Publications

Zahariev and Wang [Phys. Rev. A, 70, 042503 (2004)] discuss the density functional theory of noninteger average particle numbers. Among their many results is one we dispute: that the exact exchange-correlation potential (more precisely, the exact functional derivative of the exchange-correlation energy with respect to the density) cannot have a discontinuity as the particle number crosses an integer, in contradiction to works by two of us (J.P.P. and M.L.) in collaboration with co-workers [Phys. Rev. Lett. 49, 1691 (1982); Phys. Rev. Lett.51, 1884 (1983)] and by Sham and Schl\"uter [Phys. Rev. Lett. 51, 1888 (1983)]. We point to a counterexample to Zahariev and Wang's claim, which two of us (E.S. and J.P.P.) have presented in a separate paper: A rigorous proof that, in the absence of external magnetic fields, the exchange-correlation potential jumps by the difference between the ionization potential $(I)$ and electron affinity $(A)$ when the particle number crosses 1, given that $I\ensuremath{\geqslant}A$. We point out that Zahariev and Wang's derivation neglects an order-of-limits problem. We also prove that $I>A$ for any one-electron system in the absence of magnetic fields.

For a spherical metallic cluster of large radius R, the total energy is E=\ensuremath{\alpha}4\ensuremath{\pi}${\mathit{R}}^{3}$/ 3+\ensuremath{\sigma}4\ensuremath{\pi}${\mathit{R}}^{2}$+\ensuremath{\gamma}2\ensuremath{\pi}R, the chemical potential is \ensuremath{\mu}=-W-c/R, and the first ionization energy I and electron affinity A are -\ensuremath{\mu}\ifmmode\pm\else\textpm\fi{}1/2(R+d). By solving the Euler equation within the Thomas-Fermi-Dirac-Gombas-Weizs\"acker-4 approximation for jellium spheres with up to ${10}^{6}$ electrons, we extract the surface energy \ensuremath{\sigma}, curvature energy \ensuremath{\gamma}, work function W, and constants c and d. The constant c is not zero, but neither is it -1/8, the prediction of the image-potential argument. We trace c to the second- and fourth-order density-gradient terms in the kinetic energy, which are present even in systems with no image potential. However, the constant d is found to be the distance from a planar surface to its image plane. In the absence of shell-structure oscillations, the asymptotic forms hold accurately even for very small clusters; this fact suggests a way to extract the curvature energy of a real metal from its surface and monovacancy-formation energies. We also discuss asymptotic ${\mathit{R}}^{\mathrm{\ensuremath{-}}1}$ corrections to the electron density profile and electrostatic potential of a planar surface.

The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] obeys all 17 known exact constraints for meta-generalized-gradient approximations (meta-GGAs), and it includes some medium-range correlation effects. Long-range London dispersion interactions are still missing, but they can be accounted for via an appropriate correction scheme. In this study, we combine SCAN with an efficient London dispersion correction and show that lattice energies of simple organic crystals can be improved with the applied correction by 50%. The London-dispersion corrected SCAN meta-GGA outperforms all other tested London-dispersion corrected meta-GGAs for molecular geometries. Our method yields mean absolute deviations (MADs) for main group bond lengths that are consistently below 1 pm, rotational constants with MADs of 0.2%, and noncovalent distances with MADs below 1%. For a large database of general main group thermochemistry and kinetics ($\ensuremath{\sim}800$ chemical species), one of the lowest weighted mean absolute deviations for long-range corrected meta-GGA functionals is achieved. Noncovalent interactions are of average quality, and hydrogen bonded systems in particular seem to suffer from overestimated polarization related to the self-interaction error of SCAN. We also discuss some consequences of numerical sensitivity encountered for meta-GGAs.

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

Modern meta-GGAs based on the local kinetic energy density can predict properties of diverse systems with near experimental accuracy, but unexpectedly describe properties of metallic solids poorly due to their underestimation of screening in metals. In this work, the authors replace the kinetic energy dependence of a sophisticated meta-GGA with an approximation based on the electronic density gradient and Laplacian. This Laplacian-level meta-GGA is tested on a diverse set of solid-state properties: geometries, cohesive energies, bulk moduli, ferromagnetic moments, monovacancy formation energies, and formation enthalpies. Most deficiencies of the parent meta-GGA in describing metals are remedied with its Laplacian-level variant.

