Numerical calculations for electronic transport through molecular systems [Elektronische Ressource] / Robert Dahlke

Numerical calculations forelectronic transport throughmolecular systemsRobert DahlkeMun¨ chen 2004Numerical calculations forelectronic transport throughmolecular systemsRobert DahlkeDissertationder Fakult¨at fu¨r Physikder Ludwig–Maximilians–Universit¨atMunc¨ henvorgelegt vonRobert Dahlkeaus AachenMunc¨ hen, den 23. April 2004Erstgutachter: Prof. Dr. Ulrich Schollw¨ockZweitgutachter: Prof. Dr. Axel SchenzleTag der mundlic¨ hen Prufung:¨ 8. Juli 2004ContentsZusammenfassung ix1 Introduction 12 Description of charge transport 52.1 Perturbative approaches . . . . . . . . . . . . . . . . . . . . . 52.1.1 Rate equations . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Bardeen formula . . . . . . . . . . . . . . . . . . . . . 82.1.3 Tersoff-Hamann formula . . . . . . . . . . . . . . . . . 92.1.4 Beyond the Tersoff-Hamann approximation . . . . . . . 102.2 Scattering approaches. . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Definition of the scattering matrix . . . . . . . . . . . . 112.2.2 Landauer-Buttik¨ er formalism . . . . . . . . . . . . . . 123 Quantum-chemical description of nanoscale systems 173.1 Ab-initio quantum-chemical methods . . . . . . . . . . . . . . 183.1.1 Separating nuclear and electronic problem . . . . . . . 183.1.2 Approximations to the electronic problem . . . . . . . 193.1.3ns to the molecular orbitals . . . . . . . . 213.2 Density functional theory. . . . . . . . . . . . . . . . . . . . . 223.2.