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Saddle Points (saddle + point)
Terms modified by Saddle Points Selected AbstractsTheoretical study of the reactions BF3 + BX, where X = H or NINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2005Patrícia R. P. Barreto Abstract This work presents the rate constant for the gas-phase reaction BF3 + BX, where X = H or N, over the temperature range of 200,4,000 K. Conventional transition state theory (TST) is used to study these reactions. Geometries, frequencies, and the potential energy for reactant, products, and saddle point are obtained from accurate electronic structure calculations performed with the GAUSSIAN 98 program. The reaction rate for these reactions are determined using a simple code developed for this task. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Isomers of C20: An energy profile IIIJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2004Jennifer I. Chavez Abstract Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C20 isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C20 that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require ,15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C20 structures on the potential surface, relative to the ring, bowl, and cage isomers. © 2003 Wiley Periodicals, Inc. J Comput Chem 25: 322,327, 2004 [source] Isomers of C20: An energy profile IIJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2003Kyle A. Beran Abstract Semi-empirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C20 isomers that are predicted to exist in and around the bowl and cage isomers. Using the optimized Cartesian coordinates for the bowl and the cage isomers, a saddle-point calculation was performed. The output file generated, containing energy, distance, and geometry information, is then organized into a graphical format. The resulting graph, which plots the energy of the 20-atom system as a function of the distance from the geometric midpoint, is a two-dimensional energy profile. This profile illustrates an estimation of the contours on the potential energy surface, showing energy minima and maxima that are encountered as the bowl evolves into the cage structure, or vice-versa. To expand the surface into three dimensions, geometry optimizations were performed on the sets of Cartesian coordinates that correspond to energy minima in the bowl-cage profile. Based on these optimizations, eight additional isomers of C20 have been identified and are predicted to be energetically stable. These additional isomers were subsequently subjected to saddle-point calculations in order to identify those isomers that lie adjacent to one another on the three-dimensional surface. Two isomers that are adjacent to each other will exhibit an energy profile that progresses smoothly from the potential well of each isomer up to the saddle point separating them. Consequently, these adjacent pairs of isomers establish a step-wise transformation between the bowl and the cage. This process, which extends out over the three-dimensional surface, is predicted to require less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1287,1290, 2003 [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] STABILITY ANALYSIS OF A TRITROPHIC FOOD CHAIN MODEL WITH AN ADAPTIVE PARAMETER FOR THE PREDATORNATURAL RESOURCE MODELING, Issue 2 2009JEAN M. TCHUENCHE Abstract The study of three-species communities have become the focus of considerable attention, and because the studies of ecological communities start with their food web, we consider a tritrophic food chain model comprised of the prey, the predator, and the super-predator. The classical assumption of the domino effect is supplemented with an adaptive parameter for the predator (in the absence of prey). Thus, the model exhibits an equilibrium with the predator-top-predator steady state, which is a saddle point. Dynamical behaviors such as boundedness, existence of periodic orbits, persistence, as well as stability are analyzed. The long-term coexistence of the three interacting species is addressed, and the stability analysis of the model shows that the biologically most relevant equilibrium point is globally asymptotically stable whenever it satisfies a certain criterion. Practical implications are explored and related to real populations. [source] Scope and Mechanistic Insights into the Use of Tetradecyl(trihexyl)phosphonium Bistriflimide: A Remarkably Selective Ionic Liquid Solvent for Substitution ReactionsCHEMISTRY - A EUROPEAN JOURNAL, Issue 36 2006James McNulty Abstract A survey of substitution reactions conducted in a phosphonium bistriflimide ionic liquid is presented. The results demonstrate high selectivity favoring substitution over typically competitive elimination and solvolytic processes even when challenging secondary and tertiary electrophiles are employed. The first reports of Kornblum substitution reactions in an ionic liquid are described that proceed with very high chemoselectivity in favor of nitro over nitroso products and elimination side products. The structure,reactivity study indicates that these reactions proceed through a narrow spectrum of pathways ranging from straight SN2 to a preassociation pathway along a saddle point that approaches the SN1 limit. The barrier to the formation of dissociated carbocations is attributed to the structural features of this ionic liquid that favor intervention of the associated nucleophile over dissociation, also preventing cross over to E1 processes. The lack of any basic entity in the phosphonium bistriflimide ionic liquid appears to prevent any potential base-mediated elimination reactions, which makes this a highly selective medium for use in general substitution reactions. [source] The Diels,Alder Reaction of Ethene and 1,3-Butadiene: An Extended Multireference ab initio InvestigationCHEMPHYSCHEM, Issue 9 