Riesz potential - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T21:13:55Z

References: replace mr template with mr parameter in CS1 templates; using AWB

← Older revision		Revision as of 23:13, 25 September 2014
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	~~'''Fluxional molecules''' are [[molecule]]s that undergo dynamics such that some or all~~ of their [[atom]]s interchange between symmetry-equivalent positions. Because virtually all molecules are fluxional in some respects, e.g. bond rotations in most [[organic compound]]s, the term fluxional depends on the context and the method used to assess the ~~dynamics. Often, a molecule~~ is ~~considered fluxional if its spectroscopic signature exhibits line-broadening (beyond that dictated by the [[Heisenberg Uncertainty Principle]]) due to chemical exchange~~. ~~In some cases, where the rates are slow, fluxionality is not detected spectroscopically, but by [[isotopic labeling]].~~		The title of the writer is Garland. The favorite pastime for my kids and me is dancing and now I'm trying to earn money with it. She is currently a cashier but soon she'll be on her own. Alabama is where he and his wife live and he has every thing that he needs there.<br><br>My website: [http://www.Creativecats.com/UserProfile/tabid/331/userId/19522/Default.aspx auto extended warranty]

	~~==Carbonium ion==~~
	The ~~prototypical fluxional molecule~~ is the [[carbonium ion]], which is protonated methane, CH<sub>5</sub><sup>+</sup>.<ref>{{cite journal \| author = Kramer, G. M. \| journal = Science \| year = 1999 \| volume = 286 \| pages = 1051}}</ref><ref>{{cite journal \| author = Oka, T.; White, E. T. \| journal = Science \| year = 1999 \| volume = 286 \| pages = 1051}}</ref><ref>{{cite journal \| author1 = Marx, D. \| author2 = Parrinello, M. \| journal = Science \| volume = 286 \| pages = 1051 \| year = 1999}}</ref> In this unusual species, whose [[IR spectrum]] was recently experimentally observed<ref>{{cite journal \| author = D. W. Boo, Z. F. Liu, A. G. Suits, J. S. Tse, Y. T. Lee \| journal = Science \| volume = 269 \| pages = 57–9 \| year = 1995 \| doi = 10.1126/science.269.5220.57 \| pmid = 17787703 \| title = Dynamics of Carbonium Ions Solvated by Molecular Hydrogen: CH5+(H2)n (n = 1, 2, 3) \| issue = 5220\|bibcode = 1995Sci...269...57B }}</ref><ref>{{cite journal \| author = E. T. White, J. Tang, T. Oka \| journal = Science \| volume = 284 \| pages = 135–7 \| year = 1999 \| doi = 10.1126/science.284.5411.135 \| pmid = 10102811 \| title = CH5+: The infrared spectrum observed \| issue = 5411\|bibcode = 1999Sci...284..135W }}</ref> and more recently understood,<ref>{{ cite journal \| journal = [[Science (journal)\|Science]] \| volume = 309 \| issue = 5738 \| pages = 1219–1222 \| title = Understanding the Infrared Spectrum of Bare CH<sub>5</sub><sup>+</sup> \| first1 = O. \| last1= Asvany \| first2= P. \| last2= Kumar P \| first3= B. \| last3= Redlich \| year = 2005 \| first4= I~~. \| last4= Hegemann \| first5= S. \| last5= Schlemmer \| first6= D. \| last6= Marx \| doi = 10.1126/science.1113729 \| pmid=15994376\|bibcode = 2005Sci...309.1219A }}</ref> the barriers~~ to proton exchange are lower than the [[zero point energy]]. Thus, even at [[absolute zero]] there is no rigid molecular structure, the H atoms are always in motion. More precisely, the spatial distribution of protons in CH<sub>5</sub><sup>+</sup> is many times broader than its parent molecule CH<sub>4</sub>, methane.<ref>{{cite journal \| journal = J. Am. Chem. Soc. \| volume = 127 \| issue = 13 \| pages = 4954–4958 \| year = 2005 \| doi = 10.1021/ja0482280 \| pmid = 15796561 \| last1 = Thompson \| first1 = KC \| last2 = Crittenden \| first2 = DL \| last3 = Jordan \| first3 = MJ \| title = CH5+: Chemistry's chameleon unmasked}}</ref><ref>For an animation of the dynamics of CH<sub>5</sub><sup>+</sup>, see http://www.theochem.ruhr-uni-bochum.de/research/marx/topic4b.en.html</ref>

