On unicyclic conjugated molecules with minimal energies

The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let U(k) be the set of all unicyclic graphs with a perfect matching. Let C _g(G) be the unique cycle of G with length g(G), and M(G) be a perfect matching of G. Let U ⁰(k) be the subset of U(k) such that g(G)≡ 0 (mod 4), there are just g/2 independence edges of M(G) in C _g(G) and there are some edges of E(G)\ M(G) in G\ C _g(G) for any G∈U ⁰(k). In this paper, we discuss the graphs with minimal and second minimal energies in U ^*(k) = U(k)\ U ⁰(k), the graph with minimal energy in U ⁰(k), and propose a conjecture on the graph with minimal energy in U(k).      

The forcing number of toroidal polyhexes

The forcing number, denoted by f(G), of a graph G with a perfect matching is the minimum number of independent edges that completely determine the perfect matching of G. In this paper, we consider the forcing number of a toroidal polyhex H(p,q,t) with a torsion t, a cubic graph embedded on torus with every face being a hexagon. We obtain that f(H(p,q,t)) ≥ min{p,q}, and equality holds for p ≤ q or p > q and t∈{ 0,p−q,p−q + 1,..., p−1}. In general, we show that f(H(p,q,t)) is equal to the side length of a maximum triangle on H(p,q,t). Based on this result, we design a linear algorithm to compute the forcing number of H(p,q,t).     

Asymmetric Phase-Transfer Catalysis by Quaternary Ammonium Ions Derived from Cinchona-Alkaloid Analogs Containing 1,1′-Binaphthalene Moieties

The synthesis and catalytic properties of a new type of enantioselective phase-transfer catalysts, incorporating both the quinuclidinemethanol fragment of Cinchona alkaloids and a 1,1′-binaphthalene moiety, are described. Catalyst (+)-(aS,3R,4S,8R,9S)- 4 with the quinuclidine fragment attached to C(7′) in the major groove of the 1,1′-binaphthalene residue was predicted by computer modeling to be an efficient enantioselective catalyst for the unsymmetric alkylation of 6,7-dichloro-5-methoxy-2-phenylindanone ( 1 ; Scheme 1, Fig. 1). Its synthesis involved the selective oxidative cross-coupling of two differently substituted naphthalen-2-ols to afford the asymmetrically substituted 1,1′-binaphthalene derivative (±)- 17 in high yield (Scheme 3). Chromatographic optical resolution via formation of diastereoisomeric camphorsulfonyl esters and functional-group manipulation gave access to the 7-bromo-1,1′-binaphthalene derivative (−)-(aS)- 11 (Scheme 4). Nucleophilic addition of lithiated (−)-(aS)- 11 to the quinuclidine Weinreb amide (+)-(3R,4S,8R)- 8 afforded the two ketones (aS,3R,4S,8R)- 27 and (aS,3R,4S,8S)- 28 as an inseparable mixture of diastereoisomers (Scheme 6). Stereoselective reduction of this mixture with DIBAL-H (diisobutylaluminum hydride; preferred formation of the C(8)−C(9) erythro-pair of diastereoisomers with 18% de) or with NaBH₄ (preferred formation of the threo-pair of diastereoisomers with 50% de) afforded the four separable diastereoisomers (+)-(aS,3R,4S,8S,9S)- 29 , (+)-(aS,3R,4S,8R,9R)- 30 , (−)-(aS,3R,4S,8S,9R)- 31 , and (+)-(aS,3R,4S,8R,9S)- 32 (Scheme 6). A detailed conformational analysis, combining ¹H-NMR spectroscopy and molecular-mechanics computations, revealed that the four diastereoisomers displayed distinctly different conformational preferences (Figs. 2 and 3). These novel Cinchona-alkaloid analogs were quaternized to give (+)-(aS,3R,4S,8R,9S)- 4 , (+)-(aS,3R,4S,8S,9S)- 5 , (+)-(aS,3R,4S,8R,9R)- 6 , and (−)-(aS,3R,4S,8S,9R)- 7 (Scheme 7) which were tested as phase-transfer agents in the asymmetric allylation of phenylindanone 1 . Without any optimization work, (+)-(aS,3R,4S,8R,9S)- 4 was found to catalyze the allylation of 1 yielding the predicted enantiomer (+)-(S)- 3b in 32% ee. The three diastereoisomeric catalysts (+)- 5 , (+)- 6 , and (−)- 7 gave access to lower enantioselectivities (6 to 22% ee's), which could be rationalized by computer modeling (Fig. 4).     

