Slater Determinants and the Pauling 3-Electron Bond

Although it is not needed for a reading of much of this book, it is useful here to elaborate further the discussion of the Pauli exclusion principle in order to forma- 

Our concern here is with orbital occupancies, and therefore this equivalence is appropriate whether or not atomic orbital overlap integrals are included in the normalization constants for the molecular orbitals. See Section 3-10 for a discussion on the inclusion of atomic orbital overlap integrals on the energies of Pauling 3-electron bonds . 

The Pauli exclusion principle (Section 3-4) requires that the total wave-function for an Welectron system be antisymmetric with respect to the interchange of the coordinates of any two electrons, i.e., 

For a two-electron atom or molecule, the total wave-function may be written as the product of a spatial wave-function with a spin wave-function, i.e. 

For the ground-state molecular orbital and Heitler-London valence bond wave-functions of Hj, the antisymmetrized product wave-functions are given by Eqs. (21) and (22) (cf Eqs. (10) and (11), with / =als = SA +Sb and a = 1 etc.). 

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