	~~==NMR spectroscopy==~~
	~~Temperature dependent changes in the NMR spectra result from dynamics associated~~ with ~~the fluxional molecules when those dynamics proceed at rates comparable to the frequency differences observed by NMR~~. ~~The experiment~~ is ~~called~~ '''DNMR''' and typically involves recording spectra at varying temperatures. In the ideal case, low temperature spectra are assigned to the "frozen equilibrium" whereas spectra recorded at high temperatures correspond to molecules at "fast exchange limit". Typically spectra recorded at high temperature spectra are simpler than those at low temperatures, since at high temperatures, equivalent sites are averaged out. Prior to the advent of DNMR, kinetics of reactions were measured on nonequilibrium mixtures, monitoring the approach to equilibrium.

	~~Many molecular processes exhibit fluxionality that can~~ be ~~probed~~ on ~~the NMR time scale~~. ~~Beyond the examples highlighted below, other classic examples include the [[cope rearrangement]] in [[bullvalene]] and the [[cyclohexane conformation\|chair inversion]] in [[cyclohexane]].~~

	~~===Dimethylformamide===~~
	~~A classic example of a fluxional molecule~~ is ~~[[dimethylformamide]].<ref>{{cite journal \| author1 = H. S. Gutowsky \| author2 = C. H. Holm \| title = Rate Processes~~ and Nuclear Magnetic Resonance Spectra. II. Hindered Internal Rotation of Amides \| journal = J. Chem. Phys. \| year = 1956 \| volume = 25 \| pages = 1228–1234 \| doi=10.1063/1.1743184 \| issue = 6\|bibcode = 1956JChPh..25.1228G }}</ref>
	~~[[Image:DmfDNMR.png\|center\|300px]]~~
	At temperatures near 100 °C, the 500 MHz NMR spectrum of this compound shows only one signal for the methyl groups. Near room temperature however, separate signals are seen for the non-equivalent methyl groups. The rate of exchange can be readily calculated at the temperature where the two signals are just merged. This "coalescence temperature" depends on the measuring field. The relevant equation is:
	~~:<math>k = \frac{\pi \Delta \nu_\circ}{2^{1/2}} \sim 2 \Delta \nu_\circ</math>~~
	where Δν<sub>o</sub> is the difference in Hz between the frequencies of the exchanging sites. These frequencies are obtained from the limiting low-temperature NMR spectrum. At these lower temperatures, the dynamics continue, of course, but the contribution of the dynamics to line broadening is negligible.

	~~For example, if Δν<sub>o</sub> = 1ppm @ 500 MHz~~
	~~:<math>k \sim 2(500) = 1000 \mathrm{s}^{-1}</math> (ca. 0.5 millisecond [[half-life]])~~

	~~===Ring whizzing in organometallic chemistry===~~
	~~Many [[organometallic compound]]s exhibit fluxionality.<ref>John W. Faller "Stereochemical Nonrigidity of Organometallic Complexes" ''Encyclopedia of Inorganic~~ and ~~Bioinorganic Chemistry'' 2011, Wiley-VCH, Weinheim. {{DOI\|10~~.~~1002/9781119951438.eibc0211}}~~<~~/ref> The compound Fe(η<sup~~>5<~~/sup~~>~~-C<sub>5</sub>H<sub>5</sub>) (η<sup>1</sup>- C<sub>5</sub>H<sub>5</sub>)(CO)<sub>2</sub> exhibits the phenomenon of "ring whizzing".~~
	~~[[File~~:~~Fe Habcd.jpg\|thumb\|The structure of the ring whizzer Fe(η<sup>5</sup>-C<sub>5</sub>H<sub>5</sub>) (η<sup>1</sup>-C<sub>5</sub>H<sub>5</sub>)(CO)<sub>2</sub>.]]~~

