Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.Comment: 17 pages, 4 figures, REVTe

Free energy barrier for molecular motions in bistable [2]rotaxane molecular electronic devices

Donor−acceptor binding of the π-electron-poor cyclophane cyclobis(paraquat-p-phenylene) (CBPQT^(4+)) with the π-electron-rich tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP) stations provides the basis for electrochemically switchable, bistable [2]rotaxanes, which have been incorporated and operated within solid-state devices to form ultradense memory circuits (ChemPhysChem 2002, 3, 519−525; Nature 2007, 445, 414−417) and nanoelectromechanical systems. The rate of CBPQT^(4+) shuttling at each oxidation state of the [2]rotaxane dictates critical write-and-retention time parameters within the devices, which can be tuned through chemical synthesis. To validate how well computational chemistry methods can estimate these rates for use in designing new devices, we used molecular dynamics simulations to calculate the free energy barrier for the shuttling of the CBPQT^4+ ring between the TTF and the DNP. The approach used here was to calculate the potential of mean force along the switching pathway, from which we calculated free energy barriers. These calculations find a turn-on time after the rotaxane is doubly oxidized of ~10^9−7) s (suggesting that the much longer experimental turn-on time is determined by the time scale of oxidization). The return barrier from the DNP to the TTF leads to a predicted lifetime of 2.1 s, which is compatible with experiments

Kernspintomographisches Ganzkörper-Screening ossärer Metastasen bei Kindern

Unter dem Aspekt der Darstellung kindlicher Skelettmetastasen sollten kernspintomographische Ganzkörper-Untersuchungen in der STIR-Sequenz mit den Befunden aus der Skelettszintigraphie retrospektiv verglichen werden. Dazu werteten zwei unabhängige erfahrene Beobachter die Aufnahmen aus je 22 Ganzkörper-STIR-Magnetresonanztomographien bzw. Skelettszintigraphien aus, die jeweils während eines Gesamtzeitraumes von 30 Monaten an elf Patienten entstanden waren. Direkt korreliert wurden die Untersuchungen der Ganzkörper-STIR-MRT bzw. der Skelettszintigraphien, die jeweils innerhalb eines Zeitintervalls von maximal drei Wochen stattgefunden hatten. Die Kinder im Alter zwischen einem und 15 Jahren befanden sich aufgrund ihrer malignen Grunderkrankung (4 Rhabdomyosarkome, 2 Osteosarkome, 1 Ewing-Sarkom, 1 PNET, 1 undifferenziertes Sarkom, 1 Malignes Lymphom, 1 T-Zell-Lymphom) in stationärer Behandlung bzw. Nachbehandlung. Das Protokoll der Ganzkörper-STIR-MRT umfasste das gesamte Skelett, nicht abgebildet waren die distalen Abschnitte der Extremitätenknochen. Die Beurteilung der ossären Einzelläsionen erfolgte unter dem Gesichtspunkt „positiv“ bzw. „negativ“ in Bezug auf eine mögliche Knochenmetastase. In analoger Weise wurden die STIR-MRT und Szintigraphien getrennt voneinander ausgewertet. Ein Herd wurde in der Ganzkörper-STIR-MRT bei Vorliegen einer pathologischen fokalen Signalhyperintensität als positiv bewertet. In der Skelettszintigraphie galt die fokale Mehrspeicherung des Radiopharmakons als Kriterium für einen positiven Befund. Die Ergebnisse der einzelnen Modalitäten wurden zusätzlich im Rahmen einer kombinierten Befundung bewertet. In den Fällen mit diskrepanten Untersuchungsergebnissen wurde im Konsens aufgrund des höheren Wertes der diagnostischen Sicherheit entschieden. Als Goldstandard dienten die Verlaufskontrolle über sechs Monate und der histologische Nachweis. Die Gesamtzahl aller beschriebenen Knochenherde lag bei 118 Läsionen. Die Sensitivität der Ganzkörper-STIR-MRT lag mit 89 % deutlich über der Sensitivität der Skelettszintigraphie (50%). Dagegen betrug die Spezifität der Ganzkörper-STIR-MRT nur 48 %, während sie bei der Skelettszintigraphie einen Wert von 75% erreichte. Durch die kombinierte Befundung konnte die Spezifität auf 87% verbessert werden. Falsch-negative Befunde der Ganzkörper-STIR-MRT beruhten auf patienten- bzw. technisch bedingten Bildartefakten im Bereich der Wirbelsäule, in zwei Fällen war die erschwerte Beurteilbarkeit der Knochenstruktur im Rippenthorax die Ursache für eine Fehlinterpretation. Signalanhebungen durch unspezifische intraossäre ödematöse Veränderungen, entzündliche Prozesse, Epiphysenfugen und schichtführungsabhängige Gelenkanschnitte führten zu falsch-positiven MRT-Befunden. Die falsch-negativen Befunde der Skelettszintigraphie waren auf den initialen Befall des Knochenmarks bzw. auf eine noch fehlende Kortikalisbeteiligung zurückzuführen. Entzündlich bedingte, posttraumatische, postoperative sowie durch Fehlbelastung induzierte ossäre Mehrspeicherungen waren die Hauptursachen der falsch-positiven skelettszintigraphischen Befunde. Die Ganzkörper-STIR-MRT erbrachte nach den vorgelegten Ergebnissen bei vergleichbarem Zeitaufwand und fehlender Strahlenexposition gegenüber der Skelettszintigraphie eine deutlich höhere Sensitivität bei der Detektion ossärer Metastasen; sie erscheint damit geeignet für ein Knochenmetastasen-Screening bei Kindern mit maligner Grunderkrankung

