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Precision is given to the concept of electronegativity. It is the negative of the chemical potential (the Lagrange multiplier for the normalization constraint) in the Hohenberg–Kohn density functional theory of the ground state: χ=−μ=−(∂E/∂N)v. Electronegativity is constant throughout an atom or molecule, and constant from orbital to orbital within an atom or molecule. Definitions are given of the concepts of an atom in a molecule and of a valence state of an atom in a molecule, and it is shown how valence-state electronegativity differences drive charge transfers on molecule formation. An equation of Gibbs–Duhem type is given for the change of electronegativity from one situation to another, and some discussion is given of certain relations among energy components discovered by Fraga.

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is shown to be the universal functional for the electron-electron repulsion energy of an N-representable trial first-order density matrix y, where the actual external potential may be nonlocal as well as local. These universal functions do not require that a trial function for a variational calculation be associated with a ground state of some external potential: Thus, the v-representability problem, which is especially severe for trial firstorder density matrices, has been solved. Universal variational functionals in Hartree-Fock and other restricted wavefunction theories are also presented. Finally, natural spin-orbital functional theory is compared with traditional orbital formulations in density functional theory. This paper addresses the problem of generating adequate representations of the electronic structure of atoms, molecules, and solids without explicit recourse to many-particle wavefunctions. Instead, electron densities and first-order density matrices (one-matrices) are used directly for ground-state variational calculations. Densities and one-matrices are computationally attractive because their dimensions are smaller than those of the full wavefunctions.Formal justification for utilizing the three-dimensional electron density directly in variational calculations arises from the important theorems of Hohenberg and Kohn (1)

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