	At 30 °C, the <sup>1</sup>H NMR spectrum shows only two peaks, one typical (δ5.6) of the η<sup>5</sup>-C<sub>5</sub>''H''<sub>5</sub> and the other assigned η<sup>1</sup>-C<sub>5</sub>''H''<sub>5</sub>. The singlet assigned to the η<sup>1</sup>-C<sub>5</sub>H<sub>5</sub> ligand splits at low temperatures owing to the slow hopping of the Fe center from carbon to carbon in the η<sup>1</sup>-C<sub>5</sub>H<sub>5</sub> ligand.<ref>Bennett, Jr. M. J.; [[F. Albert Cotton\|Cotton, F. A.]]; Davison, A.; Faller, J. W.; Lippard, S. J.; Morehouse, S. M. "Stereochemically Nonrigid Organometallic Compounds. I. π-Cyclopentadienyliron Dicarbonyl σ-Cyclopentadiene" ''J. Am. Chem. Soc.'' 1966, 88,4371. {{DOI\|10.1021/ja00971a012}}</ref> Two mechanisms have been proposed, with the consensus favoring the 1,2 shift pathway.<ref name="Robert">Robert B. Jordan, Reaction Mechanisms of Inorganic and Organometallic Systems (''Topics in Inorganic Chemistry''), 2007. ISBN 978-0195301007</ref>

	~~===Berry pseudorotation===~~
	~~[[Image~~:~~Iron-pentacarbonyl-Berry-mechanism.png\|500px\|center\|Iron-pentacarbonyl-Berry-mechanism]]~~
	Pentacoordinate molecules of trigonal pyramidal geometry typically exhibit a particular kind of low energy fluxional behavior called [[Berry pseudorotation]]. Famous examples of such molecules are [[iron pentacarbonyl]] (Fe(CO)<sub>5</~~sub>) and [[phosphorus pentafluoride]] (PF<sub>5<~~/~~sub>). At higher temperatures, only one signal is observed for the ligands (e~~.g.~~, by <sup>13<~~/sup>C or <sup>19</sup>F NMR) whereas at low temperatures, two signals in a 2:3 ratio can be resolved. Molecules that are not strictly pentacoordinate are also subject to this process, such as SF<sub>4</sub>.

	~~==IR spectroscopy==~~
	Although less common, some dynamics are also observable on the time-scale of [[IR spectroscopy]]. One example is [[electron transfer]] in a mixed valence dimer of metal clusters. Application of above equation for coalescence of two signals separated by 10 cm<sup>−1</sup> gives the following result:<ref>{{cite journal \| author1 = Casey H. Londergan \|author2 = Clifford P. Kubiak \| title = Electron Transfer and Dynamic Infrared-Band Coalescence: It Looks Like Dynamic NMR Spectroscopy, but a Billion Times Faster \| journal = Chemistry, a European Journal \| year = 2003 \| volume = 9 \| pages = 5969ff \| doi = 10.1002/~~chem.200305028 \|issue = 24}}<~~/~~ref>~~
	~~:<math>k \sim \Delta \nu_\circ \sim 2(10 \mathrm{cm}^{-1}) (300 \cdot 10^8 \mathrm{cm~~/~~s}) \sim 6 \times 10^{11} \mathrm{s}^{-1} \cdot<~~/~~math>~~
	~~Clearly, processes that induce line-broadening on the IR time-scale must be extremely rapid~~.


