Energy Hypersurface

2016 ◽  
Author(s):  
S. E. Braslavsky
Keyword(s):  
2011 ◽  
Vol 172-174 ◽  
pp. 1214-1219
Author(s):  
Nataliya Perevoshchikova ◽  
Benoît Appolaire ◽  
Julien Teixeira ◽  
Sabine Denis

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.


2009 ◽  
Vol 113 (40) ◽  
pp. 10818-10825 ◽  
Author(s):  
Rodrigo D. Tosso ◽  
Miguel A. Zamora ◽  
Fernando D. Suvire ◽  
Ricardo D. Enriz

2009 ◽  
Vol 131 (14) ◽  
pp. 144309 ◽  
Author(s):  
Adrián Varela-Álvarez ◽  
V. M. Rayón ◽  
P. Redondo ◽  
C. Barrientos ◽  
José A. Sordo

1991 ◽  
Vol 69 (9) ◽  
pp. 1376-1387 ◽  
Author(s):  
Daniel Peeters ◽  
Georges Leroy

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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