Gas electron diffraction: Difference between revisions

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'''Gas electron diffraction''' (GED) is one of the applications of [[electron diffraction]] techniques.<ref name=":0">{{Cite book|last=Rankin, David W. H.|url=https://www.worldcat.org/oclc/810442747|title=Structural methods in molecular inorganic chemistry|others=Morrison, Carole A., 1972-, Mitzel, Norbert W., 1966-|isbn=978-1-118-46288-1|___location=Chichester, West Sussex, United Kingdom|oclc=810442747}}</ref> 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. 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. The detremination of accurate molecular structures<ref>{{Cite book|url=https://www.worldcat.org/oclc/26264763|title=Accurate molecular structures : their determination and importance|date=1992|publisher=International Union of Crystallography|others=Domenicano, Aldo., Hargittai, István.|isbn=0-19-855556-3|___location=[Chester, England]|oclc=26264763}}</ref> by GED studies are fundamental for a understanding of [[structural chemistry]].<ref>{{Cite book|last=Wells, A. F. (Alexander Frank), 1912-|url=https://www.worldcat.org/oclc/801026482|title=Structural inorganic chemistry|isbn=978-0-19-965763-6|edition=Fifth edition|___location=Oxford|oclc=801026482}}</ref><ref name=":0" />{{Multiple issues|

{{Multiple issues|

{{citation style|date=December 2018}}

{{one source|date=December 2018}}

}}

== Introduction ==

'''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.

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]], [[Nuclear magnetic resonance spectroscopy|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.

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]].<ref name=":1">{{Cite book|last=Bonham|first=R.A.|title=High Energy Electron Scattering|publisher=Van Nostrand Reinhold|year=1974|isbn=|___location=|pages=}}</ref> 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|___location=Weinheim|pages=}}. {{isbn|3-527-26691-7|0-89573-337-4}}</ref>

== '''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|___location=Weinheim|pages=}}. {{isbn|3-527-26691-7|0-89573-337-4}}</ref><ref name=":1" /> ==

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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So it is the molecular scattering intensity that is of interest, and this is obtained by calculation all other contributions and subtracting them from the experimentally measured total scattering function.

== Results ==

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

* Structure of [[diborane]] B₂H₆<ref>{{Cite journal|last=Hedberg|first=Kenneth|last2=Schomaker|first2=Verner|date=1951-04|title=A Reinvestigation of the Structures of Diborane and Ethane by Electron Diffraction 1,2|url=https://pubs.acs.org/doi/abs/10.1021/ja01148a022|journal=Journal of the American Chemical Society|language=en|volume=73|issue=4|pages=1482–1487|doi=10.1021/ja01148a022|issn=0002-7863}}</ref>

* Structure of the planar trisilylamine<ref>{{Cite journal|last=Hedberg|first=Kenneth|date=1955-12-01|title=The Molecular Structure of Trisilylamine (SiH3)3N1,2|url=https://doi.org/10.1021/ja01629a015|journal=Journal of the American Chemical Society|volume=77|issue=24|pages=6491–6492|doi=10.1021/ja01629a015|issn=0002-7863}}</ref>

* Determinations of the structures of gaseous elemental [[phosphorus]] P₄ and of the binary P₃As<ref>{{Cite journal|last=Cossairt|first=Brandi M.|last2=Cummins|first2=Christopher C.|last3=Head|first3=Ashley R.|last4=Lichtenberger|first4=Dennis L.|last5=Berger|first5=Raphael J. F.|last6=Hayes|first6=Stuart A.|last7=Mitzel|first7=Norbert W.|last8=Wu|first8=Gang|date=2010-06-23|title=On the Molecular and Electronic Structures of AsP3 and P4|url=https://doi.org/10.1021/ja102580d|journal=Journal of the American Chemical Society|volume=132|issue=24|pages=8459–8465|doi=10.1021/ja102580d|issn=0002-7863}}</ref>

