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We establish rigorous inequalities between different electronic properties linked to optical sum rules, and organize them into weak and strong bounds on three characteristic properties of insulators: electron localization length $\ell$ (the quantum fluctuations in polarization), electric susceptibility $\chi$, and optical gap $E_{\rm G}$. All-electron and valence-only versions of the bounds are given, and the latter are found to be more informative. The bounds on $\ell$ are particularly interesting, as they provide reasonably tight estimates for an ellusive ground-state property -- the average localization length of valence electrons -- from tabulated experimental data: electron density, high-frequency dielectric constant, and optical gap. The localization lengths estimated in this way for several materials follow simple chemical trends, especially for the alkali halides. We also illustrate our findings via analytically solvable harmonic oscillator models, which reveal an intriguing connection to the physics of long-ranged van der Waals forces.

High-resolution angle- and spin-resolved photoemission spectroscopy reveals new features of the electronic structure of the ferromagnetic triple-layered ruthenate Sr$_4$Ru$_3$O$_{10}$. There are narrow spectral peaks $\sim$30 meV below the Fermi-level in two regions of the Brillouin zone: a hole-like band at the zone-center and a saddle-point van Hove singularity at the zone edge. Below T$_c$ each feature is almost completely spin-polarized, with opposite sign polarization and with strong Kondo-coherence-like temperature-dependent spectral weight variation suggestive of strong Hund's metal correlations. In addition, there are distinct Fermi surfaces for wide electron-like minority spin bands around the zone center and narrow hole-like majority spin Fermi surface contours around the zone corners. The origin of these features is in general agreement with density functional calculations, if they are shifted to reduce the exchange splitting, and scaled to take into account effects of correlation. Furthermore, the deduced narrow band origins from the tri-layer splitting of $d_{xz/yz}$ orbitals implies a layer-specific spin-polarization contribution from the narrow bands. Over a larger energy range, net spin-majority polarization of incoherent Ru $d$-bands is observed to extend down to the top of the oxygen bands, where additional narrow oxygen bands contribute to the magnetism with spin-minority polarization., Comment: 11 pages, 5 figures plus supplement 8 pages, 4 figures

We report electronic band structure calculations for Sr$_{4}$Ru$_{3}$O$_{10}$ that displays both ferromagnetic and metamagnetic behavior. The density functional calculations find the ground state to be ferromagnetic in agreement with the experiment and we find that the inclusion of Coulomb Hubbard interaction U applied to the Ru 4d states has dramatic effects on the Fermi surface, which reveal the role of Coulomb interactions and correlated many-body physics. The minority spin bands are mainly empty with Fermi surfaces in the outer areas of the Brillouin zone away from the $\Gamma$ point with bands that disperse steeply upward. The majority spin bands are full or nearly fully occupied and form narrow bands near the Fermi energy around the $\Gamma$ point, which could be the electronic origin of the metamagnetism. The results are in qualitative agreement with recent angle resolved photoemission spectroscopy (ARPES) experiments and show the need for a combined theoretical study and experimental ARPES investigation with better energy resolution to reveal the nature of the narrow bands close to the Fermi-level, which is critical for understanding the exotic magnetic properties observed in this material.

Physical growth traits can be naturally represented by continuous functions. In a large dataset of infancy growth patterns, we develop a practical approach to infer statistical associations between growth-trajectories and IQ performance in early childhood. The main objective of this study is to show how to assess physical growth curves and detect if particular infancy growth patterns are associated with differences in IQ (Full-scale WASI scores) in later ages using a semi-parametric functional response model. Additionally, we investigate the association between different growth measurements in terms of their cross-correlation with each other, their correlation with later IQ, as well as their time-varying dynamics. This analysis framework can easily incorporate or learn population information in a non-parametric way, rendering the existence of prior population charts partially redundant.

