The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Excited state electronic polarization and reappraisal of the n <- pi* emission of acetone in water

Electronic polarization of the acetone molecule in the excited n -> pi* state is considered and its influence on the solvent shift in the emission spectrum is analyzed. Using an iterative procedure the electronic polarizations of both the ground and the excited states are included and compared with previous results obtained with Car-Parrinello dynamics. Analysis of the emission transition obtained using CIS(D)/aug-cc-pVDZ on statistically uncorrelated solute-solvent structures, composed of acetone and twelve explicit water molecules embedded in the electrostatic field of remaining 263 water molecules, corroborates that the solvent effect is mild, calculated here between 80 and 380 cm (1). (c) 2010 Published by Elsevier B.V.

Two-dimensional electron states bound to an off-plane donor in a magnetic field

The states of an electron confined in a two-dimensional (2D) plane and bound to an off-plane donor impurity center, in the presence of a magnetic field, are investigated. The energy levels of the ground state and the first three excited states are calculated variationally. The binding energy and the mean orbital radius of these states are obtained as a function of the donor center position and the magnetic field strength. The limiting cases are discussed for an in-plane donor impurity (i.e. a 2D hydrogen atom) as well as for the donor center far away from the 2D plane in strong magnetic fields, which corresponds to a 2D harmonic oscillator.

Study of the spectroscopic properties and first hyperpolarizabilities of disperse azo dyes derived from 2-amino-5-nitrothiazole

The solvatochromism and other spectroscopic and photophysical characteristics of four azo disperse dyes, derived from 2-amino-5-nitrothiazole, were evaluated and interpreted with the aid of experimental data and quantum mechanical calculations. For the non-substituted compound two conformers, E and Z, were proposed for the isolated molecules, being the second one considerably less stable. The optimization of these structures in combination with a SCRF methodology (IEFPCM, Simulating the molecules in a continuum dielectric with characteristics of methanol), suggests that the Z form is not stable in solution. This same behaviour is expected for the substituted compounds, which is corroborated by experimental data presented in previous investigations [A.E.H. Machado, L.M. Rodrigues, S. Gupta, A.M.F. Oliveira-Campos, A.M.S. Silva, J. Mol. Struct. 738 (2005) 239-245]. For the substituted compounds, two forms derived from E conformer (A and R) are possible. Quantum mechanical data suggest for the isolated molecules, that the low energy absorption hand of the E conformers involve at least two close electronic states. having the low-lying excited state a (1)(n,pi*) nature, and being the S-2 state attributed to a (1)(pi,pi*) transition. The data also suggest a small energy gap between the absorption peaks of A and B, related to the easy conversion between these forms. For the structures optimized in combination with the applied SCRF methodology, an states inversion is observed for the Substituted compounds, with a considerable diminish of the energy gap between A and B absorption peaks. The electronic spectra of these compounds are quite sensitive to changes in the solvent polarity. The positive solvatochromism is more evident in aprotic solvents, probably due to the polarization induced by the solute. These compounds do not fluoresce at 298 K, but present a small but perceptible fluorescence at 77 K, which seems to be favoured by the nature of the group in the 2 `-position of the phenyl ring. Moreover, such compounds present expressive values for first hyperpolarizability, which implies in good non-linear optics (NLO) responses and photoswitching capability. (C) 2008 Elsevier B.V. All rights reserved.

fac-/mer-[RuCl(3)(NO)(P-N)] (P-N = [o-(N,N-dimethylamino)phenyl]diphenylphosphine): Synthesis, characterization and DFT calculations

