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Stationary Points (stationary + point)
Selected AbstractsOxygenolysis of Flavonoid Compounds: DFT Description of the Mechanism for QuercetinCHEMPHYSCHEM, Issue 11 2004Sébastien Fiorucci Abstract Flavonoids are naturally occurring phenol derivatives present in substantial amounts in a large variety of plants, fruits and vegetables daily eaten by humans. Most of these compounds exhibit several interesting biological activities, such as antiradical and antioxidant actions. Indeed, by complexation with specific enzymes, flavonoids are notably liable to metabolize molecular dioxygen. On the basis of experimental results describing oxygenolysis of the flavonoid quercetin, activated by the enzyme quercetin 2,3-dioxygenase (2,3-QD), our attention has focused on the role of metal center in the activation of the substrate quercetin. Thus, in the present study, by means of DFT calculations at the B3LYP/6-31(+)G* level on model molecular systems, we describe different mechanisms for dioxygen metabolization by quercetin. Stationary points are described, and energetic and structural analyses along the reaction paths are reported. Our calculations show that the copper cation must act as an oxidant towards the substrate and that the reaction proceeds through a 1,3-cycloaddition. [source] Obtaining positions and widths of scattering resonances from a complex multiconfigurational self-consistent field state using the M1 methodINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2010Kousik Samanta Abstract We present a complex multiconfigurational self-consistent field (CMCSCF)-based approach to investigate electron-atom scattering resonances. It is made possible by the use of second quantization algebra adapted for biorthogonal spin orbitals, which has been applied to develop a quadratically convergent CMCSCF method. To control the convergence to the correct CMCSCF stationary point, a modified step-length control algorithm is introduced. Convergence to a tolerance of 1.0 × 10,10 a.u. for the energy gradient is found to be typically within 10 iterations or less. A method involving the first block of the M matrix defined in the multiconfigurational spin tensor electron propagator method (MCSTEP) based on the CMCSCF reference state has been implemented to investigate 2P Be, shape resonances. The position and width of these resonances have been calculated for different complete active space choices. The wide distribution of the position and width of the resonance reported in the literature is explained by the existence of two distinct resonances which are close in energy. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] OPTIMIZATION OF VACUUM PULSE OSMOTIC DEHYDRATION OF CANTALOUPE USING RESPONSE SURFACE METHODOLOGYJOURNAL OF FOOD PROCESSING AND PRESERVATION, Issue 1 2005WILMER J. FERMIN ABSTRACT The optimum levels of vacuum pressure, concentration of osmotic solution and dehydration time for vacuum pulse osmotic dehydration of cantaloupe were determined by response surface methodology (RSM). The response surface equations ( P < 0.05 and lack of fit > 0.1) explain the 97.6, 88.0 and 97.1% of the variability in weight loss, water loss and °Brix increase, respectively, at 95% confidence level. The canonical analysis for each response indicated that the stationary point is a saddle point for weight loss and °Brix increase, and a point of maximum response for water loss. The region that best satisfied all the constraints (low values in weight loss and °Brix increase, and high value in water loss) is located within the intervals from 49.5 °Brix to 52.5 °Brix for concentration and from 75 min to 84 min for dehydration time at a vacuum pulse of 740 mbar. [source] A Noncooperative Quantity-Rationing Theory of Transboundary PollutionJOURNAL OF PUBLIC ECONOMIC THEORY, Issue 3 2010SUDHIR A. SHAH We study a remedy for the problem caused by international transfrontier pollution. Our results are derived from the analysis of a noncooperative game model of the determination of emissions in a quantity-rationing setting. We model the emission capping negotiations using the best response dynamic process and provide natural conditions under which the process has a unique and globally asymptotically stable stationary point. We then analyze the link between type profiles and the stationary points of the negotiation process to derive various comparative statics results and the type-contingent ordering of emission allocations. These results are used to study the investment strategies that nations can use prior to the negotiations in order to manipulate the equilibrium emission caps. [source] Likelihood and bayesian approaches to inference for the stationary point of a quadratic response surfaceTHE CANADIAN JOURNAL OF STATISTICS, Issue 2 2008Valeria