Nonlinear Approximation with Dictionaries. II. Inverse Estimates

In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually incoherent bases introduced by Donoho and Huo. The Bernstein inequality obtained for such dictionaries is proved to be sharp, but it has an exponent that does not match that of the corresponding Jackson inequality.     

Alzheimer’s Disease,Cholesterol, and Statins: The Junctions of Important Metabolic Pathways

Recent years have seen a significant increase in published data supporting the positive effects of statins on neurodegenerative diseases, in particular on Alzheimer’s disease. Statins show neuroprotective activity by a combination of different cellular and systemic mechanisms that are based on the inhibition of the biosynthesis of cholesterol and isoprenoid by‐products. The promising results obtained in vivo and in epidemiological studies are generally not in accordance with those of placebo‐controlled randomized clinical trials. Nevertheless, these results make statins valuable assets for disease prevention rather than therapeutic agents for use when disease symptoms are already displayed. Thus, the modulation of midlife cholesterol and/or statin administration prior to the appearance of dementia or cognitive impairment may have a better long‐term outcome.     

Charge Effects in PCP Pincer Complexes of NiII bearing Phosphinite and Imidazol(i)ophosphine Coordinating Jaws: From Synthesis to Catalysis through Bonding Analysis

This contribution reports on a new family of Ni^II pincer complexes featuring phosphinite and functional imidazolyl arms. The proligands ^RPIMC^HOP^R′ react at room temperature with Ni^II precursors to give the corresponding complexes [(^RPIMCOP^R′)NiBr], where ^RPIMCOP^R=κ^P,κ^C,κ^P‐{2‐(R′₂PO),6‐(R₂PC₃H₂N₂)C₆H₃}, R=iPr, R′=iPr ( 3 b , 84 %) or Ph ( 3 c , 45 %). Selective N‐methylation of the imidazole imine moiety in 3 b by MeOTf (OTf=OSO₂CF₃) gave the corresponding imidazoliophosphine [(^iPrPIMIOCOP^iPr)NiBr][OTf], 4 b , in 89 % yield (^iPrPIMIOCOP^iPr=κ^P,κ^C,κ^P‐{2‐(iPr₂PO),6‐(iPr₂PC₄H₅N₂)C₆H₃}). Treating 4 b with NaOEt led to the NHC derivative [(NHCCOP^iPr)NiBr], 5 b , in 47 % yield (NHCCOP^iPr=κ^P,κ^C,κ^C‐{2‐(iPr₂PO),6‐(C₄H₅N₂)C₆H₃)}). The bromo derivatives 3–5 were then treated with AgOTf in acetonitrile to give the corresponding cationic species [(^RPIMCOP^R)Ni(MeCN)][OTf] [R=Ph, 6 a (89 %) or iPr, 6 b (90 %)], [(^RPIMIOCOP^R)Ni(MeCN)][OTf]₂ [R=Ph, 7 a (79 %) or iPr, 7 b (88 %)], and [(NHCCOP^R)Ni(MeCN)][OTf] [R=Ph, 8 a (85 %) or iPr, 8 b (84 %)]. All new complexes have been characterized by NMR and IR spectroscopy, whereas 3 b , 3 c , 5 b , 6 b , and 8 a were also subjected to X‐ray diffraction studies. The acetonitrile adducts 6 – 8 were further studied by using various theoretical analysis tools. In the presence of excess nitrile and amine, the cationic acetonitrile adducts 6 – 8 catalyze hydroamination of nitriles to give unsymmetrical amidines with catalytic turnover numbers of up to 95.     

Thermodynamics and molecular bases of the interaction of ampicillin and streptomycin at their binding sites of bovine serum albumin

