Gas electron diffraction

GED is one of two experimental methods (besides microwave spectroscopy) to determine the structure of free molecules, undistorted by intermolecular forces, which are omnipresent in the solid and liquid state.

[3][1] Diffraction occurs because the wavelength of electrons accelerated by a potential of a few thousand volts is of the same order of magnitude as internuclear distances in molecules.

Since the orientation of the target molecules relative to the electron beams is random, the internuclear distance information obtained is one-dimensional.

Thus only relatively simple molecules can be completely structurally characterized by electron diffraction in the gas phase.

It is possible to combine information obtained from other sources, such as rotational spectra, NMR spectroscopy or high-quality quantum-mechanical calculations with electron diffraction data, if the latter are not sufficient to determine the molecule's structure completely.

The total scattering intensity in GED is given as a function of the momentum transfer, which is defined as the difference between the wave vector of the incident electron beam and that of the scattered electron beam and has the reciprocal dimension of length.

The interferences reflect the distributions of the atoms composing the molecules, so the molecular structure is determined from this part.

The electron beam hits a perpendicular stream of a gaseous sample effusing from a nozzle of a small diameter (typically 0.2 mm).

Most of the sample is immediately condensed and frozen onto the surface of a cold trap held at -196 °C (liquid nitrogen).

The steep decent of intensity can be compensated for by passing the electrons through a fast rotation sector (Figure 3).

These data are then processed by suitable fitting software like UNEX for refining a suitable model for the compound and to yield precise structural information in terms of bond lengths, angles and torsional angles.

The outcome if applied to gases with randomly oriented molecules is provided here in short:[5][4] Scattering occurs at each individual atom (

is the scattering variable or change of electron momentum, and its absolute value is defined as with

In essence, this is a summation over the scattering contributions of all atoms independent of the molecular structure.

is the main contribution and easily obtained if the atomic composition of the gas (sum formula) is known.

The most interesting contribution is the molecular scattering, because it contains information about the distance between all pairs of atoms in a molecule (bonded or non-bonded): with

the anharmonicity constant (correcting the vibration description for deviations from a purely harmonic model), and

is a phase factor, which becomes important if a pair of atoms with very different nuclear charge is involved.

is mostly determined by fitting and subtracting smooth functions to account for the background contribution.

The molecular scattering intensity curves are used to refine a structural model by means of a least squares fitting program.

The curves below the RDC represent the diffrerence between the experiment and the model, i.e. the quality of fit.

The very simple example in Figure 5 shows the results for evaporated white phosphorus, P4.

The width of the peak represents the molecular vibration and is the result of Fourier transformation of the damping part.

Because their contributions overlap in the RDC, the peak is broader (also seen in a more rapid damping in the molecular scattering).

Some selected other examples of important contributions to the structural chemistry of molecules are provided here:

Figure 2: Diffraction pattern of gaseous benzene
Scheme 1: Schematic drawing of an electron diffraction apparatus
Scheme 2: Data reduction process from the concentric scattering pattern to the molecular scattering intensity curve
Figure 1: Gas-diffraction apparatus at the University of Bielefeld, Germany
Figure 3: Scheme of a rotating sector, placement of the rotating sector within a GED apparatus and two examples of diffraction pattrens recorded with and without rotating sector.
Figure 3: Scheme of a rotating sector, placement of the rotating sector within a GED apparatus and two examples of diffraction pattrens recorded with and without rotating sector.
Scheme 2: Schematic scattering process of an electron passing a positively charged atomic nucleus
Firgure 4. Electron wave scattered at a pair of atomic nuclei at different distances
Figure 5: Examples of molecular intensity curves (left) and their Fourier transforms, the radial distribution curves of P4 and P3As.