General Adiabatic Evolution with a Gap Condition

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable. The presence of eigenilpotents in the spectral decomposition of the generator typically leads to solutions which grow exponentially fast in some inverse power of the adiabaticity parameter, even for real spectrum. In turn, this forbids the evolution to follow all instantaneous eigenprojectors of the generator in the adiabatic limit. Making use of superadiabatic renormalization, we construct a different set of time-dependent projectors, close to the instantaneous eigenprojectors of the generator in the adiabatic limit, and an approximation of the evolution semigroup which intertwines exactly between the values of these projectors at the initial and final times. Hence, the evolution semigroup follows the constructed set of projectors in the adiabatic regime, modulo error terms we control.     

Self‐association in {2‐[3,4‐alkylenedioxy‐5‐(3‐pyridyl)]‐thienyl}alkanols: an NMR,IR, and single‐crystal X‐ray study

syn‐2,2,4,4‐Tetramethyl‐3‐{2‐[3,4‐alkylenedioxy‐5‐(3‐pyridyl)]thienyl}pentan‐3‐ols self‐associate both in the solid state and in solution. Single‐crystal X‐ray diffraction study of the 3,4‐ethylenedioxythiophene (EDOT) derivative shows that it exists as a centrosymmetric head‐to‐tail, syn dimer in the solid state. The IR spectra of the solids display only a broad OH absorption around 3300 cm^?1, corresponding to a hydrogen‐bonded species. ¹H Nuclear Overhauser Effect Spectroscopy (NOESY) NMR experiments in benzene reveal interactions between the tert‐butyl groups and the H2 and H6 protons of the pyridyl group. Two approaches have been used to determine association constants of the EDOT derivative by NMR titration, based on the concentration dependence of (i) the syn/anti ratio and (ii) the OH proton shift of the syn rotamer. Reasonably concordant results are obtained from 298 to 323 K (3.6 and 3.9 M^?1, respectively, at 298 K). Similar values are obtained from the syn OH proton shift variation for the 3,4‐methylenedioxythiophene (MDOT) derivative. Concentration‐dependent variation of the anti OH proton shift in the latter suggests that the anti isomer associates in the form of an open, singly hydrogen‐bonded dimer, with a much smaller association constant than the syn rotamer. Self‐association constants for 3‐pyridyl‐EDOT‐alkanols with smaller substituents vary by a factor of 4 from (i‐Pr)₂ up to (CD₃)₂, while the hetero‐association constants for the same compounds with pyridine vary slightly less. Copyright © 2007 John Wiley & Sons, Ltd.     

Constrained nucleic acids (CNA). Part 2. Synthesis of conformationally restricted dinucleotide units featuring noncanonical alpha/beta/gamma or delta/epsilon/zeta torsion angle combinations

Four dinucleotide building units of nucleic acids in which three out of six backbone torsion angles are included in a dioxaphosphorinane ring structure (D-CNA family) have been synthesized: two diastereoisomeric alpha,beta,gamma-D-CNA {cis and trans} and two diastereoisomeric delta,epsilon,zeta-D-CNA {(S(C4'),R(P)) and (S(C4'),S(P))}. The structural analysis of these conformationally restricted dinucleotides, using NMR spectroscopy and X-ray crystallography, shows that these D-CNA structural elements allow the stabilization of torsion angle combinations, alpha/beta/gamma and delta/epsilon/zeta, that are significantly different from those typically observed in canonical A- or B-form duplexes.     

Regioselective N-functionalization of tetraazacycloalkanes

[reaction: see text] Bisaminal type compounds obtained by condensation of pyruvic aldehyde with the suitable open-chain tetraamine followed by cyclization with either dibromoethane or dibromopropane can be regioselectively quaternized by a wide range of alkylating agents. Removal of the bisaminal bridge yields the monosubstituted tetraazamacrocycle or bismacrocycle. Further functionalization allows the preparation of bifunctional ligands or trisubstituted macrocycles. The structure of six compounds was solved by X-ray diffraction, and the unexpected results are rationalized according to the molecular modeling calculations.     

Calculation of ionization potentials of small molecules: a comparative study of different methods

With the help of various theoretical methods, ionization potentials (IPs) have been computed for a panel of small molecules containing atoms of group 14, 15, or 16 and representing different singly, doubly, or triply bonded systems with or without an interacting heteroatom lone pair. Comparison of experimental IP values to theoretical results indicates that (i) the standard outer valence green function (OVGF), density functional theory (DFT), and DeltaSCF methods lead to rather accurate values, (ii) the CASPT2 method systematically underestimates IPs, (iii) the method of deducing IPs from a shift of some standard DFT eigenvalue spectrum is a straightforward approach leading to rather accurate IPs, (iv) the eigenvalue spectrum obtained with the so-called statistical average of different orbital model potential (SAOP) exchange-correlation model potential is an efficient approach leading directly to quite accurate IPs, and (v) a good prediction of the IP spectrum can be obtained from the shifted excitation spectra of the system calculated by the time-dependent DFT (TD-DFT) method. It is also shown that the TD-DFT calculations of the ionized species bring a significant improvement over the calculations of the neutral molecules, indicating that a great part of the electronic relaxation is already taken into account (in a similar way for all ionizations). Finally, in the case of TD-DFT calculations of neutral molecules, the statistical average of different orbital model potential (SAOP) functional does not lead to significantly better results than the B3LYP functional.     

Synthesis of primary-alkyl selenols and selenides from primary-alkyl thiols involving diphenyl sulfonium salts

Hexyl thiol has been transformed to hexyl selenol and related selenides and selenocyanate by substitution of the corresponding hexyldiphenylsulfonium tetrafluoroborate with selenium nucleophiles.     

Velocity and hierarchical spread of epidemic outbreaks in scale-free networks

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.     

The N-N stretching band of hydrazine

For the first time a very weak N-N stretching band (ν₅) of hydrazine was unambiguously assigned in the Fourier-transform infrared spectrum. Almost 1500 transitions with a resolution of for K^′ from 0 to 6 and for all symmetry species have been analyzed. Despite some perturbations a global fit has been carried out successfully and the band center was determined at , much higher than previously expected.     

Bounds on isocurvature perturbations from cosmic microwave background and large scale structure data

We obtain very stringent bounds on the possible cold dark matter, baryon, and neutrino isocurvature contributions to the primordial fluctuations in the Universe, using recent cosmic microwave background and large scale structure data. Neglecting the possible effects of spatial curvature, tensor perturbations, and reionization, we perform a Bayesian likelihood analysis with nine free parameters, and find that the amplitude of the isocurvature component cannot be larger than about 31% for the cold dark matter mode, 91% for the baryon mode, 76% for the neutrino density mode, and 60% for the neutrino velocity mode, at 2sigma, for uncorrelated models. For correlated adiabatic and isocurvature components, the fraction could be slightly larger. However, the cross-correlation coefficient is strongly constrained, and maximally correlated/anticorrelated models are disfavored. This puts strong bounds on the curvaton model.