Intershell nl4f electron correlation effects

The pair correlation energies for some nl4f pairs of the ground state of the Yb atom are calculated for the first time. The partial wave (PW ) increments to the second-order pair energies are generated using numerical first-order radial pair functions obtained as the solution of two-dimensional differential equations. The analysis of the PW s contributions shows the dominant role of the df, fg, and gh PW s for the 4d4f pair, of the pf and dg PW s for the 4p4f and 5p4f pairs, and of the sf and pg PW s for the 4s4f, 5s4f, and 6s4f pairs. A discussion of the similarities and differences of the structure of the correlation energy found in this paper with those calculated earlier for smaller atoms is given.     

Embedding on alphabet overlap digraphs

Alphabet overlap digraphs can be viewed as a generalization of directed de Bruijn graphs. Given three integers α ≥ 1, k ≥ 2 and 1 ≤ i < k, the alphabet overlap digraph O(α, k ; i) is a digraph: the set of all words of length k over a certain alphabet with cardinality α is vertex set, and there is an arc from a vertex u to a vertex v if and only if the word of last k−i letters of u coincides with the word of first k−i letters of v. In this paper, we consider whether O(α, k ; i) can be embedded in O(α, k ; j) for given integers 1 ≤ i < j < k. In order to resolve this problem, we give an O(1)-time algorithm to decide whether there exists a permutation on {1, . . . ,k} from O(α, k ; i) to O(α, k ; j). If such a permutation exists, for any vertex of O(α, k ; i), we apply the permutation to change its label’s position and map it to a vertex of O(α, k ; j). Furthermore, we obtain an embedding from O(α, k ; i) to O(α, k ; j). Hence, we solve partly the problem. As a consequence, we show that every directed de Bruijn graph can be embedded in all alphabet overlap digraphs with the same parameters α and k.     

Study on Self-assembly of Poly(ethylene glycol)- block-poly(γ-benzyl L -glutamate)-graft-poly(ethylene glycol) Copolymer and Poly(γ-benzyl L -glutamate)- block-poly(ethylene glycol) Copolymer in Ethanol

Poly(ethylene glycol)-block-poly(γ-benzyl L-glutamate)-graft-poly(ethylene glycol) (PEG-b-PBLG-g-PEG) copolymer was synthesized by the ester exchange reaction of poly(γ-benzyl L-glutamate)-block-poly(ethylene glycol) (PBLG-block-PEG) copolymer with PEG chain, and PBLG-block-PEG copolymer was prepared by a standard N-carboxyl-γ-benzyl-L-glutamate anhydride (NCA) method. Nuclear magnetic resonance (NMR) spectroscopy was used to confirm the components of PBLG-block-PEG and PEG-b-PBLG-g-PEG. The self-association behaviors of PBLG-block-PEG and PEG-b-PBLG-g-PEG in ethanol were investigated by transmission electron microscopy (TEM), dynamic laser scattering (DLS), and viscometry. The experimental results revealed that the different molecular structures could exert marked effects on the self-assembly behaviors of PBLG-block-PEG and PEG-b-PBLG-g-PEG in ethanol. PBLG-block-PEG and PEG-b-PBLG-g-PEG could self-assemble to form polymeric micelles with a core-shell structure in the shapes of plump spherical and regular rice-like, respectively. Effects of the introduction of PBLG homopolymer on the average particle diameter of the micelles of PBLG-block-PEG and PEG-b-PBLG-g-PEG and influence of testing temperature on the critical micelle concentration of different copolymers were studied.     