* Determination of the structure of [[Buckminsterfullerene|C₆₀]]<ref>{{Cite journal|last=Hedberg|first=K.|last2=Hedberg|first2=L.|last3=Bethune|first3=D. S.|last4=Brown|first4=C. A.|last5=Dorn|first5=H. C.|last6=Johnson|first6=R. D.|last7=De Vries|first7=M.|date=1991-10-18|title=Bond Lengths in Free Molecules of Buckminsterfullerene, C60, from Gas-Phase Electron Diffraction|url=https://www.sciencemag.org/lookup/doi/10.1126/science.254.5030.410|journal=Science|language=en|volume=254|issue=5030|pages=410–412|doi=10.1126/science.254.5030.410|issn=0036-8075}}</ref> and C₇₀<ref>{{Cite journal|last=Hedberg|first=Kenneth|last2=Hedberg|first2=Lise|last3=Bühl|first3=Michael|last4=Bethune|first4=Donald S.|last5=Brown|first5=C. A.|last6=Johnson|first6=Robert D.|date=1997-06-01|title=Molecular Structure of Free Molecules of the Fullerene C70 from Gas-Phase Electron Diffraction|url=https://doi.org/10.1021/ja970110e|journal=Journal of the American Chemical Society|volume=119|issue=23|pages=5314–5320|doi=10.1021/ja970110e|issn=0002-7863}}</ref>

* Structure of [[tetranitromethane]]<ref>{{Cite journal|last=Vishnevskiy|first=Yury V.|last2=Tikhonov|first2=Denis S.|last3=Schwabedissen|first3=Jan|last4=Stammler|first4=Hans-Georg|last5=Moll|first5=Richard|last6=Krumm|first6=Burkhard|last7=Klapötke|first7=Thomas M.|last8=Mitzel|first8=Norbert W.|date=2017-08-01|title=Tetranitromethane: A Nightmare of Molecular Flexibility in the Gaseous and Solid States|url=http://doi.wiley.com/10.1002/anie.201704396|journal=Angewandte Chemie International Edition|language=en|volume=56|issue=32|pages=9619–9623|doi=10.1002/anie.201704396}}</ref>

* Absence of local C₃ symmetry in the simplest [[phosphonium ylide]] H₂C=PMe₃<ref>{{Cite journal|last=Mitzel|first=Norbert W.|last2=Brown|first2=Daniel H.|last3=Parsons|first3=Simon|last4=Brain|first4=Paul T.|last5=Pulham|first5=Colin R.|last6=Rankin|first6=David W. H.|date=1998|title=Differences Between Gas-Phase and Solid-State Molecular Structures of the Simplest Phosphonium Ylide, Me3P=CH2|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291521-3773%2819980703%2937%3A12%3C1670%3A%3AAID-ANIE1670%3E3.0.CO%3B2-S|journal=Angewandte Chemie International Edition|language=en|volume=37|issue=12|pages=1670–1672|doi=10.1002/(SICI)1521-3773(19980703)37:123.0.CO;2-S|issn=1521-3773}}</ref> and in [[Aminophosphine|amino-phosphanes]] like P(NMe₂₎₃ and [[Ylide|ylides]] H₂C=P(NMe₂)₃<ref>{{Cite journal|last=Mitzel|first=Norbert W.|last2=Smart|first2=Bruce A.|last3=Dreihäupl|first3=Karl-Heinz|last4=Rankin|first4=David W. H.|last5=Schmidbaur|first5=Hubert|date=1996-01|title=Low Symmetry in P(NR 2 ) 3 Skeletons and Related Fragments: An Inherent Phenomenon|url=https://pubs.acs.org/doi/10.1021/ja9621861|journal=Journal of the American Chemical Society|language=en|volume=118|issue=50|pages=12673–12682|doi=10.1021/ja9621861|issn=0002-7863}}</ref>

* Determination of intramolecular [[London dispersion force|London dispersion]] interaction effects on gas-phase and solid-state structures of diamondoid dimers<ref>{{Cite journal|last=Fokin|first=Andrey A.|last2=Zhuk|first2=Tatyana S.|last3=Blomeyer|first3=Sebastian|last4=Pérez|first4=Cristóbal|last5=Chernish|first5=Lesya V.|last6=Pashenko|first6=Alexander E.|last7=Antony|first7=Jens|last8=Vishnevskiy|first8=Yury V.|last9=Berger|first9=Raphael J. F.|last10=Grimme|first10=Stefan|last11=Logemann|first11=Christian|date=2017-11-22|title=Intramolecular London Dispersion Interaction Effects on Gas-Phase and Solid-State Structures of Diamondoid Dimers|url=https://doi.org/10.1021/jacs.7b07884|journal=Journal of the American Chemical Society|volume=139|issue=46|pages=16696–16707|doi=10.1021/jacs.7b07884|issn=0002-7863}}</ref>

==References==