Complex fac-[RuCl(3)(NO)(P-N)] (1) was synthesized from the reaction of [RuCl(3)(H(2)O)(2)(NO)] and the P-N ligand, o-[(N,N-dimethylamino)phenyl]diphenylphosphine) in refluxing methanol solution, while complex mer,trans-[RuCl(3)(NO)(P-N)] (2) was obtained by photochemical isomerization of (1) in dichloromethane solution. The third possible isomer mer, cis-[RuCl(3)(NO)(P-N)] (3) was never observed in direct synthesis as well as in photo-or thermal-isomerization reactions. When refluxing a methanol solution of complex (2) a thermally induced isomerization occurs and complex (1) is regenerated. The complexes were characterized by NMR ((31)P{(1)H}, (15)N{1H} and 1H), cyclic voltammetry, FTIR, UV-Vis, elemental analysis and X-ray diffraction structure determination. The (31)P{(1)H} NMR revealed the presence of singlet at 35.6 for (1) and 28.3 ppm for (2). The (1)H NMR spectrum for (1) presented two singlets for the methyl hydrogens at 3.81 and 3.13 ppm, while for (2) was observed only one singlet at 3.29 ppm. FTIR Ru-NO stretching in KBr pellets or CH(2)Cl(2) solution presented 1866 and 1872 cm(-1) for (1) and 1841 and 1860 cm(-1) for (2). Electrochemical analysis revealed a irreversible reduction attributed to Ru(II)-NO(+) -> Ru(II)-NO(0) at -0.81 V and -0.62 V, for (1) and (2), respectively; the process Ru(II) -> Ru(III), as expected, is only observed around 2.0 V, for both complexes. Studies were conducted using (15)NO and both complexes were isolated with (15)N-enriched NO. Upon irradiation, the complex fac-[RuCl(3)(NO)(P-N)] (1) does not exchange (14)NO by (15)NO, while complex mer, trans-[RuCl(3)(NO)(P-N)] (2) does. Complex mer, trans-[RuCl(3)((15)NO)(P-N)] (2`) was obtained by direct reaction of mer, trans-[RuCl(3)(NO)(P-N)] (2) with (15)NO and the complex fac-[RuCl(3)((15)NO)(P-N)] (1`) was obtained by thermal-isomerization of mer, trans-[RuCl(3)((15)NO)(P-N)] (2`). DFT calculation on isomer energies, electronic spectra and electronic configuration were done. For complex (1) the HOMO orbital is essentially Ru (46.6%) and Cl (42.5%), for (2) Ru (57.4%) and Cl (39.0%) while LUMO orbital for (1) is based on NO (52.9%) and is less extent on Ru (38.4%), for (2) NO (58.2%) and Ru (31.5%). (C) 2011 Elsevier B. V. All rights reserved.

Ionic Recognition by 7-Nitro-1,3,5-triaza Adamantane: First Thermodynamic Study

A thermodynamic study involving 7-nitro-1,3,5-triaza adamantane, 1, and its interaction with metal cations in nonaqueous media is first reported. Solubility data of 1 in various solvents were used to derive the standard Gibbs energies of solution, Delta G(s)degrees in these solvents. The effect of solvation in the different media was assessed from the Gibbs energy of transfer taking acetonitrile as a reference solvent. (1)H NMR studies of the interaction of 1 and metal cations were carried out in CD(3)CN and CD(3)OD and the data are reported. Conductance measurements revealed that this ligand forms lead(II) or zinc complexes of 1: 1 stoichiometry in acetonitrile. It also revealed a stoichiometry of two molecules of 1 per mercury(II) and two cadmiu (II) ions per molecule of 1. The addition of silver salt to 1 led to the precipitation of the silver-1 complex which was isolated and characterized by X-ray crystallography. At variance with conductance measurements in solution, in the solid state the X-ray structure show`s a 1:1 stoichiometry in the Hg(II) complex. The themiodynamics of complexation of 1 and these cations provide a quantitative assessment of the selective behavior of this ligand for ions of environmental relevance.

Tightened Lieb-Oxford Bound for Systems of Fixed Particle Number

The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a nonempirical tightening of that bound in both universal and electron number-dependent form. The test functional is PBE. Regarding both atomization energies (slightly worsened) and bond lengths (slightly improved), we find the PBE functional to be remarkably insensitive to the value of the Lieb-Oxford bound. This both rationalizes the use of the original Lieb-Oxford constant in PBE and suggests that enhancement factors more sensitive to sharpened constraints await discovery.

Diphenyllead(IV) thiosemicarbazonates and pyrazolonates: Synthesis and characterization

Cyclization of thiosemicarbazones derived from beta-keto esters and beta-keto amides (HTSC) in the presence of diphenyllead(IV) acetate was explored in methanol solution at room temperature and under reflux. All beta-keto ester TSCs underwent cyclization to give the corresponding pyrazolone (HL), which, except in one case, deprotonated and coordinated the PbPh(2)(2+) moiety to form homoleptic [PbPh(2)(L)(2)] or heteroleptic [PbPh(2)(OAc)(L)] derivatives. Cyclization did not occur with beta-keto amide TSCs and only [Pbph(2)(TSC)(2)] or [PbPh(2)(OAc)(TSC)] thiosernicarbazonates were isolated. The complexes were characterized by IR spectroscopy in the solid state and by (1)H, (13)C and (207)Pb NMR spectroscopy in DMSO-d(G) solution, in which they evolve and decompose with time. Additionally, crystals of p-acetoacetanisidide thiosemicarbazone (HTSC(10)), [PbPh(2)(OAc)(L(5))] center dot MeOH (HL(5) = 2,5-dihydro-3,4-dimethyl-5-oxo-1H-pyrazolone-1-carbothioamide), [PbPh(2)Cl(L(2))] (HL(2) = 2,5-dihydro-5-oxo-3-phenyl-1H-pyrazolone-1-carbothioamide), [PbPh(2)(OAc)(TSC(8))]center dot 2MeOH (HTSC(8) = acetoacetanilide thiosemicarbazone), [PbPh(2)(OAc)(TSC(10))]center dot H(2)O and [PbPh(2)(OAc)(TSC(11))] center dot 0.75MeOH (HTSO(11) = o-acetoacetotoluidide) were studied by X-ray crystallography. The complexes, monomers or dimers with almost linear C-Pb-C moieties, are compared with the corresponding derivatives of Pb(II). (C) 2009 Elsevier Ltd. All rights reserved.