Kinetic and Thermodynamic Approaches for the Efficient Formation of Mechanical Bonds

Among the growing collection of molecular systems under consideration for nanoscale device applications, mechanically interlocked compounds derived from electrochemically switchable bistable [2]rotaxanes and [2]catenanes show great promise. These systems demonstrate dynamic, relative movements between their components, such as shuttling and circumrotation, enabling them to serve as stimuli-responsive switches operated via reversible, electrochemical oxidation−reduction rather than through the addition of chemical reagents. Investigations into these systems have been intense for a number of years, yet limitations associated with their synthesis have hindered incorporation of their mechanical bonds into more complex architectures and functional materials. We have recently addressed this challenge by developing new template-directed synthetic protocols, operating under both kinetic and thermodynamic control, for the preparation of bistable rotaxanes and catenanes. These methodologies are compatible with the molecular recognition between the π-electron-accepting cyclobis(paraquat-p-phenylene) (CBPQT4+) host and complementary π-electron-donating guests. The procedures that operate under kinetic control rely on mild chemical transformations to attach bulky stoppering groups or perform macrocyclizations without disrupting the host−guest binding of the rotaxane or catenane precursors. Alternatively, the protocols that operate under thermodynamic control utilize a reversible ring-opening reaction of the CBPQT4+ ring, providing a pathway for two cyclic starting materials to thread one another to form more thermodynamically stable catenaned products. These complementary pathways generate bistable rotaxanes and catenanes in high yields, simplify mechanical bond formation in these systems, and eliminate the requirement that the mechanical bonds be introduced into the molecular structure in the final step of the synthesis. These new methods have already been put into practice to prepare previously unavailable rotaxane architectures and novel complex materials. Furthermore, the potential for utilizing mechanically interlocked architectures as device components capable of information storage, the delivery of therapeutic agents, or other desirable functions has increased significantly as a result of the development of these improved synthetic protocols

Spin Wave Instability of Itinerant Ferromagnet

We show variationally that instability of the ferromagnetic state in the Hubbard model is largely controlled by softening of a long-wavelength spin-wave excitation, except in the over-doped strong-coupling region where the individual-particle excitation becomes unstable first. A similar conclusion is drawn also for the double exchange ferromagnet. Generally the spin-wave instability may be regarded as a precursor of the metal-insulator transition.Comment: 11 pages, 8 figure

Control of Vulval Cell Division Number in the Nematode Oscheius/Dolichorhabditis sp. CEW1

Spatial patterning of vulval precursor cell fates is achieved through a different two-stage induction mechanism in the nematode Oscheius/Dolichorhabditis sp. CEW1 compared with Caenorhabditis elegans. We therefore performed a genetic screen for vulva mutants in Oscheius sp. CEW1. Most mutants display phenotypes unknown in C. elegans. Here we present the largest mutant category, which affects division number of the vulva precursors P(4-8).p without changing their fate. Among these mutations, some reduce the number of divisions of P4.p and P8.p specifically. Two mutants omit the second cell cycle of all vulval lineages. A large subset of mutants undergo additional rounds of vulval divisions. We also found precocious and retarded heterochronic mutants. Whereas the C. elegans vulval lineage mutants can be interpreted as overall (homeotic) changes in precursor cell fates with concomitant cell cycle changes, the mutants described in Oscheius sp. CEW1 do not affect overall precursor fate and thereby dissociate the genetic mechanisms controlling vulval cell cycle and fate. Laser ablation experiments in these mutants reveal that the two first vulval divisions in Oscheius sp. CEW1 appear to be redundantly controlled by a gonad-independent mechanism and by a gonadal signal that operates partially independently of vulval fate induction

Efficient Templated Synthesis of Donor−Acceptor Rotaxanes Using Click Chemistry

The mild reaction conditions, remarkable functional group compatibility, and complete regioselectivity of the Cu-catalyzed Huisgen 1,3-dipolar cycloaddition (“click chemistry”) between organic azides and terminal alkynes have led to a threading-followed-by-stoppering approach to the synthesis of donor−acceptor rotaxanes incorporating cyclobis(paraquat-p-phenylene) (CBPQT^(4+)) as the π-accepting ring component. Rotaxane formation is initiated by reacting azide-functionalized pseudorotaxanes containing π-donating 1,5-dioxynaphthalene (DNP) recognition units with appropriate alkyne-functionalized stoppers. The high yields obtained in this efficient, kinetically controlled post-assembly covalent modification, as well as the excellent convergence of the synthetic protocol, are demonstrated by the preparation of [2]-, [3]-, and [4]rotaxanes containing multiple DNP/CBPQT^(4+) donor−acceptor recognition motifs

