Energy Hypersurface

2016 ◽  
Author(s):  
S. E. Braslavsky
Keyword(s):  
Energy Hypersurface

A Convex Hull Algorithm for Minimization of Gibbs Energy in Two-Phase Multicomponent Alloys

2011 ◽  
Vol 172-174 ◽  
pp. 1214-1219
Author(s):  
Nataliya Perevoshchikova ◽  
Benoît Appolaire ◽  
Julien Teixeira ◽  
Sabine Denis
Keyword(s):  
Gibbs Energy ◽  
Convex Hull ◽  
Large Temperature ◽  
Two Phase ◽  
Multicomponent Alloys ◽  
General Dimension ◽  
Newton Raphson ◽  
Convex Hull Algorithm ◽  
Energy Hypersurface ◽  
Equilibrium Calculations

We have adapted the Quickhull algorithm with the general dimension Beneath-Beyondalgorithm [6] for computing the convex hull of the Gibbs energy hypersurface of multicomponenttwo-phase alloys. We illustrate the salient features of our method with calculations of isothermalferrite-austenite equilibria in Fe-C-Cr. Finally, successive equilibrium calculations in a Fe-C-Cr-Mosteel over a large temperature range show the benefit of computing the convex hull before performingthe conventional Newton-Raphson search.

scholarly journals Ab Initio and DFT Study of the Conformational Energy Hypersurface of Cyclic Gly-Gly-Gly

2009 ◽  
Vol 113 (40) ◽  
pp. 10818-10825 ◽  
Author(s):  
Rodrigo D. Tosso ◽  
Miguel A. Zamora ◽  
Fernando D. Suvire ◽  
Ricardo D. Enriz
Keyword(s):  
Ab Initio ◽  
Conformational Energy ◽  
Dft Study ◽  
Energy Hypersurface ◽  
Ab Initio And Dft

scholarly journals Gas-phase reaction between calcium monocation and fluoromethane: Analysis of the potential energy hypersurface and kinetics calculations

2009 ◽  
Vol 131 (14) ◽  
pp. 144309 ◽  
Author(s):  
Adrián Varela-Álvarez ◽  
V. M. Rayón ◽  
P. Redondo ◽  
C. Barrientos ◽  
José A. Sordo
Keyword(s):  
Potential Energy ◽  
Gas Phase ◽  
Phase Reaction ◽  
Gas Phase Reaction ◽  
Energy Hypersurface ◽  
Potential Energy Hypersurface

A theoretical approach to the acid-catalyzed hydration of the carbonyl group: the case of formaldehyde

1991 ◽  
Vol 69 (9) ◽  
pp. 1376-1387 ◽  
Author(s):  
Daniel Peeters ◽  
Georges Leroy
Keyword(s):  
Reaction Mechanism ◽  
Potential Energy ◽  
Water Molecules ◽  
Hydration Reaction ◽  
Second Derivatives ◽  
Hydrated Proton ◽  
Energy Reaction ◽  
Derivatives Of ◽  
Energy Hypersurface ◽  
Potential Energy Hypersurface

The analysis of the hydration of formaldehyde in the presence of a hydrated proton was performed. Molecular quantum chemistry methods were used to explore the potential energy hypersurface. Calculations were performed at RHF-4-31G level. The structures were obtained through the use of first and second derivatives of the potential energy hypersurface thereby guaranteeing the nature of the extremum. The incidence of one or two water molecules on the reaction is discussed. It has been found that a low energy reaction path exists when the hydration process is catalyzed by a proton and two water molecules. The reaction mechanism rests on successive addition/elimination processes and reveals the respective roles of the oxygen lone pairs and of the C=O double bond upon the mechanism. Key words: ab initio calculations, carbonyl reactivity, acid catalysis, hydration, reaction mechanism.

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