Overall values of conventional discrepancy indices for related and unrelated models of a non-centrosymmetric crystal with a centrosymmetric group

Theoretical expressions for the overall values of the conventional discrepancy indicesR(F) andR(I) are derived for a non-centrosymmetric crystal with a centrosymmetric group by taking the centrosymmetric group and a part of the other atoms in the unit cell as the trial structure. These results are used to obtain tables of values of these indices in terms of the parameter σ _1c ² and σ ₁ ² which define the fractional contribution to the local mean intensity from the centrosymmetric group and all the known atoms respectively. Contribution No. 561     

Structure and conformation of n‐ (t‐butoxycarbonyl)‐l‐valine‐l‐phenylalanine‐methyl ester (Boc‐Val‐Phe‐OMe)

The crystal structure of N‐ (t‐butoxycarbonyl) ‐ L‐valine‐L‐phenylalanine‐methyl ester (Boc‐Val‐Phe‐OMe), C₂₀H₃₀N₂O₅ was determined by X‐ray diffraction methods. The dipeptide crystallizes in orthorhombic space group P2₁2₁2₁, with cell parameters a = 5.0680(1) Å, b = 13.8650(1) Å and c = 28.2630(1) Å, V = 2143.8(5) ų, F.W. = 378.46, Z = 4, D_calc = 1.173 Mg/m³, μ = 0.687 mm^‐1, F₀₀₀ = 816, CuKα = 1.5418 Å. The structure was solved by direct methods and final R1 and wR2 are 0.0659 and 0.1654, respectively. The peptide unit is in trans conformation [ω = 177.4(9)°]. The conformation angles ϕ₁, ψ₁, ϕ₂ and ψ₂ for the peptide backbone are: ‐96.5(13)°, 101.2(13)°, ‐123.9(12)° and 34.0(15)°. The N‐H…O and C‐H…O hydrogen bondings influence the packing of the molecules in the dipeptide crystal. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

t‐3‐Iso­propyl‐1‐methyl‐r‐2,c‐6‐di­phenyl­piperidin‐4‐one thio­semi­carbazone

The piperidine ring in the title compound, C₂₂H₂₈N₄S, exhibits a chair conformation. The thio­semicarbazone moiety adopts an extended conformation, and the planar phenyl rings are oriented equatorially with respect to the piperidine ring. Two intermol­ecular hydrogen bonds involving the S atom form molecular pairs, and the crystal structure is stabilized by weak C—H⃛π interactions in addition to van der Waals forces.     

Thermodynamics of supramolecular naphthalenediimide nanotube formation: the influence of solvents, side chains, and guest templates

Amino-acid functionalized naphthalenediimides self-assemble into hydrogen-bonded supramolecular helical nanotubes via a noncooperative, isodesmic process; the self-assembly of ordered helical systems is usually realized through a cooperative process. This unexpected behavior was rationalized as a manifestation of entropy-enthalpy compensation. Fundamental insights into the thermodynamics governing this self-assembly were obtained through the fitting of the isodesmic model to (1)H NMR spectrometry and circular dichroism spectroscopy measurements. Furthermore, we have extended the application of this mathematical model, for the first time, to quantitatively estimate the effect of guests, solvents, and side chains on the stability of the supramolecular nanotube; most significantly, we demonstrate that C(60) acts as a template to stabilize the nanotube assembly and thereby substantially increase the degree of polymerization.     

Nonlinear compression of optical solitons

In this paper, we consider nonlinear Schrödinger (NLS) equations, both in the anomalous and normal dispersive regimes, which govern the propagation of a single field in a fiber medium with phase modulation and fibre gain (or loss). The integrability conditions are arrived from linear eigen value problem. The variable transformations which connect the integrable form of modified NLS equations are presented. We succeed in Hirota bilinearzing the equations and on solving, exact bright and dark soliton solutions are obtained. From the results, we show that the soliton is alive, i.e. pulse area can be conserved by the inclusion of gain (or loss) and phase modulation effects.