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| [[File:Karplus.svg|thumb|300px| Graph of the Karplus relation ''J''<sub>HH</sub>(φ) = 12 cos<sup>2</sup>φ - cosφ+2 obtained for ethane derivatives <ref name="Minch1994">{{cite journal | doi = 10.1002/cmr.1820060104 | journal = [[Concepts in Magnetic Resonance]] | volume = 6 |pages=41–56 | year =1994 | first=M. J.|last=Minch| title = Orientational Dependence of Vicinal Proton-Proton NMR Coupling Constants: The Karplus Relationship}}</ref>]] | | Claude is her name and she totally digs that title. Her friends say it's [http://gcjcteam.org/index.php?mid=etc_video&document_srl=654672&sort_index=regdate&order_type=desc extended auto warranty] car warranty auto warranty not great for her but what she [http://autos.jdpower.com/content/buying-tip/xa345A7/pros-and-cons-of-buying-an-extended-warranty-for-a-car.htm loves performing] is flower arranging and she is attempting to make it a occupation. Years ago we moved [http://www.jvawest.com/UserProfile/tabid/152/userId/2157/Default.aspx extended car warranty] warranty to Arizona but my spouse wants us to transfer. Managing people is auto warranty how she makes money and she will not change it [http://Autos.Jdpower.com/content/buying-tip/xa345A7/pros-and-cons-of-buying-an-extended-warranty-for-a-car.htm anytime] soon.<br><br>My web page: [http://Pchelpnow.biz/ActivityFeed/MyProfile/tabid/60/userId/48445/Default.aspx extended auto warranty] |
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| The '''Karplus equation''', named after [[Martin Karplus]], describes the correlation between <sup>3</sup>[[J-coupling]] constants and [[dihedral angle|dihedral torsion angles]] in [[nuclear magnetic resonance spectroscopy]]:<ref name="Dalton2003">{{cite journal | journal = [[Chemical & Engineering News]] | volume = 81 | issue = 51 |page=37 | date =2003-12-22 | first=Louisa |last=Dalton | title = Karplus Equation | url = http://pubs.acs.org/cen/science/8151/8151karplus.html | doi = 10.1021/cen-v081n036.p037}}</ref>
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| :<math>J(\phi) = A \cos^2 \phi + B \cos\,\phi + C</math>
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| where ''J'' is the <sup>3</sup>''J'' coupling constant, <math> \phi </math> is the [[dihedral angle]], and ''A'', ''B'', and ''C'' are empirically derived parameters whose values depend on the atoms and substituents involved.<ref name="Karplus1959">{{cite journal |last=Karplus |first=Martin | title = Contact Electron-Spin Coupling of Nuclear Magnetic Moments | year = 1959 | journal = [[J. Chem. Phys.]] | volume = 30 | issue = 1 | pages = 11–15 | doi = 10.1063/1.1729860|bibcode = 1959JChPh..30...11K }}</ref> The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2 φ rather than cos<sup>2</sup>φ —these lead to different numerical values of ''A'', ''B'', and ''C'' but do not change the nature of the relationship.
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| The relationship is used for <sup>3</sup>''J''<sub>H,H</sub> coupling constants. The superscript "3" indicates that a <sup>1</sup>H atom is coupled to another <sup>1</sup>H atom three bonds away, via H-C-C-H bonds. (Such hydrogens bonded to neighbouring carbon atoms are termed [[Vicinal (chemistry)|vicinal]]).<ref name="Karplus1963">{{cite journal |last=Karplus |first=Martin |title = Vicinal Proton Coupling in Nuclear Magnetic Resonance | year = 1963 | journal = [[J. Am. Chem. Soc.]] | volume = 85 | issue = 18 | pages = 2870–2871 | doi = 10.1021/ja00901a059}}</ref> The magnitude of these couplings are generally smallest when the torsion angle is close to 90° and largest at angles of 0 and 180°.
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| This relationship between local geometry and coupling constant is of great value throughout [[nuclear magnetic resonance]] spectroscopy and is particularly valuable for determining [[Backbone chain|backbone]] torsion angles in [[protein NMR]] studies.
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://www.stenutz.eu/conf/jhh.html Generalized Karplus calculation of proton-proton coupling constants]
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| [[Category:Nuclear magnetic resonance]]
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