A topological method for the classification of entanglements in crystal networks

A rigorous method is proposed to describe and classify the topology of entanglements between periodic networks if the links are of the Hopf type. The catenation pattern is unambiguously identified by a net of barycentres of catenating rings with edges corresponding to the Hopf links; this net is called the Hopf ring net. The Hopf ring net approach is compared with other methods of characterizing entanglements; a number of applications of this approach to various kinds of entanglement (interpenetration, polycatenation and self-catenation) both in modelled network arrays and in coordination networks are considered

How 2-periodic coordination networks are interweaved : entanglement isomerism and polymorphism

The entanglements of 1319 2-periodic coordination polymers are examined and fully classified using the extended ring nets (ERNs) approach. The ERNs characterize the entanglement to the greatest detail ever achieved: all possible classes/types/modes of entanglements observed and reported in the literature so far result in 216 ERN topologically distinct modes of entanglements with 74% of all the structures falling into only 21 of them. We also introduce the notion of entanglement isomerism to designate the coordination polymers that have the same chemical composition, local and overall topology, but differ by their catenation patterns as mapped into their ERNs

Microlensing effects and structure of gravitational lens systems

A study of gravitational microlensing of distant objects is presented. We performed simulations of light curves and trajectories of the image centroid of an extended source in the Chang–Refsdal lens with shear and continual dark matter. Various brightness distributions over the source (Gaussian, power-law, Shakura–Synyaev accretion disc) have been studied. We considered in detail approximate relations and corresponding algorithms used to fit observational data on high amplification events (HAE). The results are applied to interpretation of HAE observed by OGLE and GLITP groups. The source size and caustic crossing moment are estimated from these data, however, the determination of the brightness profile is statistically not reliable

Lattice dynamics effects on small polaron properties

This study details the conditions under which strong-coupling perturbation theory can be applied to the molecular crystal model, a fundamental theoretical tool for analysis of the polaron properties. I show that lattice dimensionality and intermolecular forces play a key role in imposing constraints on the applicability of the perturbative approach. The polaron effective mass has been computed in different regimes ranging from the fully antiadiabatic to the fully adiabatic. The polaron masses become essentially dimension independent for sufficiently strong intermolecular coupling strengths and converge to much lower values than those tradition-ally obtained in small-polaron theory. I find evidence for a self-trapping transition in a moderately adiabatic regime at an electron-phonon coupling value of .3. Our results point to a substantial independence of the self-trapping event on dimensionality.Comment: 8 pages, 5 figure

Crossover from BCS to Composite Boson (Local Pair) Superconductivity in Quasi-2D systems

The crossover from cooperative Cooper pairing to independent bound state (composite bosons) formation and condensation in quasi-2D systems is studied. It is shown that at low carrier density the critical superconducting temperature is equal to the temperature of Bose-condensation of ideal quasi-2D Bose-gas with heavy dynamical mass, meanwhile at high densities the BCS result remains valid. The evident nonmonotoneous behaviour of the critical temperature as function of the coupling constant (the energy of the two particle bound state) is a qualitative difference of quasi-2D crossover from 3D one.Comment: 9 pages, LaTeX, no figures. (The latest version which appeared in the journal

The Holstein Polaron

We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the 1d polaron energy at intermediate coupling). We compute ground and low-lying excited state properties of the model at continuous values of the wavevector $k$ in essentially all parameter regimes. Our results for the polaron energy band, effective mass and correlation functions compare favorably with those of other numerical techniques including DMRG, Global Local and exact diagonalization. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong coupling perturbation theory.Comment: 24 pages, 11 figures submitted to PR