Combined Crystallographic and Solution Molecular Dynamics Study of Allosteric Effects in Ester and Ketone p-tert-Butylcalix[4]arene Derivatives and Their Complexes with Acetonitrile, Cd(II), and Pb(II)

We describe here a procedure to bridge the gap in the field of calixarene physicochemistry between solid-state atomic-resolution structural information and the liquid-state low-resolution thermodynamics and spectroscopic data. We use MD simulations to study the kinetics and energetics involved in the complexation of lower rim calix[4]arene derivatives (L), containing bidentate ester (1) and ketone (2) pendant groups, with acetonitrile molecule (MeCN) and Cd2+ and Pb2+ ions (M2+) in acetonitrile solution. On one hand, we found that the prior inclusion of MeCN into the calix to form a L(MeCN) adduct has only a weak effect in preorganizing the hydrophilic cavity toward metal ion binding. On the other hand, the strong ion-hydrophilic cavity interaction produces a wide open calix which enhances the binding of one MeCN molecule (allosteric effect) to stabilize the whole (M2+)1(MeCN) bifunctional complex. We reach two major conclusions: (i) the MD results for the (M2+)1(MeCN) binding are in close agreement with the ""endo"", fully encapsulated, metal complex found by X-ray diffraction and in vacuo MD calculations, and (ii) the MD structure for the more flexible 2 ligand, however, differs from the also endo solid-state molecule. In fact, it shows strong solvation effects at the calixarene lower bore by competing MeCN molecules that share the metal coordination sphere with the four C=O oxygens of an ""exo"" (M2+)2(MeCN) complex.

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

gamma-zein secondary structure in solution by circular dichroism

The proline-rich N-terminal domain of gamma-zein has been reported in relevant process, which include its ability to cross the cell membranes. Evidences indicate that synthetic hexapeptide (PPPVHL), naturally found in N-terminal portion of gamma-zein, can adopt the polyproline II (PPII) conformation in aqueous solution. The secondary structure of gamma-zein in maize protein bodies had been analyzed by solid state Fourier transform infrared and nuclear magnetic resonance spectroscopies. However, it was not possible to measure PPII content in physiological environment since the beta-sheet and PPII signals overlap in both solid state techniques. Here, the secondary structure of gamma-zein has been analyzed by circular dichroism in SDS aqueous solution with and without ditiothreitol (DTT), and in 60% of 2-propanol and water with DTT The results show that gamma-zein has high helical content in all solutions. The PPII conformation was present at about 7% only in water/DTT solution. (c) 2007 Wiley Periodicals, Inc.

Crystal structure and statistical coupling analysis of highly glycosylated peroxidase from royal palm tree (Roystonea regia)

Royal palm tree peroxidase (RPTP) is a very stable enzyme in regards to acidity, temperature, H(2)O(2), and organic solvents. Thus, RPTP is a promising candidate for developing H(2)O(2)-sensitive biosensors for diverse applications in industry and analytical chemistry. RPTP belongs to the family of class III secretory plant peroxidases, which include horseradish peroxidase isozyme C, soybean and peanut peroxidases. Here we report the X-ray structure of native RPTP isolated from royal palm tree (Roystonea regia) refined to a resolution of 1.85 angstrom. RPTP has the same overall folding pattern of the plant peroxidase superfamily, and it contains one heme group and two calcium-binding sites in similar locations. The three-dimensional structure of RPTP was solved for a hydroperoxide complex state, and it revealed a bound 2-(N-morpholino) ethanesulfonic acid molecule (MES) positioned at a putative substrate-binding secondary site. Nine N-glycosylation sites are clearly defined in the RPTP electron-density maps, revealing for the first time conformations of the glycan chains of this highly glycosylated enzyme. Furthermore, statistical coupling analysis (SCA) of the plant peroxidase superfamily was performed. This sequence-based method identified a set of evolutionarily conserved sites that mapped to regions surrounding the heme prosthetic group. The SCA matrix also predicted a set of energetically coupled residues that are involved in the maintenance of the structural folding of plant peroxidases. The combination of crystallographic data and SCA analysis provides information about the key structural elements that could contribute to explaining the unique stability of RPTP. (C) 2009 Elsevier Inc. All rights reserved.

