Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

High resolution photoacoustic overtone spectroscopy of monofluoroacetylene, HCCF, with a titanium:sapphire ring laser

Intracavity photoacoustic overtone spectrum of monofluoroacetylene, HCCF, has been recorded in the wave number region 10 750–14 500 cm−1 with a titanium:sapphire ring laser. The spectrum contains many dense vibration–rotation band systems which can be resolved with Doppler limited resolution. Altogether 58 individual overtone bands have been analyzed rotationally. Many of the observed bands show perturbations of which some have been attributed to anharmonic resonance interactions. A Fermi resonance model based on conventional rectilinear normal coordinate theory has been used to assign vibrationally bands from this work and from earlier studies. Many of the observed vibrational term values and rotational constants can be reproduced well with this model. The results show the importance of the Fermi resonance interactions at the high overtone excitations.

Analytical potentials for triatomic molecules VIII. A two valued surface for the lowest 1A¢ surfaces of H2O

Ab initio calculations of the energy have been made at approximately 150 points on the two lowest singlet A' potential energy surfaces of the water molecule, 1A' and 1A', covering structures having D∞h, C∞v, C2v and Cs symmetries. The object was to obtain an ab initio surface of uniform accuracy over the whole three-dimensional coordinate space. Molecular orbitals were constructed from a double zeta plus Rydberg basis, and correlation was introduced by single and double excitations from multiconfiguration states which gave the correct dissociation behaviour. A two-valued analytical potential function has been constructed to fit these ab initio energy calculations. The adiabatic energies are given in our analytical function as the eigenvalues of a 2 2 matrix, whose diagonal elements define two diabatic surfaces. The off-diagonal element goes to zero for those configurations corresponding to surface intersections, so that our adiabatic surface exhibits the correct Σ/II conical intersections for linear configurations, and singlet/triplet intersections of the O + H2 dissociation fragments. The agreement between our analytical surface and experiment has been improved by using empirical diatomic potential curves in place of those derived from ab initio calculations.

Assembly rules for protein networks derived from phylogenetic-statistical analysis of whole genomes

Background: We report an analysis of a protein network of functionally linked proteins, identified from a phylogenetic statistical analysis of complete eukaryotic genomes. Phylogenetic methods identify pairs of proteins that co-evolve on a phylogenetic tree, and have been shown to have a high probability of correctly identifying known functional links. Results: The eukaryotic correlated evolution network we derive displays the familiar power law scaling of connectivity. We introduce the use of explicit phylogenetic methods to reconstruct the ancestral presence or absence of proteins at the interior nodes of a phylogeny of eukaryote species. We find that the connectivity distribution of proteins at the point they arise on the tree and join the network follows a power law, as does the connectivity distribution of proteins at the time they are lost from the network. Proteins resident in the network acquire connections over time, but we find no evidence that 'preferential attachment' - the phenomenon of newly acquired connections in the network being more likely to be made to proteins with large numbers of connections - influences the network structure. We derive a 'variable rate of attachment' model in which proteins vary in their propensity to form network interactions independently of how many connections they have or of the total number of connections in the network, and show how this model can produce apparent power-law scaling without preferential attachment. Conclusion: A few simple rules can explain the topological structure and evolutionary changes to protein-interaction networks: most change is concentrated in satellite proteins of low connectivity and small phenotypic effect, and proteins differ in their propensity to form attachments. Given these rules of assembly, power law scaled networks naturally emerge from simple principles of selection, yielding protein interaction networks that retain a high-degree of robustness on short time scales and evolvability on longer evolutionary time scales.

Vibrational energy levels for the electronic ground state of the diazocarbene (CNN) molecule

The vibrational energy levels of diazocarbene (diazomethylene) in its electronic ground state, (X) over tilde (3) Sigma(-) CNN, have been predicted using the variational method. The potential energy surfaces of (X) over tilde (3) A" CNN were determined by employing ab initio single reference coupled cluster with single and double excitations (CCSD), CCSD with perturbative triple excitations [CCSD(T)], multi-reference complete active space self-consistent-field (CASSCF), and internally contracted multi-reference configuration interaction (ICMRCI) methods. The correlation-consistent polarised valence quadruple zeta (cc-pVQZ) basis set was used. Four sets of vibrational energy levels determined from the four distinct analytical potential functions have been compared with the experimental values from the laser-induced fluorescence measurements of Wurfel et al. obtained in 1992. The CCSD, CCSD(T), and CASSCF potentials have not provided satisfactory agreement with the experimental observations. In this light, the importance of both non-dynamic (static) and dynamic correlation effects in describing the ground state of CNN is emphasised. Our best theoretical fundamental frequencies at the cc-pVQZ ICMRCI level of theory, v(1) = 1230, v(2) = 394, and v(3) = 1420 cm(-1) are in excellent agreement with the experimental values of v(1) = 1235, v(2) = 396, and v(3) = 1419cm(-1) and the mean absolute deviation between the 23 calculated and experimental vibrational energy levels is only 7.4 cm(-1). It is shown that the previously suggested observation of the v(3) frequency at about 2847cm(-1) was in fact the first overtone 2v(3).