2004Hans Lischka Prof. Dr. Abstract The concerted and stepwise mechanisms of the Diels,Alder reaction between 1,3-butadiene and ethene have been investigated using highly correlated multireference methods (MRAQCC) and extended basis sets. Full MRAQCC geometry optimizations have been performed in all cases. The best estimate for the energy barrier of the Diels,Alder reaction is 22 kcal,mol,1. Anti- and gauche-out minima for the biradical structures and corresponding fragmentation saddle points have been determined. The biradical anti fragmentation saddle point is located 6.5 kcal,mol,1above the concerted saddle point. The gauche-in structure does not correspond to a local minimum, but leads on geometry optimization directly to cyclohexene. [source] The winnerless competition paradigm in cellular nonlinear networks: Models and applicationsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2009Paolo Arena Abstract Starting from the biological background on the olfactory architecture of both insects and mammalians, different nonlinear systems able to respond to spatial-distributed external stimuli with spatial,temporal dynamics have been investigated in the last decade. Among these, there is a class of neural networks that produces quasi-periodic trajectories that pass near heteroclinic contours and prove to be global attractors for the system. For this reason, these networks are called winnerless competition (WLC) networks. The sequence of saddle points crossed by each trajectory depends on the spatial input presented to the network and can be used as a ,code' representing a specific class of stimuli. Thanks to the intrinsic discrimination, WLC networks are often used for classification. In this paper, this capability is exploited within a framework for action-oriented perception. WLC networks are here used as bio-inspired architectures for the association between stimuli and ,percepts'. After presenting the theoretical basis of the WLC network in the classic Lotka,Volterra system, we investigate how WLC networks can be formalized in terms of cellular nonlinear networks (CNNs) hosting different kinds of cells: the FitzHugh,Nagumo neuron, the Izhikevich neuron and the single layer CNN standard cell. In order to find efficient ways to code environmental stimuli for action generation, we analyze and compare these WLC-based CNNs in terms of number of generated classes and robustness against the initial conditions. Based on the simulation results, we apply the best-performing system to solve a perceptual task involving navigation and obstacle avoidance. We demonstrate how the large memory capacity shown by the WLC,CNN is able to contribute to the new perceptual framework for autonomous artificial agents, where the association between stimuli and sequences is learned through the experience. Copyright © 2008 John Wiley & Sons, Ltd. [source] Remarks on the updated Hessian matrix methodsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003Josep Maria Bofill Abstract Optimizing a function with respect to a set of variables using the quasi-Newton,Raphson method implies updating the Hessian matrix at each iteration. The Broyden,Fletcher,Goldfarb,Shanno update formula is used for minimization and the Murtagh,Sargent,Powell update formula for optimization of first-order saddle points. Two new formulae are proposed to update the Hessian matrix. One of these formulae is derived using exponential weights and should be used to locate first-order saddle points. The second formula is a modification of the TS,Broyden,Fletcher,Goldfarb,Shanno update and could used for both minimum and first-order saddle point optimizations. These two update Hessian matrix formulae present a performance that is the same and in many cases better that the Broyden,Fletcher,Goldfarb,Shanno and Murtagh,Sargent,Powell formulae. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 324,332, 2003 [source] A new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximationJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2004I. Fdez. Abstract A new method for calculating saddle points of reactions in solution is presented. The main characteristics of the method are: (1) the solute,solvent system is described by the averaged solvent electrostatic potential/molecular dynamics method (ASEP/MD). This is a quantum mechanics/molecular mechanics method (QM/MM) that makes use of the mean field approximation (MFA) and that permits one to simultaneously optimize the electronic structure and geometry of the solute molecule and the solvent structure around it. (2) The transition state is located by the joint use of the free-energy gradient method and the mean field approximation. An application to the study of the Menshutkin reaction between NH3 and CH3Cl in aqueous solution is discussed. The accuracy and usefulness of the proposed method is checked through comparison with other methods. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1227,1233, 2004 [source] Critical properties and stability of stationary solutions in multitransonic pseudo-Schwarzschild accretionMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2006Soumini Chaudhury ABSTRACT For inviscid, rotational accretion flows, both isothermal and polytropic, a simple dynamical system analysis of the critical points has given a very accurate mathematical scheme to understand the nature of these points, for any pseudo-potential by which the flow may be driven on to a Schwarzschild black hole. This allows us for a complete classification of the critical points for a wide range of flow parameters, and shows that the only possible critical points for this kind of flow are saddle points and centre-type points. A restrictive upper bound on the angular momentum of critical solutions has been established. A time-dependent perturbative study reveals that the form of the perturbation equation, for