Bandwidth and pathwidth of three-dimensional grids

We study the bandwidth and the pathwidth of multi-dimensional grids. It can be shown for grids, that these two parameters are equal to a more basic graph parameter, the vertex boundary width. Using this fact, we determine the bandwidth and the pathwidth of three-dimensional grids, which were known only for the cubic case. As a by-product, we also determine the two parameters of multi-dimensional grids with relatively large maximum factors.     

Phospholipid-Modified ODS Monolithic Column for Affinity Prediction of Hydrophobic Basic Drugs to Phospholipids

A phospholipid-modified octadecyl silica (ODS) monolithic column was prepared and its interaction with basic hydrophobic drugs was studied. These drugs are of interest in pharmaceutical research because of their strong interaction with biomembranes. The amount of dimyristoylphosphatidylcholine trapped on the ODS surface was reproducible, and the results of the trinitrobenzenesulfonic acid assay suggested the formation of a monolayer on the surface. Both hydrophobic and electrostatic interactions acted between the model drugs and the phosphatidylcholine. The column was stable for 10 days at least. The column was applied to the affinity screening of basic drugs to phospholipid. Good correlation was obtained between log k and log P for the basic drugs lidocaine, quinidine, propranolol, imipramine, and chlorpromazine. The monolithic silica column allowed highly hydrophobic basic drugs such as imipramine and chlorpromazine to be assayed; these are difficult to analyze by using a conventional particle-packed column. These drugs were clearly separated from acidic drugs naproxen and warfarin on the log k versus log P plots. The thermodynamic studies revealed that the retention of the drug was an enthalpy-driven process, and that the decrease in enthalpy for the phospholipid-modified ODS monolithic column was larger than those for immobilized artificial membrane columns. Our results suggest that the phospholipid-modified ODS monolithic column is applicable to affinity screening of drugs to phospholipids.     

Preparation of Functional Polyamine Scaffolds via Mitsunobu Post‐Polymerization Modification Reactions

A Mitsunobu reaction of trifluoroacetamide (TFA amide) and alcohols is used in a post‐polymerization modification process. The reaction is conducted on polystyrene (PSt) bearing 20 mol% TFA amide groups with 4‐methyl benzyl alcohol in the presence of a N,N,N′,N′‐tetramethylazodicarboxamide and tributylphosphine as mediators. The Mitsunobu reaction on polymer proceeds efficiently, as confirmed by the obvious precipitation generation during the reaction and the conversion of TFA amide moiety reached 88.6% confirmed by ¹⁹F NMR measurement, yielding PSt bearing tertiary TFA amide moieties. The obtained polymers featuring tertiary TFA amide moieties are deprotected in the presence of tetrabutylammonium hydroxide as a base to afford corresponding polymers featuring functionalized polyamine scaffolds with 92.5% conversion. In addition, the precise structural assignment is proven by synthesis and analysis of the model monomeric compounds and the respective model polymers.

     

Finite‐field method with unbiased polarizable continuum model for evaluation of the second hyperpolarizability of an open‐shell singlet molecule in solvents

The static second hyperpolarizability γ of the complexes composed of open‐shell singlet 1,3‐dipole molecule involving a boron atom and a water molecule in aqueous phase are investigated by the finite‐field (FF) method combined with a standard polarized continuum model (PCM) and with a newly proposed unbiased PCM (UBPCM). On the basis of the comparison with the results calculated by the FF method using the full quantum and the quantum‐mechanical/molecular‐mechanical and molecular‐dynamics (QM/MM‐MD) treatments, the present FF‐UBPCM method is demonstrated to remedy the artificial overestimation of the γ caused by standard FF‐PCM calculations and to well reproduce the FF‐QM/MM‐MD and FF‐full‐QM results with much lower costs. © 2013 Wiley Periodicals, Inc.     

Ultrafast Exciton Self‐Trapping and Delocalization in Cycloparaphenylenes: The Role of Excited‐State Symmetry in Electron‐Vibrational Coupling

Upon photon absorption, π‐conjugated organics are apt to undergo ultrafast structural reorganization via electron‐vibrational coupling during non‐adiabatic transitions. Ultrafast nuclear motions modulate local planarity and quinoid/benzenoid characters within conjugated backbones, which control primary events in the excited states, such as localization, energy transfer, and so on. Femtosecond broadband fluorescence upconversion measurements were conducted to investigate exciton self‐trapping and delocalization in cycloparaphenylenes as ultrafast structural reorganizations are achieved via excited‐state symmetry‐dependent electron‐vibrational coupling. By accessing two high‐lying excited states, one‐photon and two‐photon allowed states, a clear discrepancy in the initial time‐resolved fluorescence spectra and the temporal dynamics/spectral evolution of fluorescence spectra were monitored. Combined with quantum chemical calculations, a novel insight into the effect of the excited‐state symmetry on ultrafast structural reorganization and exciton self‐trapping in the emerging class of π‐conjugated materials is provided.     

