On maximal resonance of polyomino graphs

A polyomino graph is a finite plane 2-connected bipartite graph every interior face of which is bounded by a regular square of side length one. Let k be a positive integer, a polyomino graph G is k-resonant if the deletion of any i ≤ k vertex-disjoint squares from G results in a graph either having perfect matchings or being empty. If graph G is k-resonant for any integer k ≥ 1, then it is called maximally resonant. All maximally resonant polyomino graphs are characterized in this work. As a result, the least integer k such that a k-resonant polyomino graph is maximally resonant is determined.     

Short diastereoselective synthesis of cis- and trans-hexahydropyrido[2,1-a]isoindole derivatives

A new and highly stereoselective access to 4,10b-trans or 4,10b-cis hexahydropyrido[2,1-a]isoindole derivatives is reported, both requiring an intramolecular Mannich-type reaction as key step. The cis diastereoisomer is obtained in three steps from a 2-alkyl benzaldehyde through the stereoselective formation of a 2,6-cis-disubstituted piperidine, while the trans stereomer is efficiently obtained, in a single step, if a 2-formyl benzoic acid is involved in the Mannich cyclization process.     

The drag of the row of parallel chains of spherical particles in the Stokes flow

The drag of thin-layered porous deposit consisting of dendrites of identical spherical particles with respect to the flow of viscous incompressible liquid is calculated. The deposit is approximated by a model system, a row of parallel chains of particles oriented perpendicular to a flow direction. The expression is derived for the dimensionless drag force acting on the unit chain length as a function of the ratio of a particle radius to a half-distance between chain axes, a/h. It is shown that, at a/h < 0.5, the hydrodynamic equivalent of the chains is the smooth cylinder whose radius is 1.16 times smaller than the particle radius that agrees with the experiment. It is also shown that, at a/h = 1, the drag force of a particle contacting with four adjacent particles in the layer with square packing is equal to F = 44F _St, where F _St is the Stokes drag force of a spherical particle. The pressure drop in this single layer is by 3.5% higher than in the layer of spherical particles with cubic packing. At a/h = 2/√3, drag force F of the particle contacting with six particles in a single layer with hexagonal packing is equal to 340F _St.     

A copper-catalyzed domino radical cyclization route to benzospiro-indolizidinepyrrolidinones

In this Letter the synthesis of benzospiro-indolizidinepyrrolidinones is described by a domino atom transfer radical cyclization reaction using a copper catalyst. The structure of one of the products was established by single crystal X-ray diffraction. The investigated precursors, bearing a homo allyl substituent on the N-indole, result in a 5-exo-trig, followed by a 6-endo-trig cyclization. When the N-indole is substituted with an allyl group, only the spiro-cyclization occurs.     

Synthesis of enantiomeric pure lithium and potassium benzamidinate complexes

A new synthesis leading to the chiral amidines (S,S)- and (R,R)-N,N-bis-(1-phenylethyl)benzamidine ((S)- and (R)-HPEBA) in good yields is presented. Further reaction of (S)-HPEBA with n-BuLi gave the chiral lithium salt (S)-LiPEBA. Treatment of KH with (S)-HPEBA in boiling THF afforded the corresponding potassium salt (S)-KPEBA. In contrast by performing the reaction in boiling toluene a fast racemization was observed. In the solid state racemic KPEBA formed a dimer, in which all four nitrogen atoms are in a plane. To each potassium atom a toluene molecule is η⁶-coordinated.     

Microwave-assisted guanidinylation in solid phase peptide synthesis: comparison of various reagents

The guanidinylation of a peptide chain on a polymeric support under microwave conditions using derivatives of thioureas—S-alkylisothioureas, pyrazole-carboxamidine, and guanidine as guanidinylating reagents is described. The best results are obtained with N,N′-di-Z-S-methylisothiourea and N,N′-di-Z(2-Cl)-S-methylisothiourea. It is found that guanidinylation with reagents containing Boc groups is accompanied by side reactions.     

Packing in honeycomb networks

Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K ₂, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing of HC(n) with P ₆ and K _1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.     

An alternate route to substituted 6,7-dihydro 5H-dibenz[c,e]azepines from allylbenzamides derived from the Morita–Baylis–Hillman adducts

An acid-catalyzed modular synthesis of substituted 5H-dibenz[c,e]azepines from a biaryl allylbenzamides prepared from the MBH adducts via a cascade dearoylation and intramolecular cyclization is described. The utility of the product for preparing 7,9-dihydro-4bH-dibenz[c,e]pyrrolo[1,2-a]azepine is also presented.     