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transformation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation., Comment: 25 pages, 6 figures

We compute the electrical conductivity for liquid hydrogen at high pressure using quantum Monte Carlo. The method uses Coupled Electron-Ion Monte Carlo to generate configurations of liquid hydrogen. For each configuration correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give AC electrical conductivity directly. The extrapolated DC conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data., Comment: 4 pages, 5 figures

Transport measurements of the two-dimensional electron gas (2DEG) at the LaAlO$_3$/SrTiO$_3$ interface have found a density of carriers much lower than expected from the "polar catastrophe" arguments. From a detail density-functional study, we suggest how this discrepancy may be reconciled. We find that electrons occupy multiple subbands at the interface leading to a rich array of transport properties. Some electrons are confined to a single interfacial layer and susceptible to localization, while others with small masses and extended over several layers are expected to contribute to transport., Comment: 4 pages, 7 figures, Accepted in Phys. Rev. Lett

By carrying out extensive lattice regularized diffusion Monte Carlo calculations, we study the spin and density dependence of the ground state energy for a quasi-one-dimensional electron gas, with harmonic transverse confinement and long-range $1/r$ interactions. We present a parametrization of the exchange-correlation energy suitable for spin density functional calculations, which fulfills exact low and high density limits., Comment: 9 pages, 3 figures, corrected Eq. 17, added new reference, submitted to J. Phys. A: Math. Theor. as proceedings of the SCCS2008 conference in Camerino, Italy

We calculate the momentum distribution of the Fermi liquid phase of the homogeneous, two-dimensional electron gas. We show that, close to the Fermi surface, the momentum distribution of a finite system with $N$ electrons approaches its thermodynamic limit slowly, with leading order corrections scaling as $N^{-1/4}$. These corrections dominate the extrapolation of the renormalization factor, $Z$, and the single particle effective mass, $m^*$, to the infinite system size. We show how convergence can be improved analytically. In the range $1 \le r_s \le 10$, we get a lower renormalization factor $Z$ and a higher effective mass, $m^*>m$, compared to the perturbative RPA values., Comment: 4 pages, 3 figures

We present a quantum Monte Carlo study of the hydrogen-benzene system where binding is very weak. We demonstrate that the binding is well described at both variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) levels by a Jastrow correlated single determinant geminal wave function with an optimized compact basis set that includes diffuse orbitals. Agreement between VMC and fixed-node DMC binding energies is found to be within 0.18 mHa, suggesting the calculations are well-converged with respect to the basis. Essentially the same binding is also found in independent DMC calculations using a different trial wave function of a more conventional Slater-Jastrow form, supporting our conclusion that the binding energy is accurate and includes all effects of correlation. We compare with empirical models and previous calculations, and we discuss the physical mechanisms of the interaction, the role of diffuse basis functions, and the charge redistribution in the bond., Comment: 12 pages, 4 figures

We present an approach to calculate total energies of nanoclusters based on first principles estimates. For very large clusters the total energy can be separated into surface, edge and corner energies, in addition to bulk contributions. Using this separation and estimating these with direct, first principles calculations, together with the relevant chemical potentials, we have calculated the total energies of Cu and CdSe tetrahedrons containing a large number of atoms. In our work we consider polyhedral clusters so that in addition our work provides direct information on relaxation. For Cu the effects are very small and the clusters vary uniformly from very small to very large sizes. For CdSe there are important variations in surface and edge structures for specific sizes; nevertheless, the approach can be used to extrapolate to large non-stoichiometric clusters with polar surfaces., Comment: 5 pages, 3 figures and 2 tables

We present a theoretical study of diluted magnetic semiconductors that includes spin-orbit coupling within a realistic host band structure and treats explicitly the effects of disorder due to randomly substituted Mn ions. While spin-orbit coupling reduces the spin polarization by mixing different spin states in the valence bands, we find that disorder from Mn ions enhances the spin polarization due to formation of ferromagnetic impurity clusters and impurity bound states. The disorder leads to large effects on the hole carriers which form impurity bands as well as hybridizing with the valence band. For Mn doping 0.01 < x < 0.04, the system is metallic with a large effective mass and low mobility.

We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon., Comment: 4 pages, 4 figures, submitted to PRL; corrected typos

Our it ab initio calculations show that spin-orbit coupling is crucial to understand the electronic structure of the Si(557)-Au surface. The spin-orbit splitting produces the two one-dimensional bands observed in photoemission, which were previously attributed to spin-charge separation in a Luttinger liquid. This spin splitting might have relevance for future device applications. We also show that the apparent Peierls-like transition observed in this surface by scanning tunneling microscopy is a result of the dynamical fluctuations of the step-edge structure, which are quenched as the temperature is decreased.

