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.

The Hohenberg–Kohn theorem implies the existence of an energy functional based solely on the first-order reduced density matrix of the ground state of an atomic or molecular system. Application of the variational principle for the functional EvM[γ] generates a set of coupled Euler equations for the representation coefficients and spin orbitals of a rank-M approximation to the exact ground-state density matrix. Defining the (assumed Hermitian) kernel FM[γ;x′,x]≡δEvM/δγ (x,x′), the equations in an arbitrary representation for the approximate density matrix, γ (x,x′) =ΣijMψ1(x) γijψj* (x′) are the following: ℱdξFM[γ;x′,ξ]ψi(ξ) =μψi(x′); i=1, 2,...,M; ℱdξFM[γ;x′,ξ] ΣMiψi(ξ) γ ij=ΣMiψi(x′) λij; j=1, 2, ...,M. The quantity μ is the chemical potential of the system of interest and the λij are a set of M2 Lagrange multipliers constraining the orthonormality of the spin orbital basis {ψ}. The coefficients γij must be chosen such that FM has the degenerate eigenvalue spectrum, FiiM=μ, i=1, 2,...,M, for all partially occupied orbitals. The spin orbitals, for a fixed set of coefficients, must be simultaneously determined so that λ is Hermitian. Provided all occupation numbers lie on the open interval (0,1), the stationary density matrix itself obeys the eigenvalue equation ℱdξFM[γ;x,ξ]γ (ξ,x′) =μγ (x,x′), and for any stationary density matrix the following commutation rules are valid: [FM[γ], γ]=0; [λ, γ]=0. The matrices γ and λ consequently can be brought simultaneously to diagonal form, and the canonical representation of the energy functional provides an eigenvalue equation determining the natural spin orbitals. The value of the chemical potential is μ=εi/ni, i=1, 2, ...,M; ε=diag (λ); from which follows the distribution function governing the occupation numbers of a stationary density matrix. Two limiting forms of the variational principle are examined, the exact and Hartree–Fock functionals, and related previous work by Gilbert is discussed. The physical content of the equations is illuminated by identification of the chemical potential as the negative of the electronegativity; Sanderson’s Principle of Electronegativity Equalization follows.

It is now widely appreciated that the real poles of the electron propagator G(E) yield information on the ionization potentials and electron affinities of the stationary states of an atom or molecule. It is herein shown that application of the Aguilar-Balslev-Combes-Simon coordinate transformation, r-r exp(i8), to G(E) yields an analytically continued complex propagator G(Z, 8) whose complex poles correspond to the complex electron affinities associated with nonstationary, resonance states of an atomic or molecular anion. As an initial application of the coordinate rotation technique we derive and discuss the working equations for a coordinate rotated propagator which is correct to second order in the electron-electron interaction. This is followed by use of the formalism in a model study of a 2p shape resonance in the Be atom. Our second-order results for this system are then compared to those obtained by previous authors employing static exchange, and static-exchange plus cutoff polarization methods.

The Euler equations and kernel F[γ] of an energy functional of the first-order density matrix are compared to the corresponding quantities which result from Löwdin’s treatment of the extended Hartree–Fock equations (the latter are based on an energy functional ▪v dependent on the second-order density matrix). Comparison of the functionals Ev and ▪v, facilitated by transformation of Löwdin’s kernel to the Hermitian kernel ▪[γ] which is central to the extended Koopmans’ theorem, leads to a clarification of the fundamental difference between ionization and chemical potentials. A definition of chemical potential (electronegativity) appropriate to Hartree–Fock theory is proposed. Denoting the Fock operator by the symbol FN[γ;x′,x], this definition is μ=−χ=ℱℱdxdx′ FN[γ;x′,x] [∂γ (x,x′)/∂N]. This reduces, in the special case of a system with a single valence electron, to a measure of the Hartree–Fock electronegativity proposed originally by Mulliken and by Moffitt; namely χ=−ε−J/2, where ε is an eigenvalue of the Fock operator, and J is a Coulomb integral evaluated for the canonical valence orbital χN.

This article reports the results of a calculation in the doublet pi shape resonance occurring near I .70 eV for the carbon monoxide molecule. The method employed is coordinate rotation as applied to the second-order electron propagator. We have obtained results for the resonance energy within a small Gaussian molecular basis set which are in substantial agreement with experiment. The width of this state is less-well represented by the small basis employed in the calculation.