Processus concurrents de photoisomerisation d'hexatrienes polymethyles: effet de longueur d'one

The ground-state conformer composition is shown to play a determining role in the orientation of the photochemical reactions of two hexatrienes. A pronounced wavelength effect is observed for Z-2,6-dimethyl-1,3,5-heptatriene; photocycloaddition leads to a bicyclo[3.1.0]hexene and [1,5] sigmatropic hydrogen migration occurs from an s-cis-s-trans conformation preferentially excited by longer wavelength light, whereas the Z-E interconversion is predominantly observed as a result of excitation of the s-trans-s-trans conformation by shorter wavelength light.     

Über den Einfluß der elektrostatischen Wechselwirkungen auf die α-Helixbildung von basischen Poly-[α-aminosäuren]

A theoretical treatment of the electrostatic interactions influencing the conformation of poly-[α-aminoacids] containing ionogenic side-chains is reported. Using the Gouy-Chapman-equation for the relation between the density of surface chargeσ _e and surfacepotentialψ the latter one will be determined on the surface of anα-helix of a basic poly-[α-aminoacid] in an aqueous electrolyte solution. As it could be shown,ψ decreases with the electrolyte concentrationc. The equilibrium constants for the propagation step of theα-helix-formation is expressed as a function ofψ and a parameterK ₀ containingΔS₀ andΔH₀ dependent onc, considering the electrostatic energy of neighboured basic groups. The temperature at the mid-point of the transitionT _m is a function of the reciproce ionic strengthI. In a solution of an 1-1-electrolyte,T _m depends linearly on 1/√c. The experimental data for Poly-[L-lysine] are in a very good agreement with the straight line given by this relation. However, in the case of a 1∶1 copolymer ofL-lysine andL-leucine the calculated values are much lower than the measured ones, obviously due to neglecting the hydrophobic interactions of the leucine side chains. Furthermore, a relation for the change of theα-helix-contentf _H with 1/T is given. In this case, in the well-known relation (?f _H/? (1/T))=?ΔH⁰/4Rσ ^1/2, the cooperative parameterσ is substituted by a modified parameterΣ depending on the ionic strength. According to this equation and agreeing with the experimental results,T _m increases with the ionic strength, because the electrostatic potentialψ at theα-helix-surface decreases. However, in contrast to reality, the inclination of thef _H-T-curves increases withI orc, respectively. This may be due to an increase ofσ with the electrolyte concentration.     

La methode polarovoltrique : Principes généraux et bases de la méthode

The various steps in the development of the polarovoltric method and its utilisation in an automatic titration apparatus employing 2 polarized platinum electrodes are described. The method is based on the use of 2 types of polarization relationships applied to different chemical systems. These relationships are of the type I = f(V) and V = f(U), where V is the potential measured at the electrodes and U the potential applied to the electrodes across a resistance R, and are obtained directly from 2 indicating electrodes without the need for a reference electrode.The advantage of these relationships over the classic I= f(E) curves, where E is the potential of the indicating electrode with respect to a reference electrode, is to facilitate the prediction of the titration curves as a function of the resistance R and the applied voltage U. The use of these relationships has shown that a fixed applied voltage U of 3 V and a fixed series resistance R of 0.5 megohm are the most suitable for a differential polarovoltmeter for semi-automatic titrations.A symbolic notation is described which indicates the origin of the observed variations in potential. This notation permits a simple interpretation of polarovoltric curves and the rational use of unsymmetrical electrode arrangements.     

Exact semiclassical solution for the time evolution of a quantum-mechanical system in a circularly polarized monochromatic driving field

A closed-form exact solution is presented for the time evolution operator of a nonrelativistic hydrogen atom driven by a circularly polarized monochromatic light beam. The solution has the form U(t, 0) = exp(?itF)exp(?itG), where F and G are time independent operators. All temporal effects of the oscillating field are included. Extension to other systems is easily made. A generalization of the rotating wave approximation to multilevel systems is also presented.     