Calculations of rovibrational energies and dipole transition intensities for polyatomic molecules using MULTIMODE

We report rigorous calculations of rovibrational energies and dipole transition intensities for three molecules using a new version of the code MULTIMODE. The key features of this code which permit, for the first time, such calculations for moderately sized but otherwise general polyatomic molecules are briefly described. Calculations for the triatomic molecule BF(2) are done to validate the code. New calculations for H(2)CO and H(2)CS are reported; these make use of semiempirical potentials but ab initio dipole moment surfaces. The new dipole surface for H(2)CO is a full-dimensional fit to the dipole moment obtained with the coupled-cluster with single and double excitations and a perturbative treatment of triple excitations method with the augmented correlation consistent triple zeta basis set. Detailed comparisons are made with experimental results from a fit to relative data for H(2)CS and absolute intensities from the HITRAN database for H(2)CO.

Rovibrational energy levels for the electronic ground state of A1OH

The vibrational-rotational energy levels of aluminum monohydroxide in its electronic ground state, (A) over tilde (1)A' AlOH, have been predicted using the variational method. The potential energy surface of the (X) over tilde (1)A' ground state of AlOH was determined employing the ab initio coupled cluster method with single, double, and perturbative triple excitations [CCSD(T)] and the correlation-consistent polarized valence quadruple zeta (cc-pVQZ) basis set. Low-lying J= 0 and J= 1 vibrational levels are reported. These are analyzed in terms of the quasilinearity of the molecule. Coriolis effects are shown to be significant. We hope that our predictions will be of value in the future when assigning rovibrational transitions in spectroscopic studies. (c) 2006 Elsevier B.V. All rights reserved.

Proteomic profiling of neuromas reveals alterations in protein composition and local protein synthesis in hyper-excitable nerves

Neuropathic pain may arise following peripheral nerve injury though the molecular mechanisms associated with this are unclear. We used proteomic profiling to examine changes in protein expression associated with the formation of hyper-excitable neuromas derived from rodent saphenous nerves. A two-dimensional difference gel electrophoresis ( 2D-DIGE) profiling strategy was employed to examine protein expression changes between developing neuromas and normal nerves in whole tissue lysates. We found around 200 proteins which displayed a > 1.75-fold change in expression between neuroma and normal nerve and identified 55 of these proteins using mass spectrometry. We also used immunoblotting to examine the expression of low-abundance ion channels Nav1.3, Nav1.8 and calcium channel alpha 2 delta-1 subunit in this model, since they have previously been implicated in neuronal hyperexcitability associated with neuropathic pain. Finally, S(35)methionine in vitro labelling of neuroma and control samples was used to demonstrate local protein synthesis of neuron-specific genes. A number of cytoskeletal proteins, enzymes and proteins associated with oxidative stress were up-regulated in neuromas, whilst overall levels of voltage-gated ion channel proteins were unaffected. We conclude that altered mRNA levels reported in the somata of damaged DRG neurons do not necessarily reflect levels of altered proteins in hyper-excitable damaged nerve endings. An altered repertoire of protein expression, local protein synthesis and topological re-arrangements of ion channels may all play important roles in neuroma hyper-excitability.

