Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

Structure of disocium uridine 5'-Phosphate heptahydrate

Na2[CgHllN2OgP].7H20, M r = 494.0,orthorhombic, C222~, a = 22.880 (7), b = 8.877 (3),c = 19.592 (9) A, Z = 8, V = 3979.2 A 3. The Cu Ka intensity data consisted of 1005 unique reflections. Final R -- 14.5%. This nucleotide shows no unusual conformational features. The uracil base has an anti conformation about the glycosidic bond (tpo o = 44.4°). The furanose ring conformation is C(2')-endo,gauchegauche with tpo o = -75.5 ° and ~Poc = 49"6°.

Phenyl-Ring-Bearing Cationic Surfactants: Effect of Ring Location on the Micellar Structure

A series of isomeric cationic surfactants (S1-S5) bearing a long alkyl chain that carries a 1,4-phenylene unit and a trimethyl ammonium headgroup was synthesized; the location of the phenyl ring within the alkyl tail was varied in an effort to understand its influence on the amphiphilic properties of the surfactants. The cmc's of the surfactants were estimated using ionic conductivity measurements and isothermal calorimetric titrations (ITC); the values obtained by the two methods were found to be in excellent agreement. The ITC measurements provided additional insight into the various thermodynamic parameters associated with the micellization process. Although all five surfactants have exactly the same molecular formula, their micellar properties were seen to vary dramatically depending on the location of the phenyl ring; the cmc was seen to decrease by almost an order of magnitude when the phenyl ring was moved from the tail end (cmc of S1 is 23 mM) to the headgroup region (cmc of S5 is 3 mM). In all cases, the enthalpy of micellization was negative but the entropy of micellization was positive, suggesting that in all of these systems the formation of micelles is both enthalpically and entropically favored. As expected, the decrease in cmc values upon moving the phenyl ring from the tail end to he headgroup region is accompanied by an increase in the thermodynamic driving force (Delta G) for micellization. To understand further the differences in the micellar structure of these surfactants, small-angle neutron scattering (SANS) measurements were carried out; these measurements reveal that the aggregation number of the micelles increases as the cmc decreases. This increase in the aggregation number is also accompanied by an increase in the asphericity of the micellar aggregate and a decrease in the fractional charge. Geometric packing arguments are presented to account for these changes in aggregation behavior as a function of phenyl ring location.

Interactions of tris buffer with nucleotides: the crystal structure of tris(hydroxymethyl)methylammonium adenosine 5'-diphosphate dihydrate

The crystal and molecular structures of the Tris salt of adenosine 5'-diphosphate were determined from X-ray diffraction data. The crystals are monoclinic, space P21, and Z = 2 with a=9.198 (2) A, b=6.894 (1) A, c=18.440 (4) A, and beta = 92.55 (2) degrees. Intensity data were collected on an automated diffractometer. The structure was solved by the heavy-atom technique and refined by least squares to R = 0.047. The ADP molecule adopts a folded conformation. The conformation about the glycosidic bond is anti. The conformation of the ribose ring is close to a perfect C(2')-endo-C-(3')-exo puckering. The conformation about C(4')-C(5') is gauche-gauche, similar to other nucleotide structures. The pyrophosphate chain displays a nearly eclipsed geometry when viewed down the P-P vector, unlike the staggered conformation observed in crystal structures of other pyrophosphates. The less favorable eclipsed conformation probably results from the observed association of Tris molecules with the polar diphosphate chain through electrostatic interactions and hydrogen bonds. Such interactions may play an important role in Tris-buffered aqueous solutions of nucleotides and metal ions.

A norbornadiene–cyclobutadiene cycloaddition cascade: novel intramolecular σ2+π2 trapping of a cyclobutane ring

Norbornadiene and 1,2-bismethoxycarbonylcyclobutadiene furnish a novel heptacyclic system 3(whose X-ray crystal structure has been determined)and an annulated pterodactylane derivative 4 in a single step.

Quinoxaline: Z `=1 form

A new Z' = 1 crystal structure of quinoxaline (or 1,4-diazanaphthalene), C8H6N2, with one-fifth the volume of the earlier known Z' = 5 structure was obtained by means of an in situ cryocrystallization technique.

Palladium(II) chloride complexes of bis(pyrazolyl)cyclotriphosphazenes

Reactions of the bis(3,5-dimethylpyrazolyl)cyclotriphosphazene derivatives gem-N3P3(MeNCH(2)CH(2)O)(2)(dmp)(2) (1) and nongeminal cis-N3P3(OPh)(4)(dmp)(2) (2) with PdCl2 afford complexes of the type [PdCl2.(L)] (L = 1 or 2). In these complexes, the phosphazenes act as bidentate NN-donor ligands with the two pyrazolyl pyridinic nitrogen atoms bonded to the metal, thus forming a six- and an eight-membered chelate ring, respectively. The structures of 2 and [PdCl2.(2)] (4) have been confirmed by single-crystal X-ray diffraction. Crystal data for 2: a = 16.759(2) Angstrom, b = 10.788(3) Angstrom, c = 19.635(9) Angstrom, beta = 101.61(3)degrees, P2(1/c), Z = 4, R = 0.038 for 4688 reflections with F > 5 sigma(F). Crystal data for 4: a = 9.701(3) Angstrom, b = 24.853(4) Angstrom, c = 15.794(4) Angstrom, beta = 101.46(2)degrees, P2(1/n), Z = 4, R = 0.030 for 5416 reflections with F > 5 sigma(F).