Sambucini Abstract In response surface analysis, a second order polynomial model is often used for inference on the stationary point of the response function. The standard confidence regions for the stationary point are due to Box & Hunter (1954). The authors propose an alternative parametrization, in which the stationary point is the parameter of interest; likelihood techniques and Bayesian analysis are then easier to perform. The authors also suggest an approximate method to get highest posterior density regions for the maximum point (not simply for the stationary point). Furthermore, they study the coverage probabilities of these Bayesian regions through simulations. Approches vraisemblantiste et bayésienne pour I'inference portant sur le point stationnaire d'une surface de réponse quadratique Résumé: Dans l'analyse des surfaces de réponse, un polyn,me du second degré est souvent utilisé pour l'inférence portant sur le point stationnaire de la fonction de réponse. Les régions de confiance standards pour le point stationnaire sont dues à Box & Hunter (1954). Les auteurs proposent une paramétrisation différente dans laquelle le point stationnaire est le paramètre d'intér,t; ceci facilite l'emploi des techniques de vraisemblance et l'analyse bayésienne. Les auteurs suggèrent aussi une façon d'approximer les régions de plus haute densité a posteriori pour le point maximum (et non seulement pour le point stationnaire). De plus, ils étudient les propriétés de couverture des régions bayésiennespar voie de simulation. [source] EXPERIMENTAL EVIDENCE FOR MULTIVARIATE STABILIZING SEXUAL SELECTIONEVOLUTION, Issue 4 2005Robert Brooks Abstract Stabilizing selection is a fundamental concept in evolutionary biology. In the presence of a single intermediate optimum phenotype (fitness peak) on the fitness surface, stabilizing selection should cause the population to evolve toward such a peak. This prediction has seldom been tested, particularly for suites of correlated traits. The lack of tests for an evolutionary match between population means and adaptive peaks may be due, at least in part, to problems associated with empirically detecting multivariate stabilizing selection and with testing whether population means are at the peak of multivariate fitness surfaces. Here we show how canonical analysis of the fitness surface, combined with the estimation of confidence regions for stationary points on quadratic response surfaces, may be used to define multivariate stabilizing selection on a suite of traits and to establish whether natural populations reside on the multivariate peak. We manufactured artificial advertisement calls of the male cricket Teleogryllus commodus and played them back to females in laboratory phonotaxis trials to estimate the linear and nonlinear sexual selection that female phonotactic choice imposes on male call structure. Significant nonlinear selection on the major axes of the fitness surface was convex in nature and displayed an intermediate optimum, indicating multivariate stabilizing selection. The mean phenotypes of four independent samples of males, from the same population as the females used in phonotaxis trials, were within the 95% confidence region for the fitness peak. These experiments indicate that stabilizing sexual selection may play an important role in the evolution of male call properties in natural populations of T. commodus. [source] A practical grid-based method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2006M. De Kool SUMMARY We present a practical grid-based method in 3-D spherical coordinates for computing multiple phases comprising any number of reflection and transmission branches in heterogeneous layered media. The new scheme is based on a multistage approach which treats each layer that the wave front enters as a separate computational domain. A finite-difference eikonal solver known as the fast-marching method (FMM) is reinitialized at each interface to track the evolving wave front as either a reflection back into the incident layer or a transmission through to the adjacent layer. Unlike the standard FMM, which only finds first arrivals, this multistage approach can track those later arriving phases explicitly caused by the presence of discontinuities. Notably, the method does not require an irregular mesh to be constructed in order to connect interface nodes to neighbouring velocity nodes which lie on a regular grid. To improve accuracy, local grid refinement is used in the neighbourhood of a source point where wave front curvature is high. The method also provides a way to trace reflections from an interface that are not the first arrival (e.g. the global PP phase). These are computed by initializing the multistage FMM from both the source and receiver, propagating the two wave fronts to the reflecting interface, and