Core molecule dependence of energy migration in phenylacetylene nanostar dendrimers: Ab initio molecular orbital-configuration interaction based quantum master equation study

The core molecule dependence of energy (exciton) migration in phenylacetylene nanostar dendrimers is investigated using the ab initio molecular orbital (MO)-configuration interaction based quantum master equation approach. We examine three kinds of core molecular species, i.e., benzene, anthracene, and pentacene, with different highest occupied MO-lowest unoccupied MO (HOMO-LUMO) gaps, which lead to different orbital interactions between the dendron parts and the core molecule. The nanostars bearing anthracene and pentacene cores are characterized by multistep exciton states with spatially well-segmented distributions: The exciton distributions of high-lying exciton states are spatially localized well in the periphery region, whereas those of low-lying exciton states are done in the core region. On the other hand, for the nanostar bearing benzene core, which also has multistep exciton states, the spatial exciton distributions of low-lying exciton states are delocalized over the dendron and the core regions. It is found that the former nanostars exhibit nearly complete exciton migration from the periphery to the core molecule in contrast to the latter one, in which significant exciton distribution remains in the dendron parts attached to the core after the exciton relaxation, although all these dendrimers exhibit fast exciton relaxation from the initially populated states. It is predicted from the analysis based on the MO correlation diagrams and the relative relaxation factor that the complete exciton migration to the core occurs not only when the HOMO-LUMO gap of the core molecule is nearly equal to that of the dendron parts attached to the core (anthracene case) but also when fairly smaller than that (pentacene case), whereas the complete migration is not achieved when the HOMO-LUMO gap of the core is larger than that of the dendron parts (benzene case). These results suggest that the fast and complete exciton migration of real dendrimers could be realized by adjusting the HOMO-LUMO gap of the core molecule to be smaller than that of dendron parts, although there exist more complicated relaxation processes as compared to simple dendritic aggregate models studied so far.     

Investigation of the dominant hydration structures among the ionic species in aqueous solution: novel quantum mechanics/molecular mechanics simulations combined with the theory of energy representation

In the present work, we have performed quantum chemical calculations to determine preferable species among the ionic complexes that are present in ambient water due to the autodissociation of water molecule. First, we have formulated the relative population of the hydrated complexes with respect to the bare ion (H(3)O(+) or OH(-)) in terms of the solvation free energies of the relevant molecules. The solvation free energies for various ionic species (H(3)O(+), H(5)O(2) (+), H(7)O(3) (+), H(9)O(4) (+) or OH(-), H(3)O(2) (-), H(5)O(3) (-), H(7)O(4) (-), H(9)O(5) (-)), categorized as proton or hydroxide ion in solution, have been computed by employing the QM/MM-ER method recently developed by combining the quantum mechanical/molecular mechanical (QM/MM) approach with the theory of energy representation (ER). Then, the computed solvation free energies have been used to evaluate the ratio of the populations of the ionic complexes to that of the bare ion (H(3)O(+) or OH(-)). Our results suggest that the Zundel form, i.e., H(5)O(2) (+), is the most preferable in the solution among the cationic species listed above though the Eigen form (H(9)O(4) (+)) is very close to the Zundel complex in the free energy, while the anionic fragment from water molecules mostly takes the form of OH(-). It has also been found that the loss of the translational entropy of water molecules associated with the formation of the complex plays a role in determining the preferable size of the cluster.     

Activation of C–H and H–H bonds by dinuclear iridium complexes. Oxidative addition to highly active unsaturated 32e− diiridium species

Reactions of [(Cp¹Ir)₂(μ-dmpm)(μ-H)₂][OTf]₂ (1) with NaO^tBu in aromatic solvent at room temperature give [(Cp¹Ir)(H)(μ-dmpm)(μ-H)(Cp¹Ir)(Ar)][OTf] [Ar = Ph (3), p-Tol (4a), m-Tol (4b), 2-furyl (5a), 3-furyl (5b)] via intermolecular aromatic C–H activation. Treatment of [(Cp¹Ir)₂(μ-dppm)(μ-H)₂][OTf]₂ (2) with weak base (Et₂NH) results in intramolecular C–H activation of a phenyl group in the dppm ligand to give [(Cp¹Ir)(H){μ-PPh(C₆H₄)CH₂PPh₂}(μ-H)(Cp¹Ir)][OTf] (6). Reaction of 1 with NaO^tBu in tetrahydrofuran under H₂ (1 atm) results in activation of the H–H bond to give [{(Cp¹Ir)(H)}₂(μ-dmpm)(μ-H)][OTf] (7). Reaction of 1 with NaO^tBu in dichloromethane under carbon monoxide (1 atm) gives a carbonyl-bridged Ir^II–Ir^II complex, [(Cp¹Ir)₂(μ-dmpm)(μ-H)(μ-CO)][OTf] (8-OTf). These results strongly suggest that the active species in C–H and H–H bond activation starting with 1 and 2 would be unsaturated 32e^? diiridium species. The structures of 3, 5a, 6, 7, and 8-BPh₄ have been determined by X-ray diffraction methods.