Hydrolysis Reaction of N-Phosphoryl-α-, β- and γ-amino Acids Studied by HPLC

The hydrolysis reactions of N-（O,O＇diisopropyl）phosphoryl-L-α-alanine （DIPP-L-α-Ala）, N-（O,O＇diisopropyl）- phosphoryl-D-α-alanine （DIPP-D-α-Ala）, N-（O,O＇-diisopropyl）phosphoryl-β-alanine （DIPP-β-Ala） and N-（O,O＇-diisopropyl）phosphoryl-γ-amino butyric acid （DIPP-γ-Aba）, were studied by HPLC and their hydrolysis reaction kinetic equations were obtained. Under acid conditions, the reaction rate of DIPP-L-α-Ala was close to that of DIPP-D-α-Ala and the same rule was true between DIPP-β-Ala and DIPP-γ-Aba. Meantime, the reaction rate of DIPP-L/D-α-Ala was as 10 times as that of DIPP-β-Ala or DIPP-γ-Aba. Under basic conditions, the hydrolysis reactions of DIPP-β-Ala and DIPP-γ-Aba almost did not take place and the reaction rate of DIPP-L/D-α-Ala was about 1/10 of that under acid conditions. Moreover, theoretical calculation further illuminated the differences of the hydrolysis rate from the view of energy. The results would provide some helpful clues to why nature chose a-amino acids but not other kinds of analogs as protein backbones.     

Rogiolol Acetate: A Novel β-Chamigrene-Type Sesquiterpene Isolated from a Marine Sponge

The marine sponge Spongia zimocca SCHMIDT , 1862, collected in front of the torrent II Rogiolo, south of Livorno, contains the sesquiterpene rogiolol acetate (= (+)-(2R,3S,6R,8R,9R)-2,8-dibromo-9-chloro-1,1,9-trimethyl-5-methylidenespiro[5.5]undec-3-yl acetate; (+)- 3a ), which represents the first chamigrane isolated from a sponge. Although compounds of this class are common in red seaweeds of the genus Laurencia, and our sponge actually contains 9-bromochamigrene and a variety of other metabolites of nearby growing Laurencia sp., (+)- 3a is unique to our sponge.     

The stability condition of phase equilibrium for various concentration variables

The stability conditions of phase equilibrium for various concentration variables are educed according to thermodynamic principle. When a system with k components arrives at stable equilibrium, if the mole number n_i or the mole fraction y_i(=n_i/n_k) or molality m_i[= n_i/(n_kM_k)] of component i(i = 1,2,...,k − 1) are elected as concentration variables, thermodynamic theory is able to confirm that the sign of every order determinant composed of the second-order partial differential of chemical potential with respect to these concentration variables is positive; if the mole fraction x_i(= n_i/n) or mass fraction w_i(= n_iM_i/W are elected as the concentration variables, thermodynamic theory is only able to confirm that the sign of (k−1) order determinant is positive; if molarity c_i(= n_i/V are elected as the concentration variables, thermodynamic theory is not able to confirm the sign of every order determinant.     

S‐endo‐2‐Norbornyl‐N‐n‐butylcarbamate as a Potential Pseudomonas Lipase Inhibitor to Probe the Enantioselectivity of the Enzyme by Kinetic and Molecular Docking Evaluation

