The Interplay between Spectroscopy and Electron Diffraction

Morino and his co-workers established a systematic treatment for the calculation of mean amplitudes of vibration from harmonic force fields, based on the widely used Wilson GF matrix method, which is still the foundation for the majority of such calculations. The theory of such calculations has been developed considerably since, notably by Cyvin and coworkers. With the advent of modern computers, the calculation of mean amplitudes using these methods has become a routine procedure. The resultant extensive literature has been reviewed by Cyvin.  

Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations , McGraw-Hill, New York, 1955. 

As far as mean amplitudes are concerned, interplay between spectroscopy and electron diffraction may come about in two ways. Firstly, even for comparatively simple polyatomic molecules e.g. the methyl halides ) the general harmonic force field is not well determined from all the spectroscopic data available, i.e. vibration frequencies, isotopic frequency shifts, Coriolis zfita constants, and centrifugal distortion constants. In principle, experimental mean amplitudes from electron diffraction studies should provide valuable additional data. In practice, however, the experimental amplitudes have as yet rarely been of sufficient precision to be helpful. Secondly, for more complex molecules, mean amplitudes calculated from spectroscopic data (by way of what are inevitably very approximate force fields in many cases) are sometimes used as fixed parameters in the electron diffraction analysis in order to reduce the total number of parameters refined. 

These three major topics— mean amplitudes of vibration, the interrelation of molecular structures obtained from spectroscopic and electron diffraction data, and the shrinkage effect in electron diffraction studies— comprise the main areas of interplay between spectroscopy and electron diffraction. Cyvin s book treats the first and third topics at length. This chapter concentrates on the second topic, which had until very recently not been reviewed at all. An article by Kuchitsu now deals with molecular structure determination by spectroscopic and electron diffraction methods Kuchitsu and Cyvin have summarized the notation and definitions of the varied bond-length parameters employed in gas-phase molecular structure determination. 

In the sections which follow, the level of theoretical development is intended to be adequate to account for effects on interatomic distances of the order of 0.001 A or greater. Error analysis in experimental electron diffraction work is still in a somewhat unsatisfactory state (see also Chapter 1, Section 2). Recent work - on the influence of correlation between data points has, however, indicated that estimated standard deviations have frequently been over-optimistic in the past. This author does not feel that many structure determinations can realistically claim an accuracy of better than 0.001 A when all sources of random and systematic error are taken into account. The same is true of molecular structure determination by spectroscopic techniques, apart from diatomic molecules and a very few small polyatomic molecules. Thus, although the level of theoretical sophistication in many areas permits the calculation of various effects on molecular structure at the level of 10 A, such developments are given only a passing reference in the text. 

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Recent synergetic studies between computational simulations and spectroscopic techniques will be also discussed. Experimental techniques (FT IR spectroscopy, NMR, neutron scattering, neutron diffraction, and X-ray absorption spectroscopy) will also be discussed. Computer simulations often are able to provide an excellent interpretation of what is obtained from spectroscopy. Examples of this interplay between experiment and simulation are listed. In presenting the results of computer simulations, visualization of the molecular structure or electronic structure and animations of the MD trajectories are often used. Some of these also are discussed, in terms of technical aspects and software available for visualization. One of the most up-to-date visualization techniques, virtual reality (VR), is also discussed in the context of computational chemistry. 

Qearly silicon compounds have proved a fruitful area for study. The results seem to highlight the need to consider carefully, in parallel with many electron-difhaction studies, any relevant spectroscopic observations. During the seventies, generally, a much closer interplay may be expected between electron-diffraction and vibrational and rotational spectroscopy. 

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