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Unformatted text preview: Vicinal 1 H 1 H coupling constants ( 3 J HH ) are particularly useful for molecular structure studies In the late 1950s and early 1960s, Martin Karplus established a relationship between the dihedral (torsion) angle between vicinal hydrogens and the 3 J HH coupling constant using a largely theoretical (valencebond) approach This important relationship is now called the Karplus relationship Karplus, Martin (1959). "Contact ElectronSpin Coupling of Nuclear Magnetic Moments". J Chem. Phys . 30 (1), 1115 *Karplus, Martin (1963). "Vicinal Proton Coupling in Nuclear Magnetic Resonance". J. Am. Chem. Soc . 85 (18), 28702871. * This is the 17 th most cited article in JACS history 3 J HH large (~ 15 Hz) 3 J HH small (~ 5 Hz) The dependence of the vicinal coupling constant on the dihedral angle, as formulated by Karplus, is without doubt one of the most important relationships in conformational analysis, possibly more so than any other.  Horst Freibolin, from Basic Oneand TwoDimensional NMR Spectroscopy, Fourth Edition, 2005. The general form of the Karplus relationship is: where the coef f cients (A, B, and C) are parameterized for particular molecule types, atoms and substitutents. Karplus curve for ethane derivatives, 3 J HH ( ) = 12 cos 2 ( ) cos ( ) + 2 Karplus curve parameterized for de f ning the main chain angle (CO i1N iC iCO i ) in protein molecules ( 3 J( ) = 7.0 cos 2 ( ) 1.4 cos ( ) + 1.7) 3 J ( ) = A cos 2 ( ) + B cos( ) + C Minch, M. J. (1994). "Orientational Dependence of Vicinal ProtonProton NMR Coupling Constants: The Karplus Relationship. Concepts in Magnetic Resonance 6 , 4146. Wang, A. C., and Bax, A. (1996) Determination of the Backbone Dihedral Angles in Human Ubiquitin from Reparametrized Empirical Karplus Equations . J. Am. Chem. Soc . 118 , 24832494. The dihedral angle dependence of the magnitude of vicinal couplings results from molecular orbital overlap the CC bond and the CH bonds are nearly perpendicular, so there is little overlap overlap of the sp 3 hybrid orbitals governs the magnitude of the coupling maximum orbital overlap occurs when the dihedral angle is 0 and 180 ( 3 J HH is large) the orbital overlap is minimal when the dihedral angle is 90 ( 3 J HH is small) Ethane derivatives, rotameric states, and rotameric averaging In ethane derivatives (ethyl groups), the dihedral angle for gauche rotamers 1 and 3 is about 60, whereas for the trans rotamer the dihedral angle is 180 Therefore, according to the Karplus curve: the 1 H 1 H coupling constant is about 4 Hz for rotamers 1 and 3 ( 3 J 1 = 3 J 3 4 Hz) the 1 H 1 H coupling constant is about 13 Hz for rotamer 2 ( 3 J 2 13 Hz) The fraction of the total compound that adopts each of the three rotameric conformations will depend on the substitutents these fractions will be represented as F 1 , F 2 , and F...
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This note was uploaded on 11/13/2011 for the course CHEM 4190 taught by Professor Staff during the Fall '08 term at University of Georgia Athens.
 Fall '08
 Staff
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