Abstract
It is argued that the matrix PS is to be considered as the proper linear combination of atomic orbitals (LCAO) representation of the first-order density matrix, P and S being the usual molecular “density matrix” and the overlap matrix, respectively. This conclusion is in line with the fact that Hermitian operators are represented by non-Hermitian matrices if an overlapping basis is used. (The matrix representation of an operator is to be distinguished from the matrix of its integrals.) The diagonal elements of the matrix PS are Mulliken's gross orbital populations and the elements of this matrix are also necessary to define the bond order between a pair of atoms and the actual total and free valences of an atom in a molecule.
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