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structure - Vicinal 1H-1H coupling constants(3JHH are...

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Vicinal 1 H- 1 H coupling constants ( 3 J HH ) are particularly useful for molecular structure studies In the late 1950’s and early 1960’s, Martin Karplus established a relationship between the dihedral (torsion) angle between vicinal hydrogens and the 3 J HH coupling constant using a largely theoretical (valence-bond) approach This important relationship is now called the “Karplus relationship” Karplus, Martin (1959). "Contact Electron-Spin Coupling of Nuclear Magnetic Moments". J Chem. Phys . 30 (1), 11-15 *Karplus, Martin (1963). "Vicinal Proton Coupling in Nuclear Magnetic Resonance". J. Am. Chem. Soc . 85 (18), 2870-2871. * 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 One-and Two-Dimensional NMR Spectroscopy”, Fourth Edition, 2005.
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The general form of the Karplus relationship is: where the coef fi cients (A, B, and C) are parameterized for particular molecule types, atoms and substitutents. “Karplus curve” for ethane derivatives, 3 J HH ( φ ) = 12 cos 2 ( φ ) - cos ( φ ) + 2 Karplus curve parameterized for de fi ning the main chain angle φ (CO i -1 -N i -C α i -CO i ) in protein molecules ( 3 J( φ ) = 7.0 cos 2 ( φ ) 1.4 cos ( φ ) + 1.7) 3 J ( φ ) = A cos 2 ( φ ) + B cos( φ ) + C Minch, M. J. (1994). "Orientational Dependence of Vicinal Proton-Proton NMR Coupling Constants: The Karplus Relationship”. Concepts in Magnetic Resonance 6 , 41-46. 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 , 2483-2494.
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The dihedral angle dependence of the magnitude of vicinal couplings results from molecular orbital overlap • the σ C-C bond and the σ C-H 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)
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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 3 (F 1 + F 2 + F 3 = 1) The observed coupling constant (assuming fast rotation about the C-C bond) is given by: 3 J observed = F 1 3 J 1 + F 2 3 J 2 + F 3 3 J 3
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Example 2: • the observed value of 3 J HH for either isomer ( erythro or threo ) of
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