Meso-[2.2]paracyclophanyltriphenylporphyrin: A simple representative of cyclophanylporphyrins

(R + S)Meso-[2.2]Paracyclophanyltriphenylporphyrin 3 , a member of a novel class of cyclophanylporphyrins, was obtained and characterized by spectroscopic and electrochemical methods. Compared to meso-tetra[2.2]paracyclophanylporphyrin 1, it represents a simplified structure designed for the investigation of electronic interactions between the [2.2]paracyclophane moiety and porphyrin core and for use in metallation reactions.     

Solid-state molecular organization and solution behavior of methane-1,1-diphosphonic acid derivatives of heterocyclic amines: the role of the topochemical ring modification and the intramolecular hydrogen bonds in monosubstituted piperid-1-ylmethane-1,1-diphosphonic acids

The crystal structures of 3-methylpiperid-1-ylmethane-1,1-diphosphonic (2), 4-methylpiperid-1-ylmethane-1,1-diphosphonic (3), 2-ethylpiperid-1-ylmethane-1,1-diphosphonic (4), and 2-methylpiperid-1-ylmethane-1,1-diphosphonic (5) acids have been determined and are discussed with respect to their molecular organization and crystal-packing preferences. The chair conformation, predominant also in solution, favors equatorial positioning of the bulky substituents of the heterocyclic N and C atoms. The molecular geometry also provides access to intramolecular hydrogen-bond formation between the axial protons located on the nitrogen atoms, as well as the carbon atoms closest to it, and phosphonic/phosphonate oxygen atoms. The molecules preferably arrange in monolayers, observed in all crystals with an exception of 3. The layers are held in place in the third direction through van der Waals interactions. The analysis of two-dimensional hydrogen-bonded networks is concentrated on revealing how the substituent's topology of the molecule affects the solid-state organization in well-defined structures and is aimed at unraveling the consequences and the possible conformational changes by stepwise network disruption upon crystal dissolution in water. The solution NMR studies are focused on revealing the role that the topochemistry of the substituent plays for the stereodynamics in 2-5. It is demonstrated that in contrast to piperid-1-ylmethane-1,1-diphosphonic acid (1), in which the ring inversion/rotation around the C-N bond concerted with the N-H...O hydrogen-bond breaking/formation process leads to a mixture of two interconverting conformers, the concerted N-H...O breaking/rotation/N-H...O formation process in 2 and 3 allows for a predominance of one conformer in solution. However, placement of a substituent at 2-position in the ring hampers the rotation around the C-N bond; this makes 4 and 5 significantly less flexible relative to compounds 1-3. In addition, both compounds 4 and 5 are proved to exist as a mixture of two conformers, the equilibrium of which in acidic solution is shifted towards the conformer found in solid state. In alkaline solutions of 4 and 5, the equilibrium is shifted towards the conformer that is forced by the flipping of the heterocyclic ring. These results correlate well with recently documented differences in the biological potency of this group of compounds.     

(Higgs)2,3 quantum fields in a finite volume

This is the second part of the paper entitled, “(Higgs)_2,3 Quantum Fields in a Finite Volume.” The proof of an upper bound for vacuum energy is completed with the exception of some technical estimates.     

Natural bond orbital (NBO) analysis of the angular group induced bond alternation (AGIBA) substituent effect

The geometries, natural charges, and resonance structures of 11 monosubstituted benzene derivatives were analyzed at the B3LYP/6‐311++G(d,p) and HF/6‐311++G(d, p) levels of theory. The following angular substituents were chosen: OCH₃, CH₂CH₃, OH, SH, NHCH₃, NHNH₂, N?O, CH?CH₂, N?CH₂, N?NH, and CHO. The analysis of resonance structures was performed by using two different methodologies: harmonic oscillator stabilization energies (HOSE) and natural resonance theory (NRT). Also, the natural bond orbital (NBO) donor–acceptor stabilization energies for different resonance structures were calculated. We found that for all the substituents, the purely geometric resonance stabilization parameter (HOSE) is linearly correlated with quantum chemically derived resonance structure weight (NRT) of a given structure. Also, the calculations provide qualitative support for the earlier assumption of a through space angular group induced bond alternation (AGIBA) effect. Copyright © 2010 John Wiley & Sons, Ltd.     

Field asymmetric waveform ion mobility spectrometry studies of proteins: Dipole alignment in ion mobility spectrometry?

Approaches to separation and characterization of ions based on their mobilities in gases date back to the 1960s. Conventional ion mobility spectrometry (IMS) measures the absolute mobility, and field asymmetric waveform IMS (FAIMS) exploits the difference between mobilities at high and low electric fields. However, in all previous IMS and FAIMS experiments ions experienced an essentially free rotation; thus the separation was based on the orientationally averaged cross-sections Omega(avg) between ions and buffer gas molecules. Virtually all large ions are permanent electric dipoles that will be oriented by a sufficiently strong electric field. Under typical FAIMS conditions this will occur for dipole moments >400 D, found for many macroions including most proteins above approximately 30 kDa. Mobilities of aligned dipoles depend on directional cross-sections Omega(dir) (rather than Omega(avg)), which should have a major effect on FAIMS separation parameters. Here we report the FAIMS behavior of electrospray-ionization-generated ions for 10 proteins up to approximately 70 kDa. Those above 29 kDa exhibit a strong increase of mobility at high field, which is consistent with predicted ion dipole alignment. This effect expands the useful FAIMS separation power by an order of magnitude, allowing separation of up to approximately 10(2) distinct protein conformers and potentially revealing information about Omega(dir) and ion dipole moment that is of utility for structural characterization. Possible approaches to extending dipole alignment to smaller ions are discussed.     

Effect of temperature on spectroscopic features relevant to laser performance of YVO4:Tm3+, GdVO4:Tm3+, and LuVO4:Tm3+ crystals

Optical spectra and luminescence decay curves were measured for thulium-doped YVO(4), GdVO(4), and LuVO(4) single crystals as a function of temperature in the 300-670 K temperature region. In spite of structural similarity, the three systems studied display significantly different transition intensities and nonradiative relaxation rates. It was found, in particular, that the peak value of the pump band absorption intensity diminishes by about 30% for Tm:YVO(4) and Tm:GdVO(4), and the effective emission cross section for the laser transition of Tm(3+) diminishes by a factor of 2 roughly when temperature increases from 300 to 500 K. An unusually small quantum efficiency of the upper laser level in Tm:LuVO(4) has been derived from the analysis of luminescence decay curves.     

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

In the paper, the classical exact absolute value function method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value penalty function method is analyzed under assumption that the functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value penalty function are given.     

Codimension-two critical behavior in vacuum gravitational collapse

We consider the critical behavior at the threshold of black-hole formation for the five-dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a discretely self-similar solution with two unstable modes.