Structure of a steriod fungal metabolite

3a,7a, 14a-Trihydroxypregn-16-en-20-one, C21H3204, M r = 348.48, orthorhombic, P212121, a = 9.211 (1), b = 13.201 (1), c = 16.031 (1),~, V = 1949.28 (29)/~3, Z = 4, Dx = 1.187 g cm -3, A(Cu Ka), = 1.5418 ,~,/z = 6.07 cm-l, F(000) = 760, T= 293 K, R = 0.061 for 1337 observations. The A, B and C rings adopt normal chair conformations with the D ring in a 14a-envelope conformation. The molecules are held together by two hydrogen bonds [0(3)..'0(20) = 2.879 and O(7).--O(14)= 2.612 A,].

Structure of pregna-4,16-diene-7[alpha],14[alpha]-diol-3,20-dione

7a,14a-Dihydroxypregna-4,16-diene-3,20- dione, C21H2804, M r = 344.45, orthorhombic, P212121, a = 7.136 (1), b = 12.342 (1), c = 20.049 (3)/k, V= 1765.7 (3)/k 3, Z = 4, Dx = 1.295 g cm -3, A(Cu Kte) = 1.5418/k, /z = 6.7 cm- a, F(000) = 744, T = 293 K, R = 0.048 for 1345 observations. The A ring may be described as in a l a,2flhalf- chair conformation or a l a-sofa conformation. The B and C rings adopt normal chair conformations and the D ring has a 14a-envelope conforma tion. The molecules are held together by a hydrogen bond [0(3)...0(7)= 2.767 A].

Enantiospecific approach to AB-ring system of the diterpenes fusicoccanes

Enantiospecific synthesis of the AB ring system of 5-8-5 tricyclic diterpenes fusicoccanes has been accomplished, starting from the readily available monoterpene (R)-limonene employing an reaction as the key step.

An Approach Toward Homocalystegines and Silyl-homocalystegines. Acid-Mediated Migrations of Acetates in Seven-Membered Ring Systems

A short access to homocalystegine analogues silylated at C7 is described. The synthesis involves the desymmetrization of a (phenyldimethylsilyl)methylcycloheptatriene using osmium-mediated dihydroxylation, followed by the diol protection and a cycloaddition involving the remaining diene moiety and an acylnitroso reagent. Additions of the osmium and acylnitroso reagents were shown, through X-ray diffraction studies of the resulting major isomers, to occur anti and syn, respectively, relative to the SiCH2 substituent. N-O bond cleavage on the resulting cycloadduct then produces the aminopolyol having a silylmethyl substituent. Oxidation of the C-Si bond also afforded an access to unusual amino-heptitols having five contiguous stereogenic centers. In the course of this work, we finally observed a unusual rearrangement taking place on cycloheptanone 18 substituted by two acetyl groups and a neighboring Boc-protected amine. A profound reorganization of the substituents on the seven-membered ring effectively took place under acidic conditions (TFA) leading to the thermodynamically more stable homocalystegine-type compound., DFT calculations of the conformational energy of isomeric silyl homocalystegines indicated that the product observed upon the acid-mediated rearrangement was the most stable of a series of analogues with various distributions of substituents along the seven-membered ring backbone. A tentative mechanism is proposed to rationalize the acetate migrations and inversions of the stereochemistry at various stereocenters.

Ring Resonators and Micro Fluidics: Novel Design for Drug/Disease Detection

MEMS systems are technologically developed from integrated circuit industry to create miniature sensors and actuators. Originally these semiconductor processes and materials were used to build electrical and mechanical systems, but expanded to include biological, optical fluidic magnetic and other systems 12]. Here a novel approach is suggested where in two different fields are integrated via moems, micro fluidics and ring resonators. It is well known at any preliminary stage of disease onset, many physiological changes occur in the body fluids like saliva, blood, urine etc. The drawback till now was that current calibrations are not sensitive enough to detect the minor physiological changes. This is overcome using optical detector techniques 1]. The basic concepts of ring resonators, with slight variations can be used for optical detection of these minute disease markers. A well known fact of ring resonators is that a change in refractive index will trigger a shift in the resonant wavelength 5]. The trigger for the wavelength shift in the case discussed will be the presence of disease agents. To trap the disease agents specific antibody has to be used (e. g. BSA).

1H-4,1,2-Benzothiadiazines from 1,2,3-Benzothiadiazole via Alkylbenzothiadiazolium Salts: A Novel Heterocyclic Ring Expansion Possibly via Nitrogen Ylides.

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Application of a modified z-cosy experiment for the analysis of spectra of oriented molecules - the spectrum of cis,cis-mucanonitrile

NMR spectra of cis,cis-mucanonitrile oriented in a liquid crystal have been analysed using the connectivity information obtained from a modified Z-COSY experiment which provided crucial clues for the starting parameters for the iterative analysis. The proton spectra with and without C-13 satellites and the C-13 spectra have thus been interpreted. The indirect spin-spin couplings required for the analyses have been obtained from the corresponding isotropic spectra. The H-1-H-1 and C-13-H-1 dipolar couplings so obtained have been utilized to determine the relative internuclear distances. The results indicate that the molecule is planar. (C) 1994 Academic Press, Inc.