Pressure-jump X-ray studies of liquid crystal transitions in lipids

In this paper, we give an overview of our studies by static and time-resolved X-ray diffraction of inverse cubic phases and phase transitions in lipids. In 1, we briefly discuss the lyotropic phase behaviour of lipids, focusing attention on non-lamellar structures, and their geometric/topological relationship to fusion processes in lipid membranes. Possible pathways for transitions between different cubic phases are also outlined. In 2, we discuss the effects of hydrostatic pressure on lipid membranes and lipid phase transitions, and describe how the parameters required to predict the pressure dependence of lipid phase transition temperatures can be conveniently measured. We review some earlier results of inverse bicontinuous cubic phases from our laboratory, showing effects such as pressure-induced formation and swelling. In 3, we describe the technique of pressure-jump synchrotron X-ray diffraction. We present results that have been obtained from the lipid system 1:2 dilauroylphosphatidylcholine/lauric acid for cubic-inverse hexagonal, cubic-cubic and lamellar-cubic transitions. The rate of transition was found to increase with the amplitude of the pressure-jump and with increasing temperature. Evidence for intermediate structures occurring transiently during the transitions was also obtained. In 4, we describe an IDL-based 'AXCESS' software package being developed in our laboratory to permit batch processing and analysis of the large X-ray datasets produced by pressure-jump synchrotron experiments. In 5, we present some recent results on the fluid lamellar-Pn3m cubic phase transition of the single-chain lipid 1-monoelaidin, which we have studied both by pressure-jump and temperature-jump X-ray diffraction. Finally, in 6, we give a few indicators of future directions of this research. We anticipate that the most useful technical advance will be the development of pressure-jump apparatus on the microsecond time-scale, which will involve the use of a stack of piezoelectric pressure actuators. The pressure-jump technique is not restricted to lipid phase transitions, but can be used to study a wide range of soft matter transitions, ranging from protein unfolding and DNA unwinding and transitions, to phase transitions in thermotropic liquid crystals, surfactants and block copolymers.

Potential energy surface and MULTIMODE vibrational analysis of C2H3+

A full dimensional, ab initio-based semiglobal potential energy surface for C2H3+ is reported. The ab initio electronic energies for this molecule are calculated using the spin-restricted, coupled cluster method restricted to single and double excitations with triples corrections [RCCSD(T)]. The RCCSD(T) method is used with the correlation-consistent polarized valence triple-zeta basis augmented with diffuse functions (aug-cc-pVTZ). The ab initio potential energy surface is represented by a many-body (cluster) expansion, each term of which uses functions that are fully invariant under permutations of like nuclei. The fitted potential energy surface is validated by comparing normal mode frequencies at the global minimum and secondary minimum with previous and new direct ab initio frequencies. The potential surface is used in vibrational analysis using the "single-reference" and "reaction-path" versions of the code MULTIMODE. (c) 2006 American Institute of Physics.

Thermal Fractionation and isothermal crystallization of polyethylene nanocomposites prepared by in situ polymerization

Nanocomposites of high-density polyethylene (HDPE) and carbon nanotubes (CNT) of different geometries (single wall, double wall, and multiwall; SWNT, DWNT, and MWNT) were prepared by in situ polymerization of ethylene on CNT whose surface had been previously treated with a metallocene catalytic system. In this work, we have studied the effects of applying the successive self-nucleation and annealing thermal fractionation technique (SSA) to the nanocomposites and have also determined the influence of composition and type of CNT on the isothermal crystallization behavior of the HDPE. SSA results indicate that all types of CNT induce the formation of a population of thicker lamellar crystals that melt at higher temperatures as compared to the crystals formed in neat HDPE prepared under the same catalytic and polymerization conditions and subjected to the same SSA treatment. Furthermore, the peculiar morphology induced by the CNT on the HDPE matrix allows the resolution of thermal fractionation to be much better. The isothermal crystallization results indicated that the strong nucleation effect caused by CNT reduced the supercooling needed for crystallization. The interaction between the HDPE chains and the surface of the CNT is probably very strong as judged by the results obtained, even though it is only physical in nature. When the total crystallinity achieved during isothermal crystallization is considered as a function of CNT content, it was found that a competition between nucleation and topological confinement could account for the results. At low CNT content the crystallinity increases (because of the nucleating effect of CNT on HDPE), however, at higher CNT content there is a dramatic reduction in crystallinity reflecting the increased confinement experienced by the HDPE chains at the interfaces which are extremely large in these nanocomposites. Another consequence of these strong interactions is the remarkable decrease in Avrami index as CNT content increases. When the Avrami index reduces to I or lower, nucleation dominates the overall kinetics as a consequence of confinement effects. Wide-angle X-ray experiments were performed at a high-energy synchrotron source and demonstrated that no change in the orthorhombic unit cell of HDPE occurred during crystallization with or without CNT.

Maximum induced subgraph of a recursive circulant

The recursive circulant RC(2(n), 4) enjoys several attractive topological properties. Let max_epsilon(G) (m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. In this paper, we show that max_epsilon(RC(2n,4))(m) = Sigma(i)(r)=(0)(p(i)/2 + i)2(Pi), where p(0) > p(1) > ... > p(r) are nonnegative integers defined by m = Sigma(i)(r)=(0)2(Pi). We then apply this formula to find the bisection width of RC(2(n), 4). The conclusion shows that, as n-dimensional cube, RC(2(n), 4) enjoys a linear bisection width. (c) 2005 Elsevier B.V. All rights reserved.

