A New Class of Exactly Solvable Interacting Fermion Models in One Dimension

We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be salved exactly via a simple unitary transformation. Nevertheless, correlation functions exhibit nontrivial interaction-dependent exponents. A similar model defined on a lattice is introduced and solved. Various generalizations, e.g., to the case of internal symmetries of the fermions, are discussed. The present treatment also clarifies certain aspects of Luttinger's original solution of the "Luttinger model."

Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics

In this paper, the critical budding temperature of single-walled carbon nanotubes (SWCNTs), which are embedded in one-parameter elastic medium (Winkler foundation) is estimated under the umbrella of continuum mechanics theory. Nonlocal continuum theory is incorporated into Timoshenko beam model and the governing differential equations of motion are derived. An explicit expression for the non-dimensional critical buckling temperature is also derived in this work. The effect of the nonlocal small scale coefficient, the Winkler foundation parameter and the ratio of the length to the diameter on the critical buckling temperature is investigated in detail. It can be observed that the effects of nonlocal small scale parameter and the Winkler foundation parameter are significant and should be considered for thermal analysis of SWCNTs. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the thermal buckling properties of embedded single-walled carbon nanotubes. (C) 2011 Elsevier B.V. All rights reserved.

Spin state and exchange in the quasi-one-dimensional antiferromagnet KFeS2

We report the optical spectra and single crystal magnetic susceptibility of the one-dimensional antiferromagnet KFeS2. Measurements have been carried out to ascertain the spin state of Fe3+ and the nature of the magnetic interactions in this compound. The optical spectra and magnetic susceptibility could be consistently interpreted using a S = 1/2 spin ground state for the Fe3+ ion. The features in the optical spectra have been assigned to transitions within the d-electron manifold of the Fe3+ ion, and analysed in the strong field limit of the ligand field theory. The high temperature isotropic magnetic susceptibility is typical of a low-dimensional system and exhibits a broad maximum at similar to 565 K. The susceptibility shows a well defined transition to a three dimensionally ordered antiferromagnetic state at T-N = 250 K. The intra and interchain exchange constants, J and J', have been evaluated from the experimental susceptibilities using the relationship between these quantities, and chi(max), T-max, and T-N for a spin 1/2 one-dimensional chain. The values are J = -440.71 K, and J' = 53.94 K. Using these values of J and J', the susceptibility of a spin 1/2 Heisenberg chain was calculated. A non-interacting spin wave model was used below T-N. The susceptibility in the paramagnetic region was calculated from the theoretical curves for an infinite S = 1/2 chain. The calculated susceptibility compares well with the experimental data of KFeS2. Further support for a one-dimensional spin 1/2 model comes from the fact that the calculated perpendicular susceptibility at 0K (2.75 x 10(-4) emu/mol) evaluated considering the zero point reduction in magnetization from spin wave theory is close to the projected value (2.7 x 10(-4) emu/mol) obtained from the experimental data.

Synthesis based on cyclohexadienes .23. Total synthesis of 5-epi-pupukean-2-one

A new strategy for the construction of the isotwistane skeleton is reported from easily available cyclohexadienes which involves stereoselective alkylation of a bicyclooctenone derivative and a decarboxylative 5-exo-trig radical cyclisation as the key steps in the total synthesis of 5-epi-pupukean-2-one.

Exact spectral functions of a non-Fermi liquid in one dimension

We study the exact one-electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give spectral functions that turn out to be computable, interesting, and nontrivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.

