New developments in the synthesis of pyrrolizidinone-based dipeptide isosteres

1,3-Dipolar cycloaddition of acrylamide with the cyclic nitrone derived from proline tert-butyl ester has been employed in the synthesis of bicyclic Gly-(s-cis)Pro isosteres suitably protected for the Fmoc-based solid phase peptide synthesis. (R)-1-Phenylethylamine was introduced as chiral auxiliary to resolve racemic intermediates and obtain enantiopure compounds. Using methacrylamide as dipolarophile, the analogous Ala-Pro mimetics have been prepared in racemic form, whereas the same strategy applied to methyl itaconate failed to give the corresponding Asp-Pro mimetic.     

Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

A nonadiabatic lower bound calculation of H 2 + and D 2 +

Accurate nonadiabatic lower and upper bounds for groundstate energies of H ₂ ⁺ and D ₂ ⁺ are calculated with the linearized method of variance minimization. The results in a.u. are –0.59713906₃<E ₀(H ₂ ⁺ )<–0.59713899₄ –0.59878877₅<E ₀(D ₂ ⁺ )<–0.59877873₈ i.e. the values are determined with an absolute error smaller than 0.02 cm^–1 for H ₂ ⁺ and 0.01 cm^–1 for D ₂ ⁺ .     

Optically active rhodium complexes with indenyl-linked phosphane ligands

The optically active indenyl-linked phosphane ligands (S)-[2-(3H-inden-1-yl)-1-phenylethyl]diphenylphosphane (L₁) and (S)-[2-(4,7-dimethyl-3H-inden-1-yl)-1-phenyl-ethyl]diphenylphosphane (L₂) were synthesized in three steps from (R)-1-phenylethane-1,2-diol in excellent yields. Their lithium salts reacted with [Rh(μ-Cl)(η²-CH₂CH₂)₂]₂ at −78 °C in THF affording the planar chiral complexes (S,R_pl + S_pl)-[Rh(η⁵-indenyl-CH₂CH(Ph)PPh₂-kP)(η²-CH₂CH₂)] and (S,R_pl + S_pl)-[Rh(η⁵-4,7-dimethylindenyl-CH₂CH(Ph)PPh₂-kP)(η²-CH₂CH₂)] as 61:39 and 15:85 mixtures of diastereomers. The complexes were isolated in optically pure form by column chromatography. The stereochemical configuration of one of the diastereomers was determined by X-ray crystallography. The complexation of L₂ was studied in different solvents and with several Rh precursors and diastereomeric excesses up to 76% were achieved. The ability of the chiral ligands to control the stereochemistry at the metal center was tested by oxidative addition of methyl iodide. Diastereomeric excesses greater than 98% were observed.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Linear Group 13 E≡E Triple Bonds in E2Li62+

The triply bonded heavier main-group compounds have a textbook trans-bent geometry, in contrast to a familiar linear form found for the lightest analogues. Strikingly, the unexpected linear group 13 E≡E triple bonds were herein found in the D_4h-symmetry E₂Li₆²⁺ clusters, and they possess a large barrier (>18.0 kcal/mol) towards the dissociation of Li⁺. The perfectly surrounded Li₄ motifs and two linear coordinated Li atoms strongly suppress the increasing nonbonded electron density of heavier E atoms, making two degenerate π bonds and one multi-center σ bond in linear heavier main-group triple bonds. The surrounding Li₆ motifs not only creates an effective electronic structure to form a linear E≡E triple bond, but the resulting electrostatic interactions account for the highly stable global E₂Li₆²⁺ clusters.     

Global X2A′ potential energy surface of Li2H and quantum dynamics of H + Li2 (X1Σg+) → Li + LiH (X1Σ+) reaction

A global potential energy surface (PES) for the electronic ground state of Li₂H system is constructed over a large configuration space. About 30 000 ab initio energy points have been calculated by MRCI‐F12 method with aug‐cc‐pVTZ basis set. The neural network method is applied to fit the PES and the root mean square error of the current PES is only 1.296 meV. The reaction dynamics of the title reaction has been carried out by employing time‐dependent wave packet approach with second order split operator on the new PES. The reaction probability, integral cross section and thermal rate constant are obtained from the dynamics calculation. In most of the collision energy regions, the integral cross sections are in well agreement with the results reported by Gao et al. The rate constant calculated from the new PES increases in the temperature range of present investigation.     

二组分混合物的最小流化特性 Ⅰ.混合/分离状态与最小流化空隙率

分析了二组分混合物的３种混合／分离状态及在完全混合时发生连续相转变的极限组成。提出一个判别非等密度体系混合／分离状态的法则与确定混合物空隙率简易可行的随意松散堆积方法。     

A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane

The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de Vries as a model for long-crested small-amplitude long waves propagating on the surface of water. The same partial differential equation has since arisen as a model for unidirectional propagation of waves in a variety of physical systems. In mathematical studies, consideration has been given principally to pure initial-value problems where the wave profile is imagined to be determined everywhere at a given instant of time and the corresponding solution models the further wave motion. The practical, quantitative use of the Korteweg-de Vries equation and its relatives does not always involve the pure initial-value problem. Instead, initial-boundary-value problems often come to the fore. A natural example arises when modeling the effect in a channel of a wave maker mounted at one end, or in modeling near-shore zone motions generated by waves propagating from deep water. Indeed, the initial-boundary-value problem

studied here arises naturally as a model whenever waves determined at an entry point propagate into a patch of a medium for which disturbances are governed approximately by the Korteweg-de Vries equation. The present essay improves upon earlier work on (0.1) by making use of modern methods for the study of nonlinear dispersive wave equations. Speaking technically, local well-posedness is obtained for initial data in the class for \frac34$"> and boundary data in , whereas global well-posedness is shown to hold for when , and for when . In addition, it is shown that the correspondence that associates to initial data and boundary data the unique solution of (0.1) is analytic. This implies, for example, that solutions may be approximated arbitrarily well by solving a finite number of linear problems.

     

The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a vertical cylindrical jet

The numerical solution of the thin film flow surrounding a horizontal cylinder resulting from a single vertical cylindrical jet is obtained. This is effected by transforming the domain of the flow, which contains a free surface, onto a rectangular parallelepiped and using a marching strategy to solve the ensuing parabolic equations. The flow terminates at a finite distance along the cylinder, its position depending on the velocity and mass flux of the jet. A comparison with the usual two-dimensional model in which the jet is replaced by a vertical sheet shows that such a representation is valid provided the overall width of the flow is not too large. In particular, the differences in heat transfer characteristics amount to a few per cent, thus validating the use of the two-dimensional model when applied to heat exchanger tubes. A comparison with the more usual multicolumn case is also considered.