Karplus relationship bonds

NOEs or NOESY cross peaks can be used to define distances between protons. It is well known that the three-bond scalar coupling constants 3Jjj between nuclei / and J obey a Karplus relationship of the type [39,40]... 

The Karplus Relationship and the Correlation of Two Anomalous 13C-Vicinal H Coupling Constants with Bonding Electron Density Distribution Found by Accurate X-Ray Analysis, L. T. J. Delbaere, M. N. G. James, and R. U. Lemieux, J. Am. Chem. Soc., 95 (1973) 7866-7868. 

Coupling is largest at 180° the Karplus relationship J vs. dihedral angle when the orbitals of the two C-H bonds are perfectly parallel... 

Figure 9.6. Graphical depiction of Eq. (9.4) the Karplus relationship for vicinal (three-bond) H-H coupling.

Figure 12.11. Illustration of the Karplus relationship between three-bond scalar coupling constants and the dihedral angle of the intervening bond. The relationship is indicated for the torsion angle of the H2 and H3 protons within the rigid core of taxol and related derivatives. See Fig. 12.6 for the structure of taxol.

B. Bose, S. Zhao, R. Stenutz, F. Cloran, P. B. Bondo, G. Bondo, B. Hertz, I. Carmichael, and A. S. Serianni, Three-bond C-O-C-C spin-coupling constants in carbohydrates Development of a Karplus relationship,./. Am. Chem. Soc., 120 (1998) 11158—11173. 

The observed three-bond coupling constants may be analyzed with a proton-phosphorus Karplus relationship to determine the C4 -C3 -O-P torsional angle c (28). As shown by Dickerson (10) there is a strong correlation (R = -0.92) between torsional angles C4 -C3 -O3 -P (c) and C3 -O3 -P-O5 (C) in the crystal structures of various duplexes. Thus both torsional angles c and ( can often be calculated from the measured P-H3 coupling constant. 

The dependence of the coupling constant on the angle between the two C—H bonds is called the Karplus relationship after Martin Karplus, who first observed the relationship. Karplus was bom in 1930. He received a B.A. from Harvard University and a Ph.D. from the California Institute of Technology. He is currently a professor of chemistry at Harvard University. 

Three-bond long-range H-i5N couplings obey a Karplus relationship with maxima near 0° and 180° [81]. 

The Karplus relationship makes perfect sense according to the Dirac model. When the two adjacent C—H cr bonds are orthogonal (a= 90°, perpendicular), there should be minimal orbital overlap, with little or no spin interaction between the electrons in these orbitals. As a result, nuclear spin information is not transmitted, and Vhh = 0- Conversely, when these two bonds are parallel (a= 0°) or antiparallel (a= 180°), the couphng constant should have its greatest magnitude ( hh = max). 

Karplus relationship. A mathe matical function based on orbital overlap that relates the magnitude of J-coupling as a function of the gemi-nal bond angle or the vicinal dihedral angle. 

THE KARPLUS RELATIONSHIP FOR SPINS SEPARATED BY THREE BONDS... 

The parameters a, b, and c were analyzed as a function of the electronegativities of X and Y. The hydrogen-bonded H) values decreased nearly 100-fold from the covalent V(H, H) values, but they followed closely a Karplus relationship. 

Figure 8 The Karplus relationship for three-bond proton-proton coupling relating dihedral angle and J. (Adapted from Campbell ID and Dwek RA (1984) Biological Spectroscopy. Menlo Park, CA Benjamin/Cummings.)...

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