Obesity is a complex health issue and it can cause many health and social problems. Previous studies reported that lipase is a main target for obesity treatment. We synthesized R‐exo‐2‐norbornyl‐N‐n‐butylcarbamate and S‐exo‐2‐norbornyl‐N‐n‐butylcarbamate as potential pseudomonas lipase inhibitors to probe the enantioselectivity of the enzyme and demonstrated that R‐exo‐2‐norbornyl‐N‐n‐butylcarbamate had better enzyme enantioselectivity, ki and the docking model with Pseudomonas species lipase in our previous studies. In this article, we reported the property of the Pseudomonas species lipase inhibitors, R‐and S‐endo‐2‐norbornyl‐N‐n‐butylcarbamate and compared the docking models of these two compounds with R‐ and S‐exo‐2‐norbornyl‐N‐n‐butylcarbamates by AutoDock. We found that S‐endo‐2‐norbornyl‐N‐n‐butylcarbamate has the best enantioselectivity, ki and docking model and this study could provide useful information about enzyme enantioselectivity for the development of Pseudomonas species lipase inhibitors for obesity treatment.     

Theoretical investigation into the coordination of R‐/S‐asymmetric uranyl–salophens containing six‐membered ring lactam with cis−/trans‐cyclohexylamines

A six‐membered ring lactam derivative was introduced in a parallel manner into uranyl–salophens with R/S configuration (R‐/S‐AUSRLs), which were used as receptors to coordinate with guests of cis?/trans‐methylcyclohexylamines (cis?/trans‐MCHAs). Using density functional theory calculations at the B3LYP/6‐311G** level and RECP, an insight into the coordination complexes of the R‐/S‐AUSRLs with cis?/trans‐MCHAs was obtained. The results showed that the U atoms of receptors could coordinate with the N atoms of four kinds of cis?/trans‐1,2 or ? 1,4 guests, but the two kinds of cis?/trans‐1,3 guests could not be converged by the same method in the process of structural optimization due to steric hindrance, and thus the cis?/trans‐1,3 guests could not be coordinated with the R‐/S‐AUSRLs. The mode of coordination of the R‐/S‐AUSRLs with the guests displayed a significant difference. And the change of R‐AUSRL coordination ability to the cis?/trans‐MCHAs was very large, but that of S‐AUSRL was small. Overall, the stability of the R‐series coordination complexes was higher than that of the corresponding S‐series coordination complexes, and the R‐AUSRL receptor had better coordination selectivity and higher molecular recognition to the cis?/trans‐MCHA guests than the S‐AUSRL receptor. However, the coordination ability of S‐AUSRL with the cis?/trans‐MCHAs was stronger than that of R‐AUSRL. It was expected that these results could provide insightful information and theoretical guidance for understanding the molecular recognition of R‐/S‐AUSRLs for cis?/trans‐type cyclohexylamine derivatives.     

Diffusion of nonionic azo dyes in nylon-6

Diffusion of 2,4-dinitroaniline and three nonionic azo dyes in Nylon-6 film was studied by analysis of the concentration-distance curves (profiles) of penetrants in the polymer. Actual diffusivities D_(c) of penetrants in polymer, diffusion coefficients as a function of the concentration C_f of penetrant in polymer, were calculated from the profile. It was found that D_(c) is almost constant or decreases gradually with decreasing C_f in the range of high-medium C_f but decreases appreciably with decreasing C_f at low C_f. The change in D_(c) with C_f was explained in terms of the dual-mode sorption-diffusion model. The penetrants diffuse in the polymer as two distinct species, i.e., a dissolved species and an adsorbed species. The former is the penetrant taken up by the polymer by a partition mechanism (dissolved species) and the latter is that taken up by Langmuir sorption (adsorbed species). The actual diffusivity D_P(c) of the dissolved species decreases with decreasing C_f. While the actual diffusivity D_L(c) of the adsorbed species normally increases gradually with decreasing C_f. D_P(c) is usually larger than D_L(c). © 1993 John Wiley & Sons, Inc.     

