The effect of nitrogen atom on double bond pyramidalization

The title compound 6-phenyl-4,6,8-triazatetracyclo[9.2.1.0^2,10.0^4,8]tetradec-2(10)-ene-5,7-dione (6) has been synthesized by the addition of 4-phenyl-1,2,4-triazole-3,5-dione (PTAD) to 2,3-dimethylenebicyclo[2.2.1]heptane. The cell parameters are a = 9.991(5), b = 11.754(9), c = 6.549(5) Å, = 101.08(7)°, = 103.31(5)°, = 98.24(5)°. The crystal structure of 6 was determined. The obtained geometrical parameters were highly correlated with the DFT calculations. The experimentally determined folding angle of the double bond was found to be 8.44°. The effect of the electron-withdrawing ability of nitrogen atom on the degree of pyramidalization is discussed.     

Natural frequencies of a multi-degree-of-freedom vibration system

A chain structured mass-spring vibration system with N degrees of freedom is considered where massesM _j = m_jm = m/j and spring stiffnesses k_j = c_jk = (N + 1 - j)k, j = 1, …, N, have been applied. The conjecture of Mikota [1] on the natural frequencies is discussed showing how difficult it is to find an explicit solution of the related eigenvalue problem. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A <Emphasis Type="Italic">q</Emphasis>-deformed particle algebra with a unique <Emphasis Type="Italic">d</Emphasis>-dimensional representation

We present an algebra generated by a single pair of creation and annihilation operators b and b*. We prove that the algebra has a unique d-dimensional representation. Physically this algebra corresponds to a system where there are at most d − 1 particles in a state with otherwise same quantum numbers.     

Nonlinear pressure dependence of the interaction potential of dense protein solutions

The influence of pressure on the structure and protein-protein interaction potential of dense protein solutions was studied and analyzed using small-angle x-ray scattering in combination with a liquid state theoretical approach. The structural as well as the interaction parameters of dense lysozyme solutions are affected by pressure in a nonlinear way. The structural properties of water lead to a modification of the protein-protein interactions below 4?kbar, which might have significant consequences for the stability of proteins in extreme natural environments.     

Intercalation in layered metal-organic frameworks: reversible inclusion of an extended π-system

We report the synthesis of layered [Zn(2)(bdc)(2)(H(2)O)(2)] and [Cu(2)(bdc)(2)(H(2)O)(2)] (bdc = benzdicarboxylate) metal-organic frameworks (MOF) carried out using the liquid-phase epitaxy approach employing self-assembled monolayer (SAM) modified Au-substrates. We obtain Cu and Zn MOF-2 structures, which have not yet been obtained using conventional, solvothermal synthesis methods. The 2D Cu(2+) dimer paddle wheel planes characteristic for the MOF are found to be strictly planar, with the planes oriented perpendicular to the substrate. Intercalation of an organic dye, DXP, leads to a reversible tilting of the planes, demonstrating the huge potential of these surface-anchored MOFs for the intercalation of large, planar molecules.     

Density functional theory and Raman spectroscopy applied to structure and vibrational mode analysis of 1,1',3,3'-tetraethyl-5,5',6,6'-tetrachloro- benzimidazolocarbocyanine iodide and its aggregate

We have measured electronic and Raman scattering spectra of 1,1',3,3'-tetraethyl-5,5',6,6'-tetrachloro-benzimidazolocarbocyanine iodide (TTBC) in various environments, and we have calculated the ground state geometric and spectroscopic properties of the TTBC cation in the gas and solution phases (e.g., bond distances, bond angles, charge distributions, and Raman vibrational frequencies) using density functional theory. Our structure calculations have shown that the ground state equilibrium structure of a cis-conformer lies ～200 cm(-1) above that of a trans-conformer and both conformers have C(2) symmetry. Calculated electronic transitions indicate that the difference between the first transitions of the two conformers is about 130 cm(-1). Raman spectral assignments of monomeric- and aggregated-TTBC cations have been aided by density functional calculations at the same level of the theory. Vibrational mode analyses of the calculated Raman spectra reveal that the observed Raman bands above 700 cm(-1) are mainly associated with the in-plane deformation of the benzimidazolo moieties, while bands below 700 cm(-1) are associated with out-of-plane deformations of the benzimidazolo moieties. We have also found that for the nonresonance excited experimental Raman spectrum of aggregated-TTBC cation, the Raman bands in the higher-frequency region are enhanced compared with those in the nonresonance spectrum of the monomeric cation. For the experimental Raman spectrum of the aggregate under resonance excitation, however, we find new Raman features below 600 cm(-1), in addition to a significantly enhanced Raman peak at 671 cm(-1) that are associated with out-of-plane distortions. Also, time-dependent density functional theory calculations suggest that the experimentally observed electronic transition at ～515 nm (i.e., 2.41 eV) in the absorption spectrum of the monomeric-TTBC cation predominantly results from the π → π? transition. Calculations are further interpreted as indicating that the observed shoulder in the absorption spectrum of TTBC in methanol at 494 nm (i.e., 2.51 eV) likely results from the ν(") = 0 → ν' = 1 transition and is not due to another electronic transition of the trans-conformer-despite the fact that measured and calculated NMR results (not provided here) support the prospect that the shoulder might be attributable to the 0-0 band of the cis-conformer.     

Synthesis of dipyrrolo-diazepine derivatives via intramolecular alkyne cyclization

A regioselective approach was developed for the synthesis of dipyrrolo-diazepine derivatives. The synthetic route to dipyrrolo-diazepines first involves the synthesis of dipyrromethanes, followed by reaction of propargyl bromide in the presence of NaH to attach one alkyne functionality to the pyrrole nitrogen atom. Intramolecular heterocyclization with NaH in DMF between the alkyne functionality and pyrrole nitrogen atom gave the desired structures in good yields.     

Spinning solutions of classical Yang-Mills theory

A class of 0(4)-covariant solutions is found to Yang-Mills field equations in Minkowski space. The solutions have finite energy, contain the 0(4)-invariant solutions including the meron as special cases, and have an unexpected new feature: they possess angular momentum. Their physical properties are examined and numerical solutions are displayed graphically.