Among the biological parameters of chemotherapeutics, serum albumin binding is a critical factor in determining drug distribution and bioavailability. In this study, the binding properties as well as the interaction of ampicillin and streptomycin at their binding sites of bovine serum albumin (BSA) were investigated. The binding constant varied from 3.2 × 10³ M^?1 at 298 K to 37.5 × 10³ M^?1 at 313 K for ampicillin, and from 10.7 × 10³ M^?1 at 298 K to 3.5 × 10³ M^?1 at 313 K for streptomycin. By increasing the temperature, from 298 to 313 K, the binding affinity decreased by about 11-fold for ampicillin. Conversely, streptomycin showed stronger binding at higher temperature, which is decreased by threefold at 298 K. Interestingly, the affinity of ampicillin with the free BSA was ~4-fold higher than the binding with BSA/streptomycin complex. In contrast, the affinity of streptomycin with the free BSA was ~6-fold lower than the binding with BSA/ampicillin complex. Mutual binding experiments indicate that ampicillin and streptomycin are sharing both of common and different binding sites on BSA. Dissection of the forces of interactions indicated that rigid-body binding was the mode of binding of ampicillin and streptomycin with BSA with minor degree of conformational changes. Both of ampicillin and streptomycin can bind with free BSA. Furthermore, the binding of ampicillin with BSA improves the binding of streptomycin, while the binding of streptomycin with BSA adversely affect the binding of ampicillin.     

Functional carbo‐Butadienes: Nonaromatic Conjugation Effects through a 14‐Carbon, 24‐π‐Electron Backbone

A systematic study of carbo‐butadiene motifs not embedded in an aromatic carbo‐benzene ring is described. Dibutatrienylacetylene (DBA) targets R¹?C(R)?C?C?C(Ph)?C≡C?C(Ph)?C?C?C(R)?R² are devised, in which R is C≡CSiiPr₃ and R¹ and R² are R, H, or 4‐X‐C₆H₄, with the latter including three known representatives (X: H, NMe₂, or NH₂). The synthesis method is based on the SnCl₂‐mediated reduction of pentaynediols prepared by early or late divergent strategies; the latter allows access to a OMe–NO₂ push–pull diaryl‐DBA. If R¹ and R² are H, an over‐reduced dialkynylbutatriene (DAB) with two allenyl caps was isolated instead of the unsubstituted DBA. If R¹=R²=R, the tetraalkynyl‐DBA target was obtained, along with an over‐reduced DBA product with a 12‐membered 1,2‐alkylidene‐1H₂,2H₂‐carbo‐cyclobutadiene ring. X‐ray crystallography shows that all of the acyclic DBAs adopt a planar trans–transoid–trans configuration. The maximum UV/Vis absorption wavelength is found to vary consistently with the overall π‐conjugation extent and, more intriguingly, with the π‐donor character of the aryl X substituents, which varies consistently with the first (reversible) reduction potential and first (irreversible) oxidation peak, as determined by voltammetry.     

Aromaticity and electron affinity of Carbo(k)-[3]radialenes, k=0, 1, 2

Aromaticity enhancement is a possible driving force for the low reduction potentials of buta-1,3-diynediyl-expanded [N]radialenes: this hypothesis is theoretically analyzed for the expanded [3]radialene prototype. This study is undertaken within a more general prospect, namely the evaluation of the variation of aromaticity with endocyclic and peripheral carbomeric expansion of [3]radialene and its mono- and dianions. The structures, denoted as [C-H](6) (h)[C-C](3) (k)carbo-[3]radialene(q) (h=0, 1; k=0, 1, 2; q=0, -1, -2), were optimized in relevant singlet, doublet, or triplet spin states at the B3PW91/6-31G** level. They were found to be all planar. The structural aromaticity was measured through the average bond length d(av) over the [C-C](3) (k)carbo-[3]radialene core, and by the corresponding bond-length equalization parameter sigma(d), related to Krygowski's GEO. The magnetic aromaticity was measured by Schleyer's NICS values at the center of the rings. Regarding the relative variation of NICS and sigma(d), two classes of species can be distinguished according to their endocyclic expansion level. The species with a nonexpanded (k=0) or doubly expanded (k=2) ring constitute the first class: they exhibit D(3h) symmetry and a strong correlation of NICS with sigma(d). The species with a singly expanded ring (k=1) fall far from the correlation line, and constitute the second class. This class distinction is related to the degeneracy scheme of the frontier orbitals of the neutral representative. A finer appraisal of the electron (de)localization is brought by the ELF (Electron Localization Function) analysis of the electron density. It allows for a weighting of relevant resonance forms. Unsubstituted species are well described by the superimposition of two or three resonance forms. For (doublet spin state) monoanionic species, their respective weights are validated by comparison with AIM spin density. The weighted mean, n, of the formal numbers of paired pi(z) electrons in the resonance forms was calculated and compared with the closest even integer of either forms 4m+2 or 4m. A density-based continuous generalization of the orbital-based discrete Hückel rule is then heuristically proposed through an analytical correlation of NICS versus sigma(d), n, and S, the spin of the species. The frontier-orbital-degeneracy pattern of neutral species is discussed with respect to structural and magnetic aromaticity criteria. A decreasing HOMO-LUMO gap versus endocyclic expansion is obtained, but [C-C](3) (1)carbo-[3]radialene possesses the highest HOMO and LUMO energies. Vertical and adiabatic electron affinities of neutral and monoanionic species were also computed and compared with related experimental data.     

