CHAPTER 1
Electron Diffraction Determinations of Gas-phase Molecular Structures
BY L. SCHÄFER
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 techniques, which makes the results of hybrid studies relatively reliable, but the quality of investigations of this kind depends profoundly on the quality of the applied techniques. Molecular mechanics calculations, for example, can in general provide satisfactory results when the conformational stituation of a particular test case represents an interpolation with respect to the model systems which were used to define the empirical force field involved, but in extrapolative cases they have often led to disaster. Unfortunately, it is often not clear whether a particular model of interest represents an interpolative or an extrapolative situation. In quantum mechanical calculations when ab initio procedures are used, uncertainties can often arise from the choice of basis sets and because it is in most cases not possible to optimize molecular geometries fully by relaxing all relevant parameters. When semi-empirical procedures are applied, one has often the impression that an indefinite range of possible models may be derived by adjusting the empirical parameters. In computations of mean amplitudes of vibration, finally, the force fields applied are generally underdetermined or affected by uncertainties of spectroscopic assignments. Because of this long list of potential dangers, hybrid theoretical–GED procedures must be used with caution. The results of such studies can only be as good as investigators are careful. To make use of published GED results requires, therefore, more than the reading of the abstract of a paper.
Many of the papers quoted in the following sections of this Report will demonstrate the changed methodology. Whenever possible, investigators are no longer satisfied merely to fit theoretical models to experimental radial distributions, as once was the conventional course, and indeed, the only practicable one. One has now the computional means to require, as a basic rule, that no GED study is concluded by a final molecular model which is energetically unstable, without giving special justification, and that no GED study is concluded, again without special justification, by a final theoretical model that reproduces experimental intensity only by using mean amplitudes of vibration which differ by orders of magnitude from calculated ones.
In observing these developments, the impression is conveyed that responsibly applied joint spectroscopic–GED and hybrid theoretical-GED procedures have created the effect of a quantum jump in the versatility of gas-phase electron diffraction that can be compared to the improvements which, in the earlier history of the field, were achieved by the invention of the rotating sector or by the fist application of automated densitometry. It seems safe to predict that the hybrid techniques mentioned will be found to be increasingly useful.
2 Structural Results from GED Studies of Individual Molecules
This Report departs from the conventions which have been followed in previous surveys of results. We present the structural results of the papers reviewed by tabulating the significant geometrical parameters of each molecule. Each molecule is identified in the Table by its gross formula and by its name. The names given are those used in the original papers; if no names were used originally, the I.U.P.A.C. recommendations for the nomenclature of molecules are applied. Following the name is a schematic formula or figure for each molecule to indicate its primary structure. Furthermore, there are some verbal comments and a summary, as seems useful, concerning the structural results and the procedures employed to obtain them.
We have chosen this format for the convenience of our readers. If there is interest in a particular molecule, a quick check of the gross formula register will tell whether or not this molecule has been the object of an investigation during the period covered by this volume. At the same time the most significant parameters of a molecule listed or details of its conformational behaviour will be quickly available at a glance.
The parameters reported are selected parameters chosen by a very critical and rather conservative evaluation of each paper. Numerical values are listed only for those parameters which were clearly resolved in significant features of the diffraction data. If a particular molecule contains a number of similar bond distances, for example, their values are given here only if they could be resolved in some way, for example by the analysis of non-bonded distance peaks or by the inclusion of spectroscopic observables in the analysis of the diffraction data. In many cases a comment is, therefore, made indicating that further unresolved parameters can be found in the original paper which are not reproduced in our table. In some of these cases the reader may feel that our evaluation and selection of parameters may have been too careful, but it is always easy to over-ride our personal opinion by reading the original papers. One should keep in mind, however, that an underdetermined set of experimental parameters does not represent a unique solution of the structural problem. On the other hand even an unresolved structure may give a helpful description of a particular molecule. Our restrictive procedure for the selection of molecular parameters to be presented here is, therefore, never a criticism of authors and their procedures but an attempt to avoid giving to numerical values an authority which their authors did not intend them to have.