Car-Parinello molecular dynamics simulations of thionitroxide and S-nitrosothiol in the gas phase, methanol, and water—A theoretical study of S-nitrosylation

A dilemma about whether thionitroxide radical (RSNHO) or S-nitrosothiol (RSNO) is observed in protein S-nitrosylation has arisen recently. To illustrate the effect of chemical environment on these structures, this paper presents quantum mechanical molecular dynamics of thionitroxide, and cis-and trans-S-nitrosothiols in the gas phase, methanol, and water. By using Car-Parrinello molecular dynamics (CPMD), we have observed that there is free rotation about the S-N bond at 300 K in thionitroxide, but no such rotation is observed for S-nitrosothiol. The C-S-N-O torsion angle distribution in thionitroxide is s-ignificantly dependent upon the surrounding environment, leading to either gauche-, cis-, or trans-conformation. In the case of S-nitrosothiol the C-S-N-O plane is twisted slightly by 5°-15° in the cis-isomer, while the periplanar structure is well-retained in the trans-isomer. The calculated results are in agreement with the X-ray crystallographic data of small molecular RSNO species. Interestingly, for both compounds, the CPMD simulations show that solvation can cause a decrease in the S-N bond length. Moreover, the oxygen atom of thionitroxide is found to be a good hydrogen-bond acceptor, forming an oxyanion-hole-like hydrogen bonding network.     

A simple approach for the synthesis of new pyrimidinyl α-amino acids

A simple synthetic method for the preparation of optically active pyrimidinyl α-amino acids is presented. A nucleophilic ipso-substitution reaction between 2-(benzylsulfonyl)-4-isopropoxypyrimidines and a nucleophilic side chain of several protected natural α-amino acids is investigated to obtain new pyrimidin-2-yl α-amino acids. A detailed optimisation study of this reaction is discussed. Moreover, the selective O-alkylation of 2-(benzylsulfanyl)-4(3H)pyrimidinones with a hydroxylic side chain of some natural α-amino acids under Mitsunobu conditions is studied as a method to prepare new pyrimidin-4-yl α-aminoesters.     

Partition of symmetric powers of G-sets into orbits: application to the enumeration of force constants

Using the theory of actions of groups on sets this paper describes an efficient method to obtain the partition of the symmetric powers of a G-set into orbits, where G is a finite group. In this method, a generating function is obtained for each representative of the conjugacy classes of subgroups of G. The coefficients of the generating function corresponding to a representative subgroup H?≤ G give the number of orbits isomorphic to the coset G/H that are contained in the successive symmetric powers of the G-set. A direct application of this approach is the attainment of the number and isotropy group of the vibrational force constants associated with a set of internal coordinates for a given molecule. As illustration, the method has been applied to XYZ ₃?(C _3v ) molecules.     

Enhancement and quenching of photoionization in rare gas mixtures

Admixing a sufficient amount of a light rare gas to a heavier rare gas effects the photoionization current measured at the absorption lines of the latter. This current is enhanced if hv > E_c and quenched if hv <E_c where hv is the energy of the exciting photons. E_c is approximately equal to the ionization potential of the corresponding heteronuclear van der Waals molecule. Both homonuclear and heteronuclear dimer ion formation are discussed.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers I. Configuration distribution and density profiles of adsorbed chains

Monte Carlo simulations for the adsorption of symmetric triblock copolymers from a nonselective solvent at a solid-liquid interface have been performed on a lattice model. In simulations, triblock copolymer molecules are modeled as self-avoiding linear chains composed of m segments of A and n segments of B arranged as A_m/2B_nA_m/2. Either segment A or segment B is attractive, while the other is non-attractive to the surface. The microstructure of the adsorbed layers, including the segment-density profiles and the size distribution of loops, tails and trains are presented. The effect of the adsorption energy, the bulk concentration, the chain composition, as well as the chain length on various adsorption properties has been studied. The results have shown that the size distribution of various configurations is dependent of the adsorption energy, the chain composition and the chain length. The mean length of the loops, trains and tails is insensitive to the bulk concentration. The mean length of the trains increases and that of the tails decreases as the adsorption energy and the length of the attractive segments increase. The mean length of the loops for the end-adsorbed copolymers appears a maximum and that for middle-adsorbed copolymers appears a minimum as the length of attractive segments increases. The length of the non-attractive segments affects mostly the size distribution of the tails. The longer the chain is, the larger the tail appears. The mean length of the tails and loops increases linearly as the length of the non-attractive segments increases, but that of the trains approximately is unchanged.     

An enantioselective enzymatic desymmetrization route to hexahydro-4H-furopyranol,a high-affinity ligand for HIV-1 protease inhibitors

An enantioselective synthesis of (3aS,4S,7aR)-hexahydro-4H-furo[2,3-b]pyran-4-ol, a high-affinity nonpeptide ligand for a variety of potent HIV-1 protease inhibitors is described. The key steps involved a highly enantioselective enzymatic desymmetrization of meso-diacetate, an efficient transacetalization, and a highly diastereoselective reduction of a ketone. This route is amenable to large-scale synthesis using readily available starting materials.