Direct Minimization Generating Electronic States with Proper Occupation Numbers

We carry out the direct minimization of the energy functional proposed by Mauri, Galli and Car to derive the correct self-consistent ground state with fractional occupation numbers for a system degenerating at the Fermi level. As a consequence, this approach enables us to determine the electronic structure of metallic systems to a high degree of accuracy without the aid of level broadening of the Fermi-distribution function. The efficiency of the method is illustrated by calculating the ground-state energy of C$_2$ and Si$_2$ molecules and the W(110) surface to which a tungsten adatom is adsorbed.Comment: 4 pages, 4 figure

One-way multigrid method in electronic structure calculations

We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each finer level. The only changes compared to a single grid calculation are interpolation and orthonormalization steps outside the original total energy calculation and required only for transferring between grids. This feature results in a minimal amount of code change, and enables us to employ a sophisticated interpolation method and noninteger ratio of grid spacings. Calculations employing a preconditioned conjugate gradient method are presented for two examples, a quantum dot and a charged molecular system. Use of three grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication

Kohn Anomalies in Superconductors

I present the detailed behavior of phonon dispersion curves near momenta which span the electronic Fermi sea in a superconductor. I demonstrate that an anomaly, similar to the metallic Kohn anomaly, exists in a superconductor's dispersion curves when the frequency of the phonon spanning the Fermi sea exceeds twice the superconducting energy gap. This anomaly occurs at approximately the same momentum but is {\it stronger} than the normal-state Kohn anomaly. It also survives at finite temperature, unlike the metallic anomaly. Determination of Fermi surface diameters from the location of these anomalies, therefore, may be more successful in the superconducting phase than in the normal state. However, the superconductor's anomaly fades rapidly with increased phonon frequency and becomes unobservable when the phonon frequency greatly exceeds the gap. This constraint makes these anomalies useful only in high-temperature superconductors such as $\rm La_{1.85}Sr_{.15}CuO_4$.Comment: 18 pages (revtex) + 11 figures (upon request), NSF-ITP-93-7

Electron correlation in the Si(100) surface

Motivated by the controversy between quantum chemists and solid-state physicists, and by recent experimental results, spin-polarized density-functional (DFT) calculations are used to probe electron correlation in the Si(100) reconstructed surface. The ground state displays antiferromagnetic spin polarization for low dimer inclinations indicating, not magnetic order, but the importance of Mott-like correlations among dangling bonds. The lowest energy corresponds to a higher dimer inclination with no spin. DFT energies, however, should be taken with caution here. Our results together with quantum-chemical findings suggest dimers with highly correlated electrons that tend to buckle due to interactions with other dimers.Comment: 5 pages, 1 eps figure, 1 table; RevTeX v3.1. To appear in Surface Science (proceedings of the European Conference On Surface Science, ECOSS-19, Madrid, Sept. 5-8, 2000

DFT calculation of the intermolecular exchange interaction in the magnetic Mn4_4 dimer

The dimeric form of the single-molecule magnet [Mn$_4$O$_3$Cl$_4$(O$_2$CEt)$_3$(py)$_3$]$_2$ recently revealed interesting phenomena: no quantum tunneling at zero field and tunneling before magnetic field reversal. This is attributed to substantial antiferromagnetic exchange interaction between different monomers. The intermolecular exchange interaction, electronic structure and magnetic properties of this molecular magnet are calculated using density-functional theory within generalized-gradient approximation. Calculations are in good agreement with experiment.Comment: 4 page

Towards a Linear-Scaling DFT Technique: The Density Matrix Approach

A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.Comment: REVTeX file, 27 pages with 4 uuencoded postscript figure

Transformation elastodynamics and active exterior acoustic cloaking

This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with "torque springs", which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.Comment: Submitted as a chapter for the volume "Acoustic metamaterials: Negative refraction, imaging, lensing and cloaking", Craster and Guenneau ed., Springe

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc

Domain-swapped T cell receptors improve the safety of TCR gene therapy

T cells engineered to express a tumor-specific {alpha}{beta} T cell receptor (TCR) mediate anti-tumor immunity. However, mispairing of the therapeutic {alpha}{beta} chains with endogenous {alpha}{beta} chains reduces therapeutic TCR surface expression and generates self-reactive TCRs. We report a general strategy to prevent TCR mispairing: swapping constant domains between the {alpha} and {beta} chains of a therapeutic TCR. When paired, domain-swapped (ds)TCRs assemble with CD3, express on the cell surface, and mediate antigen-specific T cell responses. By contrast, dsTCR chains mispaired with endogenous chains cannot properly assemble with CD3 or signal, preventing autoimmunity. We validate this approach in cell-based assays and in a mouse model of TCR gene transfer-induced graft-versus-host disease. We also validate a related approach whereby replacement of {alpha}{beta} TCR domains with corresponding {gamma}{delta} TCR domains yields a functional TCR that does not mispair. This work enables the design of safer TCR gene therapies for cancer immunotherapy

A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters

We have studied the fragmentation of Li11+ clusters into the two experimentally observed products (Li9+,Li2) and (Li10+,Li) The ground state structures for the two fragmentation channels are found by Molecular Dynamics Simulated Annealing in the framework of Local Density Functional theory. Energetics considerations suggest that the fragmentation process is dominated by non-equilibrium processes. We use a real-space approach to solve the Kohn-Sham problem, where the Laplacian operator is discretized according to the Mehrstellen scheme, and take advantage of a Full MultiGrid (FMG) strategy to accelerate convergence. When applied to isolated clusters we find our FMG method to be more efficient than state-of-the-art plane wave calculations.Comment: 9 pages + 6 Figures (in gzipped tar file