A simple formalism for the evaluation of 〈S2〉 in terms of the two-particle density matrix is presented. The implementation of the formalism in the restricted open-shell Hartree–Fock (ROHF), unrestricted HF (UHF) and density functional (DFT) based theories is discussed. Rules governing the nonzero S2 matrix elements in the UHF based methods are presented. Further examples are given of 〈S2〉 in several atomic and radical systems from very simple density functional models.

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The dependence of net atomic charges, as derived from least‐squares fitting to electrostatic potentials, on molecular orientation and potential site location is critically examined. A unique rotationally invariant algorithm, in which the charges may be constrained to reproduce the molecular dipole moment, is presented and the results for several basis sets compared to previous work. Significant improvements in dipole moments derived from the unconstrained charges are noted.

The Laplacian of the spherically averaged charge density ∇2ρ̄(r) has been computed from nonrelativistic SCF wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium, in order to examine the shell structure. ∇2ρ̄(r) exhibits a number of extremal points and zeros with the absolute value of the function becoming smaller at each successive extremal point. The zeros, in particular the odd numbered zeros, are shown to exhibit good correlation with the Bohr theory of an atom while the extremal points correlate to a lesser extent. At most five shells are seen in the studied atomic cases based on the fact that the odd numbered zeros are the topological feature of ∇2ρ̄(r) most indicative of a shell.