Publications

The optimized effective potential (OEP) is the exact Kohn-Sham potential for explicitly orbital-dependent energy functionals, e.g., the exact exchange energy. We give a proof for the OEP equation which does not depend on the chain rule for functional derivatives and directly yields the equation in its simplest form: a certain first-order density shift must vanish. This condition explains why the highest-occupied orbital energies of Hartree-Fock and exact exchange OEP are so close. More importantly, we show that the exact OEP can be constructed iteratively from the first-order shifts of the Kohn-Sham orbitals and that these can be calculated easily. The exact exchange potential ${v}_{\mathrm{x}}(\mathbf{r})$ for spherical atoms and three-dimensional sodium clusters is calculated. Its long-range asymptotic behavior is investigated, including the approach of ${v}_{\mathrm{x}}(\mathbf{r})$ to a nonvanishing constant in particular spatial directions. We calculate total and orbital energies and static electric dipole polarizabilities for the sodium clusters employing the exact exchange functional. Exact OEP results are compared to the Krieger-Li-Iafrate and local density approximations.

An expression for the contact density, or Fermi-surface electron probability density at the nucleus, is developed to first order in the pseudopotential for a metal with a spherical Fermi surface, and applied to solid alkali metals and liquid binary alkali alloys at all concentrations. The explicit orthogonalization of the pseudo-wave-functions to the ionic core states permits the use of a local empirical pseudopotential. The contact density samples the Fourier transform of the pseudopotential primarily in the region just above $2{k}_{F}$; consequently the large changes in ${k}_{F}$ which occur upon alloying in the alkali metals are dominant over the details of the ionic environment in determining the behavior of the contact density. The calculated contact densities, when combined with measured alloy Knight shifts, imply a unique and roughly free-electron-like dependence of the Pauli electron-spin susceptibility upon the interelectron spacing ${r}_{s}$ in the range $4.0<{r}_{s}<5.8$. The polarizability of the ions may introduce an effective value of ${r}_{s}$ in the range $3.8<r_{}^{*}{}_{s}{}^{}<4.6$. The deduced susceptibilities are consistent with a simple picture in which the electron-ion effective masses of Na, K, Rb, and Cs are close to unity; the susceptibilities agree in this picture with a recent analysis of the observed enhancement of the Korringa constant. The calculation is in some important respects insensitive to the choice of pseudopotentials, structure factors, and core-state wave functions. The temperature dependence and change upon melting of the Knight shift are also estimated, and the extension of the calculation to other metals is briefly discussed.

All wired up! High-quality colloidal PbS and CdS nanowires were grown from Bi nanoparticles by the solution–liquid–solid (SLS) mechanism. The single-source-precursor strategy could provide a general approach for the synthesis of colloidal semiconductor nanowires. Supporting information for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2002/2008/z705142_s.pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Received 9 December 2008DOI:https://doi.org/10.1103/PhysRevLett.101.269902©2008 American Physical Society

Abstract Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of “gold standard” coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.

On the Jacob’s Ladder of density functional approximations to the exchangecorrelation energy, each higher rung adds another local ingredient which can be used to satisfy further exact constraints. The rst rung is the local density approximation. The second rung or generalized gradient approximation (GGA) adds the gradient of the density. The third rung or meta-GGA further adds the Kohn-Sham orbital kinetic energy density. I will review the nonempirical construction of a recent meta-GGA [1] and its mostly-successful numerical tests for molecules [2,3] and solids [4].

We consider the energy needed to form a spherical hole or void in a simple metal, modeled as ordinary jellium or stabilized jellium. (Only the latter model correctly predicts positive formation energies for voids in high-density metals.) First we present two Hellmann-Feynman theorems for the void-formation energy 4\ensuremath{\pi}${\mathit{R}}^{2}$${\mathrm{\ensuremath{\sigma}}}_{\mathit{R}}^{\mathit{v}}$(n\ifmmode\bar\else\textasciimacron\fi{}) as a function of the void radius R and the positive-background density n\ifmmode\bar\else\textasciimacron\fi{}, which may be used to check the self-consistency of numerical calculations. They are special cases of more-general relationships for partially emptied or partially stabilized voids. The difference between these two theorems has an analog for spherical clusters. Next we link the small-R expansion of the void surface energy (from perturbation theory) with the large-R expansion (from the liquid drop model) by means of a Pad\'e approximant without adjustable parameters. For a range of sizes (including the monovacancy and its ``antiparticle,'' the atom), we compare void formation energies and cohesive energies calculated by the liquid drop expansion (sum of volume, surface, and curvature energy terms), by the Pad\'e form, and by self-consistent Kohn-Sham calculations within the local-density approximation, against experimental values. Thus we confirm that the domain of validity of the liquid drop model extends down almost to the atomic scale of sizes. From the Pad\'e formula, we estimate the next term of the liquid drop expansion beyond the curvature energy term. The Pad\'e form suggests a ``generalized liquid drop model,'' which we use to estimate the edge and step-formation energies on an Al (111) surface.

This dataset contains all VASP inputs and outputs for the paper "Improved Laplacian-level meta-GGA for the weakly-nonlocal solid and liquid metals." For the preprint, see arXiv:2203.09403, and for the reference densities, fitting routines, and analysis scripts, see the Gitlab code repository. Description of individual tarballs: AE6: 6-molecule set of atomization energies ferro: relaxed geometries and magnetic moments for the ferromagnetic solids Fe, Ni, and Co intermetallics: formation energies of three intermetallic solids, HfOs, ScPt, and VPt₂ LC20: relaxed geometries and equilibrium bulk moduli for the LC20 set of cubic solids. Equilibrium geometries by equation of state fit. Bandgaps for select insulators are included here. LC20_stress_tensor: same as LC20, but equilibrium geometries found by minimizing forces on unit cell computed with Laplacian-dependent stress tensor LC23: equilibrium geometries, bulk moduli, and cohesive energies for the LC23 set (LC20 + K, Rb, and Cs) found by equation of state fit. Bandgaps for select insulators are included here. Pt_monovac: monovacancy formation energies for Pt, computed in a few different ways described in the text