Laconicity and redundancy of Toeplitz matrices

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46295/1/209_2005_Article_BF01111000.pd

New Strategies in Modeling Electronic Structures and Properties with Applications to Actinides

This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic Hamiltonians that are frequently applied to account for relativistic effects. Then, we scrutinize various quantum chemistry methods that approximate the $N$-electron wave function. In this respect, we will review the most popular single- and multi-reference approaches that have been developed to model the multi-reference nature of heavy element compounds and their ground- and excited-state electronic structures. Specifically, we introduce various flavors of post-Hartree--Fock methods and optimization schemes like the complete active space self-consistent field method, the configuration interaction approach, the Fock-space coupled cluster model, the pair-coupled cluster doubles ansatz, also known as the antisymmetric product of 1 reference orbital geminal, and the density matrix renormalization group algorithm. Furthermore, we will illustrate how concepts of quantum information theory provide us with a qualitative understanding of complex electronic structures using the picture of interacting orbitals. While modern quantum chemistry facilitates a quantitative description of atoms and molecules as well as their properties, concepts of quantum information theory offer new strategies for a qualitative interpretation that can shed new light onto the chemistry of complex molecular compounds.Comment: 43 pages, 3 figures, Version of Recor

Selected Open Problems in Discrete Geometry and Optimization

A list of questions and problems posed and discussed in September 2011 at the following consecutive events held at the Fields Institute, Toronto: Workshop on Discrete Geometry, Conference on Discrete Geometry and Optimization, and Workshop on Optimization. We hope these questions and problems will contribute to further stimulate the interaction between geometers and optimizers

Theoretical study of the bridging in β-Halo Ethyl

Large-acale multi-reference configuration interaction (MRD-CI) calculations in a quite flexible AO basis are employed to study the energy hypersurface for the reaction intermediates XC$_3$H$_4$ with X = Cl, Br and F. Particular emphasis is therby placed on determining the equilibrium conformations, the CH$_2$ rotation barrier and the energy surface for a possible bridging (shuttling motion (1a] of X between the two carbon centers). The absolute minimum in the potential energy surface is found in all three cases for the asymmetric ß-halo radical in general agreement with ESR data at an XCC angle of ca. 110°, a c-c separation somewhat shorter than a single bond and an approximate sp3 type hybridization ($\alpha _2 \approx$ 135-140°). In FC$_2$H$_4$ the energy difference between the minimum in the symmetric conformation and the absolute minimum is found to be more than 30 kcal so that shuttling seems impossible in agreement with experimental findings. In BrC$_2$H$_4$ the difference between these two potential minima is only between 1-2 kcal, i.e., smaller than the barrier to CH$_2$, rotation, so that· shuttling is favored, while ClC$_2$H$_4$ takes an intermediate position between these extremes. The use of correlated wavefunctions is found to be quite important for such a study; the results are related to various kinetic studies of these radicals

CONFIGURATION INTERACTION CALCULATIONS OF ELECTRONIC SPECTRA: VALENCE AND RYDBERG STATES AND INFLUENCE OF VIBRATIONS

Author Institution: Lehrstuhl f\""{u}r Theoretische Chemie, der Untversit\""{a}t Bon