Using first-principles total-energy methods, we investigate Jahn-Teller distortions in III-V dilute magnetic semiconductors, GaAs:Mn and GaN:Mn in the cubic zinc blende structure. The results for an isolated Mn impurity on a Ga site show that there is no appreciable effect in GaAs, whereas, in GaN there is a Jahn-Teller effect in which the symmetry around the impurity changes from T$_{d}$ to D$_{2d}$ or to C$_{2v}$. The large effect in GaN occurs because of the localized d$^4$ character, which is further enhanced by the distortion. The lower symmetry should be detectable experimentally in cubic GaN with low Mn concentration, and should be affected by charge compensation (reductions of holes and conversion of Mn ions to d$^5$ with no Jahn-Teller effect). Jahn-Teller effect is greatly reduced because the symmetry at each Mn site is lowered due to the Mn-Mn interaction. The tendency toward ferromagnetism is found to be stronger in GaN:Mn than in GaAs:Mn and to be only slightly reduced by charge compensation., Comment: 6 pages, 3 figures

We present a theoretical study of diluted magnetic semiconductors that treats the local sp-d exchange interaction J between the itinerant carriers and the Mn d electrons within a realistic band structure and goes beyond previous mean-field approaches. In case of (Ga,Mn)As, we find that strong exchange potentials tightly bind carriers near impurity sites. Spin-orbit coupling is found to have a more pronounced effect on spin polarization at weak coupling and this feature can be exploited for magnetotransport. For low doping regime, we predict that spin-orbit coupling splits impurity bands and can induce a novel insulating phase., Comment: 4 pages, 5 figures

We present {\it ab initio} density-functional calculations of molecular solids formed from C$_{28}$-derived closed-shell fullerenes. Solid C$_{28}$H$_4$ is found to bind weakly and exhibits many of the electronic structure features of solid C$_{60}$ with an enhanced electron-phonon interaction potential. We show that chemical doping of this structure is feasible, albeit more restrictive than its C$_{60}$ counterpart, with an estimated superconducting transition temperature exceeding those of the alkali-doped C$_{60}$ solids., Comment: Lower quality postscript file for Figure 1 is used in the manuscript in order to meet submission quota for pre-print server. Higher quality postscript file available from author: naromero@alum.mit.edu This article has been updated to reflect changes incorporated during the peer review process. It is published in PRB 70, 140504(R) 2004

We have performed a density functional study of fifteen different structural models of the Si(557)-Au surface reconstruction. Here we present a brief summary of the main structural trends obtained for the more favourable models, focusing afterwards in a detailed description of the atomic structure, electronic properties and, simulated STM images of the most stable model predicted by our calculations. This structure is in very good agreement with that recently proposed from X-ray diffraction measurements by Robinson et al. [Phys. Rev. Lett. 88, (2002) 096194]., Comment: 12 pages, including two figures, in preprint format. Submitted to Surface Science on July 2002 (Proceedings of the ECOSS-21 conference)

We report on a general method for the calculation of the frequency-dependent optical response of clusters based upon time-dependent density functional theory (TDDFT). The implementation is done using explicit propagation in the time domain and a self-consistent program that uses a linear combination of atomic orbitals (LCAO). Our actual calculations employ the SIESTA program, which is designed to be fast and accurate for large clusters. We use the adiabatic local density approximation to account for exchange and correlation effects. Results are presented for the imaginary part of the linear polarizability, Im [\alpha(w)], and the dipole strength function, S(w), of C60 and Na8, compared to previous calculations and to experiment. We also show how to calculate the integrated frequency-dependent second order non-linear polarizability for the case of a step function electric field, \gamma_{step}(w), and present results for C60., Comment: 11 pages with 6 postscript figures. Submitted for publication

The ``14-1-11'' phase compounds based on magnetic Mn ions and typified by Ca14MnBi11 and Ba14MnBi11 show unusual magnetic behavior, but the large number (104) of atoms in the primitive cell has precluded any previous full electronic structure study. Using an efficient, local orbital based method within the local spin density approximation to study the electronic structure, we find a gap between a bonding valence band complex and an antibonding conduction band continuum. The bonding bands lack one electron per formula unit of being filled, making them low carrier density p-type metals. The hole resides in the MnBi4 tetrahedral unit and partially compensates the high spin d^5 Mn moment, leaving a net spin near 4 \mu_B that is consistent with experiment. These manganites are composed of two disjoint but interpenetrating `jungle gym' networks of spin 4/2 MnBi4^{9-} units with ferromagnetic interactions within the same network, and weaker couplings between the networks whose sign and magnitude is sensitive to materials parameters. Ca14MnBi11 is calculated to be ferromagnetic as observed, while for Ba14MnBi11 (which is antiferromagnetic) the ferro- and antiferromagnetic states are calculated to be essentially degenerate. The band structure of the ferromagnetic states is very close to half metallic., Comment: 17 pages, containing 10 postscript figures and 5 tables. Two additional figures (Fig.8 and 11 of the paper) are provided in JPG format in separate files. Submitted to Phys. Rev. B on September 20th 2001

