2-Designs and a differential equation

We show that 2-designs with given parameters v, k, are in one-to-one correspondence to polynomials that solve a certain differential equation and have coefficients equal to zero or one. From this result we derive an existence theorem whereby designs correspond to integer points on a sphere in Euclidean space.     

Notiz zur Darstellung von 4-Hydroxy-6-methyl-5,6-dihydro-2H-pyran-2-on

Meldrum's acid (2) is acylated by diketen affording the acylMeldrum's acid3. In aqueous bicarbonate its 3-oxogroup is selectively reduced by sodium tetrahydroborate giving the alcohol4, which readily undergoes cyclization in refluxing dioxane leading to the title pyrone7. Under identical conditions3 produces the pyrone6 with the pyrone carboxylic acid5 as intermediate.

     

Primary reaction dynamics of halorhodopsin,observed by sub-picosecond IR – vibrational spectroscopy

The primary all-trans to 13-cis chromophore isomerization of the light driven chloride pump halorhodopsin has been studied by means of transient absorption spectroscopy in the visible and mid-infrared regime at a time resolution of better than 100 and 220 fs, respectively. The picosecond vibrational dynamics are dominated by two time constants, i.e., 2 and 7.7 ps in accordance with the biphasic decay of the retinal excited electronic state and electronic ground state formation with 1.5 and 6.6 ps. The transient vibrational spectra of the participating electronic states strongly suggest the existence of two distinct S₁ populations as a result of an early branching reaction. It is shown that the 13-cis product is formed with the fast time constant, whereas the all-trans educt state is repopulated via both time constants. Concomitant protein dynamics are indicated by spectral changes on a similar time scale in the amide region.     

Amino substituted 1-oxa-3-azabutatrienium salts: preparation, structure and reaction with carbonyl compounds

N,N-Dimethylformamide ($\text{4a}$) and N,N-dimethylpivalamide ($\text{4b}$) react with carbonyl chloride isocyanate ($\text{5}$) in the presence of antimony pentachloride to afford the amino substituted 1-oxa-3-azabutatrienium hexachloroantimonates $\text{6a}$,$\text{b}$. An X-ray diffraction analysis of $\text{6a}$ confirms the proposed structure. The heterocumulenes $\text{6a}$,$\text{b}$ react with aldehydes, ketones and tertiary carboxamides to give the amino substituted 2-azaallenium salts $\text{13a}$-$\text{O}$ in high yields.     

Resonances and microlocal analysis

In this paper we outline briefly how microlocal analysis can be applied to give a general approach to the mathematical theory of resonances in the semiclassical limit. We also describe recent results about the asymptotic behavior of resonances generated by closed trajectories and stationary points in the classical flow.     

Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding

In this study, we investigate the performance of the frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] to model the solvent effects on the electron-spin-resonance hyperfine coupling constants (hfcc's) of the H2NO molecule. The hfcc's for this molecule depend critically on the out-of-plane bending angle of the NO bond from the molecular plane. Therefore, solvent effects can have an influence on both the electronic structure for a given configuration of solute and solvent molecules and on the probability for different solute (plus solvent) structures compared to the gas phase. For an accurate modeling of dynamic effects in solution, we employ the Car-Parrinello molecular-dynamics (CPMD) approach. A first-principles-based Monte Carlo scheme is used for the gas-phase simulation, in order to avoid problems in the thermal equilibration for this small molecule. Calculations of small H2NO-water clusters show that microsolvation effects of water molecules due to hydrogen bonding can be reproduced by frozen-density embedding calculations. Even simple sum-of-molecular-densities approaches for the frozen density lead to good results. This allows us to include also bulk solvent effects by performing frozen-density calculations with many explicit water molecules for snapshots from the CPMD simulation. The electronic effect of the solvent at a given structure is reproduced by the frozen-density embedding. Dynamic structural effects in solution are found to be similar to the gas phase. But the small differences in the average structures still induce significant changes in the computed shifts due to the strong dependence of the hyperfine coupling constants on the out-of-plane bending angle.     

Electronic energy transfer and collection in luminescent molecular rods containing ruthenium(II) and osmium(II) 2,2':6',2"-terpyridine complexes linked by thiophene-2,5-diyl spacers

The electronic absorption spectra, luminescence spectra and lifetimes (in MeCN at room temperature and in frozen n-C3H7CN at 77 K), and electrochemical potentials (in MeCN) of the novel dinuclear [(tpy)Ru(3)Os(tpy)]4+ and trinuclear [(tpy)Ru(3)Os(3)Ru(tpy)]6- complexes (3 = 2,5-bis(2,2':6',2'-terpyridin-4-yl)thiophene) have been obtained and are compared with those of model mononuclear complexes and homometallic [(tpy)Ru(3)Ru(tpy)]4+, [(tpy)Os(3)Os(tpy)]4+ and [(tpy)Ru(3)Ru(3)Ru(tpy)]6+ Complexes. The bridging ligand 3 is nearly planar in the complexes, as seen from a preliminary X-ray determination of [(tpy)Ru(3)Ru(tpy)][PF6]4, and confers a high degree of rigidity upon the polynuclear species. The trinuclear species are rod-shaped with a distance of about 3 nm between the terminal metal centres. For the polynuclear complexes, the spectroscopic and electrochemical data are in accord with a significant intermetal interaction. All of the complexes are luminescent (phi in the range 10(-4)-10(-2) and tau in the range 6-340 ns, at room temperature), and ruthenium- or osmium-based luminescence properties can be identified. Due to the excited state properties of the various components and to the geometric and electronic properties of the bridge, Ru --> Os directional transfer of excitation energy takes place in the complexes [(tpy)Ru(3)Os(tpy)]4+ (end-to-end) and [(tpy)Ru(3)Os(3)Ru(tpy)]6+ (periphery-to-centre). With respect to the homometallic case, for [(tpy)Ru(3)Os(3)Ru(tpy)]6+ excitation trapping at the central position is accompanied by a fivefold enhancement of luminescence intensity.