Gases, electron diffraction

Hargittai, I. Gas Electron Diffraction A Tool of Structural Chemistry in Perspectives, 96, 43-78 (1981). 

In general, all observed intemuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. 

To illustrate how the operations of an experimental technique affect the nature of its observables, gas electron diffraction shall be used as an example. Considering the mechanics... 

Structural Observables Derived from Gas Electron Diffraction... 

In Eq. (5.2), the function i iv(r) 2/r = P(r)/r is an example of a so-called radial distribution (RD) function, in the form in which it is obtained from gas-electron diffraction, in this case for a particular vibrational state of a diatomic molecule. It is seen that the molecular intensity curve is the Fourier transform of Pf. The reverse, by inversion, the RD function is the Fourier transformation of the molecular intensities ... 

Equations (5.2)—(5.4) and Figs. 5.1-5.3 illustrate the nature of the structural observables obtained from gas-electron diffraction the intensity data provide intemuclear distances which are weighted averages of the expectation values of the individual vibrational molecular states. This presentation clearly illustrates that the temperature-dependent observable distribution averages are conceptually quite different from the singular, nonobservable and temperature independent equilibrium distances, usually denoted r -type distances, obtained from ab initio geometry optimizations. 

During the last decades, a large body of structural information has been derived from gas-electron diffraction studies. The corresponding results are nearly exclusively reported in the literature in terms of r distances, or the equivalent thermal average intemuclear distances, which are denoted r. The r distances are defined by the relation, r = r — If. Alternative methods for interpreting gas-electron diffraction data are possible, for example, in terms of -geometries5, but they are currently too complex to apply in routine stmctural analyses, because they require detailed information on the molecular potential energy surface which is not usually available. 

For structures obtained by gas-electron diffraction, it is not meaningful to compare intemuclear distances to within several thousandths of an A. This is particularly true when bond lengths are closely spaced and not resolved in the diffraction data. In such cases the uncertainties can be >0.05 A, even though they may be reported with higher precision. 

A. A. Ischenko, J. D. Ewbank, and L. Schafer, Direct Evaluation of Equilibrium Molecular Geometries Using Real-Time Gas Electron Diffraction, J. Phys. Chem., 98 (1994) 4287-4300. 

Kitano, M., and K. Kuchitsu. 1974. Molecular Structure of Formamide as Studied by Gas Electron Diffraction. Bull. Chem. Soc. Japan 47, 67-72. 

Kohata, K., T. Fukuyama, and K. Kuchitsu. 1979. Molecular Structure and Conformation of 1,2-Dimethylhydrazine Studied by Gas Electron Diffraction. Chem. Lett. 257-260. 

Nakata, M., H. Takeo, C. Matsumura, K. Yamanouchi, K. Kuchitsu, and T. Fukuyama. 1981. Structures of 1,2-Dimethylhydrazine Conformers as Determined by Microwave Spectroscopy and Gas Electron Diffraction. Chem. Phys. Letters 83, 246-249. 

Schafer, L., I. S. Bin Drees, R. F. Frey, C. Van Alsenoy, and J. D. Ewbank. 1995c. Molecular Orbital Constrained Gas Electron Diffraction Study of N-Acetyl N -MEthyl Alanine Amide. J. Mol. Struct. (Theochem) 338, 71-82. 

Van Hemelrijk, D., L. Van den Enden, H. J. Geise, H. L. Sellers, and L. Schafer. 1980. Structure Determination of 1-Butene by Gas Electron Diffraction, Microwave Spectroscopy, Molecular Mechanics, and Molecular Orbital Constrained Electron Diffraction. J. Am. Chem. Soc. 102, 2189-2195. 

Fig. 7.8 Structural parameters for formamide determined from gas-electron diffraction (values with uncertainty estimates in parentheses taken from M. Kitano and K. Kuchitsu, Bull. Chem. Soc. Japan, 47 (1974) 67) and HF/4-21G calculations (values taken from H. L. Sellers, V. J. Klimkowski, and L. Schafer, Chem. Phys. Lett. 58 (1978) 541).

Nakata, M., H. Takeo, C. Matsumura, K. Yamanouchi, K. Kuchitsu, andT. Fukuyama. 1981. Structures of 1,2-Dimethylhydrazine Conformers as Determined by Microwave Spectroscopy and Gas Electron Diffraction, Chem. Phys. Letters 83, 246-249. Norden, T. D., S. W. Staley, W. H. Taylor, and M. D. Harmony. 1986. On the Electronic Character of Methylenecyclopropene Microwave Spectrum, Structure, and Dipole Moment, J. Am. Chem. Soc. 108, 7912-7918. 

Bartell and coworkers investigated the structures of a series of noncyclic alkanes by means of gas electron diffraction (14, 44, 45) and invoked for the interpretation of their results a simple force field which contained to a high extent vibrational spectroscopic constants of Snyder and Schachtschneider. This force field reproduces bond lengths and bond angles of acyclic hydrocarbons well, energies of isomerisation satisfactorily. As an example, Fig. 8 shows geometry parameters of tri-t-butylmethane as observed by electron diffraction and calculated with this force field (14). 

Experimental structural data are available for two crystalline derivatives of c/s,cis-cyclo-octadiene-1,5 (86). The distorted-boat form occurs in both crystals (observed C—CH2—CH2—C torsion angles 65 and 74°, respectively). Hedberg and Hedberg have performed a gas-electron diffraction study and found that the distorted boat conformation predominates also in the gas-phase (87). For the dibenzo derivative, however, there are crystallographic indications that in the solid state the eight-membered ring has the chair conformation (88). 

Table 2 Structural data of selected dialkylzinc compounds from gas electron diffraction (GED) and computational (DFT) studies...

The amount of high precision experimental structural data on conjugated polyenes is limited. Some structure results are presented in Table 5. In gas electron diffraction studies it is difficult to determine closely spaced bond distances accurately, because these parameters are highly correlated with the corresponding vibrational amplitudes. Today it is possible to calculate the vibrational amplitudes accurately, if the vibrational frequencies are known. This was, however, not the case when the GED studies presented in Table 5 were carried out. The observed differences between the terminal and central C=C bonds in the GED studies of traw.s-l,3,5-hexatriene and c/s-l,3,5-hexatricne are probably too large29. A very accurate X-ray study of traw.s-l,3,5-hexatriene has, however, been carried out also in connection with the preparation of this chapter4. Figure 4 shows the molecular structures of trans-1,3-butadiene and trans-l,3,5-hexatriene as found in the crystal lattice. 

FVP-gas electron diffraction (FVP-GED), 21 139. See also Flash vacuum pyrolysis (FVP)... 

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