Dirac equation with a Coulomb plus scalar potential in D + 1 dimensions

We generalize the Dirac equation to D + 1‐dimensional spacetime. The exact solutions of the D‐dimensional radial equations with a Coulomb plus scalar potential taking the form 1/r are analytically presented by studying the Tricomi equations. The energies E(n, l, D) are exactly presented. The dependences of the energies E(n, l, D) on the dimension D are analyzed in some detail. The energies E(n, 0, D) first decrease and then increase when increasing dimension D, but the energies E(n, l, D) (l ≠ 0) increase when increasing dimension D. The energies E(n, 0, D) are symmetric with respect to D = 1 for D ∈ (0, 2). It is shown that the energies E(n, l, D) (l ≠ 0) are almost independent of the quantum number l for large D and are completely independent of it if the Coulomb potential is equal to the scalar one. The energies E(n, l, D) almost overlap for large D. The dependences of the energies E(n, l, v) and E(n, l, s) on the vector potential parameter v and scalar potential one s are also studied for D = 3. All are found to decrease when these parameters are increased. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Synthesis,Isolation, and Full Spectroscopic Characterization of Eleven (Z)-Isomers of (3R,3′R)-Zeaxanthin

Developmental efforts to improve the yield of the chemical synthesis of (3R,3′R)-zeaxanthin resulted in the isolation, partly by chromatography from reaction mixtures, and full spectroscopic characterization by ¹H-NMR, UV/VIS, and CD spectrosocpy of eleven (Z/E)-isomers of zeaxanthin: (7Z)-, (9Z), (13Z)-, (15Z)-, (7Z,7′Z)-, (9Z,9′Z)- (7Z,9Z,7Z)-, (7Z,11Z,7′Z)-, (9Z,13Z,9′Z)-, (7Z,9Z,7′Z,9′Z)-, and (7Z,9Z,11Z,7′Z,9′Z)-zeaxanthin. Five of these isomers were obtained by specific synthesis, namely the (7Z)-, (7Z,7′Z)-, (9Z,9′Z)-, (7Z,9Z,7′Z)-, and (7Z,9Z,7′Z-9Z)-isomers.     

Optisch aktive 4,5-Epoxy-4,5-dihydro-α-ionone und Synthese der stereoisomeren 4,5:4′,5′-Diepoxy-4,5,4′,5′-tetrahydro-ϵ,ϵ-carotine und der sterische Verlauf ihrer Hydrolyse

Optically Active 4,5-Epoxy-4,5-dihydro-α-ionones; Synthesis of the Stereoisomeric 4,5:4′,5′-Diepoxy-4,5,4′,5′-tetrahydro-?,?-carotenes and the Steric Course of their Hydrolysis We prove that epoxidation with peracid of α-ionone, contrary to a recently published statement, predominantly leads to the cis-epoxide. Acid hydrolysis affords a single 4,5-glycol whose structure, established by an X-ray analysis, shows that oxirane opening occurred with inversion at the least substituted position (C(4)). Stable cis-and trans-epoxides are prepared by epoxidation of the C₁₅-phosphonates derived from α-ionone. Both the racemic and optically active form are used for the synthesis of the 4,5:4′,5′-diepoxy-4,5,4′,5′-tetrahydro-?,?-carotenes having the following configuration in the end groups: meso-cis/cis, meso-trans/trans, rac-cis/trans, rac- and (6R, 6′ R)-cis/cis, rac- and (6R, 6′R)-trans/trans, rac- and (6R, 6′R)-cis/trans, and (6R, 6′ R)-cis/?. Acid hydrolysis of the cis/cis-epoxycarotenoids under relatively strong conditions occurs again with inversion at C(4)/C(4′) in case of the cis/cis-epoxycarotenoids, but at C(5)/C(5′) in case of the trans/trans-epoxycarotenoids. An independent synthesis of this 4,5,4′,5′-tetrahydro-?,?-carotene-4,5,4′,5′-tetrol is presented. The irregular results of the oxirane hydrolysis are explained by assumption of neighbouring effects of the lateral chain. 400-Mz-¹H-NMR data are given for each of the stereoisomeric sets. In the visible range of the CD spectra, the (6R, 6R′)-epoxycarotenoids compared with (6R, 6R′)-?,?-carotene exhibit an inversion of the Cotton effects.     

