Recently Joyce J. Kaufman put forward the hypothesis that for the equilibrium configuration of a molecular system the total overlap population should have a maximum [ 11. Similar criteria for molecular energies and geometries have also been used by Mortimer [2] and Quinn and McCann [3]. Since the evidence for Kaufman's criterion consists of extended Huckel calculations [4,5] it is of some interest to note that the criterion is identical to the ordinary Huckel energy criterion-that the sum of occupied orbital energies should have a minimum-for a very special case, i.e. when the diagonal elements of the effective Hamiltonian are all equal.With the expansion of the molecular orbitals C$i in the basis system {xk} given by where N is the number of electrons. I t is convenient to split the density matrix into two parts R(l) and R(2). R ( l ) is chosen diagonal and can be thought of *