Karplus relationship

The dependence of on dihedral angle is re ferred to as the Karplus relationship after Martin Karplus (Harvard University) who offered the presently accepted theoretical treat ment of it... 

Fig. 11. (A) Coupling constant versus cf> angle from Karplus relationship. (B) Simu-...

The so-called Karplus relationship expresses approximately, the angular dependence of the vicinal coupling constant as ... 

The 7hh spin coupling constants (Table 7) also provide valuable insight into the structure of aUyhnagnesium compounds. Assuming the Karplus relationship holds, the magnitude of the coupling between the unique hydrogen, H, and the two equivalent... 

This equation was predicted on theoretical grounds, but the constants, A, B, and C are empirical.450 Other forms of the equation, some of them simplified, have also been proposed.451 The Karplus relationship is often used to estimate time-averaged torsion angles in peptides. For a CaH - NH torsion angle the parameters A, B and C of Eq. 3-52 are 6.4,1.4, and 1.9, respectively. For a CaH - CpH they are 9.5,1.6, and... 

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... 

Numerical values of J vary with substitution, ring size, etc., but the Karplus relationship still works—it gives good relative values... 

Although this is the only chapter in which stereoelectronics appears in the title, you will soon recognize the similarity between the ideas we cover here and concepts like the stereospecificity of E2 elimination reactions (Chapter 19), the Karplus relationship (Chapter 32), the Felkin-Anh transition state (Chapter 33), and the conformational requirements for rearrangement (Chapter 37) and fragmentation (Chapter 38) reactions. 

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

Cyclic carbodiimide 48 theoretically exists as two conformational isomers. Comparison of the coupling constant values, calculated using AMI Hamiltonian and Karplus relationship, with the experimental vicinal coupling constants of 8.33 and 1.05 Hz, undoubtedly prove its methyl-out structure 48 <1996JOC4289>. 

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.

Slightly more difficult determination of stereochemistry moving from two dimensions to three Revision of the Karplus relationship and of conjugate addition. 

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