finding stationary points of the sum of the two traveltime fields on the reflecting interface. A series of examples are presented to test the efficiency, accuracy and robustness of the new scheme. As well as efficiently computing various global phases to an acceptable accuracy through the ak135 model, we also demonstrate the ability of the scheme to track complex crustal phases that may be encountered in coincident reflection, wide-angle reflection/refraction or local earthquake surveys. In one example, a variety of phases are computed in the presence of a realistic subduction zone, which includes several layer pinch-outs and a subducting slab. Our numerical tests show that the new scheme is a practical and robust alternative to conventional ray tracing for finding various phases in layered media at a variety of scales. [source] Ab initio conformational study of the P6 potential surface: Evidence for a low-lying one-electron-bonded isomerHETEROATOM CHEMISTRY, Issue 2 2007Philippe C. Hiberty The low-lying isomers of the P6 species are investigated at various levels of calculations, ranging from MP2/6-31G(d) to CCSD(T) in triple-zeta basis set involving polarization functions up to f. In addition to the five possible normal-valent isomers, which obey the octet rules, several other conformations are found to be stationary points on the potential energy surface. Among the five normal-valent isomers, the benzvalene structure is found to be the most stable one, in agreement with former studies. The benzene-like D6h planar hexagon is the least stable one, lying 32.3 kcal/mol over benzvalene, and spontaneously distorts to a less symmetrical, nonplanar six-membered ring. Above the benzvalene structure, and lying, respectively, 5.8 and 15.8 kcal/mol higher, the two lowest lying isomers are the prismane and the chair-like forms. This latter conformation, which does not obey the octet rule, exhibits two one-electron PP hemibonds and can be considered as a generic model for a new category of heterobenzene analogs, among which is the recently discovered dimer of diphosphirenyl radical. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:129,134, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20324 [source] On the convergence of stationary sequences in topology optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005Anton Evgrafov Abstract We consider structural topology optimization problems including unilateral constraints arising from non-penetration conditions in contact mechanics. The resulting non-convex non-smooth problems are instances of mathematical programs with equilibrium constraints (MPEC), or bi-level programs. Applying nested (implicit programming) algorithms to this class of problems is problematic owing to the singularity of the feasible set. We propose a perturbation strategy combining the relaxation of the equilibrium constraint with the restriction of the design domain to its regular part only. This strategy allows us to attack the problem numerically using standard non-linear programming algorithms. We rigorously study the optimality conditions for the original singular problem as well as the convergence of stationary points and globally optimal solutions to approximating problems towards respective stationary points and globally optimal solutions to the original problem. A limited numerical benchmarking of the algorithm is performed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Direct ab initio dynamics calculations of the rate constants for the reaction of CHF2CF2OCH3 with ClINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 4 2007Lei Yang A dual-level direct dynamics method is employed to reveal the dynamical properties of the reaction of CHF2CF2OCH3 (HFE-254pc) with Cl atoms. The optimized geometries and frequencies of the stationary points and the minimum energy path (MEP) are calculated at the B3LYP/6-311G(d,p) level by using GAUSSIAN 98 program package, and energetic information is further refined by the G3(MP2) method. Two H-abstraction channels have been identified. For the reactant CHF2CF2OCH3 and the two products, CHF2CF2OCH2 and CF2CF2OCH3, the standard enthalpies of formation are evaluated with the values of ,256.71 ± 0.88, ,207.79 ± 0.12, and ,233.43 ± 0.88 kcal/mol, respectively, via group-balanced isodesmic reactions. The rate constants of the two reaction channels are evaluated by means of canonical variational transition-state theory (CVT) including the small-curvature tunneling (SCT) correction over a wide range of temperature from 200 to 2000 K. The calculated rate constants agree well with the experimental data, and the Arrhenius expressions for the title reaction are fitted and can be expressed as k1 = 9.22 × 10,19 T2.06 exp(219/T), k2 = 4.45 × 10,14T0.90 exp(,2220/T), and k = 4.71 × 10,22 T3.20) exp(543/T) cm3 molecule,1 