Estimating local bonding/antibonding character of canonical molecular orbitals from their energy derivatives. The case of coordinating lone pair orbitals

According to Koopmans theorem, the derivative of the energy of a canonical molecular orbital (MO) with respect to nuclear coordinates quantifies its bonding/antibonding character. This quantity allows predictions of bond length variation on ionisation in a panel of 19 diatomic species. In polyatomic molecules, the derivative of a MO energy with respect to a given bond length reveals the nature and the degree of the bonding/antibonding contribution of this MO with respect to this bond. Accordingly, the HOMO “lone pairs” of CO and CN^? and the HOMO‐2 of CH₃CN are found to be antibonding with respect to the C? X bond (X = N, O), whereas the HOMO of N₂ is found to be bonding. With the same approach, the variation of the bonding character in the MOs of CO and CH₃CN on interaction with an electron acceptor (modeled through the approach of a proton) or by applying an electric field was studied. © 2016 Wiley Periodicals, Inc.     

Chemical algebra III: Thermochemical approach to completely G-invariant distances

The search for a definition of distances over sets of skeletal analogs (identified to G-Hilbert spaces of vector ligand parameters) is initiated from the algebraic formulation of the constant of stereogenic pairing equilibria (pairing product). A basic definition equation is devised from thermodynamical speculations. The equation is proved to have always a single potential distance solution D_p as soon as the pairing product is discriminating. The equation of D_p is constructed in order to satisfy three consistency requirements: completeG-invariance (arbitrary orientations selected to describe skeletal analogs do not affect the value of D_p); extension properties (D_p coincides with two standard completelyG-invariant distances or with the Euclidean distance in borderline cases); all the distance properties except, perhaps, the triangular inequality. The latter point remains challenging in general, and is computationally verified in some examples.     

Bioinspired Mechanical Gradients in Cellulose Nanofibril/Polymer Nanopapers

Mechanical gradients are important as tough joints, for strain field engineering in printable electronics, for actuators, and for biological studies, yet they are difficult to prepare and quantitatively characterize. We demonstrate the additive fabrication of gradient bioinspired nanocomposites based on stiff, renewable cellulose nanofibrils that are bottom‐up toughened via a tailor‐made copolymer. Direct filament writing of different nanocomposite hydrogels in patterns, and subsequent healing of the filaments into continuous films while drying leads to a variety of linear, parabolic and striped bulk gradients. In situ digital image correlation under tensile deformation reveals important differences in the strain fields regarding asymmetry and step heights of the patterns. We envisage that merging top‐down and bottom‐up structuring of nanocellulose hybrids opens avenues for aperiodic and multiscale, bioinspired nanocomposites with optimized combinations of stiffness and toughness.     

Description of carbo-oxocarbons and assessment of exchange-correlation functionals for the DFT description of carbo-mers

Mono- and polycyclic valence isomers of carbo-[3]oxocarbon C(9)O(3) and carbo-[5]oxocarbon C(15)O(5) have been characterized on the singlet spin state potential energy surface. By contrast to their geometry, their relative stability is highly sensitive to the calculation level. The performance of LDA, GGA, meta-GGA, and hybrid functionals is compared to that of HF, post-HF, and multiconfigurational calculations. The results obtained for C(9)O(3) are compared to those obtained for hydrocarbon analogues such as &[3]pericyclyne C9(H2)3 and carbo-[3]radialene C9(CH2)3 and are analyzed on the basis of an energy decomposition scheme. The respective role of the exchange and correlation counterparts of the functional in the discrepancy of the results is discussed.