Gradient corrections to the local spin density (LSD) approximation for the exchange-correlation energy are making density functional theory as useful in quantum chemistry as it is in solid-state physics. But which of the many gradient-corrected density functionals should be preferred a priori? We make a graphical comparison of the gradient dependencies of some popular approximations, discussing the exact formal conditions which each obeys and identifying which conditions seem most important. For the exchange energy, there is little formal or practical reason to choose among the Perdew-Wang 86, Becke 88, or Perdew-Wang 91 functionals. But, for the correlation energy, the best formal properties are displayed by the nonempirical PW91 correlation functional. Furthermore, the real-space foundation of PW91 yields an insight into the character of the gradient expansion which suggests that PW91 should work especially well for solids. Indeed, while improving dissociation energies over LSD, PW91 remains the most “local” of the gradient-corrected exchange-correlation functionals and, thus, the least likely to overcorrect the subtle errors of LSD for solids. To show that our analysis of spin-unpolarized functionals is sufficient, we also compute spin-polarization energies for atoms, finding PW91 values only slightly more negative than LSD values. © 1996 John Wiley & Sons, Inc.

The extra-electron binding energies of the ground-state monatomic negative ions with $Z<86$ are calculated using the self-interaction correction (SIC) to the local spin-density approximation (LSD) for exchange and correlation. The results agree reasonably with experiment, and the errors reflect the familiar "interconfigurational energy error" common to LSD and SIC. Some of the rare earths, e.g., Ce and possibly Gd, are predicted to form stable negative ions. In addition we have the following: (1) Relativistic (other than spin-orbit) contributions to the electron affinities are included and discussed. In Au the relativistic effects boost the calculated affinity from 1.5 to 2.5 eV. (2) The doubly negative ions ${\mathrm{O}}^{2\ensuremath{-}}$ and ${\mathrm{Te}}^{2\ensuremath{-}}$ are predicted to have no stable ground state. (3) Electron affinities are calculated for a few excited atomic states. (4) The calculated ground-state densities $n(r)$ of all the neutral atoms and negative ions are monotonically decreasing functions of $r$. (5) Corrections to the random-phase-approximation electron-gas correlation energy are shown to cancel out of SIC calculations for atoms.

Research Article| January 01, 2010 Density Functional Theory of Electronic Structure: A Short Course for Mineralogists and Geophysicists John P. Perdew; John P. Perdew Department of Physics and Engineering Physics Tulane University New Orleans, Louisiana 70118, U.S.A., perdew@tulane.edu Search for other works by this author on: GSW Google Scholar Adrienn Ruzsinszky Adrienn Ruzsinszky Department of Physics and Engineering Physics Tulane University New Orleans, Louisiana 70118, U.S.A., perdew@tulane.edu Search for other works by this author on: GSW Google Scholar Reviews in Mineralogy and Geochemistry (2010) 71 (1): 1–18. https://doi.org/10.2138/rmg.2010.71.1 Article history first online: 09 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation John P. Perdew, Adrienn Ruzsinszky; Density Functional Theory of Electronic Structure: A Short Course for Mineralogists and Geophysicists. Reviews in Mineralogy and Geochemistry 2010;; 71 (1): 1–18. doi: https://doi.org/10.2138/rmg.2010.71.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyReviews in Mineralogy and Geochemistry Search Advanced Search Mineralogists and geophysicists need to understand and predict the properties of solids and liquids at normal and especially at high pressures and temperatures. For example, they need to know the equilibrium structure, equation of state, phase transitions, and vibrational properties of solids, and the interatomic or intermolecular interaction needed for a molecular dynamics study of liquids (Stixrude et al. 1994; Soederlind and Ross 2000; Karki et al. 2001; Alfè et al. 2002; Steinle-Neumann et al. 2004; Sha and Cohen 2006; Carrier et al. 2007). This information, in sufficient detail, is not always... You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Solid, liquid and alloyed phases of gallium play a role in a variety of important technological applications. While many of the gallium phases involved in these applications are metallic, some have been proposed or are known to contain covalently bound Ga dimers. Thus, understanding the nature of bonding in Ga is crucial to the development of Ga-based materials. The solid phase of gallium at ambient conditions, <i>α</i>-Ga, is metallic and composed of molecular dimers, and can serve as a testing ground for studying gallium bonding with electronic structure calculations. We use density functional theory-based molecular dynamics simulations in conjunction with maximally localised Wannier functions to examine the nature of chemical bonding in <i>α</i>-Ga. We propose a geometric criterion for defining various bonding environments, which enables the quantification of covalent and weak bonds in solid gallium. We additionally connect the bonding structure of <i>α</i>-Ga to its phonon density of states and discuss similarities and differences with diatomic halogen crystals.