Theory of bound polarons in oxide compounds

We present a multilateral theoretical study of bound polarons in oxide compounds MgO and \alpha-Al_2O_3 (corundum). A continuum theory at arbitrary electron-phonon coupling is used for calculation of the energies of thermal dissociation, photoionization (optically induced release of an electron (hole) from the ground self-consistent state), as well as optical absorption to the non-relaxed excited states. Unlike the case of free strong-coupling polarons, where the ratio \kappa of the photoionization energy to the thermal dissociation energy was shown to be always equal to 3, here this ratio depends on the Froehlich coupling constant \alpha and the screened Coulomb interaction strength \beta. Reasonable variation of these two parameters has demonstrated that the magnitude of \kappa remains usually in the narrow interval from 1 to 2.5. This is in agreement with atomistic calculations and experimental data for hole O^- polarons bound to the cation vacancy in MgO. The thermal dissociation energy for the ground self-consistent state and the energy of the optically induced charge transfer process (hops of a hole between O^{2-} ions) have been calculated using the quantum-chemical method INDO. Results obtained within the two approaches for hole O$^-$ polarons bound by the cation vacancies (V^-) in MgO and by the Mg^{2+} impurity (V_{Mg}) in corundum are compared to experimental data and to each other. We discuss a surprising closeness of the results obtained on the basis of independent models and their agreement with experiment.Comment: 13 pages, 2 figures, 2 tables, E-mail addresses: [email protected], [email protected]

Mass Renormalization in the Su-Schrieffer-Heeger Model

This study of the one dimensional Su-Schrieffer-Heeger model in a weak coupling perturbative regime points out the effective mass behavior as a function of the adiabatic parameter $\omega_{\pi}/J$, $\omega_{\pi}$ is the zone boundary phonon energy and $J$ is the electron band hopping integral. Computation of low order diagrams shows that two phonons scattering processes become appreciable in the intermediate regime in which zone boundary phonons energetically compete with band electrons. Consistently, in the intermediate (and also moderately antiadiabatic) range the relevant mass renormalization signals the onset of a polaronic crossover whereas the electrons are essentially undressed in the fully adiabatic and antiadiabatic systems. The effective mass is roughly twice as much the bare band value in the intermediate regime while an abrupt increase (mainly related to the peculiar 1D dispersion relations) is obtained at $\omega_{\pi}\sim \sqrt{2}J$.Comment: To be published in Phys.Rev.B - 3 figure

Topochemical Synthesis of Single-Crystalline Hydrogen-Bonded Cross-Linked Organic Frameworks and Their Guest-Induced Elastic Expansion

Covalently linked single-crystalline porous organic materials are highly desired for structure-property analysis; however, periodically polymerizing organic entities into high dimensional networks is challenging. Here, we report a series of topologically divergent single-crystalline hydrogen-bonded cross-linked organic frameworks (HCOFs) with visible guest-induced elastic expansions, which mutually integrate high structural order and high flexibility into one framework. These HCOFs are synthesized by photo-cross-linking molecular crystals with alkyldithiols of different chain lengths. Their detailed structural information was revealed by single-crystal X-ray analysis and experimental investigations of HCOFs and their corresponding single-crystalline analogues. Upon guest adsorption, HCOF-2 crystals composed of a 3D self-entangled polymer network undergo anisotropic expansion to more than twice their original size, while the 2D-bilayer HCOF-3 crystals exhibit visible, layered sorption bands and form delaminated sheets along the plane of its 2D layers. The dynamic expansion of HCOF networks creates guest-induced porosity with over 473% greater volume than their permanent voids, as calculated from their record-breaking aqueous iodine adsorption capacities. Temperature-gated DMSO sorption investigations illustrated that the flexible nature of cross-linkers in HCOFs provides positive entropy from the coexistence of multiple conformations to allow for elastic expansion and contraction of the frameworks

Topologically guided tuning of Zr-MOF pore structures for highly selective separation of C6 alkane isomers

As an alternative technology to energy intensive distillations, adsorptive separation by porous solids offers lower energy cost and higher efficiency. Herein we report a topology-directed design and synthesis of a series of Zr-based metal-organic frameworks with optimized pore structure for efficient separation of C6 alkane isomers, a critical step in the petroleum refining process to produce gasoline with high octane rating. Zr6O4(OH)4(bptc)3 adsorbs a large amount of n-hexane but excluding branched isomers. The n-hexane uptake is ~70% higher than that of a benchmark adsorbent, zeolite-5A. A derivative structure, Zr6O4(OH)8(H2O)4(abtc)2, is capable of discriminating all three C6 isomers and yielding a high separation factor for 3-methylpentane over 2,3-dimethylbutane. This property is critical for producing gasoline with further improved quality. Multicomponent breakthrough experiments provide a quantitative measure of the capability of these materials for separation of C6 alkane isomers. A detailed structural analysis reveals the unique topology, connectivity and relationship of these compounds