s,1. Our results indicate that H-abstraction from CH3 group is the main reaction pathway in the lower temperature range, while H-abstraction from CHF2 group becomes more competitive in the higher temperature range. © 2007 Wiley Periodicals, Inc. 39: 221,230, 2007 [source] Theoretical studies on the mechanism and kinetics of the reaction of F atom with NCO radicalINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 2 2003Zheng-Yu Zhou The reaction of a F atom with an NCO radical was studied at 6-311+g* level, using DFT methods. All geometries, vibrational frequencies, and energies of different stationary points were calculated by HF, UMP2, and DFT methods, and the results agreed with the experimental values. The vibrational frequencies and vibrational modes of the reactant, intermediates, transition states, and products were calculated and the changes of these frequencies and modes were analyzed. Simultaneously, the vibrational modes of various species were assigned. The relationship and the change among these confirmed the mechanism of the reaction and the process of electron transfer. The major channel for the reaction was found to be the cis-channel. At the same time the rate constant was estimated. A new method of analyzing reaction mechanism is also presented. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 52,60, 2003 [source] Interaction of FeO+ cation with benzene, aniline, and 3-methylaniline: DFT study of oxygen insertion mechanismINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2008Karolina Kwapien Abstract The reaction pathways and energetics for oxygen insertion into CH bond in benzene, aniline, and 3-methylaniline by FeO+ in the gas phase were investigated by means of the DFT methodology with the B3LYP exchange-correlation functional and 6-311G** basis set. The main aim of this work was to elucidate the influence of substituents in phenyl ring on stationary points along the energy profile on sextet and quartet surfaces for the reaction of FeO+ with substituted benzenes. The studies show that the amino and methyl groups change the energetics of oxygen insertion by lowering the energy profile along the reaction pathway. The substituents studied in this work facilitate the insertion of oxygen into the aromatic CH bond by stabilizing the intermediate sigma complex (,-complex), the amino group being by far more effective. On the other hand, both functional groups increase the activation energy of the rate-determining step in the gas phase, so that they have unfavorable influence on the kinetics. The comparison of the energy diagrams for the sextet and quartet spin states indicates the dominance of the low-spin reactivity in oxygen insertion into aromatic CH bond. Aniline and 3-methylaniline oxidation occurs via electrophilic addition while the conversion of benzene to phenol by FeO+ is mediated by a ,-complex with mixed radical and cationic character. Present results are also discussed in the context of oxyferryl group reactivity. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Mechanisms and kinetics for preparing carbohydrazide by reacting dimethyl carbonate with hydrazine: A theoretical studyINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2008Jianguo Zhang Abstract The mechanism and kinetic modeling for preparing carbohydrazide from dimethyl carbonate and hydrazine has been declared. The geometries of all the stationary points (reactants, intermediates, transition states, and products) are optimized by using the B3LYP method with the cc-pVDZ basis set, and the harmonic vibrational frequencies as well as infrared intensities are predicted with the same method. The minimum-energy paths are obtained by using the intrinsic reaction coordinate (IRC) theory at the B3LYP/cc-pVDZ level of theory with the step length 0.02 (amu)1/2·bohr. The rate constants are evaluated by using the TST, TST/Eckart, and RRKM (T)/Eckart methods. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Study of conformational and optical rotation for the alaninamideINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2007Shulei Zhao Abstract Six stationary points of alaninamide have been located on the potential surface energy (PES) at the B3LYP/6-311++G(2d,2p) level of theory both in the gas phase and in aqueous solution. In the aqueous solution, to take the water solvent effect into account, the polarizable continuum model (PCM) method has been used. Accurate geometric structures and their relative stabilities have been investigated. The results show that the intramolecular hydrogen bond plays a very important role in stabilizing the global minimum of the alaninamide. Moreover, the consistent result in relative energy using high-level computations, including the MP2 and MP3 methods with the same basis set [6-311++G(2d,2p)], indicates that the B3LYP/6-311++G(d,p) level