	~~==See also==~~
	* [[Bailar twist]]
	* [[Ray-Dutt twist]]
	* [[Bartell mechanism]]
	* [[Pseudorotation]]

	~~==References==~~
	~~<references/>~~

	~~[[Category:Chemical compounds]~~]

en>Billlion: another c_\alpha

2013-12-02T18:37:07Z

another c_\alpha

← Older revision		Revision as of 20:37, 2 December 2013
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	Hi there, ~~I am Felicidad Oquendo~~. ~~One~~ of the ~~issues I adore most~~ is ~~climbing~~ and ~~now I have time~~ to ~~consider~~ on ~~new issues~~. ~~Delaware~~ is ~~our birth place~~. ~~His day occupation~~ is ~~a cashier~~ and ~~his wage has~~ been ~~really fulfilling~~.<br><br>~~Visit my site extended car warranty~~ ([~~http:~~//~~chilevisual~~.~~net~~/~~index~~.~~php?mod~~=~~users~~&~~action~~=~~view&id~~=~~7096 simply click~~ the ~~next web page~~])		'''Fluxional molecules''' are [[molecule]]s that undergo dynamics such that some or all of their [[atom]]s interchange between symmetry-equivalent positions. Because virtually all molecules are fluxional in some respects, e.g. bond rotations in most [[organic compound]]s, the term fluxional depends on the context and the method used to assess the dynamics. Often, a molecule is considered fluxional if its spectroscopic signature exhibits line-broadening (beyond that dictated by the [[Heisenberg Uncertainty Principle]]) due to chemical exchange. In some cases, where the rates are slow, fluxionality is not detected spectroscopically, but by [[isotopic labeling]].

			==Carbonium ion==
			The prototypical fluxional molecule is the [[carbonium ion]], which is protonated methane, CH<sub>5</sub><sup>+</sup>.<ref>{{cite journal \| author = Kramer, G. M. \| journal = Science \| year = 1999 \| volume = 286 \| pages = 1051}}</ref><ref>{{cite journal \| author = Oka, T.; White, E. T. \| journal = Science \| year = 1999 \| volume = 286 \| pages = 1051}}</ref><ref>{{cite journal \| author1 = Marx, D. \| author2 = Parrinello, M. \| journal = Science \| volume = 286 \| pages = 1051 \| year = 1999}}</ref> In this unusual species, whose [[IR spectrum]] was recently experimentally observed<ref>{{cite journal \| author = D. W. Boo, Z. F. Liu, A. G. Suits, J. S. Tse, Y. T. Lee \| journal = Science \| volume = 269 \| pages = 57–9 \| year = 1995 \| doi = 10.1126/science.269.5220.57 \| pmid = 17787703 \| title = Dynamics of Carbonium Ions Solvated by Molecular Hydrogen: CH5+(H2)n (n = 1, 2, 3) \| issue = 5220\|bibcode = 1995Sci...269...57B }}</ref><ref>{{cite journal \| author = E. T. White, J. Tang, T. Oka \| journal = Science \| volume = 284 \| pages = 135–7 \| year = 1999 \| doi = 10.1126/science.284.5411.135 \| pmid = 10102811 \| title = CH5+: The infrared spectrum observed \| issue = 5411\|bibcode = 1999Sci...284..135W }}</ref> and more recently understood,<ref>{{ cite journal \| journal = [[Science (journal)\|Science]] \| volume = 309 \| issue = 5738 \| pages = 1219–1222 \| title = Understanding the Infrared Spectrum of Bare CH<sub>5</sub><sup>+</sup> \| first1 = O. \| last1= Asvany \| first2= P. \| last2= Kumar P \| first3= B. \| last3= Redlich \| year = 2005 \| first4= I. \| last4= Hegemann \| first5= S. \| last5= Schlemmer \| first6= D. \| last6= Marx \| doi = 10.1126/science.1113729 \| pmid=15994376\|bibcode = 2005Sci...309.1219A }}</ref> the barriers to proton exchange are lower than the [[zero point energy]]. Thus, even at [[absolute zero]] there is no rigid molecular structure, the H atoms are always in motion. More precisely, the spatial distribution of protons in CH<sub>5</sub><sup>+</sup> is many times broader than its parent molecule CH<sub>4</sub>, methane.<ref>{{cite journal \| journal = J. Am. Chem. Soc. \| volume = 127 \| issue = 13 \| pages = 4954–4958 \| year = 2005 \| doi = 10.1021/ja0482280 \| pmid = 15796561 \| last1 = Thompson \| first1 = KC \| last2 = Crittenden \| first2 = DL \| last3 = Jordan \| first3 = MJ \| title = CH5+: Chemistry's chameleon unmasked}}</ref><ref>For an animation of the dynamics of CH<sub>5</sub><sup>+</sup>, see http://www.theochem.ruhr-uni-bochum.de/research/marx/topic4b.en.html</ref>

