Publications

Material scientists and condensed matter physicists have long been divided on the issue of choosing the conceptual framework for explaining why open-shell transition-metal oxides tend to be insulators, whereas otherwise successful theories such as DFT often predict them to be (false) metals. Strong correlation becomes the recommended medicine. We point out that strong correlation can be mitigated by allowing DFT to lower the energy by breaking structural, magnetic or dipolar symmetries. Such local motifs are observed experimentally by local probes beyond the 'average structure' determined by X-Ray diffraction. Observed broken symmetries can arise from slow fluctuations that persist over the observation time or longer. The surprising fact is that when symmetry breaking motifs are used as input to electronic structure calculations, false metals are converted into real insulators without the recommended medicine of strong correlation. Consistently, DFT calculations that show energy lowering symmetry breaking correct most cases where DFT, even with advanced exchange-correlation functionals, previously missed the correct metal vs insulator designation. Total energy calculations distinguish systems that support energy-lowering symmetry breaking from those that do not. This approach distinguishes between paramagnetic insulating and metallic phases and shows mass enhancement in Mott metals. The reason is that symmetry breaking removes many of the degeneracies that exist in a symmetry-unbroken system, reducing significantly the need for strong correlation. If one chooses to ignore symmetry breaking, the persistent degeneracies often call for strong correlation treatment. Thus, symmetry breaking transforms strong to normal correlation and false metals to true insulators. This view sheds light on the historic controversy between Mott and Slater that still reverberates today.

In the general case, quantum-mechanical quantities are represented by operators in position- or momentum-space representations, but in phase space they are represented by functions. The correspondence between classical mechanics and quantum mechanics is non-unique as a consequence of [

Low-temperature synthesis of crystalline silicon and silicon-containing nanowires remains a challenge in synthetic chemistry due to the lack of sufficiently reactive Si precursors. We report that colloidal Si nanowires can be grown using tris(trimethylsilyl)silane or trisilane as the Si precursor by a Ga-mediated solution-liquid-solid (SLS) approach at temperatures of about 200 °C, which is more than 200 °C lower than that reported in the previous literature. We further demonstrate that the new Si chemistry can be adopted to incorporate Si atoms into III-V semiconductor lattices, which holds promise to produce a new Si-containing alloy semiconductor nanowire. This development represents an important step toward low-temperature fabrication of Si nanowire-based devices for broad applications.

Abstract Density functional theory (DFT) is now the most commonly used method of electronic structure calculation in both condensed matter physics and quantum chemistry, thanks in part to the focus it has received over the first 50 years of the Sanibel Symposium. We present a short history, and review fourteen short and easy but important lessons about nonrelativistic DFT, with some partiality but with a minimum of technical complication. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

How can the fundamental band gap of an insulator be predicted? As a difference of ground-state energies, the fundamental gap seems to fall within the reach of density functional theory, yet the predicted gaps from band structure calculations within the local density approximation (LDA) are about 40% too small. It is argued here that even the exact Kohn-Sham potential veff(r), which generates the exact density in a self-consistent-field calculation, generates a band structure which underestimates the gap. Within the context of the band gap problem, several recent developments in the density-functional theory of many-electron systems are reviewed: (1) The Langreth-Mehl approximation to the Kohn-Sham exchange-correlation energy and potential, based upon the Langreth-Perdew wavevector analysis of the density gradient expansion. This functional leads to more accurate ground-state energies and densities than those of the LDA with little change in the calculated band structures of solids. (2) The derivative discontinuity of the exchange-correlation energy, which is responsible for substantial underestimation of the fundamental gap by even the exact Kohn-Sham potential. (3) The self-interaction correction, which yields accurate gaps in insulators only by virtue of its orbital-dependent potential. (4) The density response function of the uniform electron gas, which suggests that the LDA gives a good estimate of the exact Kohn-Sham potential for a semiconductor with a weak periodic potential. In short, several very different (but admittedly approximate) numerical calculations suggest that most of the error in the LDA fundamental gap would persist in the gap of the exact Kohn-Sham band structure. This error would persist in any attempt to calculate the gap from LDA total energy differences for clusters of increasing size.

Expressions for the kinetic energy $T$ (and incidentally also for the exchange energy ${E}_{x}$) of a ground-state inhomogeneous electron gas as a functional of the electron density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, and for $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ as a functional of the one-electron potential $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, are readily generalized to the case of two unequal spin densities ${n}_{\ensuremath{\uparrow}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ and ${n}_{\ensuremath{\downarrow}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. As an example the authors consider the expansions of $T$ up to fourth order in the gradients of $n$, and of $n$ up to fourth order in the gradients of $V$. These expansions are tested for the extreme case of one- and two-electron atoms. It is found that (i) The $n[V]$ expansion contains serious pathologies, while the $T[n]$ expansion leads to much more reasonable results when applied to either the exact density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ or to an $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ obtained by minimization of the approximate total-energy functional $E[n]$. (ii) Good approximations to $E$ and $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ in one-electron atoms are obtained only when the complete spin polarization of a single electron is taken into account via $T[{n}_{\ensuremath{\uparrow}}, {n}_{\ensuremath{\downarrow}}]$. (iii) Within a variational calculation, the inclusion of second- and fourth-order gradient corrections to the zeroth-order (Thomas-Fermi) approximation for $T$ leads to systematic improvements in the analytic behavior of $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ near the nucleus. The authors also compare the local-exchange approximation with the local-exchange-correlation approximation in one- and two-electron atoms, and find that correlation should not be neglected.

Binding energy curves have been calculated for the ground-state rare-gas diatomics Ne(2) and Ar(2) and for the alkaline-earth diatomic Be(2) using the nonempirical density functionals from the first three rungs of a ladder of approximations: the local spin density (LSD) approximation, the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. Binding energy curves in reasonable agreement with those constructed from experiment are found from PBE and TPSS, which incorporate inhomogeneity corrections that satisfy the Lieb-Oxford bound and so describe the short-range part of the van der Waals interaction. At large internuclear separation, these functionals produce an exponentially decaying attraction in place of the correct long-range -C(6)/R(6). Basis-set and exchange-only effects are also discussed.

A new exchange and correlation functional, called ISIN here, of the fifth rung of Jacob’s ladder is presented. It is based on the explicit approximation of Wλ, the integrand in the adiabatic connection (AC) with λ representing the coupling constant. Besides utilizing the two leading terms of each asymptotic expansion of Wλ at λ = 0 and ∞, the ISIN extends the coupling constant λ to negative values (i.e., to attractive electron−electron interactions). For the simple system of two electrons on the surface of a sphere (2ESS), the correlation energies yielded by the ISIN are in excellent agreement with the exact values. However, the ISIN seriously fails to approximate Wλ when W0′, the slope at λ = 0, goes to −∞, which leads to much more negative correlation energies for real systems.