We also found it useful to list the techniques applied in each structural study. We have used abbreviations for gas-phase electron diffraction (GED), microwave spectroscopy (MW), molecular mechanics conformational analyses (mol. mech.), quantum mechanical computations (for example, ab initio or CNDO/2), and calculations of vibrational molecular parameters employing methods of vibrational analysis (vib. calc.). The temperature of the diffraction experiment is also recorded since GED distances are thermal average values and since many studies are concerned with temperature-dependent conformational properties. The nozzle temperature is usually reported but no specific comment is made when only the temperature of the reservoir rather than that of the nozzle is specified in a particular paper. (In some papers T was not reported at all.)
The symbols used to define molecular structures, such as ra, rαetc., follow the usual conventions. Interatomic distances are represented by a solid line for a pair of directly bonded atoms [for example ra(C — C) is a bond between two carbon atoms]. This line does usually not indicate the multiplicity of the bond since this may often be difficult to define exactly. Multiplicities are indicated by a double or triple bar (for double and triple bonds, respectively) only for organic molecules with well defined bond distance systems and when a molecule contains different bonds between the same kinds of atoms so that a symbolic distinction is needed. Non-bonded distances are indicated by a dotted line between two atom pairs [for example ra (H ··· H)]. A bond angle between atoms X, Y, and Z is symbolized by [angle] (XYZ). Torsional angles are usually defined in detail. All distances are given in Å (0.1 nm) and all angles are given in degrees. Estimated errors are given in parentheses following each value and refer to the last significant figure of the parameter [ra(C — C)= 1.536(2) Å, means ra(C — C) = 1.536 [plus or minus] 0.002 Å, for example]. The quoted error estimates are those found in the primary papers. This should not be taken to mean that they should not be larger in some studies. In fact, in a few cases where reported error limits were obviously too small, we have increased their values, for example to indicate the actual reproducibility of molecular parameters. Mean amplitudes are usually not listed in this Report. For these, as for all the details of a particular structural study, the reader is referred to the original papers.
Compounds are arranged in two groups, containing inorganic and organic (or organometallic) molecules. In the gross formulae of organic molecules first the number of carbon atoms and then the number of hydrogen atoms is given followed by the symbols of other elements in alphabetical order. In inorganic compounds all elements are ordered alphabetically to construct the gross formula. For the same alphabetical sequence containing several molecules, the simplest systems are recorded first.
The papers reviewed in this part were published in the period August 1976 to July 1977. Because of the date of submission requested by the editors, some of the most recent issues of journals which are not so easily available to this Reporter (for example Eastern European journals) could not be reviewed. Personal contacts made it possible to present an updated list of some but not all of the references of this kind. The same problem obviously existed also for the Reporter of this part of the previous volume (Vol. 5) of this series. We have, therefore, also included in our Report those references which appeared shortly before August 1976 but which were not available to the previous Reporter.
3 GED Papers of a General Nature without a Specific Molecule
In addition to the papers listed in Section 2, a number of publications should be mentioned here which are somehow involved with high-energy gas-phase electron diffraction work without being primarily concerned with a single structural problem. These are review-type papers, procedure-related publications, and theoretical papers and reports on calculations referring directly to a particular GED study.
In the first category reviews and summaries have been published of the GED papers which appeared between August 1975 and August 1976; of some aspects of the experimental determination of average and equilibrium structures of polyatomic gas molecules by diffraction and spectroscopic methods; 1 of some results of applying hybrid theoretid–GED procedures to the conformational analysis of some cyclic systems; and of some of the structural parameters obtained for a number of unsaturated organo-tin compounds.
A book has been issued dealing with the molecular geometries of co-ordination compounds in the vapour phase incorporating the results of both GED and MW studies. In addition to presenting some general concepts, the book offers a systematic discussion of the structural trends observed for co-ordination compounds in the vapour phase.
Furthermore, an introduction to GED as a tool of structural chemistry has been written as one of a series of feature articles directed to non-specialists.
Special emphasis must be given in this context to an excellent compilation of the structure data of free polyatomic molecules published between 1960 and June 1974. Parameters were listed in this publication after a critical re-estimation of their uncertainties. For free molecules, these tables are a very useful continuation of the complete listing of molecular structures published up to 1959. This volume is also noteworthy because an excellent discussion of the characteristics of some of the techniques used in vapour-phase structural chemistry is given in its introductory section (see also these sections of ref. 97).
