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4PI2,but not of 9,’. This is because either ,s2 = 1 or s2 = 0 can couple with s1 = 1 to give S = 1. Rather than containing a pure contribution from st = 1 or s2 = 0, the YK functions O2 and O3 contain mixtures of both. D. Practicality of Spin-Coupling Techniques The genealogical construction of spin functions is inconvenient because it is recursive. In order to make an N-electron spin function, one must first generate every predecessor in the genealogical scheme. It can be seen from the branching diagrams that the complexity of the problem increases rapidly with N .

References . . . . . ' . . . . . 64 67 69 70 72 72 74 76 79 81 83 83 85 87 92 I. Introduction A. Indistinguishability of Electrons Electrons are identical in the sense that no experiment can tell them apart. This implies that expectation values are independent of any electron numbering scheme. Suppose that Y( 1, 2, . . , N ) is the exact wavefunction (a solution of the Schrodinger equation) for an N electron system, and that P is any of the N ! permutations of the electrons. Then for any observable operator W , (PY(1,2,.

But a more interesting case arises when the two sets N and N' of equivalent nuclei can be exchanged by a symmetry operation s. : ss,,s-' = s,,,, and it can be said that the operation s conjugates S,, and S,,, . The appropriate NMR symmetry group G is the semidirect product (Serre, 1967) (represented by the symbol w ) of the invariant subgroup S,, x S,,, and a subgroup of two elements, 1 and s: G = (S,, x S,,,) Y (1, s). In general there is more than one operation exchanging the two sets Nand N' and the subgroup (1, s) is not an invariant subgroup of the total groups.