We argue that when one divides a molecular property into atom‐in‐a‐molecule contributions, one should perform the division based on the property density of the quantity being partitioned. This is opposition to the normal approach, where the electron density is given a privileged role in defining the properties of atoms‐in‐a‐molecule. Because partitioning each molecular property based on its own property density is inconvenient, we design a reference‐free approach that does not (directly) refer atomic property densities. Specifically, we propose a stockholder partitioning method based on relative influence of a molecule's atomic nuclei on the electrons at a given point in space. The resulting method does not depend on an “arbitrary” choice of reference atoms and it has some favorable properties, including the fact that all of the electron density at an atomic nucleus is assigned to that nucleus and the fact all the atoms in a molecule decay at a uniform asymptotic rate. Unfortunately, the resulting model is not easily applied to spatially degenerate ground states. Furthermore, the practical realizations of this strategy that we tried here gave disappointing numerical results. © 2017 Wiley Periodicals, Inc.

We review information on methods for constructing the exact density functional mathematically and computationally. While it is generally accepted that no explicit analytic form for the exact functional exists, we argue, based on what is known about the classical many-body problem, that this is not necessarily the case.

International Journal of Quantum ChemistryVolume 1, Issue S1 p. 163-165 Article Remark on the analytical form of Isorbitals in atoms and molecules John H. Weare, John H. Weare Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland Sonneborn Fellow, 1966–1967.Search for more papers by this authorRobert G. Parr, Robert G. Parr Department of Chemistry, The Johns Hopkins University, Baltimore, MarylandSearch for more papers by this author John H. Weare, John H. Weare Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland Sonneborn Fellow, 1966–1967.Search for more papers by this authorRobert G. Parr, Robert G. Parr Department of Chemistry, The Johns Hopkins University, Baltimore, MarylandSearch for more papers by this author First published: 16/21 January 1967 https://doi.org/10.1002/qua.560010617Citations: 4 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume1, IssueS1Supplement: Proceedings of the International Symposium on Atomic, Molecular, and Solid-State Theory16/21 January 1967Pages 163-165 RelatedInformation

International Journal of Quantum ChemistryVolume 12, Issue S11 p. 29-37 Article Erich Hückel and Friedrich Hund—Pioneers in quantum chemistry† Robert G. Parr, Robert G. Parr Department of Chemistry, University of North Carolina. Chapel Hill, North Carolina 27514, U. S. ASearch for more papers by this author Robert G. Parr, Robert G. Parr Department of Chemistry, University of North Carolina. Chapel Hill, North Carolina 27514, U. S. ASearch for more papers by this author First published: 16/22 January 1977 https://doi.org/10.1002/qua.560120808 † Delivered January 16, 1977, at 1977 Sanibel International Symposium in honor of W. Heitler, F. Hund, and E. Hückel. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume12, IssueS11Supplement: Proceedings of the International Symposium on Atomic, Molecular, and Solid‐state Theory, Collision Phenomena, and Computational Methods16/22 January 1977Pages 29-37 RelatedInformation

International Journal of Quantum ChemistryVolume 7, Issue S7 p. 123-126 Article The scientific contributions of S. F. Boys Robert G. Parr, Robert G. Parr Department of Chemistry, Johns Hopkins University, Baltimore, MarylandSearch for more papers by this author Robert G. Parr, Robert G. Parr Department of Chemistry, Johns Hopkins University, Baltimore, MarylandSearch for more papers by this author First published: 21/27 January 1973 https://doi.org/10.1002/qua.560070717AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume7, IssueS7Supplement: Proceedings of the International Symposium on Atomic, Molecular and Solid-State Theory and Quantum Biology21/27 January 1973Pages 123-126 RelatedInformation

In the density-functional theory of chemical reactivity, the local hardness is known to be an ambiguous concept. The mathematical structure associated with this problematic situation is elaborated and three common definitions for the local hardness are critically examined: the frontier local hardness [S. K. Ghosh, Chem. Phys. Lett. 172, 77 (1990)], the total local hardness [S. K. Ghosh and M. Berkowitz, J. Chem. Phys. 83, 2976 (1985)], and the unconstrained local hardness [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000)]. The frontier local hardness has particularly nice properties: (a) it has smaller norm than most, if not all, other choices of the local hardness and (b) it is "unbiased" in an information-theoretic sense. For the ground electronic state of a molecular system, the frontier local hardness is equal to the global hardness. For an electronic system in its ground state, both the chemical potential and the frontier local hardness are equalized. The frontier local hardness equalization principle provides a computational approach for designing reagents with desirable chemical reactivity profiles.

Higher-order global softnesses, local softnesses, and softness kernels are defined along with their hardness inverses. The local hardness equalization principle recently derived by the authors is extended to arbitrary order. The resulting hierarchy of equalization principles indicates that the electronegativity/chemical potential, local hardness, and local hyperhardnesses all are constant when evaluated for the ground-state electron density. The new equalization principles can be used to test whether a trial electron density is an accurate approximation to the true ground-state density and to discover molecules with desired reactive properties, as encapsulated by their chemical reactivity indicators.

Ground-state atomic correlation energies, and their kinetic energy and potential energy components, are shown to be well-represented by empirical formulas of the form CN rho(0)Z(-gamma), where C and gamma are constants that are largely invariant within various sets of atoms and positive ions, Z is the atomic number, N is the number of electrons, and rho(0) is the electron density at the nucleus. Results are given for neutral atoms, singly charged positive ions, and many isoelectronic series-315 atomic species in all.

A comprehensive analysis is presented for the acid-base double-exchange reaction as well as the associated acid-displacement and base-displacement “half-reactions” with the goal of elucidating the meaning of the hard/soft acid/base (HSAB) principle and the conditions for its validity. When electron-transfer effects are important and other effects are negligible, the HSAB principle is driven by the surpassing stability of the soft acid/soft base product. When electrostatic effects dominate the reactivity, the HSAB principle is driven by the surpassing stability of the hard acid/hard base product. Because electron-transfer effects favor soft/soft interactions, while electrostatic effects favor hard/hard interactions, acid-base exchange reactions may be used to determine whether a reagent’s reactivity is dominated by electron-transfer or by electrostatic effects. Because electron-transfer and electrostatic considerations separately favor the HSAB principle whenever the electronic chemical potentials of the acids and bases involved in the reaction are similar, our analysis provides strong support for the HSAB principle. The electronic chemical potential measures the intrinsic strength of acids and bases.

Revealed are scaling properties for T(c)[rho], the kinetic-energy component of the correlation energy density functional for atoms, in terms of the total number of electrons N, the nuclear charge Z, and the total electron density at the nucleus rho(0). T(c) scales well as Nrho(0)/Z(8/3) for both neutral atoms up to Z=18 and the four-electron Be-like cationic species. A model is given that describes these findings, involving a density encoding the cusp information and an effective potential going like r(-4/3).

Motivated by recent work on asymptotic correct exchange-correlation potentials, this paper investigates properties of the Fermi-Amaldi model for the exchange-correlation potential. It compares atomic excitation energies for Hydrogen through Argon to orbital energy differences computed using the exact Kohn-Sham potential and the Fermi-Amaldi approximation to the Kohn-Sham potential. While the Fermi-Amaldi model is not a particularly good model for the exchange-correlation energy, its eigenvalue spectrum is semi-quantitatively correct for alkali metals and alkaline earths. However, it is not accurate for p-block atoms, which suggests that the Fermi-Amaldi model may not be a superior choice for asymptotically correcting exchange-correlation potentials. It is suggested that asymptotic correction involving the Fukui function would give better results.