A Redox-Switchable α-Cyclodextrin-Based [2]Rotaxane

A bistable [2]rotaxane comprising an α-cyclodextrin (α-CD) ring and a dumbbell component containing a redox-active tetrathiafulvalene (TTF) ring system within its rod section has been synthesized using the Cu(I)-catalyzed azide−alkyne cycloaddition, and the redox-driven movements of the α-CD ring between the TTF and newly formed triazole ring systems have been elucidated. Microcalorimetric titrations on model complexes suggested that the α-CD ring prefers to reside on the TTF rather than on the triazole ring system by at least an order of magnitude. The fact that this situation does pertain in the bistable [2]rotaxane has not only been established quantitatively by electrochemical experiments and backed up by spectroscopic and chiroptical measurements but also been confirmed semiquantitatively by the recording of numerous cyclic voltammograms which point, along with the use of redox-active chemical reagents, to a mechanism of switching that involves the oxidation of the neutral TTF ring system to either its radical cationic (TTF^(•+)) or dicationic (TTF^(2+)) counterparts, whereupon the α-CD ring, moves along the dumbbell to encircle the triazole ring system. Since redox control by both chemical and electrochemical means is reversible, the switching by the bistable [2]rotaxane can be reversed on reduction of the TTF^(•+) or TTF^(2+) back to being a neutral TTF

Structural and Co-conformational Effects of Alkyne-Derived Subunits in Charged Donor−Acceptor [2]Catenanes

Four donor−acceptor [2]catenanes with cyclobis(paraquat-p-phenylene) (CBPQT^(4+)) as the π-electron-accepting cyclophane and 1,5-dioxynaphthalene (DNP)-containing macrocyclic polyethers as π-electron donor rings have been synthesized under mild conditions, employing Cu^+-catalyzed Huisgen 1,3-dipolar cycloaddition and Cu^(2+)-mediated Eglinton coupling in the final steps of their syntheses. Oligoether chains carrying terminal alkynes or azides were used as the key structural features in template-directed cyclizations of [2]pseudorotaxanes to give the [2]catenanes. Both reactions proceed well with precursors of appropriate oligoether chain lengths but fail when there are only three oxygen atoms in the oligoether chains between the DNP units and the reactive functional groups. The solid-state structures of the donor−acceptor [2]catenanes confirm their mechanically interlocked nature, stabilized by [π···π], [C−H···π], and [C−H···Ο] interactions, and point to secondary noncovalent contacts between 1,3-butadiyne and 1,2,3-triazole subunits and one of the bipyridinum units of the CBPQT^(4+) ring. These contacts are characterized by the roughly parallel orientation of the inner bipyridinium ring system and the 1,2,3-triazole and 1,3-butadiyne units, as well as by the short [π···π] distances of 3.50 and 3.60 Å, respectively. Variable-temperature ^1H NMR spectroscopy has been used to identify and quantify the barriers to the conformationally and co-conformationally dynamic processes. The former include the rotations of the phenylene and the bipyridinium ring systems around their substituent axes, whereas the latter are confined to the circumrotation of the CBPQT^(4+) ring around the DNP binding site. The barriers for the three processes were found to be successively 14.4, 14.5−17.5, and 13.1−15.8 kcal mol^(-1). Within the limitations of the small dataset investigated, emergent trends in the barrier heights can be recognized:  the values decrease with the increasing size of the π-electron-donating macrocycle and tend to be lower in the sterically less encumbered series of [2]catenanes containing the 1,3-butadiyne moiety

Enzyme-Responsive Snap-Top Covered Silica Nanocontainers

Mesoporous silica nanoparticles, capable of storing a payload of small molecules and releasing it following specific catalytic activation by an esterase, have been designed and fabricated. The storage and release of the payload is controlled by the presence of [2]rotaxanes, which consist of tri(ethylene glycol) chains threaded by α-cyclodextrin tori, located on the surfaces of the nanoparticles and terminated by a large stoppering group. These modified silica nanoparticles are capable of encapsulating guest molecules when the [2]rotaxanes are present. The bulky stoppers, which serve to hold the tori in place, are stable under physiological conditions but are cleaved by the catalytic action of an enzyme, causing dethreading of the tori and release of the guest molecules from the pores of the nanoparticles. These snap-top covered silica nanocontainers (SCSNs) are prepared by a modular synthetic method, in which the stoppering unit, incorporated in the final step of the synthesis, may be changed at will to target the response of the system to any of a number of hydrolytic enzymes. Here, the design, synthesis, and operation of model SCSNs that open in the presence of porcine liver esterase (PLE) are reported. The empty pores of the silica nanoparticles were loaded with luminescent dye molecules (rhodamine B), and stoppering units that incorporate adamantyl ester moieties were then attached in the presence of α-cyclodextrin using the copper-catalyzed azide−alkyne cycloaddition (CuAAC), closing the SCSNs. The release of rhodamine-B from the pores of the SCSN, following PLE-mediated hydrolysis of the stoppers, was monitored using fluorescence spectroscopy