Session H31: Focus Session: Simulation of Complex Materials II

Persistent Current and Drude Weight in Mesoscopic Rings

We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a DMRG algorithm for complex fields. We find that the persistent current changes from an algebraic to an exponential decay with the system size, as the system crosses from the Luttinger Liquid (LL) to the Charge Density Wave (CDW) phase with increasing interaction $U$. We also find that in the interacting system the persistent current is invariant under the impurity transformation $\rho\rightarrow 1/\rho $, for large system sizes, where $\rho $ is the defect strength. In the LL phase the Drude weight decreases algebraically with the number of lattice sites $N$, due to the interplay of the electron interaction with the impurity, while in the CDW phase it decreases exponentially, defining a localization length which decreases with increasing interaction and impurity strength. Our results show that the impurity and the interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit $N\rightarrow\infty $, in both phases.   

Applying Time-dependent DMRG to Calculate the Conductance of Nanostructures

DMRG provides a powerful tool to study quantum 1D systems. We present a detailed procedure for applying the recently developed time-dependent DMRG to calculate the conductance of nanostructures, such as quantum dots (QD's). The leads are modelled using tight-binding Hamiltonians. The ground state at time zero is calculated at zero bias. Then a small bias is applied between the two leads, the wave-function is evolved in time and the current is measured as a function of time. Typically, the current saturates at a steady state after a short period of time. The conductance is obtained from the steady-state current. To test this approach We study several cases of interacting and non-interacting systems. Our results show excellent agreement with the exact results in the non-interacting case. We also reproduce quantitatively the well-established results in the case of one interacting QD and two coupled interacting QD's. [1] K. A. Al-Hassanieh {\it et al}, in preparation. [2] Steven R. White and Adrian E. Feiguin, Phys. Rev. Lett. {\bf 93}, 076041 (2004).   

Structural and electronic properties of solvated benzene and hexafluorobenzene from \textit{ab initio} simulations

We have studied the aqueous solvation of benzene and hexafluorobenzene using extensive first principles molecular dynamics simulations. By employing a rigid water approximation [1], we have been able to efficiently address long time-scale simulations ($\sim $100 ps) within a first-principles context. Our analysis of radial, spatial and tilt angle distribution functions of first shell water molecules reveals structural details in the axial and equatorial regions of the solute. In particular, we have identified strong orientational ordering near the faces of the rings and cage-like spacial structures in the equatorial regions. The structural properties of the first solvation shell lead to subtle changes in the electronic structure of water, e.g. changes in dipole moments. [1] M. Allesch, et al. J. Chem. Phys. 120, 5192 (2004) This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

Boron: do we know the ground state structure?

Boron is only the fifth element in the periodic table, having a simple electronic configuration, yet, it is known to form one of the most complicated crystal structures, $\beta$-rhombohedral structure. Up to date, the best estimate on the number of atoms in its hexagonal unit cell is 320.1, not even an integer number. The key concept to understand its complexity is covalency and electron deficiency: It does not have enough valence electrons to form a simple covalent crystal, like carbon or silicon. Instead it forms a complicated packing of icosahedrons. The structural model of $\beta$-boron was developed in the 1960s based on X-ray experiment. Although this model structure captures the most of the structural characteristics of $\beta$-boron, it has a crucial pitfall; the number of atoms per cell estimated by X-ray experiment does not agree with the number of atoms estimated by the pycnometric density. In 1988, Slack et al. discovered four more POS, by which the discrepancy in the number of atoms is reconciled [J. of Solid State Chem. 76, 52 (1988)]. There still remains an unanswered question; how are these POS atoms configured? Is it completely random? Or there is some kind of order as it has been suggested in Slack’s paper? A major challenge here is the astronomical number of possible configurations, roughly 150 million even for the irreducible cell. We tackle this problem using {\it ab-initio} simulated annealing coupled with a Lattice Model Monte Carlo simulated annealing. Our results reveal that the stable structure, indeed, has a certain type of correlation in its POS configuration. More detail on the structural property and its impact on electronic property of $\beta$-boron will be discussed at the presentation. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/ LLNL under contract no. W-7405-Eng-48.   

First principles thermodynamics studies on the surface structures of Pt-alloy catalyst as a function of the surface segregation, co-adsorption and particle size

Segregation in alloy catalysts can be significantly affected by the chemical environments. Using density functional theory coupled to the cluster expansion technique we study how adsorption of chemical species and bulk alloying change the surface structures and hence reactivity of Pt. We find that chemical adsorbates (O, OH, CO and water etc,) can change surface segregation energy of alloy elements dramatically in both bulk and nano-sized Pt. It implies that the interactions between adsorbates and surface atoms are important to understand the surface morphology and catalyst activities. We also find that Pt oxide (Pt-O or Pt-OH) has a higher reactivity to CO oxidation than pure Pt. On the other hands, Ru alloying on the Pt surface without adsorbates enhances the CO adsorption on Pt. We also investigate the effect of nanoparticle size of the on surface segregation and CO oxidation.   

