Robert G. Parr

Electronegativity: The density functional viewpoint

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.

A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II

The theory of electronic spectra and electronic structure, the elucidation of which was begun in the first paper of this series, is further developed and applied to ethylene, butadiene, benzene, pyridine, pyrimidine, pyrazine, and s‐triazine.A realistic and consistent LCAO‐MO π‐electron theory should allow the σ‐electrons to adjust themselves to the instantaneous positions of the mobile π‐electrons. This is accomplished in the theory by assignment of empirical values to the Coulomb electronic repulsion integrals and Coulomb penetration integrals which enter the formulas, these values being obtained in a prescribed way from valence state ionization potentials and electron affinities of atoms. Use of the empirical values in the molecular orbital theory reduces the magnitude of computed singlet‐triplet splittings and the effects of configuration interaction without complicating the mathematics. From the valence‐bond point of view, ionic structures may be said to be enhanced.The applications to hydrocarbons a...

Density-functional theory of the electronic structure of molecules.

Recent fundamental advances in the density-functional theory of electronic structure are summarized. Emphasis is given to four aspects of the subject: (a) tests of functionals, (b) new methods for determining accurate exchange-correlation functionals, (c) linear scaling methods, and (d) developments in the description of chemical reactivity.

New alternative to the Dunham potential for diatomic molecules

A new systematic procedure for constructing potential curves for diatomic molecules is developed. The procedure is similar to the well‐known Dunham method, except that the expansion parameter is (R‐Re)/R instead of (R‐Re)/Re. The new expansion, which has a formal theoretical basis, is shown to be superior in terms of both rate of convergence and region of convergence. It is shown how the expansion coefficients may be obtained from spectroscopic data, and the proper behavior of the potential at large R is shown to allow one to determine additional coefficients and to determine dissociation energies. To illustrate the method, the ground states of hydrogen flouride and carbon monoxide are treated. Possible extensions to polyatomic molecules are briefly discussed.

Electron density, Kohn–Sham frontier orbitals, and Fukui functions

In this note we shall show that the ground-state electron density \(\rho ({\mathbf r})\) is a functional of the highest occupied orbital in Kohn–Sham (Phys Rev 140:A1133, 1965, [1]) theory, \(\psi _{\mathrm {max}}\). The functionals \(\rho [\psi _{\mathrm {max}}]\) for an \((M+\delta )\)-electron system are resolved into three cases and connected to three Fukui functions defined by Parr and Yang (J Am Chem Soc, 106(14):4049, 1984, [2]).

Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities

Hardness and softness kernels η(r,r’) and s(r,r’) are defined for the ground state of an atomic or molecular electronic system, and the previously defined local hardness and softness η(r) and s(r) and global hardness and softness η and S are obtained from them. The physical meaning of s(r), as a charge capacitance, is discussed (following Huheey and Politzer), and two alternative ‘‘hardness’’ indices are identified and briefly discussed.

Calculation of ionization potentials from density matrices and natural functions, and the long‐range behavior of natural orbitals and electron density

Given an exact eigenfunction ψ for some system with N electrons, a procedure is developed for determining ionization potentials of the system to various states of the corresponding system having N−p electrons. The long−range behavior of the electron density and of the natural spin orbitals is shown to involve a set of eigenvalues which are obtained by this procedure. Following is the procedure. First determine the pth−order natural functions for ψ, Xm(p), and their occupation numbers nm(p), by diagonalization of the pth−order density matrix Γ(p). Calculate the quantities where ? ≡ (x1x2⋅⋅⋅xp) and ?ξ ≡ (ξ1ξ2⋅⋅⋅ξp). Then diagonalize the Hermitian matrix μ(p)kl = λ(p)kl / (n(p)kn(p)l)1/2. The resultant eigenvalues μα(p) are approximations to the negative of the p−electron ionization potentials of the system, with successive μα(p) (from the highest to the lowest) being lower bounds to the negative successive p−electron ionization potentials (from the lowest to the highest). For an approximate eigenfunction ?,...

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

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...

Theory of Separated Electron Pairs

Electron pairs in a molecule are said to be separated if (i) the molecular electronic wave function is accurately expressible as an antisymmetrized product of individual pair wave functions, and (ii) the individual pair functions are mutually exclusive in the sense that if all pair functions are linearily expressed in terms of Slater determinants built from some orthogonal one‐electron spin orbitals, no spin orbital enters the description of more than one pair function. It is shown that the electronic energy of a system of separated electron pairs may be written in a particularly simple form, and the problem of determining the best separated electron‐pair description of a particular molecule is discussed.The best orbital description of an electron‐pair bond is defined to be the best wave function for the pair that can be built from two atomic orbitals, one on each of two atoms. Systematic adjustment of individual pair descriptions one at a time is shown to provide a rigorous yet practicable procedure for ...

Molecular Orbital Calculations of the Lower Excited Electronic Levels of Benzene, Configuration Interaction Included

The lower excited π‐electron levels of benzene are calculated by the non‐empirical method of antisymmetrized products of molecular orbitals (in LCAO approximation) including configuration interaction. All configurations arising from excitation of one or two electrons from the most stable configuration are considered, and all many‐center integrals are retained. The results are in better agreement with experiment and valence‐bond calculations than those obtained previously by Craig in a calculation neglecting many‐center integrals. Configuration interaction is found to change the order of the 1B1u and 1E2g states but leave unchanged the order of the 3B1u and 3B2u states, in agreement with the assignments 1A1g—3B1u and 1A1g—1E2g for the experimental bands at 3.8 and 6.2 ev.