New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Additions- und Umlagerungsreaktionen des Lewis-aciden Dihypersilylplumbandiyls in Umsetzungen mit monodenten und ambidenten Lewis-Basen

Die chemische Reaktivität des Dihypersilylplumbylens Pb[Si(Si(CH3)3)3]2 wird durch seine besondere elektronische Struktur bestimmt. Im Unterschied zu Carbenen (Triplett-Grundzustand) liegen Plumbylene im Grundzustand als Singulett vor, mit einem energetisch hochliegenden HOMO (freies Elektronenpaar mit hohem s-Charakter) und einem tiefliegenden LUMO (näherungsweise: freies p-Orbital des Pb-Atoms). Daraus resultiert das amphotere Lewis-Säure/Lewis-Base-Verhalten der Verbindung, mit der Besonderheit, dass sich die beiden Lewis-Zentren am selben Atom befinden. rnIn Umsetzungen mit monodenten und ambidenten Lewis-Basen wurden die Lewis-aciden Eigenschaften des Dihypersilylplumbandiyls Pb[Si(Si(CH3)3)3]2 untersucht. Reaktionen mit den sterisch anspruchsvollen O-Nucleophilen KOtBu (Kalium-tert-Butanolat) und KOiPrPh (4-Kaliumisopropylphenolat) führten bei tiefen Temperaturen zur primären Adduktbildung. Die aus der Strukturanalyse erhaltenen Bindungsdaten zeigen die extreme sterische Überfrachtung des zentralen Blei-Atoms. Der Abbau der sterischen Spannung ist möglicherweise die Ursache für offensichtlich stattfindende Umlagerungsfolgereaktionen (bei Reaktionsführungen bei T>-60°C), die aufgrund spektroskopische Untersuchungen zu vermuten sind.rnEingehender wurden diese Umlagerungsreaktionen in Umsetzungen des Pb[Si(Si(CH3)3)3]2 mit ambidenten Lewis-Basen untersucht. In Übereinstimmung und Erweiterung mit früheren Ergebnissen von Klinkhammer (K. Klinkhammer, Polyhedron, 2002, 21, 587) konnte beispielsweise die Migration einer (mit der ambidenten Lewis-Base tert-Butylisonitril) bzw. beider Hypersilylgruppen (mit p-Tolylisocyanat) unter Bildung hetero- bzw. homoleptischer Plumbylene nachgewiesen werden.rnReaktionen des Pb[Si(Si(CH3)3)3]2 mit den anorganischen ambidenten Salz-Ionen CN-, OCN-, SCN-, N3-, NO2- führen zur Bildung salzartiger Plumbanide der Zusammensetzung Me{Pb[Si(Si(CH3)3)3]2}Nu (Me: Na bzw. K, Nu: CN, OCN, SCN, N3, NO2). Die Verbindungen liegen im Kristall monomer als Kontaktionenpaar vor. Auf diese Weise gelang erstmalig die gezielte Synthese eines Blei(II)cyanids sowie die Darstellung eines Blei(II)isocyanats. rn

Novel porphyrin amino acids as building blocks for artificial photosynthetic reaction centers : photoinduced energy and electron transfer

This thesis reports on the synthesis and characterisation of trans-(M)AB2C meso-substituted porphyrin amino acid esters (PAr) (M = 2H or Zn) with tunable electron donating and electron withdrawing Ar substituents at B positions (Ar = 4-C6H4OnBu, 4-C6H4OMe, 2,4,6-C6H2Me3, 4-C6H4Me, C6H5, 4-C6H4F, 4-C6H4CF3, C6F5). These porphyrins were used as key building blocks for photosynthetic LHC (LHC = light-harvesting antenna complex) and RC (RC = reaction center) model compounds.rnBased on free-base or zinc(II) porphyrin amino acid esters and porphyrin acids several amide linked free-base bis(porphyrins) PAr1-PAr2 (Ar1 = 2,4,6-C6H2Me3, C6F5 and Ar2 = 2,4,6-C6H2Me3, 4-C6H4F, 4-C6H4CF3, C6F5), mono metallated bis(porphyrin) PAr1-(Zn)PAr2 (Ar1 = 2,4,6-C6H2Me3 and Ar2 =4-C6H4F) and its doubly zincated complexes (Zn)PAr1-(Zn)PAr2 were prepared. In the fluorescence spectra of free-base bis(porphyrins) the porphyrin with the strongest electron donating power of Ar substituents at B positions is the light emitting unity. The emission of mono metallated bis(porphyrin) occurs only from the free-base porphyrin building block. This phenomenon is caused by an efficient energy transfer likely via the Dexter through-bond mechanism.rnLinking of anthraquinone (Q) as electron acceptor (A) to the N-terminus of porphyrin amino acid esters ((M)PAr) and aminoferrocene (Fc) as electron donor (D) to the C-terminus of the porphyrin resulting in Q-(M)PAr-Fc triads (M = 2H or Zn, Ar = 4-C6H4OnBu, 4-C6H4OMe, 2,4,6-C6H2Me3, 4-C6H4Me, C6H5, 4-C6H4F, 4-C6H4CF3, C6F5) with tunable electron density at the porphyrin chromophore. In these triads initial oxidative PET (Q←(M)PAr) and reductive PET ((M)PAr→Fc) (PET = photoinduced electron transfer) are possible. Both processes leads to an emission quenching of (M)PAr. The efficiency of the PET pathways occurring in the Marcus normal region is controlled by the specific porphyrin electron density.rnAmide-linked conjugates PAr-Fc (Ar = 2,4,6-C6H2Me3, C6F5) and Fmoc-Fc-PAr1 (N-Fmoc-Fc = N-Fmoc protected 1,1’-ferrocene amino acid; Ar1 = C6H5, 4-C6H4F, 4-C6H4CF3, C6F5) as well as hinges PAr2-Fc-PAr1 (Ar1 = C6H5, 4-C6H4F and Ar2 = 2,4,6-C6H2Me3) were studied with respect to the reductive PET. The PET driving force (−GET) in dyads increases with the increasing electron withdrawing character of Ar substituents. Additionally, intramolecular energy transfer between porphyrins PAr1 and PAr2 is feasible in the hinges via the Förster mechanism.rn