INDEX exchange coupled

Here the indices a and b stand for the valence orbitals on the two atoms as before, n is a number operator, c+ and c are creation and annihilation operators, and cr is the spin index. The third and fourth terms in the parentheses effect electron exchange and are responsible for the bonding between the two atoms, while the last two terms stand for the Coulomb repulsion between electrons of opposite spin on the same orbital. As is common in tight binding theory, we assume that the two orbitals a and b are orthogonal we shall correct for this neglect of overlap later. The coupling Vab can be taken as real we set Vab = P < 0. 

Fig. 6. Structural analysis of Vc 1.1 by NMR. (A) The aH secondary shifts. (B) Structural information from NOEs, chemical shift index (CSI), amide exchange, and scalar coupling, are summarized (adapted from ref. 58). (C) A stereoview of the 20 low-energy structures. Some residues are numbered for orientation. (D) Ribbon representation of the peptide the cysteine residues are in yellow. The N-terminus and C-terminus are marked N and C, respectively. (E) The surface of the peptide with selected residues labeled.

Equation (32) gives the phase of the vector in question for a single nucleus at the time of exchange. In the case of weakly coupled spin systems, this relationship remains valid and just has to be amended with index j (the value of tojP is either oofP or o>j depending on the parity of r). 

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