Proton hyperfine coupling and conformation

The contact hyperfine shift contains information on conformational arrangements because it is somehow related to chemical bonds. The information, however, is generally hidden, with the exception of few cases. For example, if we have a CH moiety of an sp3 carbon bound to an sp2 carbon which bears spin density in the pz orbital, we have already seen that a spin density of the same sign is transferred to the methyl protons (Section 2.3.2). A mechanism to originate spin density at the methyl proton is the direct overlap between the sp2 carbon pz and the Is hydrogen orbital [51-54] (Fig. 2.14). Such overlap depends on the dihedral angle between the pz(axis)-C-C plane and the C-C-H plane (Fig. 2.14). The relationship is described by the general Karplus equation [55] 

Q values (MHz) for fragments involved in n electron spin delocalization systems  

In the case of Fe4S2+ clusters it has indeed been found that the contact shifts of the PCH2 protons of coordinated cysteines depend on 0 as 

The relative values of the c and a constants give an idea of the importance of the two processes of electron delocalization, through M—D o and D jt bonds, the latter being dominant. 

In the case of blue proteins there is a plane with Cu(II), two histidine nitrogens and one cysteine sulfur, with the x and y directions defined as in Fig. 2.16A. The dx2 y2 orbital contains the unpaired electron. The sulfur donor atom has a ir orbital which overlaps the dx2 y2 orbital (Fig. 2.16(B)). Large downfield shifts are observed (see also Chapter 5), and again the angular dependence of the shifts of the CH2 protons is expected to be mainly of sin2 type [61]. 

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