may be applied to the analogue system. More importantly, the optical rotation of the optimized conformers (both in the gas phase and in aqueous solution) of alaninamide have been calculated using the density functional theory (DFT) and Hartree,Fock (HF) method at various basis sets (6-31+G*, 6-311++G(d,p), 6-311++G(2d,2p) and aug-cc-pvdz). The results show that the selection of the computation method and the basis set in calculation has great influence on the results of the optical rotations. The reliability of the HF method is less than that of DFT, and selecting the basis set of 6-311++G(2d,2p) and aug-cc-pvDZ produces relative reliable results. Analysis of the computational results of the structure parameters and the optical rotations yields the conclusion that just the helixes in molecules caused the chiral molecules to be optical active. The Boltzmann equilibrium distributions for the six conformers (both in the gas phase and in the aqueous solution) are also carried out. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Theoretical studies of mechanisms of cycloaddition reaction between difluoromethylene carbene and acetoneINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2007Xiu Hui Lu Abstract Mechanisms of the cycloaddition reaction between singlet difluoromethylene carbene and acetone have been investigated with the second-order Møller,Plesset (MP2)/6-31G* method, including geometry optimization and vibrational analysis. Energies for the involved stationary points on the potential energy surface (PES) are corrected by zero-point energy (ZPE) and CCSD(T)/6-31G* single-point calculations. From the PES obtained with the CCSD(T)//MP2/6-31G* method for the cycloaddition reaction between singlet difluoromethylene carbene and acetone, it can be predicted that path B of reactions 2 and 3 should be two competitive leading channels of the cycloaddition reaction between difluoromethylene carbene and acetone. The former consists of two steps: (i) the two reactants first form a four-membered ring intermediate, INT2, which is a barrier-free exothermic reaction of 97.8 kJ/mol; (ii) the intermediate INT2 isomerizes to a four-membered product P2b via a transition state TS2b with an energy barrier of 24.9 kJ/mol, which results from the methyl group transfer. The latter proceeds in three steps: (i) the two reactants first form an intermediate, INT1c, through a barrier-free exothermic reaction of 199.4 kJ/mol; (ii) the intermediate INT1c further reacts with acetone to form a polycyclic intermediate, INT3, which is also a barrier-free exothermic reaction of 27.4 kJ/mol; and (iii) INT3 isomerizes to a polycyclic product P3 via a transition state TS3 with an energy barrier of 25.8 kJ/mol. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Theoretical study of the mechanism of CH2CO + CN reactionINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2006Hao Sun Abstract The potential energy surface information of the CH2CO + CN reaction is obtained at the B3LYP/6-311+G(d,p) level. To gain further mechanistic knowledge, higher-level single-point calculations for the stationary points are performed at the QCISD(T)/6-311++G(d,p) level. The CH2CO + CN reaction proceeds through four possible mechanisms: direct hydrogen abstraction, olefinic carbon addition,elimination, carbonyl carbon addition,elimination, and side oxygen addition,elimination. Our calculations demonstrate that R,IM1,TS3,P3: CH2CN + CO is the energetically favorable channel; however, channel R,IM2,TS4,P4: CH2NC + CO is considerably competitive, especially as the temperature increases (R, IM, TS, and P represent reactant, intermediate, transition state, and product, respectively). The present study may be helpful in probing the mechanism of the CH2CO + CN reaction. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] Quantum chemical studies on molecular structural conformations and hydrated forms of salicylamide and O-hydroxybenzoyl cyanideINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 3 2005K. Anandan Abstract Ab initio and density functional theory (DFT) methods have been employed to study the molecular structural conformations and hydrated forms of both salicylamide (SAM) and O-hydroxybenzoyl cyanide (OHBC). Molecular geometries and energetics have been obtained in the gaseous phase by employing the Møller,Plesset type 2 MP2/6-311G(2d,2p) and B3LYP/6-311G(2d,2p) levels of theory. The presence of an electron-releasing group (SAM) leads to an increase in the energy of the molecular system, while the presence of an electron-withdrawing group (OHBC) drastically decreases the energy. Chemical reactivity parameters (, and ,) have been calculated using the energy values of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) obtained at the Hartree,Fock (HF)/6-311G(2d,2p) level of theory for all