			==NMR spectroscopy==
			Temperature dependent changes in the NMR spectra result from dynamics associated with the fluxional molecules when those dynamics proceed at rates comparable to the frequency differences observed by NMR. The experiment is called '''DNMR''' and typically involves recording spectra at varying temperatures. In the ideal case, low temperature spectra are assigned to the "frozen equilibrium" whereas spectra recorded at high temperatures correspond to molecules at "fast exchange limit". Typically spectra recorded at high temperature spectra are simpler than those at low temperatures, since at high temperatures, equivalent sites are averaged out. Prior to the advent of DNMR, kinetics of reactions were measured on nonequilibrium mixtures, monitoring the approach to equilibrium.

			Many molecular processes exhibit fluxionality that can be probed on the NMR time scale. Beyond the examples highlighted below, other classic examples include the [[cope rearrangement]] in [[bullvalene]] and the [[cyclohexane conformation\|chair inversion]] in [[cyclohexane]].

			===Dimethylformamide===
			A classic example of a fluxional molecule is [[dimethylformamide]].<ref>{{cite journal \| author1 = H. S. Gutowsky \| author2 = C. H. Holm \| title = Rate Processes and Nuclear Magnetic Resonance Spectra. II. Hindered Internal Rotation of Amides \| journal = J. Chem. Phys. \| year = 1956 \| volume = 25 \| pages = 1228–1234 \| doi=10.1063/1.1743184 \| issue = 6\|bibcode = 1956JChPh..25.1228G }}</ref>
			[[Image:DmfDNMR.png\|center\|300px]]
			At temperatures near 100 °C, the 500 MHz NMR spectrum of this compound shows only one signal for the methyl groups. Near room temperature however, separate signals are seen for the non-equivalent methyl groups. The rate of exchange can be readily calculated at the temperature where the two signals are just merged. This "coalescence temperature" depends on the measuring field. The relevant equation is:
			:<math>k = \frac{\pi \Delta \nu_\circ}{2^{1/2}} \sim 2 \Delta \nu_\circ</math>
			where Δν<sub>o</sub> is the difference in Hz between the frequencies of the exchanging sites. These frequencies are obtained from the limiting low-temperature NMR spectrum. At these lower temperatures, the dynamics continue, of course, but the contribution of the dynamics to line broadening is negligible.

			For example, if Δν<sub>o</sub> = 1ppm @ 500 MHz
			:<math>k \sim 2(500) = 1000 \mathrm{s}^{-1}</math> (ca. 0.5 millisecond [[half-life]])

			===Ring whizzing in organometallic chemistry===
			Many [[organometallic compound]]s exhibit fluxionality.<ref>John W. Faller "Stereochemical Nonrigidity of Organometallic Complexes" ''Encyclopedia of Inorganic and Bioinorganic Chemistry'' 2011, Wiley-VCH, Weinheim. {{DOI\|10.1002/9781119951438.eibc0211}}</ref> The compound Fe(η<sup>5</sup>-C<sub>5</sub>H<sub>5</sub>) (η<sup>1</sup>- C<sub>5</sub>H<sub>5</sub>)(CO)<sub>2</sub> exhibits the phenomenon of "ring whizzing".
			[[File:Fe Habcd.jpg\|thumb\|The structure of the ring whizzer Fe(η<sup>5</sup>-C<sub>5</sub>H<sub>5</sub>) (η<sup>1</sup>-C<sub>5</sub>H<sub>5</sub>)(CO)<sub>2</sub>.]]

