Synthesis and NMR spectra of the syn and anti isomers of substituted cyclobutanes—evidence for steric and spatial hyperconjugative interactions

The syn and anti isomers of cis,cis-tricyclo[5.3.0.0^2,6]dec-3-ene derivatives have been synthesized and their ¹H and ¹³C NMR spectra unequivocally analyzed. Both their structures and their ¹H and ¹³C NMR chemical shifts were calculated by DFT, the latter two calculations employing the GIAO perturbation method. Additionally, calculated NMR shielding values were partitioned into Lewis and non-Lewis contributions from the bonds and lone pairs involved in the molecules by accompanying NBO and NCS analyses. The differences between the syn and anti isomers were evaluated with respect to steric and spatial hyperconjugation interactions.     

The anisotropic effect of functional groups in H NMR spectra is the molecular response property of spatial NICS—the frozen conformational equilibria of 9-arylfluorenes

Rotation about the single bond adjoining the aryl and fluorene moieties in 9-arylfluorenes can be frozen out on the NMR timescale if methyl groups are located at either one or both of the ortho positions of the aryl substituent. In the ground-state of these rotamers, the planes of the aryl and fluorene moieties are perpendicular to each other and the methyl substituents are consequently positioned either above the fluorene moiety or in-plane with it; thus, the methyl protons are either shielded or deshielded, respectively, due to the ring current effect of the fluorene moiety. This anisotropic effect on the ¹H chemical shifts of the methyl protons has been quantified on the basis of through-space NMR shieldings (TSNMRS) and subsequently Δδ_calcd compared with the experimentally observed chemical shift differences, Δδ_exp. In this context, the experimental anisotropic effects of functional groups in the ¹H NMR have proven to quantitatively be the molecular response property of theoretical spatial nucleus independent chemical shieldings (NICS). Differences between Δδ_calcd and Δδ_exp were, for the first time, also quantified as arising from steric compression.     

Relation between two-photon absorption and dipolar properties in a series of fluorenyl-based chromophores with electron donating or electron withdrawing substituents

We investigate two-photon absorption (2PA) in a series of fluorenyl-based 9,9-diethyl-2-ethynyl-7-((4-R-phenyl)ethynyl)-9,9a-dihydro-4aH-fluorene chromophores with R being various electron donating (ED) and electron withdrawing (EW) groups. We use wavelength-tunable femtosecond laser pulses to measure the 2PA cross sections in the lowest dipole-allowed transition and show that the substituents with stronger ED or EW character enhance the peak 2PA cross section (up to σ(2) ～ 60-80 GM) while the neutral substituents lead to smaller cross sections, σ(2) < 10 GM. We apply two-level approximation to establish a quantitative relation between the 2PA in the pure electronic transition (0-0) and the corresponding change of the permanent electric dipole moment upon the excitation (Δμ). This relation is elucidated by comparing Δμ values obtained from the 2PA measurements with quantum-chemical calculations and with measurements of solvatochromic shifts in a series of solvents. We show that the calculated Δμ correlate well with the values obtained from the 2PA spectroscopy. The Δμ values obtained from the solvatochromic shifts agree well with the above two methods for the chromophores with neutral or weak EW or ED substituents. On the other hand, stronger EW or ED end groups give much larger Stokes shifts, which lead to an overestimation of the Δμ values. We tentatively attribute this effect to the excitation-induced electronic density change occurring predominantly at the substituent side of the molecule, which causes the effective point dipole associated with the Δμ to interact more strongly with the surrounding solvent.     

Chelatoaromaticity--existing: yes or no? An answer given by spatial magnetic properties (through space NMR shieldings--TSNMRS)

The spatial magnetic properties (through space NMR shieldings--TSNMRS) of metal complexes (with ligands such as acetylacetone, 3-hydroxy-pyran(4)one) and "metallobenzenes" have been calculated by the GIAO perturbation method and visualized as Iso-Chemical-Shielding Surfaces (ICSS) of various sizes and directions. The TSNMRS values, thus obtained, can be successfully employed to quantify and visualize partial aromaticity of the metallocyclic ring by comparison with the spatial magnetic properties of the corresponding non-complexed ligands in comparable structural and electronic situations, and benzene, respectively. Because anisotropy/ring current effects in (1)H NMR spectra proved to be the molecular response property of TSNMRS, the results obtained concerning partial "chelatoaromaticity" are experimentally ensured.     

Strong Static Stability of Liquid Layers

For a class of disjoining pressure potentials we show that liquid layers in equilibrium with positive second variation for nonvanishing variations (called stable by definition) are in fact strong minimizers of the associated energy functional. In a previous paper, explicit stable layers are obtained for some cases of solid configurations with simple geometries, in particular for a single cylindrical or spherical cavity. From this note it follows that all these “stable” equilibria are strong energy minimizers. No smallness for the thickness of the layer is assumed.     

The curse of dimensionality for the class of monotone functions and for the class of convex functions

We study the integration and approximation problems for monotone or convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function values. We prove that these problems suffer from the curse of dimensionality. That is, one needs exponentially many (in $d$) function values to achieve an error $\epsilon$.     

A theoretical description of elastic pillar substrates in biophysical experiments.

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.     

Automorphisms of split Cayley algebras over real closed fields

Research supported in part by NSERC Canada grant A7251.     

Endliche projektive Ebenen gerader Ordnung mit Polaritäten

Ohne ZusammenfassungHerrn Herbert Zeitler zum 70. Geburtstag gewidmet