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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/20352

Title: Limit cycles in slow-fast codimension 3 bifurcations
Authors: Huzak, Renato
Advisors: De Maesschalck, Peter
Dumortier, Freddy
Issue Date: 2013
Abstract: Summary excerpt: In the first part of the present thesis we have re-investigated the issue of Half-Metallicity for zig-zag graphene nanoribbons (ZGNRs) of finite width and periodicity in one dimension as well as for zig-zag graphene nanoislands (ZGNIs), such as bisanthrene and tetrabenzo[bc,ef,kl,no]coronene. This issue is currently very popular among material scientists due to theoretical predictions published in major scientific journals (Nature [1], Physical Review B [2]) that are based on spin-unrestricted Density Functional Theory calculations, which invariably predict a symmetry-broken electronic wave function with spinpolarized edge states. Because these states are localized on opposite zig-zag edges, they respond differently to a transversal electric field, hence the very unusual property of half-metallicity, i.e. the coexistence of metallic nature for electrons with one spin orientation and insulating nature for the electrons of opposite spin. Based on these predictions a new generation of electronic devices exploiting the electron spin for carrying binary information is already envisioned. ZGNRs and ZGNIs would thus open the way to a new field in electronics, referred to as spintronics (i.e. spin transport electronics). It has been made clear within the frame of this thesis that these views are the outcome of a too approximate treatment of electron correlation within a onedeterminantal approach such as unrestricted Density Functional Theory (which has been introduced in Chapter 2, along with Hartree-Fock theory and manybody theories of improving quality). In the absence of a symmetry-breaking spin-dependent potential (e.g. spin orbit interactions), symmetry breakings in the spin densities of a system exhibiting a singlet state are necessarily artefactual in origin. In Chapter 3, the formalism of crystalline orbitals for extended systems with periodicity in one dimension has been applied in order to demonstrate that any antiferromagnetic and half-metallic spin-polarization of edge states in n-acenes, and more generally in zig zag graphene nanoislands and nanoribbons of finite width, would imply a spin contamination. In Chapter 4, we have presented a benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of n-acenes (C4n+2H2n+4) ranging from octacene (n=8) to undecacene (n=11). In Chapter 5, we have presented a benchmark theoretical study of the ionization energies, electron affinities and singlet-triplet energy gaps of azulene, phenanthrene, pyrene, chrysene and perylene. In Chapter 6, we have applied the principles of a Focal Point Analysis to finite field calculations in order to estimate the static electric dipole polarizabilities of naphthalene, anthracene and tetracene up to the level of Coupled Cluster theory including single, double and perturbative triple excitations [CCSD(T)] in the limit of an asymptotically complete basis set, again using a symmetry-restricted depiction.
URI: http://hdl.handle.net/1942/20352
Category: T1
Type: Theses and Dissertations
Appears in Collections: PhD theses
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