Hydrothermal synthesis and structure of organically templated one-dimensional and three-dimensional iron fluorophosphate

Two new open-framework iron fluorophosphates, [C(4)N(2)H(12)](0.5) [FeF(HPO(4))(H(2)PO(4))] (I) and [C(4)N(2)H(12)][Fe(4)F(2)(H(2)O)(4)(PO(4))(4)]. 0.5H(2)O (II), were synthesized hydrothermally using piperazine as a templating agent. The structures were determined by single-crystal X-ray diffraction. Compound I crystallizes in the orthorhombic space group Pbca, a = 7.2126(2) Angstrom, b = 14.2071(4) Angstrom, c = 17.1338(2) Angstrom, Z = 8. The structure is composed of infinite anionic chains of [FeF(HPO(4))(H(2)PO(4))](n)(-) built by trans-fluorine sharing FeF(2)O(4) octahedra. These chains are similar to those found in tancoite-type minerals. Compound II crystallizes in the monoclinic space group P2(1)/n, a = 9.9045(3) Angstrom, b = 12.3011(3) Angstrom, c = 17.3220(4) Angstrom, beta = 103.7010(10)degrees, Z = 4. The structure of compound II has a three-dimensional (3D) architecture with an eight-membered channel along the b axis, in which protonoted piperazine molecules reside. The complex framework is built from two types of secondary building unit (SBU): one hexamer [Fe(3)F(2)(H(2)O)(2)(PO(4))(3)] (SBU6), and one dimer [FeO(4)(H(2)O)(2)PO(4)] (SBU2). The vertex sharing between these SBUs create the 3D structure.

Study of translational and rotational mobility and orientational preference of ethane in one-dimensional channels

Structural and dynamical properties of ethane in one-dimensional channels of AlPO4-5 and carbon nanotube have been investigated at dilute concentration with the help of molecular dynamics simulation. Density distributions and orientational structure of ethane have been analyzed. Repulsive interactions seem to play an important role when ethane is located in the narrow part of the AlPO4-5 channel. In AlPO4-5, parallel orientation is predominant over perpendicular orientation except when ethane is located in the broader part of the channel. Unlike in the case of single-file diffusion, our results in carbon nanotube show that at dilute concentrations the mean squared displacement, mu(2)(t) approximate to t(alpha), alpha = 1.8. The autocorrelation function for the z-component of angular velocity of ethane in space-fixed frame of reference shows a pronounced negative correlation. This is attributed to the restriction in the movement of ethane along the x- and y- directions. It is seen that the ratio of reorientational correlation times does not follow the Debye model for confined ethane but it is closer to the predictions of the Debye model for bulk ethane.

A Layered Zinc Phosphate, [C6N4H22][Zn6(PO4)4(HPO4)2], Formed by One-Dimensional Tubes

An open-framework zinc phosphate, [C6N4H22][Zn6(PO4)4(HPO4)2] (I), with alternating inorganic and organic layers has been synthesized hydrothermally from a starting mixture of ZnO, HCl, H3PO4, H2C2O4, and triethylenetetramine. Single-crystal data for I: monoclinic, space GROUP =P21/c (No. 14), a=9.881(1), b=16.857(1), c=8.286(1) Å, β=96.7(1)°, V=1370.8(1) Å3, Z=2, R1=0.06, and wR2=0.13 [1408 observed reflections with I>2σ(I)]. The structure of I comprises a network of ZnO4, PO4, and PO3(OH) tetrahedra forming one-dimensional tubes. The tubes, in turn, are linked via oxygen atoms forming macroanionic inorganic layers with eight-membered apertures. The one-dimensional tube-like architecture in I is a novel feature worthy of note.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

Transformations of the layered zinc phosphates of the compositions [C6N4H22](0.5) [Zn-2 (HPO4)(3)], I, [C3N2H12][Zn-2 (HPO4)(3)], II and [C3N2OH12][Zn-2 (HPO4)(3)], III, containing triethylenetetramine, 1,3-diaminopropane, and 1,3-diamino-2-hydroxypropane, respectively, have been investigated under different conditions. On heating in water, I transforms to a one-dimensional (1-D) ladder and a three-dimensional (3-D) structure, while II gives rise to only a two-dimensional (2-D) layered structure. In the transformation reaction of I with zinc acetate, the same ladder and 3-D structures are obtained along with a tubular layer. Under similar conditions II gives a layered structure formed by the joining of two ladder motifs. III, on the other hand, is essentially unreactive when heated with water and zinc acetate, probably because the presence of the hydroxy group in the amine which hydrogen bonds to the framework. In the presence of piperazine, I, II and III give rise to a four-membered, corner-shared linear chain which is likely to be formed via the ladder structure. In addition, 2-D and 3-D structures derived from the 1-D linear chain or ladder structures are also formed. The primary result from the study is that the layers produce 1-D ladders, which then undergo other transformations. It is noteworthy that in the various transformations carried out, most of the products are single-crystalline.

