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R G Parr

Publications and source records attributed to R G Parr.

15 recordsLinked to original sources
PubMed2001

Variational principles for describing chemical reactions. Reactivity indices based on the external potential.

In a recent paper [J. Am. Chem. Soc. 2000, 122, 2010], the authors explored variational principles that help one understand chemical reactivity on the basis of the changes in electron density associated with a chemical reaction. Here, similar methods are used to explore the effect changing the external potential has on chemical reactivity. Four new indices are defined: (1) a potential energy surface that results from the second-order truncation of the Taylor series in the external potential about some reference, Upsilon(R(1),R(2),.,R(M)()); (2) the stabilization energy for the equilibrium nuclear geometry (relative to some reference), Xi; (3) the flexibility, or "lability", of the molecule at equilibrium, Lambda; and (4) the proton hardness, Pi, which performs a role in the theory of Brönsted-Lowry acids and bases that is similar to the role of the chemical hardness in the theory of Lewis acids and bases. Applications considered include the orientation of a molecule in an external electric field, molecular association reactions, and reactions between Brönsted-Lowry acids and bases.

Journal Article↗
PubMed2000

Information theory, atoms in molecules, and molecular similarity.

Using information theory, it is argued that from among possible definitions of what an atom is when it is in a molecule, a particular one merits special attention. Namely, it is the atom defined by the "stockholders partitioning" of a molecule invented by Hirshfeld [(1977) Theor. Chim. Acta 44, 129]. The theoretical tool used is the minimum entropy deficiency principle (minimum missing information principle) of Kullback and Liebler [(1951) Ann. Math. Stat. 22, 79]. A corresponding analysis is given of the problem of assessing similarity between molecules or pieces of molecules.

Journal Article↗
PubMed1986

Thomas-Fermi theory for atomic systems.

The classical Thomas-Fermi theory of the electrons in an atom is amended in a manner that produces continuity of the electron density rho. This is done by imposing the constraint that e(-2kr) [unk](2) rho dr should be finite, with k determined by the nuclear cusp condition, followed or preceded by an optimum coordinate scaling. Electron densities and total energies are shown to be vastly improved.

Journal Article↗
PubMed1985

Electronegativity and hardness as coordinates in structure stability diagrams.

With electronegativity and hardness of an atom defined as 1/2(I + A) and 1/2(I - A), respectively, where I and A are the ionization potential and electron affinity, electronegativity difference and hardness sum are proposed as coordinates in structure stability diagrams. With these coordinates a successful topological classification of the crystal structures of octet and suboctet binary compounds is obtained, and a clear delineation of the structural classes portraying chemical periodicity is found.

Crystallography↗
PubMed1985

Hardness, softness, and the fukui function in the electronic theory of metals and catalysis.

The concepts of hardness eta = (2E/N2)nu and fukui function f(r) = [rho (r)/N]nu, which have recently been associated with the theory of chemical reactivity in molecules, are extended to the theory of metals. It is shown that at T = 0, 1/eta = g(epsilon F) and f(r) = g(epsilon F, r)/g(epsilon F), where g(epsilon F), and g(epsilon F, r) are the density of states and the local density of states, at the Fermi energy epsilon F. Softness S and local softness s(r) are defined as 1/eta and Sf(r), respectively, and it is shown that (formula; see text) where the averages are over a grand canonical ensemble. It is pointed out that the postulate that f(r) or g(epsilon F, r) determines site selectivity for metals in chemisorption and catalysis is synonymous with the recent argument by Falicov and Somorjai [Falicov, L. M. & Somorjai, G. A. (1985) Proc. Natl. Acad. Sci. USA 82, 2207-2211] that such selectivity is determined by low-energy density fluctuations.

Chemical Phenomena↗
PubMed1984

Transcription of ground-state density-functional theory into a local thermodynamics.

The concepts of local temperature, local entropy, and local free energy density are introduced within the framework of the ground-state density-functional theory of many-electron systems, and a complete local thermodynamic picture is then developed. A view emerges of the electron cloud, as analogous to a classical inhomogeneous fluid moving under gradients of temperature, pressure, and an effective potential, described by a locally Maxwellian distribution.

Kinetics↗
PubMed1982

Circulant orbitals and the electron-correlation problem.

Circulant, as well as canonical, orbitals are used in the different orbitals for different spins method for treating electron correlation. Circulant orbitals provide a theoretical justification for the use of a single parameter, even when the canonical orbitals have widely different orbital energies. Illustrative calculations on the ground state of the Be atom show the importance of choosing the correct "pairs" in the method. A two-parameter version of the conventional method gives 74% of the improvement obtained by a full configuration-interaction treatment using 20 linear parameters, while a one-parameter linear combination of two different coupling schemes of the circulant method gives approximately 61%. The latter wavefunction provides a compact description of the electron correlation.

Journal Article↗
PubMed1981

The kinetic energy change on covalent bond formation.