Relation between the critical point and the precipitation threshold

The relationship between the critical point and the precipitation threshold is examined in the Flory—Huggins approximation with concentration-independent interaction parameter χ. Approximate explicit expressions for the difference between the critical point and the threshold can be derived by series expansion of threshold conditions. In the first-order approximation, the concentration difference depends only on the chainlength averages x_w, x_z, and x_z+1, in the second-order approximation it depends on x_w, x_z, x_z+1, and x_z+2, etc. For polymers of low polydispersity, the second-order approximation gives a good estimate of the concentration difference; for instance, for polymers with exponential distribution and x_w/x_n < 1.25, the error is lower than ca. 1%. The approximation is not suitable for polymers with x_z+1 ? x_z (including polymers whose cloud-point curve exhibits a triple point). Irrespective of the polydispersity of the polymer, the threshold as well as the whole cloud-point curve depend only on the weight-average and higher averages, x_w, x_z, x_z+1, …, x_z+k, where k → ∞; they are, however, independent of the number average x_n.     

The PI index of phenylenes

The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n _eu (e|G) and n _ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ _e∈E(G)[n _eu (e|G) + n _ev (e|G)], where n _eu (e|G) is the number of edges of G lying closer to u than to v and n _ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of phenylenes is given, and a simple relation is established between the PI index of a phenylene and of the corresponding hexagonal squeeze.     

Geminal systems. 50. Synthesis and alcoholysis of N-acyloxy-N-alkoxy derivatives of ureas,carbamates, and benzamides

Procedures were developed for the synthesis of N-acyloxy-N-alkoxy derivatives of ureas, carbamates, and benzamides by the reactions of the corresponding N-alkoxy-N-chloro derivatives with sodium carboxylates in MeCN. N-Chloro-N-ethoxy-p-toluenesulfonamide was inert in this reaction. Alcoholysis of N-acyloxy-N-alkoxy derivatives of ureas, carbamates, and tert-alkylamines afforded the corresponding N,N-dialkoxy derivatives, whereas alcoholysis of N-acetoxy-N-ethoxybenzamide gave rise to alkyl benzoates.     

Ordering chemical unicyclic graphs by Wiener polarity index

Suppose G is a chemical graph with vertex set V(G). Define D(G) = {{u, v} ⊆ V (G) | d _G (u, v) = 3}, where d _G (u, v) denotes the length of the shortest path between u and v. The Wiener polarity index of G, W _p (G), is defined as the size of D(G). In this article, an ordering of chemical unicyclic graphs of order n with respect to the Wiener polarity index is given.     

NANOSTRUCTURES OF FUNCTIONAL BLOCK COPOLYMERS

Nanostructure fabrication from block copolymers in my group normally involves polymer design, synthesis, self-assembly, selective domain crosslinking, and sometimes selective domain removal. Preparation of thin films withnanochannels was used to illustrate the strategy we took. In this particular case, a linear triblock copolymer polyisoprenc-block-poly(2-cinnamoylethyl methacrylate)-block-poly(t-butyl acrylate), PI-b-PCEMA-b-PtBA, was used. Films, 25 to50 μm thick, were prepared from casting on glass slides a toluene solution of PI-b-PCEMA-b-PtBA and PtBA homopolymer,hPtBA, where hPtBA is shorter than the PtBA block. At the hPtBA mass faction of 20% relative to the triblock or the totalPtBA (hPtBA and PtBA block) volume fraction of 0.44, hPtBA and PtBA formed a seemingly continuous phase in the matrixof PCEMA and Pl. Such a block segregation pattern was locked in by photocrosslinking the PCEMA domain. Nanochannelswere formed by extracting out hPtBA with solvent. Alternatively. larger channels were obtained from extracting out hPtBAand hydrolyzing the t-butyl groups of the PtBA block. Such membranes were not liquid permeable but had gas permeabilityconstants ～6 orders of magnitude higher than that of low-density polyethylene films.