the conformers and the principle of maximum hardness (MHP) has been tested. The condensed Fukui functions have been calculated using the atomic charges obtained through the natural bond orbital (NBO) analysis scheme for all the optimized structures at the B3LYP/6-311G(2d,2p) level of theory, and the most reactive sites of the molecules have been identified. Nuclear magnetic resonance (NMR) studies have been carried out at the B3LYP/6-311G(2d,2p) level of theory for all the conformers in the gaseous phase on the basis of the method of Cheeseman and coworkers. The calculated chemical shift values have been used to discuss the delocalization activity of the electron clouds. The dimeric structures of the most stable conformers of both SAM and OHBC in the gaseous phase have been optimized at the B3LYP/6-311G(2d,2p) level of theory, and the interaction energies have been calculated. The most stable conformers of both compounds bear an intramolecular hydrogen bond, which gives rise to the formation of a pseudo-aromatic ring. These conformers have been allowed to interact with the water molecule. Special emphasis has been given to analysis of the intermolecular hydrogen bonds of the hydrated conformers. Self-consistent reaction field (SCRF) theory has been employed to optimize all the conformers in the aqueous phase (, = 78.39) at the B3LYP/6-311G(2d,2p) level of theory, and the solvent effect has been studied. Vibrational frequency analysis has been performed for all the optimized structures at MP2/6-311G(2d,2p) level of theory, and the stationary points corresponding to local minima without imaginary frequencies have been obtained for all the molecular structures. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] McLafferty rearrangement of the radical cations of butanal and 3-fluorobutanal: A theoretical investigation of the concerted and stepwise mechanismsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2008Daniel Norberg Abstract The stepwise and concerted pathways for the McLafferty rearrangement of the radical cations of butanal (Bu+) and 3-fluorobutanal (3F-Bu+) are investigated with density functional theory (DFT) and ab initio methods in conjunction with the 6-311+G(d,p) basis set. A concerted transition structure (TS) for Bu+, (H), is located with a Gibbs barrier height of 37.7 kcal/mol as computed with CCSD(T)//BHandHLYP. Three pathways for the stepwise rearrangement of Bu+ have been located, which are all found to involve different complexes. The barrier height for the H, transfer is found to be 2.2 kcal/mol, while the two most favorable TSs for the C,,C, cleavage are located 8.9 and 9.2 kcal/mol higher. The energies of the 3F-Bu+ system have been calculated with the promising hybrid meta-GGA MPWKCIS1K functional of DFT. Interestingly, the fluorine substitution yields a barrier height of only 20.5 kcal/mol for the concerted TS, (3F-H). A smaller computed dipole moment, 12.1 D, for (3F-H) compared with 103.2 D for (H) might explain the stabilization of the substituted TS. The H, transfer, with a barrier height of 4.9 kcal/mol, is found to be rate-determining for the stepwise McLafferty rearrangement of 3F-Bu+, in contrast to the unsubstituted case. By inspection of the spin and charge distributions of the stationary points, it is noted that the bond cleavages in the concerted rearrangements are mainly of heterolytic nature, while those in the stepwise channels are found to be homolytic. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] OH hydrogen abstraction reactions from alanine and glycine: A quantum mechanical approachJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2001Annia Galano Abstract Density functional theory (B3LYP and BHandHLYP) and unrestricted second-order Møller,Plesset (MP2) calculations have been performed using 3-21G, 6-31G(d,p), and 6-311 G(2d,2p) basis sets, to study the OH hydrogen abstraction reaction from alanine and glycine. The structures of the different stationary points are discussed. Ring-like structures are found for all the transition states. Reaction profiles are modeled including the formation of prereactive complexes, and very low or negative net energy barriers are obtained depending on the method and on the reacting site. ZPE and thermal corrections to the energy for all the species, and BSSE corrections for B3LYP activation energies are included. A complex mechanism involving the formation of a prereactive complex is proposed, and the rate coefficients for the overall reactions are calculated using classical transition state theory. The predicted values of the rate coefficients are 3.54×108 L,mol,1,s,1 for glycine and 1.38×109 L,mol,1,s,1 for alanine. