How tight is the Lieb-Oxford bound?

Density-functional theory requires ever better exchange-correlation (xc) functionals for the ever more precise description of many-body effects on electronic structure. Universal constraints on the xc energy are important ingredients in the construction of improved functionals. Here we investigate one such universal property of xc functionals: the Lieb-Oxford lower bound on the exchange-correlation energy, $E_{xc}[n] \ge -C \int d^3r n^{4/3}$, where $C\leq C_{LO}=1.68$. To this end, we perform a survey of available exact or near-exact data on xc energies of atoms, ions, molecules, solids, and some model Hamiltonians (the electron liquid, Hooke's atom and the Hubbard model). All physically realistic density distributions investigated are consistent with the tighter limit $C \leq 1$. For large classes of systems one can obtain class-specific (but not fully universal) similar bounds. The Lieb-Oxford bound with $C_{LO}=1.68$ is a key ingredient in the construction of modern xc functionals, and a substantial change in the prefactor $C$ will have consequences for the performance of these functionals.Comment: 10 pages, 3 figure

Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully non-empirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.Comment: v2: Major revison. Added information on relation to the gradient expansion and to local hybrids, improved discussion of size consistency and of performance relative to other functional

Induction of tumours by administration of N-dibutylnitrosamine and derivatives to infant mice.

Pulse doses of N-dibutylnitrosamine(DBN), N-butyl-N-(4-hydroxybutyl)nitrosamine(BBN) and N-butyl-N-(3carboxypropyl)nitrosamine(BCPN) suspended in 1% gelatin, were administered s.c. to infant CDF1 mice, and the experiment terminated at one year of age. Tumours were induced in lungs and liver. The incidences of lung adenomas were 73-95% in all treated mice, with no sex differences. Hepatocellular adenomas and a carcinoma were found with an incidence of 81% (21/26) in DBN, 59% (13/22) in BBN, and 32% (9/28) in BCPN-treated males and the incidence was 23% (5/22) in DBN-treated females. Only one papilloma of the fore-stomach was induced in mice treated with DBN. These results indicated that the s.c. administration of DBN, BBN, and BCPN induced tumours of the lung and liver, but no tumours of the urinary bladder, under these experimental conditions. The carcinogenic effect on mice at the treated dose level was DBN greater than BBN greater than BCPN

Effect of nonmagnetic impurities on stripes in high-Tc cuprates

We perform the numerically exact diagonalization study of the t-J model with nonmagnetic impurities to clarify the relation between Zn impurities and the stripes. By examining the hole-hole correlation function for a two-hole \sqrt{18}x\sqrt{18} cluster with a single impurity, we find that the impurity has a tendency to stabilize vertical charge stripes. This tendency is caused by the gain of the kinetic energy of holes moving along the stripes that are formed avoiding the impurity.Comment: 3 pages including 2 figures. Proceedings for ISS2000 (Tokyo, October 2000). To be published in Physica

Tightened Lieb-Oxford bound for systems of fixed particle number

The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a non-empirical tightening of that bound in both universal and electron-number-dependent form. The test functional is PBE. Regarding both atomization energies (slightly worsened) and bond lengths (slightly bettered), we find the PBE functional to be remarkably insensitive to the value of the Lieb-Oxford bound. This both rationalizes the use of the original Lieb-Oxford constant in PBE and suggests that enhancement factors more sensitive to sharpened constraints await discovery.Comment: six figures (color

Hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound: Implementation via local hybrids and thermochemical assessment

In 2009 Odashima and Capelle (OC) showed a way to design a correlation-only density functional that satisfies a Lieb-Oxford bound on the correlation energy, without empirical parameters and even without additional theoretical parameters. However, they were only able to test a size-inconsistent version of it that employs total energies. Here, we show that their alternative size-consistent form that employs energy densities, when combined with exact or semilocal exchange, is a local hybrid (lh) functional. We test several variants of this nonempirical OC-lh functional on standard molecular test sets. Although no variant yields enthalpies of formation with the accuracy of the semilocal Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation, OC-lh correlation with exact exchange yields rather accurate energy barriers for chemical reactions. Our purpose here is not to advocate for a new density functional, but to explore a previously published idea. We also discuss the importance of near-self-consistency for fully nonlocal functionals

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. Several of these variations are proposed here for the first time. On a test set of 60 solids we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding

Magnetic resonance peak and nonmagnetic impurities

Nonmagnetic Zn impurities are known to strongly suppress superconductivity. We review their effects on the spin excitation spectrum in $\rm YBa_2Cu_3O_{7}$, as investigated by inelastic neutron scattering measurements.Comment: Proceedings of Mato Advanced Research Workshop BLED 2000. To appear in Nato Science Series: B Physic