HARES: an efficient method for first-principles electronic structure calculations of complex systems

We discuss our new implementation of the Real-space Electronic Structure method for studying the atomic and electronic structure of infinite periodic as well as finite systems, based on density functional theory. This improved version which we call HARES (for High-performance-fortran Adaptive grid Real-space Electronic Structure) aims at making the method widely applicable and efficient, using high performance Fortran on parallel architectures. The scaling of various parts of a HARES calculation is analyzed and compared to that of plane-wave based methods. The new developments that lead to enhanced performance, and their parallel implementation, are presented in detail. We illustrate the application of HARES to the study of elemental crystalline solids, molecules and complex crystalline materials, such as blue bronze and zeolites.Comment: 17 two-column pages, including 9 figures, 5 tables. To appear in Computer Physics Communications. Several minor revisions based on feedbac

Métriques polyèdrales sur les bords de variétés hyperboliques convexes et flexibilité des polyèdres hyperboliques

Cette thèse de doctorat contient trois résultats principaux. Dans le premier chapitre on construit un polyèdre infinitésimalement flexible dans l'espace hyperbolique à trois dimensions dont le volume n'est pas stationnaire sous sa flexion infinitésimale. Dans le deuxième chapitre on obtient une condition nécessaire de flexibilité des suspensions dans l'espace hyperbolique à trois dimensions. Dans les deux derniers chapitres on démontre l'existence d'une variété quasi-Fuchsienne convexe compacte dont la métrique induite de son bord est une métrique polyèdrale hyperbolique prescrite.This thesis contains three main results. In the first chapter we construct an infinitesimally flexible polyhedron in hyperbolic 3-space such that its volume is not stationary under the infinitesimal flex. In the second chapter we obtain a necessary condition for flexibility of suspensions in hyperbolic 3-space. In the last two chapters we show the existence of a quasi-Fuchsian convex compact manifold such that the induced metric on its boundary coincides with a prescribed hyperbolic polyhedral metric

Algebra versus analysis in the theory of flexible polyhedra

Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to prove that the oriented volume remains constant during the flex. We show that none of these methods can be used to prove the both theorems. As a by-product, we prove that the total mean curvature of any polyhedron in the Euclidean 3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte

The Dehn invariants of the Bricard octahedra

We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.Comment: 13 pages, 10 figure

Effects of thermal- and spin- fluctuations on the band structure of purple bronze Li2_2Mo12_{12}O34_{34}

The band structures of ordered and thermally disordered Li$_2$Mo$_{12}$O$_{34}$ are calculated by use of ab-initio DFT-LMTO method. The unusual, very 1-dimensional band dispersion obtained in previous band calculations is confirmed for the ordered structure, and the overall band structure agrees reasonably with existing photoemission data. Dispersion and bandstructure perpendicular to the main dispersive direction is obtained. A temperature dependent band broadening is calculated from configurations with thermal disorder of the atomic positions within the unit cell. This leads a band broadening of the two bands at the Fermi energy which can become comparable to their energy separation. The bands are particularly sensitive to in-plane movements of Mo sites far from the Li-sites, where the density-of-states is highest. The latter fact makes the effect of Li vacancies on the two bands relatively small. Spin-polarized band results for the ordered structure show a surprisingly large exchange enhancement on the high DOS Mo sites. Consequences for spin fluctuations associated with a cell doubling along the conducting direction are discussed