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1138,1153, 2001 [source] The mechanism of alkaline hydrolysis of amides: a comparative computational and experimental study of the hydrolysis of N -methylacetamide, N -methylbenzamide, and acetanilideJOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 6 2009Diana Cheshmedzhieva Abstract Theoretical computations and experimental kinetic measurements were applied in studying the mechanistic pathways for the alkaline hydrolysis of three secondary amides: N -methylbenzamide, N -methylacetamide, and acetanilide. Electronic structure methods at the HF/6-31+G(d,p) and B3LYP/6-31+G(d,p) levels of theory are employed. The energies of the stationary points along the reaction coordinate were further refined via single point computations at the MP2/6-31+G(d,p) and MP2/6-311++G(2d,2p) levels of theory. The role of water in the reaction mechanisms is examined. The theoretical results show that in the cases of N -methylbenzamide and N -methylacetamide the process is catalyzed by an ancillary water molecule. The influence of water is further assessed by predicting its role as bulk solvent. The alkaline hydrolysis process in aqueous solution is characterized by two distinct free energy barriers: the formation of a tetrahedral adduct and its breaking to products. The results show that the rate-determining stage of the process is associated with the second transition state. The entropy terms evaluated from theoretical computations referring to gas-phase processes are significantly overestimated. The activation barriers for the alkaline hydrolysis of N -methylbenzamide and acetanilide were experimentally determined. Quite satisfactory agreement between experimental values and computed activation enthalpies was obtained. Copyright © 2008 John Wiley & Sons, Ltd. [source] Theoretical study of carbon atom scrambling in benzenium ions with ethyl or isopropyl groupsJOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 2 2006Bjørnar Arstad Abstract Carbon atom scrambling is observed in benzenium ions in the mass spectrometer and in isotopic labeling experiments in the methanol-to-hydrocarbons reaction over acidic zeolites. We have shown plausible scrambling mechanisms in ethyl- and isopropylbenzenium ions and various intramolecular interconversion reactions that may take place in alkylbenzenium ions. Quantum chemical Density Functional Theory (DFT) modeling at the B3LYP/cc-pVTZ//B3LYP/6-311G(d,p) level of theory has been carried out to investigate carbon atom scrambling reactions in ethyl- and isopropyl(methyl)benzenium ions. A total of 85 stationary points have been calculated (48 minima and 37 transition states). The carbon atom scrambling reactions start with an initial ring expansion of the benzenium ions to a seven-membered ring. The seven-membered ring may rearrange and at a later stage re-contract to the original benzenium species, albeit with some atoms interchanged, i.e. there has been atom scrambling. Copyright © 2005 John Wiley & Sons, Ltd. [source] A Noncooperative Quantity-Rationing Theory of Transboundary PollutionJOURNAL OF PUBLIC ECONOMIC THEORY, Issue 3 2010SUDHIR A. SHAH We study a remedy for the problem caused by international transfrontier pollution. Our results are derived from the analysis of a noncooperative game model of the determination of emissions in a quantity-rationing setting. We model the emission capping negotiations using the best response dynamic process and provide natural conditions under which the process has a unique and globally asymptotically stable stationary point. We then analyze the link between type profiles and the stationary points of the negotiation process to derive various comparative statics results and the type-contingent ordering of emission allocations. These results are used to study the investment strategies that nations can use prior to the negotiations in order to manipulate the equilibrium emission caps. [source] On-line expectation,maximization algorithm for latent data modelsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2009Olivier Cappé Summary., We propose a generic on-line (also sometimes called adaptive or recursive) version of the expectation,maximization (EM) algorithm applicable to latent variable models of independent observations. Compared with the algorithm of Titterington, this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete-data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback,Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e. that of the maximum likelihood estimator. In addition, the approach proposed is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model. [source] Self-Similar Wave of Swelling/Collapse Phase Transition along Polyelectrolyte GelMACROMOLECULAR THEORY AND SIMULATIONS, Issue 8 2004Andrey Yu. Abstract Summary: Theoretical analysis of the possibility of collapse/swelling phase transition propagation along a polyelectrolyte gel thread has been performed. A differential