Peroxymonocarbonate and Carbonate Radical Displace the Hydroxyl-like Oxidant in the Sod1 Peroxidase Activity under Physiological Conditions

Despite being one of the most important antioxidant defenses, Cu,Zn-superoxide dismutase (Sod1) has been frequently associated with harmful effects, including neurotoxicity. This toxicity has been attributed to immature forms of Sod1 and extraneous catalytic activities. Among these, the ability of Sod1 to function as a peroxidase may be particularly relevant because it is increased in bicarbonate buffer and produces the reactive carbonate radical. Despite many studies, how this radical forms remains unknown. To address this question, we systematically studied hSod1 peroxidase activity in the presence of nitrite, formate, and bicarbonate-carbon dioxide. Kinetic analyses of hydrogen peroxide consumption and of nitrite, formate, and bicarbonate-carbon dioxide oxidation showed that the Sod1-bound hydroxyl-like oxidant functions in the presence of nitrite and formate. In the presence of bicarbonate-carbon dioxide, this oxidant is replaced by peroxymonocarbonate, which is then reduced to the carbonate radical. Peroxymonocarbonate intermediacy was evidenced by (13)C NMR experiments showing line broadening of its peak in the presence of Zn,ZnSod1. In agreement, peroxymonocarbonate was docked into the hSod1 active site, where it interacted with the conserved Arg(143). Also, a reaction between peroxymonocarbonate and Cu(I)Sod1 was demonstrated by stopped-flow experiments. Kinetic simulations indicated that peroxymonocarbonate is produced during Sod1 turnover and not in bulk solution. In the presence of bicarbonate-carbon dioxide, sustained hSod1-mediated oxidations occurred with low steady-state concentrations of hydrogen peroxide (4-10 mu M). Thus, carbonate radical formation through peroxymonocarbonate may be a key event in Sod1-induced toxicity.

Absolute configuration reassignment of two chromanes from Peperomia obtusifolia (Piperaceae) using VCD and DFT calculations

Previous analysis of the ECD spectra of two prenylated benzopyrans isolated from Peperomia obtusifolia, by means of the helicity rule for the chromane chromophore, resulted in the incorrect assignment of their absolute configuration, (5) instead of (R) for a deduced P-helicity of the chromane ring for the (+)-enantiomers. This was discovered by the application of DFT calculations and VCD spectroscopy. Experimental and calculated (B3LYP/6-31G(d)) VCD and IR spectra were compared, and a definitive absolute configuration of (+)-1 and (+)-2 is reassigned directly in solution as (R). The assumption of equatorial positioning of bulky groups, shown here to be invalid for the title molecules, is the underlying cause of the previous incorrect assignment of absolute configuration. Moreover, TDDFT (B3LYP/6-311++G(2d,2p)//B3LYP/6-31G(d)) calculations of ECD spectra have shown that both P- and M-helicity of the heterocyclic ring, for a given absolute configuration, lead to the same sign for the (1)L(b) ECD band, thus bringing into question the validity of the empirical ECD helicity rule for chromane molecules. (C) 2010 Elsevier Ltd. All rights reserved.

Dinuclear Azide-Bridged Copper(II) Complex as Building Block for the Assembly of a 2D-Supramolecular Array

A novel Schiff base-copper(II) complex [Cu(2)L(2)(N(3))(2)](ClO(4))(2) 1, where L = (4-imidazolyl)ethylene-2-amino-1-ethylpyridine (apyhist), containing azide-bridges between adjacent copper ions in a dinuclear arrangement was isolated and characterized both in the solid state and in solution by X-ray crystallography and different spectroscopic techniques. Azide binding constants were estimated from titrations of the precursor [CuL(H(2)O)(2)](2+) solutions with sodium azide, giving rise to the azido-bridged species, [Cu(2)L(2)(N(3))(2)](2+). Raman spectra showed asymmetric stretching band at 2060 cm(-1), indicating the presence of azido ligands with a symmetric mu(1,) (1) binding geometry. EPA spectra, in frozen methanol/water solutions at 77 K, exhibited characteristic features of copper centers in tetragonal pyramidal coordination geometry, exhibiting magnetic interactions between them. Further, in solid state, two different values for magnetic coupling in this species were obtained, J/k = -(5.14 +/- 0.02) cm(-1) attributed to the mu(1, 1) azide-bridge mode, and J`z`/k = -(2.94 +/- 0.11) cm(-1) for the interaction between dinuclear moieties via water/perchorate bridges. Finally, an attempt was made to correlate structure and magnetic data for this dinuclear asymmetric end-on azido bridged-copper(II) 1 complex with those of another correlated dinuclear system, complex [Cu(2)L(2)Cl(2)](ClO(4))(2) 2, containing the same tridentate diimine ligand, but with chloro-bridged groups between the copper centres.