Electronic transitions and bonding properties in a series of five-coordinate “16-electron” complexes [Mn(CO)3(L2)]− (L2=chelating redox-active π-donor ligand)

In this article we present for the first time accurate density functional theory (DFT) and time-dependent (TD) DFT data for a series of electronically unsaturated five-coordinate complexes [Mn(CO)(3)(L-2)](-), where L-2 stands for a chelating strong pi-donor ligand represented by catecholate, dithiolate, amidothiolate, reduced alpha-diimine (1,4-dialkyl-1,4-diazabutadiene (R-DAB), 2,2'-bipyridine) and reduced 2,2'-biphosphinine types. The single-crystal X-ray structure of the unusual compound [Na(BPY)][Mn(CO)(3)(BPY)]center dot Et2O and the electronic absorption spectrum of the anion [Mn(CO)(3)(BPY)](-) are new in the literature. The nature of the bidentate ligand determines the bonding in the complexes, which varies between two limiting forms: from completely pi-delocalized diamagnetic {(CO)(3)Mn-L-2}(-) for L-2 = alpha-diimine or biphosphinine, to largely valence-trapped {(CO)(3)Mn-1-L-2(2-)}(-) for L-2(2-) = catecholate, where the formal oxidation states of Mn and L-2 can be assigned. The variable degree of the pi-delocalization in the Mn(L-2) chelate ring is indicated by experimental resonance Raman spectra of [Mn(CO)(3)(L-2)](-) (L-2=3,5-di-tBu-catecholate and iPr-DAB), where accurate assignments of the diagnostically important Raman bands have been aided by vibrational analysis. The L-2 = catecholate type of complexes is known to react with Lewis bases (CO substitution, formation of six-coordinate adducts) while the strongly pi-delocalized complexes are inert. The five-coordinate complexes adopt usually a distorted square pyramidal geometry in the solid state, even though transitions to a trigonal bipyramid are also not rare. The experimental structural data and the corresponding DFT-computed values of bond lengths and angles are in a very good agreement. TD-DFT calculations of electronic absorption spectra of the studied Mn complexes and the strongly pi-delocalized reference compound [Fe(CO)(3)(Me-DAB)] have reproduced qualitatively well the experimental spectra. Analyses of the computed electronic transitions in the visible spectroscopic region show that the lowest-energy absorption band always contains a dominant (in some cases almost exclusive) contribution from a pi(HOMO) -> pi*(LUMO) transition within the MnL2 metallacycle. The character of this optical excitation depends strongly on the composition of the frontier orbitals, varying from a partial L-2 -> Mn charge transfer (LMCT) through a fully delocalized pi(MnL2) -> pi*(MnL2) situation to a mixed (CO)Mn -> L-2 charge transfer (LLCT/MLCT). The latter character is most apparent in the case of the reference complex [Fe(CO)(3)(Me-DAB)]. The higher-lying, usually strongly mixed electronic transitions in the visible absorption region originate in the three lower-lying occupied orbitals, HOMO - 1 to HOMO - 3, with significant metal-d contributions. Assignment of these optical excitations to electronic transitions of a specific type is difficult. A partial LLCT/MLCT character is encountered most frequently. The electronic absorption spectra become more complex when the chelating ligand L-2, such as 2,2'-bipyridine, features two or more closely spaced low-lying empty pi* orbitals.

Necessary and sufficient conditions for realizability of point processes

We give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.

Origin of electronic absorption spectra of MLCT-excited and one-electron reduced 2,2′-bipyridine and 1,10-phenanthroline complexes

UV–Vis absorption spectra of one-electron reduction products and 3MLCT excited states of [ReICl(CO)3- (N,N)] (N,N = 2,20-bipyridine, bpy; 1,10-phenanthroline, phen) have been measured by low-temperature spectroelectrochemistry and UV–Vis transient absorption spectroscopy, respectively, and assigned by open-shell TD-DFT calculations. The characters of the electronic transitions are visualized and analyzed using electron density redistribution maps. It follows that reduced and excited states can be approximately formulated as [ReICl(CO)3(N,Nÿ)]ÿ and ⁄[ReIICl(CO)3(N,Nÿ)], respectively. UV–Vis spectra of the reduced complexes are dominated by IL transitions, plus weaker MLCT contributions. Excited-state spectra show an intense band in the UV region of 50% IL origin mixed with LMCT (bpy, 373 nm) or MLCT (phen, 307 nm) excitations. Because of the significant IL contribution, this spectral feature is akin to the principal IL band of the anions. In contrast, the excited-state visible spectral pattern arises from predominantly LMCT transitions, any resemblance with the reduced-state visible spectra being coincidental. The Re complexes studied herein are representatives of a broad class of metal a-diimines, for which similar spectroscopic behavior can be expected.