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'''Gas electron diffraction''' (GED) is one of the applications of [[electron diffraction]] techniques. The target of this method is the determination of the structure of [[gaseous molecules]] i.e. the [[Molecular geometry|geometrical arrangement of the atoms]] from which a molecule is built up.
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. The principle is the same as that of other electron diffraction methods such as [[Low-energy electron diffraction|LEED]] and [[RHEED]], but the obtainable diffraction pattern is considerably weaker than those of LEED and RHEED because the density of the target is about one thousand times smaller. 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 spectroscopy|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 (mathematics)|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 total scattering intensity is composed of two parts: the [[atomic scattering intensity]] and [[the molecular scattering intensity]]. The former decreases [[monotonically]] and contains no information about the molecular structure. The latter has [[sinusoidal]] modulations as a result of the [[Interference (wave propagation)|interference]] of the scattering [[spherical waves]] generated by the scattering from the atoms included in the target molecule. The interferences reflect the distributions of the atoms composing the molecules, so the molecular structure is determined from this part.
'''Theory'''<ref>{{Cite book|title=Stereochemical Applications of Gas‐Phase Electron Diffraction, Part A: The Electron Diffraction Technique|last=Hargittai|first=I.|publisher=VCH Verlagsgesellschaft|year=1988|isbn=
GED can be described by scattering theory. The outcome if applied to gases with randomly oriented molecules is provided here in short:
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</math>), or triples (<math> I_t(s)
</math>), of atoms.
<math> s
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</math> being the electron wavelength defined above and <math> \theta
</math> being the scattering angle
The above mentionend contributions of scattering add up to the total scattering (<math> I_{tot}(s)
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</math>, whereby (<math> I_b(s)
</math>is the experimental background intensity, which is needed to describe the experiment completely
The contribution of individual atom scattering is called atomic scattering and easy to calculate.
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</math> being the scattering amplitude of the i-th atom. In essence theis is a summation over the scattering contributions of all atoms independent of the molecular structure. <math> I_a(s)
</math>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)
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The first part is simlilar to the atomic scattering, but contains two scattering factors of the involved atoms. Summation is performed over all atom pairs.
<math> I_t(s)
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