The Ground State Energy of a Dilute Two-Dimensional Bose Gas

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E₀/N=(2²/m)|ln(a²)|^–1, to leading order, with a relative error at most O(|ln(a²)|^–1/5). Here N is the number of particles, =N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E₀ is not simply N(N–1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger.     

Stringent tests of shell model calculations in fp shell nuclei (46, 48)Ti and (50,52)Cr from measurements of g factors and B(E2) values

Measurements of magnetic moments and lifetimes of 2(+)(1) and 4(+)(1) states of (46,48)Ti and (50,52)Cr were performed with high accuracy via projectile Coulomb excitation and the technique of transient magnetic fields. The high quality of the data allows for the first time to establish stringent constraints on large scale shell model calculations. Whereas the global behavior of the data is well explained by full fp shell model calculations, distinct deviations in the g factors and B(E2) values of (46,48)Ti from theoretical predictions can be attributed to excitations of the 40Ca core. This suggestion is supported by recent Monte Carlo calculations which provide evidence that 48Ca is a better inert core.     

The Photoenolization of 2-Methylacetophenone and Related Compounds

A reinvestigation of 2-methylacetophenone ( 1 ) by ns flash photolysis has provided detailed evidence for the reaction sequence of photoenolization. The triplet reaction proceeds adiabatically from the lowest excited triplet state of the ketone, ³ K (1) , to the enol excited triplet state, ³ E (1) , which decays both to enol and ketone ground state. The Z- and E-isomers of the photoenol, Z- E (1) and E- E (1) are formed in about equal yield by the triplet pathway, while direct enolization from the lowest excited singlet state of 1 yields (predominantly) the Z-isomer. Intramolecular reketonization from Z- E (1) to 1 proceeds at a rate of ca. 10⁸s^?1 in cyclohexane, but can be retarded to ca. 10⁴s^?1 in hydrogen-bond-acceptor solvents. The proposed mechanism is summarized in Scheme 1 and rationalized on the basis of a state correlation diagram, Scheme 2. 3,3,6,8-Tetramethyl-1-tetralone ( 2 ) was used as a reference compound with fixed conformational position of the carbonyl group, and some results from a brief investigation of 2,4-dimethylbenzophenone ( 3 ) are also reported.     

Total synthesis of (+/-)-mersicarpine

The first total synthesis of the indole alkaloid mersicarpine is reported. Key steps include a beta-dicarbonyl radical cyclization, as well as an oxidation of the benzopyrrole moiety to establish the masked 1,2-dicarbonyl functionality. An X-ray crystal structure and discussion of the 1H NMR behavior of the natural product are also presented.     

Comparative molecular dynamics and Monte Carlo study of statistical properties for coarse-grained heteropolymers

Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nosé-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nosé-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nosé-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.     

Double N-H bond activation of N,N'-bis-substituted hydrazines with stable N-heterocyclic silylene

The reaction of N-heterocyclic silylene (NHSi) L [L = CH{(C[double bond, length as m-dash]CH(2))(CMe)(2,6-iPr(2)C(6)H(3)N)(2)}Si] with benzoylhydrazine, 1,2-dicarbethoxyhydrazine, 1,2-diacetylhydrazine and 1,2-bis(tert-butoxycarbonyl)hydrazine in 1 : 1 molar ratio resulted in compounds 1-4 with an almost quantitative yield and five coordinate silicon atoms. Compounds 1-4 were formed by double N-H bond activation by deliberate selection of N,N'-bis-substituted hydrazine compounds bearing the -C(O)NHNH- unit. Compounds 1-4 were characterized by NMR spectroscopy, EI-MS and elemental analysis. The molecular structures of compounds 1-3 were unambiguously established by single crystal X-ray structural analysis.     

Individual strings of conducting carbon cones and discs in a polymer matrix: Electric field‐induced alignment and their use as a strain sensor

We demonstrate micromechanical strain sensors with integrated readout based on carbon nanocones and discs (CNCs) which are aligned into a string‐like formation using an alternating electric field and studied by AC impedance spectroscopy and electromechanical methods. The CNC particles are first dispersed into a polymer matrix with a particle fraction of 0.1 vol %. This value is well below the percolation threshold (～ 2 vol %), which suppresses particle aggregation and facilitates transparency allowing the use of an UV‐curable polymer. Alignment was carried out with a 1 kHz, 4 kV/cm electric field and is a consequence of dielectrophoretic effect. It develops in minutes and makes the initially insulating, nonaligned material conductive. This is followed by UV curing of the polymer matrix, which renders a solid state device. The stretching of the aligned strings in the cured polymer leads to a reversible piezoresistive effect, and a gauge factor of about 50 is observed. This is in a sharp contrast to CNC films with particle fraction above percolation threshold (13 vol %), which are conductive but not sensitive to stretching. The strings are Ohmic in nature and moreover show higher DC conductivity (22–500 S/m) compared to identically prepared carbon black strings (1–22 S/m). © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

New air-stable planar chiral ferrocenyl monophosphine ligands: Suzuki cross-coupling of aryl chlorides and bromides

[reaction: see text] A novel class of planar chiral electron-rich monophosphine ligands has been developed. The modular design allows a short and efficient synthesis of an array of aryl-ferrocenyl derivatives carrying the donating bis(dicyclohexyl)phosphino moiety. These new ligands have successfully been applied in the palladium-catalyzed Suzuki cross-coupling of activated as well as nonactivated aryl chlorides at room temperature. The asymmetric coupling of an aryl bromide and an aryl boronic acid was also tested, giving ees up to 54%.