The Si(557)-Au surface, containing monatomic Au wires parallel to the steps, has been proposed as an experimental realization of an ideal one-dimensional metal. In fact, recent photoemission experiments on this system (Nature 402, 504 (1999)) found two peaks that were interpreted in terms of the spin-charge separation in a Luttinger liquid. Our first-principles density functional calculations reveal two metallic bands associated with Au-Si bonds, instead of the single band expected from the Au 6s states, providing an alternative explanation for the experimental observations., Comment: 5 pages with 3 postscript figures. Submitted to PRL on May 10th 2001

The adsorption of C60 on Si(111) has been studied by means of first-principles density functional calculations. A 2x2 adatom surface reconstruction was used to simulate the terraces of the 7x7 reconstruction. The structure of several possible adsorption configurations was optimized using the ab initio atomic forces, finding good candidates for two different adsorption states observed experimentally. While the C60 molecule remains closely spherical, the silicon substrate appears quite soft, especially the adatoms, which move substantially to form extra C-Si bonds, at the expense of breaking Si-Si bonds. The structural relaxation has a much larger effect on the adsorption energies, which strongly depend on the adsorption configuration, than on the charge transfer., Comment: 4 pages with 3 postscript figures, to appear in Surf. Science. (proceedings of the European Conference on Surface Science ECOSS-19, Sept 2000)

Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (D). Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wavefunction and compared to results of previous work using exact diagonalization and Hartree-Fock. We find that the model undergoes a thermodynamic transition from a band insulator (BI) to a broken-symmetry bond ordered (BO) phase as the ratio of U/D is increased. Since it is known that at D = 0 the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed ionic potential (D) and (ii) decreasing D at fixed U. We find no transition from the BO to MI state, and we propose that the MI state in 1D is unstable to bond ordering under the addition of any finite ionic potential. In real 1D systems the symmetric MI phase is never stable and the transition is from a symmetric BI phase to a dimerized BO phase, with a metallic point at the transition.

We have constructed maximally-localized Wannier functions for prototype structures of solid molecular hydrogen under pressure, starting from LDA and tight-binding Bloch wave functions. Each occupied Wannier function can be associated with two paired protons, defining a ``Wannier molecule''. The sum of the dipole moments of these ``molecules'' always gives the correct macroscopic polarization, even under strong compression, when the overlap between nearby Wannier functions becomes significant. We find that at megabar pressures the contributions to the dipoles arising from the overlapping tails of the Wannier functions is very large. The strong vibron infrared absorption experimentally observed in phase III, above ~ 150 GPa, is analyzed in terms of the vibron-induced fluctuations of the Wannier dipoles. We decompose these fluctuations into ``static'' and ``dynamical'' contributions, and find that at such high densities the latter term, which increases much more steeply with pressure, is dominant., Comment: 17 pages, two-column style with 14 postscript figures embedded. Uses REVTEX and epsf macros

We have calculated the exchange, correlation, and total electronic energy of a realistic InAs self-assembled quantum dot embedded in a GaAs matrix as a function of the number of electrons in the dot. The many-body interactions have been treated using the local spin density approximation (LSDA) to density functional theory (DFT) and diffusion quantum Monte Carlo (DMC), so that we may quantify the error introduced by LSDA. The comparison shows that the LSDA errors are about 1-2 meV per electron for the system considered. These errors are small enough to justify the use of LSDA calculations to test models of self-assembled dots against current experimental measurements., Comment: 7 pages, 6 figures, to appear in Physica E

We study metallization of molecular hydrogen under pressure using exact exchange (EXX) Kohn-Sham density-functional theory in order to avoid well-known underestimates of band gaps associated with standard local-density or generalized-gradient approximations. Compared with the standard methods, the EXX approach leads to considerably (1 - 2 eV) higher gaps and significant changes in the relative energies of different structures. Metallization is predicted to occur at a density of >= 0.6 mol/cm^3 (corresponding to a pressure of >= 400 GPa), consistent with all previous measurements., Comment: 11 pages, 4 postscript figures

