used as constraints of the least-squares GED data refinement. Alternatively, the refined, experimental mean amplitudes of vibration for a particular model were compared with the theoretical ones.

The hybrid procedures mentioned are particularly satisfactory when the same force field is consistently applied to compute both the optimized geometries and the corresponding mean amplitudes. In such studies the optimum geometry and the force field which produced it are used together in the vibrational calculations, and calculated amplitudes and optimum geometry are used together in the least-squares scheme of the GED data analysis. The first consistent studies of this kind, which combined the experiences of many groups, used force fields derived from molecular mechanics in investigations of some relatively large cyclic hydrocarbon. In several laboratories ab initio procedures are now applied in the same consistent way for relatively complicated systems, demonstrating the further advance of this technique. The co-operative effect achieved by these combined procedures has often made it possible to give a plausible description of the unperturbed conformational behaviour of relatively complicated molecules, for which no safe statement could have been made on the basis of any of the applied techniques alone. In some cases ambiguities existing in previous publications could be resolved in this way. In other cases, some older conclusions even had to be corrected. It is very pleasant to note the complementarity of theory and experiment in such studies. Whereas theoretical procedures need guidance and confirmation by experimental observation the conclusions obtained by them in turn significantly reflect upon proposed data interpretations in many specific cases.

The optimism of the previous paragraphs must be qualified by a serious warning. Vapour-phase data of relatively complicated polyatomic molecules usually do not provide anything but circumstantial evidence for structural conclusions. In most cases the number of observables is smaller than the number of unknowns. There is a certain co-operative effect in consistently combining several different...