			At 30 °C, the <sup>1</sup>H NMR spectrum shows only two peaks, one typical (δ5.6) of the η<sup>5</sup>-C<sub>5</sub>''H''<sub>5</sub> and the other assigned η<sup>1</sup>-C<sub>5</sub>''H''<sub>5</sub>. The singlet assigned to the η<sup>1</sup>-C<sub>5</sub>H<sub>5</sub> ligand splits at low temperatures owing to the slow hopping of the Fe center from carbon to carbon in the η<sup>1</sup>-C<sub>5</sub>H<sub>5</sub> ligand.<ref>Bennett, Jr. M. J.; [[F. Albert Cotton\|Cotton, F. A.]]; Davison, A.; Faller, J. W.; Lippard, S. J.; Morehouse, S. M. "Stereochemically Nonrigid Organometallic Compounds. I. π-Cyclopentadienyliron Dicarbonyl σ-Cyclopentadiene" ''J. Am. Chem. Soc.'' 1966, 88,4371. {{DOI\|10.1021/ja00971a012}}</ref> Two mechanisms have been proposed, with the consensus favoring the 1,2 shift pathway.<ref name="Robert">Robert B. Jordan, Reaction Mechanisms of Inorganic and Organometallic Systems (''Topics in Inorganic Chemistry''), 2007. ISBN 978-0195301007</ref>

			===Berry pseudorotation===
			[[Image:Iron-pentacarbonyl-Berry-mechanism.png\|500px\|center\|Iron-pentacarbonyl-Berry-mechanism]]
			Pentacoordinate molecules of trigonal pyramidal geometry typically exhibit a particular kind of low energy fluxional behavior called [[Berry pseudorotation]]. Famous examples of such molecules are [[iron pentacarbonyl]] (Fe(CO)<sub>5</sub>) and [[phosphorus pentafluoride]] (PF<sub>5</sub>). At higher temperatures, only one signal is observed for the ligands (e.g., by <sup>13</sup>C or <sup>19</sup>F NMR) whereas at low temperatures, two signals in a 2:3 ratio can be resolved. Molecules that are not strictly pentacoordinate are also subject to this process, such as SF<sub>4</sub>.

			==IR spectroscopy==
			Although less common, some dynamics are also observable on the time-scale of [[IR spectroscopy]]. One example is [[electron transfer]] in a mixed valence dimer of metal clusters. Application of above equation for coalescence of two signals separated by 10 cm<sup>−1</sup> gives the following result:<ref>{{cite journal \| author1 = Casey H. Londergan \|author2 = Clifford P. Kubiak \| title = Electron Transfer and Dynamic Infrared-Band Coalescence: It Looks Like Dynamic NMR Spectroscopy, but a Billion Times Faster \| journal = Chemistry, a European Journal \| year = 2003 \| volume = 9 \| pages = 5969ff \| doi = 10.1002/chem.200305028 \|issue = 24}}</ref>
			:<math>k \sim \Delta \nu_\circ \sim 2(10 \mathrm{cm}^{-1}) (300 \cdot 10^8 \mathrm{cm/s}) \sim 6 \times 10^{11} \mathrm{s}^{-1} \cdot</math>
			Clearly, processes that induce line-broadening on the IR time-scale must be extremely rapid.


			==See also==
			* [[Bailar twist]]
			* [[Ray-Dutt twist]]
			* [[Bartell mechanism]]
			* [[Pseudorotation]]

			==References==
			<references/>

			[[Category:Chemical compounds]]

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2010-07-09T17:56:59Z

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Hi there, I am Felicidad Oquendo. One of the issues I adore most is climbing and now I have time to consider on new issues. Delaware is our birth place. His day occupation is a cashier and his wage has been really fulfilling.<br><br>Visit my site extended car warranty ([http://chilevisual.net/index.php?mod=users&action=view&id=7096 simply click the next web page])