both isothermal and polytropic flows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid flow has been shown to be stable under an adiabatic and radially propagating perturbation. The perturbation equation has also served the dual purpose of enabling and understanding the acoustic geometry for inviscid and rotational flows. [source] Implementing a proximal algorithm for some nonlinear multicommodity flow problemsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2007Adam Ouorou Abstract In this article, we consider applying a proximal algorithm introduced by Ouorou to some convex multicommodity network flow minimization problems. This algorithm follows the characterization of saddle points introduced earlier but can be derived from Martinet's proximal algorithm. In the primal space, the algorithm can be viewed as a regularized version of the projection algorithm by Rosen. A remarkable feature of the algorithm is that the projection step for multicommodity flow problems reduces to solving independent linear systems (one for each commodity) involving the node-arc incidence matrix of the network. The algorithm is therefore amenable to parallel implementation. We present some numerical results on large-scale routing problems arising in telecommunications and quadratic multicommodity flow problems. A comparison with a specialized code for multicommodity flow problems indicates that this proximal algorithm is specially designed for very large-scale instances. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 18,27 2007 [source] Random maps, coalescing saddles, singularity analysis, and Airy phenomenaRANDOM STRUCTURES AND ALGORITHMS, Issue 3-4 2001Cyril Banderier Abstract A considerable number of asymptotic distributions arising in random combinatorics and analysis of algorithms are of the exponential-quadratic type, that is, Gaussian. We exhibit a class of "universal" phenomena that are of the exponential-cubic type, corresponding to distributions that involve the Airy function. In this article, such Airy phenomena are related to the coalescence of saddle points and the confluence of singularities of generating functions. For about a dozen types of random planar maps, a common Airy distribution (equivalently, a stable law of exponent ) describes the sizes of cores and of largest (multi)connected components. Consequences include the analysis and fine optimization of random generation algorithms for a multiple connected planar graphs. Based on an extension of the singularity analysis framework suggested by the Airy case, the article also presents a general classification of compositional schemas in analytic combinatorics. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 194,246, 2001 [source] Regio- and Stereoselective Palladium-Pincer Complex Catalyzed Allylation of Sulfonylimines with Trifluoro(allyl)borates and Allylstannanes: A Combined Experimental and Theoretical StudyCHEMISTRY - A EUROPEAN JOURNAL, Issue 26 2006Olov A. Wallner Dr. Abstract Regio- and stereoselective palladium-pincer complex catalyzed allylation of sulfonylimines has been performed by using substituted trifluoro(allyl)borates and trimethylallylstannanes. The reactions provide the corresponding branched allylic products with excellent regioselectivity. The stereoselectivity of these processes is very high when trifluoro(cinnamyl)borate and trimethyl cinnamyl stannane are employed as allylic precursors; however, the reaction with trifluoro(crotyl)borate results in poor stereoselectivity. The major diastereomer formed in these reactions was the syn isomer, while the (previously reported) reactions with aldehyde electrophiles afforded the anti products, indicating that the mechanism of the stereoselection is dependent on the applied electrophile. Therefore, we have studied the mechanistic aspects of the allylation reactions by experimental studies and DFT modeling. The experimental mechanistic studies have clearly shown that potassium trifluoro(allyl)borate undergoes transmetallation with palladium-pincer complex 1,a affording an ,1 -allylpalladium-pincer complex (1,e). The mechanism of the transfer of the allyl moiety from palladium to the sulfonylimine substrate was studied by DFT calculations at the B3PW91/LANL2DZ+P level of theory. These calculations have shown that the electrophilic substitution of sulfonylimines proceeds in a one-step process with a relatively low activation energy. The topology of the potential energy surface in the vicinity of the transition-state structure proved to be rather complicated as nine different geometries with similar energies were located as first order saddle points. Our studies have also shown that the high stereoselectivity with cinnamyl metal reagents stems from steric interactions in the TS structure of the allylation reaction. In addition, these studies have revealed that the mechanism of the stereoselection in the allylation of aldehydes and sulfonylimines is fundamentally different. [source] The Diels,Alder Reaction of Ethene and 1,3-Butadiene: An Extended Multireference ab initio InvestigationCHEMPHYSCHEM, Issue 9 2004Hans Lischka Prof. Dr. Abstract The concerted and stepwise mechanisms of the Diels,Alder reaction between 1,3-butadiene and ethene have been investigated using highly correlated multireference methods (MRAQCC) and extended basis sets. Full MRAQCC geometry optimizations have been performed in all cases. The best estimate for the energy barrier of the Diels,Alder reaction is 22 kcal,mol,1. Anti- and gauche-out minima for the biradical structures and corresponding fragmentation saddle points have been determined. The biradical anti fragmentation saddle point is located 6.5 kcal,mol,1above the concerted saddle point. The gauche-in structure does not correspond to a local minimum, but leads on geometry optimization directly to cyclohexene. [source] | |||||||||||||