The H+5potential energy hypersurface: Characterization of ten distinct energetically low‐lying stationary points

1987 ◽  
Vol 86 (9) ◽  
pp. 5072-5081 ◽  
Author(s):  
Yukio Yamaguchi ◽  
Jeffrey F. Gaw ◽  
Richard B. Remington ◽  
Henry F. Schaefer
Keyword(s):  
Stationary Points ◽  
Energy Hypersurface

scholarly journals Topological Approach to Mathematical Programs with Switching Constraints

2021 ◽  
Author(s):  
Vladimir Shikhman
Keyword(s):  
Stationary Point ◽  
Mountain Pass Theorem ◽  
Strong Stability ◽  
Complete Characterization ◽  
Stationary Points ◽  
Mathematical Programs ◽  
Linear Independence Constraint Qualification ◽  
Point Set ◽  
Stationary Level

AbstractWe study mathematical programs with switching constraints (for short, MPSC) from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous deformation of lower level sets can be performed. However, when passing a W-stationary level, the topology of the lower level set changes via the attachment of a w-dimensional cell. The dimension w equals the W-index of the nondegenerate W-stationary point. The W-index depends on both the number of negative eigenvalues of the restricted Lagrangian’s Hessian and the number of bi-active switching constraints. As a consequence, we show the mountain pass theorem for MPSC. Additionally, we address the question if the assumption on the nondegeneracy of W-stationary points is too restrictive in the context of MPSC. It turns out that all W-stationary points are generically nondegenerate. Besides, we examine the gap between nondegeneracy and strong stability of W-stationary points. A complete characterization of strong stability for W-stationary points by means of first and second order information of the MPSC defining functions under linear independence constraint qualification is provided. In particular, no bi-active Lagrange multipliers of a strongly stable W-stationary point can vanish.

Proper characterization of MCSCF stationary points

2009 ◽  
Vol 24 (S17) ◽  
pp. 645-645 ◽  
Author(s):  
Joseph T. Golab ◽  
Danny L. Yeager ◽  
Poul Jørgensen
Keyword(s):  
Stationary Points

scholarly journals Benchmark ab initio and dynamical characterization of the stationary points of reactive atom + alkane and SN2 potential energy surfaces

2020 ◽  
Vol 22 (8) ◽  
pp. 4298-4312 ◽  
Author(s):  
Gábor Czakó ◽  
Tibor Győri ◽  
Balázs Olasz ◽  
Dóra Papp ◽  
István Szabó ◽  
...  
Keyword(s):  
Potential Energy ◽  
Ab Initio ◽  
Potential Energy Surfaces ◽  
Stationary Points ◽  
Ion Molecule Reactions ◽  
Energy Surfaces ◽  
Reactive Atom

We review composite ab initio and dynamical methods and their applications to characterize stationary points of atom/ion + molecule reactions.

scholarly journals Full-dimensional potential energy surface for acetylacetone and tunneling splittings

2021 ◽  
Author(s):  
Chen Qu ◽  
Riccardo Conte ◽  
Paul L. Houston ◽  
Joel M. Bowman
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Stationary Points ◽  
Tunneling Splittings ◽  
Tunneling Dynamics

New, full-dimensional potential energy surface for acetylacetone allows for description of H-tunneling dynamics and characterization of stationary points.

Characterization of strong stability for C-stationary points in MPCC

2010 ◽  
Vol 132 (1-2) ◽  
pp. 295-308 ◽  
Author(s):  
H. Th. Jongen ◽  
V. Shikhman ◽  
S. Steffensen
Keyword(s):  
Strong Stability ◽  
Stationary Points

Nature of stationary points on CNDO/2 energy hypersurfaces of van der Waals molecules formed by polar molecules

1980 ◽  
Vol 45 (5) ◽  
pp. 1323-1330 ◽  
Author(s):  
Pavel Hobza ◽  
Jiří Pancíř ◽  
Rudolf Zahradník
Keyword(s):  
Structural Characteristics ◽  
Van Der Waals ◽  
Saddle Points ◽  
Molecular Complexes ◽  
Stationary Points ◽  
Polar Molecules ◽  
Complete Set ◽  
Experimental Values ◽  
The Individual ◽  
Energy Hypersurface

An attempt was made to find a complete set of stationary points on CNDO/2 energy hypersurface for five molecular complexes. Diagonalization of Hessian matrices served for analysis of the nature of stationary points which permits to distinguish between relative minima and saddle points. The total number of stationary points and real minima of the individual complexes is indicated in parentheses: (HF)2 (8, 1); (H2O)2 (7, 3); (LiF)2 (2, 1); (CH3OH)2 (6, 4) and CH3OH...HF (2, 1). CNDO/2 structural characteristics are compared with experimental values and with results of nonempirical calculations.

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