Structural and Vibrational Properties of Boron Nitride Analogues of Diamondoids

Diamondoids are stable cage-like hydrocabon molecules that possess a structure that is superimposable upon the diamond crystal. These highly symmetric structures have a generic structural formula C$_{4n+6}$H$_{4n+12}$, and they have been isolated from petroleum oil. Because of their various shapes and sizes, there has been speculation in the literature that diamondoids might be suitable building blocks for possible applications in nanotechnology. One could ask whether boron nitride (BN) analogues of diamondoids might exist. It is known experimentally that cyclotriborazane (B$_{3}$N$_{3}$H$_{12})$, the BN-analogue of the smallest diamondoid molecule adamantane exists, but there is no experimental evidence for the existence of higher-order BN-diamondoids at the present time. In this work we perform accurate all-electron density-functional theory (DFT) calculations to study the structural and vibrational properties of a small set of lower order BN-diamondoids (e.g. BN-adamantane (B$_{6}$N$_{4}$H$_{16})$, BN-diamantane (B$_{7}$N$_{7}$H$_{20})$, BN-triamantane (B$_{10}$N$_{8}$H$_{24})$, and BN-\textit{anti}-tetramantane (B$_{11}$N$_{11}$H$_{24}))$. We discuss the relative stability of each of these representative BN-diamondoid molecules and provide theoretical infrared and Raman spectra for future identification of this novel class of molecules.\newline *This work was supported by the National Science Foundation and the Office of Naval Research.   

High quality molecular dynamics simulation of carbon nanotubes in

Biological applications of carbon nanotubes (CNTs) rely on mechanical, electrical, and chemical interactions between CNTs and biomolecules in water. Efficient computational methods for such nanoscale disordered systems have been developed that take into account the electronic degree of freedom of the CNTs interacting with biological media with thousands of atoms. For this purpose we combined in a molecular dynamics program an empirical CNT model employing a tight-binding CNT Hamiltonian with a classical description of the biological medium (water, ions, protein, DNA). The first application of this new method [1,2] described a potassium ion-CNT complex [3] and revealed a terahertz frequency oscillation of the ion inside a 16 angstrom long CNT segment. At a greatly reduced computational expense, our result showed good agreement with a Car-Parrinello molecular dynamics simulation. [1] D. Lu, Y. Li, U. Ravaioli, and K. Schulten. J. Phys. Chem. B, 109 (2005)11461. [2] D. Lu, Y. Li, S. V. Rotkin, U. Ravaioli, and K. Schulten. Nano Lett., 4 (2004)2383. [3] D. Lu, Y. Li, U. Ravaioli, and K. Schulten. Phys. Rev. Lett., (2005) in press.   

Realistic, quantitative descriptions of electron-transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics

A general approach to calculate the diabatic surfaces for electron-transfer reactions is presented, based on first-principles molecular dynamics of the active centers and their surrounding medium. The excitation energy corresponding to the transfer of an electron at any given ionic configuration (the Marcus energy gap) is accurately assessed within ground-state density-functional theory via a novel penalty functional for oxidation-reduction reactions that appropriately acts on the electronic degrees of freedom alone. The self-interaction error intrinsic to most exchange-correlation functionals is also corrected using the same penalty functional. The free-energy diabatic surfaces are then constructed with umbrella sampling on large ensembles of configurations. As a paradigmatic case study, the self-exchange reaction between ferrous and ferric ions in water is studied in detail.   

Role of Interfaces and Effect of Impurities in Nitride-based Superhard Nanocomposites

Recently, a hardness similar to that of diamond has been reported for the ternary nitride-based nanocomposite, $nc$-TiN/ $a$-Si$_{3}$N$_{4}$/$a$- and $nc$-TiSi$_2$ [1]. The reproducibility, however, has proved difficult, as has the superhardness of the related, prototypical, binary nanocomposite $nc$-TiN/$a$-Si$_{3}$N$_{4}$. Extensive density- functional theory calculations indicate that the hardness enhancement in the latter system is due to the preferential formation of TiN(111) polar interfaces with a thin Si-layer which is N-coordinated and tetrahedrally bonded [2]. The tensile strength of TiN in the [111] direction is very similar to the weakest bonding direction in diamond. Oxygen impurities cause a significant reduction of the interface strength which could partly explain the conflicting results, and signals the importance of avoiding such contaminants for achieving super- and ultra-hard nanocomposites.\\ $[1]$ S. Veprek et al. Surf. Coat. Technol. 133-134, 152 (2000).\\ $[2]$ S. Hao, B. Delley, and C. Stampfl, to be published.   

Spectral functions of fullerene molecules and solids

There have been lots of interests in producing and engineering the fullerene materials, either because of their highly symmetric molecular geometry, the discovery of superconductivity in doped C60 materials, or their potential applications in nano devices. In this talk I will report some Quantum Monte Carlo/exact diagonalization calculations of the single-particle spectral properties on the Hubbard C20 molecule and its possible lattices. Similar calculations on the C36 and C60 materials may also be presented.   

Static Polarizabilities of Nanoclusters

In the present work, we evaluate the static polarizability of a cluster using a microscopic method that is exact within the linear and dipolar approximations. Numerical examples are presented for various shapes and sizes of clusters composed of identical atoms, where the term ``atom'' actually refers to a generic constituent, which could be any polarizable entity. The results for the clusters' polarizabilities are compared with those obtained by assuming simple additivity of the constituents' atomic polarizabilities; in many cases, the difference is large, demonstrating the inadequacy of the additivity approximation. Comparison is made (for symmetrical geometries) with results obtained from continuum models of the polarizability. Also, the surface effects due to the nonuniform local field near a surface or edge are shown to be significant.