Robert A. Donnelly

Bio: Robert A. Donnelly is an academic researcher. The author has contributed to research in topics: Shape resonance & Propagator. The author has an hindex of 6, co-authored 6 publications receiving 2667 citations.

Electronegativity: The density functional viewpoint

Abstract: 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.

Elementary properties of an energy functional of the first‐order reduced density matrix

Abstract: 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 partiall...

Complex coordinate rotation of the electron propagator

Abstract: 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(iΘ), to G(E) yields an analytically continued complex propagator G(Z, Θ) 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.

On a fundamental difference between energy functionals based on first‐ and on second‐order density matrices

Abstract: 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 Lowdin’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 Lowdin’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=−e−J/2, where e is an eigenvalue of th...

Second‐order propagator calculation of a doublet P Mg shape resonance

Abstract: We report several calculations on the doublet P shape resonance in the Mg atom by use of a second‐order, complex‐scaled electron propagator. The results agree with experiment within experimental error, and these are attained within quite small basis sets. Rules for construction of the complex scaled self‐energy are given. The diagrammatic expansion corresponds to that for a system in a scaled external potential.

Self-interaction correction to density-functional approximations for many-electron systems

Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Density-functional theory of atoms and molecules

Abstract: Current studies in density functional theory and density matrix functional theory are reviewed, with special attention to the possible applications within chemistry. Topics discussed include the concept of electronegativity, the concept of an atom in a molecule, calculation of electronegativities from the Xα method, the concept of pressure, Gibbs-Duhem equation, Maxwell relations, stability conditions, and local density functional theory.

Conceptual density functional theory.

Abstract: I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

Density Functional Theory of Electronic Structure

Abstract: Density functional theory (DFT) is a (in principle exact) theory of electronic structure, based on the electron density distribution n(r), instead of the many-electron wave function Ψ(r1,r2,r3,...). Having been widely used for over 30 years by physicists working on the electronic structure of solids, surfaces, defects, etc., it has more recently also become popular with theoretical and computational chemists. The present article is directed at the chemical community. It aims to convey the basic concepts and breadth of applications: the current status and trends of approximation methods (local density and generalized gradient approximations, hybrid methods) and the new light which DFT has been shedding on important concepts like electronegativity, hardness, and chemical reactivity index.