Stimulated by an analysis of the classical molecular orbital and valence bond descriptions of the two-electron normal covalent bond (both faulty), the argument is made that there exist good representations of the kinetic energy change DeltaT, on nonpolar covalent bond formation in a diatomic molecule, of the form DeltaT(R) = integralF(R - r')S(r')dr'. Here F is a nonlinear response function which itself involves the overlap S. The kinetic change is known to satisfy the sum rule integral(0) (infinity)DeltaT(R)dR = Z(alpha)Z(beta) exactly; it is shown how this can be built into the treatment by the use of Fourier transform methods. Also considered is integral(0) (infinity)DeltaT(R)R(2)dR, which is an important additional property of the kinetic energy change. Representation of DeltaT(R) as a Morse function, already known to be highly accurate, is shown to exactly conform to the proposed form.

Journal Article↗
PubMed1981

Circulant orbitals for atoms and molecules.

Circulant orbitals varphi(n) for a closed-shell system are the orbitals obtained when the N canonical orthonormal Hartree-Fock orbitals lambda([unk]) are subjected to a unitary transformation which is the discrete Fourier transformation: varphi(n) = 1/ radicalN Sigma([unk])lambda([unk])omega((n-1)([unk]-1)), where omega = exp(2pii/N). Electron densities associated with the orbitals varphi(n) are each close to the average total electron density. The Fock matrix, diagonal for canonical orbitals, for circulant orbitals is a Hermitian circulant matrix, epsilon(m, m+q) = 1/N Sigma([unk])epsilon([unk])omega(q([unk]-1)), where the epsilon([unk]) are the canonical orbital energies. The states ;Fvarphi(n) are uniformly distributed on the surface of a sphere in Hilbert space.

Journal Article↗
PubMed1980

Chemical potential, Teller's theorem, and the scaling of atomic and molecular energies.

FOR ATOMS AND HOMONUCLEAR DIATOMIC MOLECULES, IT IS ARGUED THAT THE ELECTRONIC ENERGIES HAVE THE FORMS [FORMULA: see text] and [Formula: see text] [Formula: see text], respectively,where Z is the atomic number, N is the number of electrons, and R is the internuclear distance. By using the Lieb-Simon theorem that the Thomas-Fermi theory is exact in the limit of large atomic number and the Teller theorem that molecules are not bound in the Thomas-Fermi theory, it is then shown, among other results, that the electron-electron repulsion energy for neutral systems has no term in Z(2) and that the nucleus-nucleus repulsion energy for neutral molecules is probably [unk](Z(5/3)). For neutral atoms, it is predicted and verified that the chemical potential (electronegativity) is [unk](Z(-1/3)) for large Z. Tetrahedral and octahedral molecules are briefly discussed.

Journal Article↗
PubMed1980

An atomic kinetic energy functional with full Weizsacker correction.

A functional is proposed for representing the electronic kinetic energy of the ground state of an N-electron atom or ion in terms of its electron density, [Formula: see text] Here T(w) is the Weizsacker quantity ((1/8))integral(nablarho.nablarho/rho)dtau and T(0) is the Thomas-Fermi quantity C(F) integral rho(5 / 3)dtau. From Hartree-Fock data on 55 neutral atoms, C = 1.412 +/- 0.033; for 1200 atoms and ions, C = 1.332 +/- 0.053. The proposed functional gives the derivative deltaT/deltarho its most important correct properties. The term T(w) is shown to give the kinetic energy of the K shell, whereas the term (C/N((1/3)))T(0) gives an incorrect statistical estimate of that energy. An alternative correction -(C/N((1/3)))T gives even better results.

Journal Article↗
PubMed1979

Local density functional theory of atoms and molecules.

A LOCAL DENSITY FUNCTIONAL THEORY OF THE GROUND ELECTRONIC STATES OF ATOMS AND MOLECULES IS GENERATED FROM THREE ASSUMPTIONS: (i) The energy functional is local. (ii) The chemical potential of a neutral atom is zero. (iii) The energy of a neutral atom of atomic number Z is -0.6127 Z(7/3). The energy functional is shown to have the form [Formula: see text] where A(0)=6.4563 and B(0)=1.0058. The first term represents the electronic kinetic energy, the second term represents the electron-electron repulsion energy for N electrons, and the third term is the nucleus-electron attraction energy. The energy E and the electron density rho are obtained and discussed in detail for atoms; their general properties are described for molecules. For any system the density becomes zero continuously at a finite distance from nuclei, and contours of the density are contours of the bare-nuclear potential v. For an atomic species of fractional charge q = 1 - (N/Z), an energy formula is obtained, [Formula: see text] which fits Hartree-Fock energies of 625 atoms and ions with root-mean-square error of 0.0270. A more general local density functional involving a coefficient B(N) = B(0)N(2/3) + B(1) is briefly considered.

Journal Article↗