Crystal and molecular structure of synthetic cholesterol compounds vitamin D3-analogues (I) 24(S)-hydroxy coprastan-3-one & (II) 24(R)-hydroxy coprastan-3-one

The title compound I (24-(S)-Hydroxy Coprastan-3-one) crystallises in orthorhombic space group P2(1)2(1)2(1) with Z = 4. The unit cell dimensions are a = 6.701(2)Angstrom, b = 11.506(8)Angstrom, c = 32.183(4)Angstrom, V = 2481(2)Angstrom (3), D-cal = 1.077 Mg/m(3). The tide compound II (24-(R)-Hydroxy Coprastan-3-one) crystallises in orthorhombic space group P212121 with two molecules per assymetric unit and with Z = 8. The Unit cell dimensions are a = 10.954(2)Angstrom, b = 21.757(6)Angstrom, c = 21.130(7)Angstrom, V = 5035.0(2)Angstrom (3), D-cal = 1.062 Mg/m(3). In compound I and in both the molecules of compound II, the rings A, B & C are in chair conformation and the five membered ring D is in envelope conformation. The priority sequence attached to the chiral carbon C24 has "S" designation in compound I and "R" designation in compound II. The structures are stabilized by C-H . . .O and O-H---O hydrogen bonds.

One-dimensional zinc phosphates with linear chain structure

Three one-dimensional zinc phosphates, [C5N2H14][Zn(HPO4)2], I, [C10N4H26][Zn(HPO4)2].2H2O II, and [C4N2H6]2[Zn(HPO4)], III, have been prepared employing hydro/solvothermal methods in the presence of organic amines. While I and II consist of linear chains of corner-shared four-membered rings, III is a polymeric wire where the amine molecule is directly bonded to the metal center. The wire, as well as the chain in these structures, are held together by hydrogen bond interactions involving the amine and the framework oxygens. The polymeric zinc phosphate with wire-like architecture, III, is only the second example of such architecture. Crystal data: I, monoclinic, P21/c (no. 14), a=8.603(2), b=13.529(2), c=10.880(1) Å, β=94.9(1)°, V=1261.6(1) Å3, Z=4, ρcalc.=1.893 gcm−3, μ(MoKα)=2.234 mm−1, R1=0.032, wR2=0.086, [1532 observed reflections with I>2σ(I)], II, orthorhombic, Pbca (no. 61), a=8.393(1), b=15.286(1), c=22.659(1) Å, V=2906.9(2) Å3, Z=8, ρcalc.=1.794 gcm−3, μ(MoKα)=1.957 mm−1, R1=0.055, wR2=0.11, [1565 observed reflections with I>2σ(I) and III, monoclinic, P21/c (no. 14), a=8.241(1), b=13.750(2), c=10.572(1) Å, β=90.9(1)°, V=1197.7(2) Å3, Z=4, ρcalc.=1.805 gcm−3, μ(MoKα)=2.197 mm−1, R1=0.036, wR2=0.10, [1423 observed reflections with I>2σ(I)].

Enantiospecific synthesis of functionalised bicyclo[3.3.1] nonanes from 10-bromocarvones via tandem intermolecular alkylation-intramolecular Michael addition sequence

A simple and convenient tandem methodology for the enantiospecific generation of functionalised bicyclo[3.3.1] nonanes 9,14-18, via intermolecular alkylation of Michael donors with 10-bromocarvones 7, 10 and 11, followed by intramolcular Michael addition, is achieved. An unsuccessful attempt for the extension of the methodology for a possible short enantiospecific approach to AB-ring system 22 of taxanes via the allyl bromide 21, is also described.