Karplus relationships for

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

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

FIGURE 6.3 the d Karplus relationship for vicinal H s. d varies as a function of the dihedral angle . 

The new empirical Karplus relationships for Vccy Vncy proteins have been obtained by Bax and co-workers. ° The couplings required to parametrize these relationships have been measured for ubiquitin and the third IgG-binding domain of protein G. The experimental Karplus curves have been confirmed by the DFT calculations including an unusual phase shift which causes the maximum Vccy - ncy couplings to occur for dihedral angles slightly smaller than 180°. The new Karplus curves permit determination of rotamer populations for the Xi torsion angles. 

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.)...

R. Suardiaz, C. Perez, J.M. de la Vega, J. San Fabian, R.H. Contreras, Theoretical Karplus relationships for vicinal coupling constants around f in valine, Chem. Phys. 

A. Wu, D. Cremer, A.A. Auer, J. Gauss, Extension of the Karplus relationship for NMR spin-spin coupling constants to nonplanar ring systems pseudo rotation of cyclopentane, J. Phys. Chem. A 106 (2002) 657. 

It was also clear that the use of NMR required a different approach to problem solving than that typically used with NMR. While the latter technique could be employed with a very general approach (e.g., the Karplus equation), NMR would, at least for the immediate future, require a relatively extensive set of model systems from which the consequences of stereochemical changes could be derived for any given carbon framework. Indeed, our own research efforts required such a set of spectral data for model, monosubstituted systems and served as the impetus for the collection of the extensive data that will be found in Chapters 5-18. With this extensive data available in computer searchable form, we are beginning to assemble the equivalent of a Karplus relationship for y substituent effects in NMR and hope to make these findings available in the not too distant future. However, the origin of such effects is not at all well defined and the observed spectral shifts may be caused by the coincidence of several relatively independent factors. 

Within the limitations just described for the general application of the Karplus relationship, the best Karplus relationship for the nucleotide H3 -P coupling constants appears to be... 

Angular restraints are another important source of structural information. Several empirical relationships between scalar couplings and dihedral angles have been found during the last decades. The most important one is certainly the Karplus relation for -couplings. Another, relaxation-based angular restraint is the so-called CCR between two dipolar vectors or between a dipolar vector and a CSA tensor. 

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... 

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. 

The important fact is that the magnitude of Vab (e.g., between Ha and Hb in Figure 9.5) is (in addition to its dependence on y values and s-character effects) a function of the dihedral angle (6) between the nuclei. The Karplus equation (named for the discoverer of the relationship) for vicinal H-H coupling has the form... 

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.

As will be seen below, a case can be made that the Karplus relationship of the form 3Jqh = IT cos2< r may usefully apply for the coupling of an aglyconic carbon with the anomeric hydrogen. 

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