We study the Mott transition in Hubbard models with a degenerate band on different 3-dimensional lattices. While for a non-degenerate band only the half-filled system may exhibit a Mott transition, with degeneracy there can be a transition for any integer filling. We analyze the filling dependence of the Mott transition and find that $U_c$ (the Hubbard interaction $U$ at which the transition takes place) decreases away from half-filling. In addition we can change the lattice structure of the model. This allows us to study the influence of frustration on the Mott transition. We find that frustration increases $U_c$, compared to bipartite systems. The results were obtained from fixed-node diffusion Monte Carlo calculations using trial functions which allow us to systematically vary the magnetic character of the system. To gain a qualitative understanding of the results, we have developed simple hopping arguments that help to rationalize the doping dependence and the influence of frustration on the Mott transition. Choosing the model parameters to describe the doped Fullerides, we can make contact with experiment and understand why some of the Fullerides are metals, while others, which according to density functional theory should also be metallic, actually are insulators., Comment: 4 pages LaTeX with 4 eps figures; submitted to Computer Physics Communications, Proceedings of the CPP'99/Centennial Meeting, Atlanta, GA; additional material available at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene/

We describe the object-oriented implementation of a higher-order finite-difference density-functional code in Fortran 90. Object-oriented models of grid and related objects are constructed and employed for the implementation of an efficient one-way multigrid method we have recently proposed for the density-functional electronic-structure calculations. Detailed analysis of performance and strategy of the one-way multigrid scheme will be presented., Comment: 24 pages, 6 figures, to appear in Comput. Phys. Comm

We investigate the behavior of three-dimensional (3D) exchange-correlation energy functional approximations of density functional theory in anisotropic systems with two-dimensional (2D) character. Using two simple models, quasi-2D electron gas and two-electron quantum dot, we show a {\it fundamental limitation} of the local density approximation (LDA), and its semi-local extensions, generalized gradient approximation (GGA) and meta-GGA (MGGA), the most widely used forms of which are worse than the LDA in the strong 2D limit. The origin of these shortcomings is in the inability of the local (LDA) and semi-local (GGA/MGGA) approximations to describe systems with 2D character in which the nature of the exchange-correlation hole is very nonlocal. Nonlocal functionals provide an alternative approach, and explicitly the average density approximation (ADA) is shown to be remarkably accurate for the quasi-2D electron gas system. Our study is not only relevant for understanding of the functionals but also practical applications to semiconductor quantum structures and materials such as graphite and metal surfaces. We also comment on the implication of our findings to the practical device simulations based on the (semi-)local density functional method., Comment: 21 pages including 9 figures, to be published in Phys. Rev. B

We develop the theory and practical expressions for the full quantum-mechanical distribution of the intrinsic macroscopic polarization of an insulator in terms of the ground state wavefunction. The central quantity is a cumulant generating function which yields, upon successive differentiation, all the cumulants and moments of the probability distribution of the center of mass X/N of the electrons, defined appropriately to remain valid for extended systems obeying twisted boundary conditions. The first moment is the average polarization, where we recover the well-known Berry phase expression. The second cumulant gives the mean-square fluctuation of the polarization, which defines an electronic localization length xi_i along each direction i. It follows from the fluctuation-dissipation theorem that in the thermodynamic limit xi_i diverges for metals and is a finite, measurable quantity for insulators. It is possible to define for insulators maximally-localized ``many-body Wannier functions'', which for large N become localized in disconnected regions of the high-dimensional configuration space, establishing a direct connection with Kohn's theory of the insulating state. Interestingly, the expression for xi_i^2, which involves the second derivative of the wavefunction with respect to the boundary conditions, is directly analogous to Kohn's formula for the ``Drude weight'' as the second derivative of the energy., Comment: 25 pages and 3 postscript figures, to appear in Phys. Rev. B. Manuscript was made more concise and some new results were added (Section V-B)

We report density-functional studies of several small molecules ($H_{2}, N_{2}, CO, H_{2}O$, and $CH_{4}$) within the Krieger-Li-Iafrate (KLI) approximation to the exact Kohn-Sham local exchange potential, using a three-dimensional real-space finite-difference pseudopotential method. It is found that exchange-only KLI leads to markedly improved eigenvalue spectra compared to those obtained within the standard local-density approximation (LDA), the generalized gradient approximation (GGA), and the Hartree-Fock (HF) method. For structural properties, exchange-only KLI results are close to the corresponding HF values. We find that the addition of LDA or GGA correlation energy functionals to the KLI exact exchange energy functional does not lead to systematic improvements., Comment: 16 pages including 1 fugure, to be published in Phys. Rev. A Nov. 1 '99