Pairing theorems and Dewars PMO theory

Coulson and Rushbrooke have derived several theorems and corollaries for AHs,286 which may be summarized as follows  

HMOs with sj a (xy/O) occur in pairs with energies s j = a The HMOs of 

Nonbonding molecular orbitals (NBMOs) are MOs with an energy sj = a, Xj = 0. The number of NBMOs is at least equal to the absolute value of the difference between the numbers of atoms in the two sets. Thus odd AHs (AHs with an odd number of atoms) have at least one NBMO. 

NBMOs must be self-paired , i.e., their coefficients must vanish on one set of atoms 

The 7t-charge densities q of neutral AHs (Equation 4.9) are unity on all atoms /jl. 

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