Interface Characteristics at an Organic/Metal Junction: Pentacene on Cu Stepped Surfaces

The adsorption of pentacene on Cu(221), Cu(511) and Cu(911) is investigated using density functional theory (DFT) with the self-consistent inclusion of van der Waals (vdW) interactions. Cu(211) is a vicinal of Cu(111) while Cu(511) and (911) are vicinals of Cu(100). For all the three surfaces, we found pentacene to prefer to adsorb parallel to the surface and near the steps. The addition of vdW interactions resulted in an enhancement in adsorption energies, with reference to the PBE functional, of around 2 eV. With vdWs inclusion, the adsorption energies were found to be 2.98 eV, 3.20 eV and 3.49 eV for Cu(211), Cu(511) and Cu(911) respectively. These values reflect that pentacene adsorbs stronger on (100) terraces with a preference for larger terraces. The molecule tilts upon adsorption with a small tilt angle on the (100) vicinals (about a few degrees) as compared to a large one on Cu(221) where the tilt angle is found to be about 20o. We find that the adsorption results in a net charge transfer to the molecule of ~1 electron, for all surfaces.Comment: 11 pages, 4 figure

Rational Formulas for Traces in zero-dimensional Algebras

We present a rational expression for the trace of the multiplication map M_r in a finite-dimensional algebra of the form A:=K[x_1,...,x_n]/I in terms of the generalized Chow form of I. Here, I is a zero-dimensional ideal of K[x_1,...,x_n] is a zero-dimensional ideal, K is a field of characteristic zero, and r(x_1,..., x_n) a rational function whose denominator is not a zero divisor in A. If I is a complete intersection in the torus, we get numerator and denominator formulas for traces in terms of sparse resultants.Comment: 11 pages, latex document, revised version accepted for publication in the AAECC Journa

Skew group algebras, invariants and Weyl Algebras

The aim of this paper is two fold: First to study finite groups $G$ of automorphisms of the homogenized Weyl algebra $B_{n}$, the skew group algebra $B_{n}\ast G$, the ring of invariants $B_{n}^{G}$, and the relations of these algebras with the Weyl algebra $A_{n}$, with the skew group algebra $A_{n}\ast G$, and with the ring of invariants $A_{n}^{G}$. Of particular interest is the case $n=1$. In the on the other hand, we consider the invariant ring \QTR{sl}{C}[X]^{G} of the polynomial ring $K[X]$ in $n$ generators, where $G$ is a finite subgroup of Gl(n,\QTR{sl}{C}) such that any element in $G$ different from the identity does not have one as an eigenvalue. We study the relations between the category of finitely generated modules over \QTR{sl}{C}[X]^{G} and the corresponding category over the skew group algebra \QTR{sl}{C}% [X]\ast G. We obtain a generalization of known results for $n=2$ and $G$ a finite subgroup of $Sl(2,C)$. In the last part of the paper we extend the results for the polynomial algebra $C[X]$ to the homogenized Weyl algebra $B_{n}$

An \emph{ab initio} study on split silicon-vacancy defect in diamond: electronic structure and related properties

The split silicon-vacancy defect (SiV) in diamond is an electrically and optically active color center. Recently, it has been shown that this color center is bright and can be detected at the single defect level. In addition, the SiV defect shows a non-zero electronic spin ground state that potentially makes this defect an alternative candidate for quantum optics and metrology applications beside the well-known nitrogen-vacancy color center in diamond. However, the electronic structure of the defect, the nature of optical excitations and other related properties are not well-understood. Here we present advanced \emph{ab initio} study on SiV defect in diamond. We determine the formation energies, charge transition levels and the nature of excitations of the defect. Our study unravel the origin of the dark or shelving state for the negatively charged SiV defect associated with the 1.68-eV photoluminescence center.Comment: 8 pages, 5 figures, 1 tabl