equation that determines the time dependence of the degree of swelling of polymer thread under the radial mechanical force has been obtained. It formally coincides with the equation of diffusion of an impurity in a medium with a certain source density that depends on excluded-volume and Coulomb interactions, osmotic pressure of counterions, and entropy of the subchains. Two stationary points of this equation correspond to contracted and swollen states. It has been shown that once activated, the phase transition between these stationary points could propagate along the thread in the form of a wave with positive speed if the initial state is characterized by a higher level of free energy than the final state. The results of numerical calculations illustrating the process of phase transition propagation along polyelectrolyte gel thread show that propagation of the swelling/collapse phase transition takes place in the form of the stepwise self-similar wave with steep front. The sharp boundary between swollen and collapsed zones is observed and does not tend to dissipate as propagation proceeds. [source] Endogenous Cycles and Menu Costs: A Dynamic Macroeconomic Model of MonopolyMETROECONOMICA, Issue 1 2002Kirsten Ralf We present a dynamic model of price setting in which price adjustments are costly for the monopolist. The general price level changes endogenously due to welfare changes. For the resulting two-dimensional dynamical system the existence of a continuum of stationary points is proven. Furthermore, simulations show that endogenous cycles of output can occur. [source] Fuzzy Sarsa Learning and the proof of existence of its stationary points,ASIAN JOURNAL OF CONTROL, Issue 5 2008Vali Derhami Abstract This paper provides a new Fuzzy Reinforcement Learning (FRL) algorithm based on critic-only architecture. The proposed algorithm, called Fuzzy Sarsa Learning (FSL), tunes the parameters of conclusion parts of the Fuzzy Inference System (FIS) online. Our FSL is based on Sarsa, which approximates the Action Value Function (AVF) and is an on-policy method. In each rule, actions are selected according to the proposed modified Softmax action selection so that the final inferred action selection probability in FSL is equivalent to the standard Softmax formula. We prove the existence of fixed points for the proposed Approximate Action Value Iteration (AAVI). Then, we show that FSL satisfies the necessary conditions that guarantee the existence of stationary points for it, which coincide with the fixed points of the AAVI. We prove that the weight vector of FSL with stationary action selection policy converges to a unique value. We also compare by simulation the performance of FSL and Fuzzy Q-Learning (FQL) in terms of learning speed, and action quality. Moreover, we show by another example the convergence of FSL and the divergence of FQL when both algorithms use a stationary policy. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Theoretical Study on the Mechanism of the Cycloaddition Reaction between Methylidenesilene and EthyleneCHINESE JOURNAL OF CHEMISTRY, Issue 3 2006Xiu-Hui Lu Abstract The mechanism of a cycloaddition reaction between singlet methylidenesilene and ethylene has been investigated with MP2/6-31G, and B3LYP/6-31G, methods, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. Energies of the involved conformers were calculated by CCSD(T)//MP2/6-31G, and CCSD(T)//B3LYP/6-31G, methods, respectively. The results show that the dominant reaction pathway of the cycloaddition reaction is that a complex intermediate is firstly formed between the two reactants through a barrier-free exothermic reaction of 13.3 kJ/mol, and the complex is then isomerized to a four-membered ring product P2.1 via a transition state TS2.1 with a barrier of 32.0 kJ/mol. [source] Moderate deviations for longest increasing subsequences: The upper tailCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2001Matthias Löwe We derive the upper-tail moderate deviations for the length of a longest increasing subsequence in a random permutation. This concerns the regime between the upper-tail large-deviation regime and the central limit regime. Our proof uses a formula to describe the relevant probabilities in terms of the solution of the rank 2 Riemann-Hilbert problem (RHP); this formula was invented by Baik, Deift, and Johansson [3] to find the central limit asymptotics of the same quantities. In contrast to the work of these authors, who apply a third-order (nonstandard) steepest-descent approximation at an inflection point of the transition matrix elements of the RHP, our approach is based on a (more classical) second-order (Gaussian) saddle point approximation at the stationary points of the transition function matrix elements. © 2001 John Wiley & Sons, Inc. [source] | ||||||||||||||||||||||