scholarly journals Steering Orbital Optimization out of Local Minima and Saddle Points Toward Lower Energy

2017 ◽  
Vol 13 (3) ◽  
pp. 1219-1228 ◽  
Author(s):  
Alain C. Vaucher ◽  
Markus Reiher
Keyword(s):  
Lower Energy ◽  
Saddle Points ◽  
Local Minima ◽  
Orbital Optimization

Gas-Phase Clustering of NO+ with H2S and H2O

2007 ◽  
Vol 72 (8) ◽  
pp. 1122-1138 ◽  
Author(s):  
Milan Uhlár ◽  
Ivan Černušák
Keyword(s):  
Hydrogen Bonds ◽  
Water Molecule ◽  
Gas Phase ◽  
Saddle Points ◽  
Solvent Molecule ◽  
Local Minima ◽  
Additional Water ◽  
Three Body ◽  
Rain Formation ◽  
Stable Structures

The complex NO+·H2S, which is assumed to be an intermediate in acid rain formation, exhibits thermodynamic stability of ∆Hº300 = -76 kJ mol-1, or ∆Gº300 = -47 kJ mol-1. Its further transformation via H-transfer is associated with rather high barriers. One of the conceivable routes to lower the energy of the transition state is the action of additional solvent molecule(s) that can mediate proton transfer. We have studied several NO+·H2S structures with one or two additional water molecule(s) and have found stable structures (local minima), intermediates and saddle points for the three-body NO+·H2S·H2O and four-body NO+·H2S·(H2O)2 clusters. The hydrogen bonds network in the four-body cluster plays a crucial role in its conversion to thionitrous acid.

scholarly journals Transition pathways connecting crystals and quasicrystals

2021 ◽  
Vol 118 (49) ◽  
pp. e2106230118
Author(s):  
Jianyuan Yin ◽  
Kai Jiang ◽  
An-Chang Shi ◽  
Pingwen Zhang ◽  
Lei Zhang
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Saddle Points ◽  
Energy Functional ◽  
Computational Method ◽  
Local Minima ◽  
Free Energy Functional ◽  
Transition Pathways ◽  
Critical Nuclei ◽  
Quasicrystalline State

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz–Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

A random walk to local minima and saddle points on a potential energy surface. A strategy based on simulated annealing

1996 ◽  
Vol 250 (2) ◽  
pp. 238-246 ◽  
Author(s):  
P. Chaudhury ◽  
P. Dutta ◽  
P. Bandyopadhyay ◽  
P. Sarkar ◽  
S.P. Bhattacharyya
Keyword(s):  
Simulated Annealing ◽  
Random Walk ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Saddle Points ◽  
Local Minima

scholarly journals Barrier Trees of Degenerate Landscapes

2002 ◽  
Vol 216 (2) ◽  
Author(s):  
Christoph Flamm ◽  
Ivo L. Hofacker ◽  
Peter F. Stadler ◽  
Michael T. Wolfinger
Keyword(s):  
Saddle Points ◽  
Local Minima ◽  
Energy Barriers ◽  
Definition Of ◽  
Barrier Trees

The heights of energy barriers separating two (macro-)states are useful for estimating transition frequencies. In non-degenerate landscapes the decomposition of a landscape into basins surrounding local minima connected by saddle points is straightforward and yields a useful definition of macro-states. In this work we develop a rigorous concept of barrier trees for degenerate landscapes. We present a program that efficiently computes such barrier trees, and apply it to two well known examples of landscapes.

scholarly journals Obtaining new local minima in lens design by constructing saddle points

2015 ◽  
Vol 23 (5) ◽  
pp. 6679 ◽  
Author(s):  
Maarten van Turnhout ◽  
Pascal van Grol ◽  
Florian Bociort ◽  
H. Paul Urbach
Keyword(s):  
Saddle Points ◽  
Lens Design ◽  
Local Minima

Non-differentiable saddle points and sub-optimal local minima exist for deep ReLU networks

2021 ◽  
Author(s):  
Bo Liu ◽  
Zhaoying Liu ◽  
Ting Zhang ◽  
Tongtong Yuan
Keyword(s):  
Saddle Points ◽  
Local Minima

Determination of the lattice translation across {110} APBs in GaAs

1988 ◽  
Vol 46 ◽  
pp. 600-601
Author(s):  
D.R. Rasmussen ◽  
N.-H. Cho ◽  
C.B. Carter
Keyword(s):  
Grain Boundaries ◽  
Lower Energy ◽  
Antiphase Boundary ◽  
The Other ◽  
Boundary Structure ◽  
Interface Plane ◽  
Inversion Symmetry ◽  
High Angle ◽  
Equilibrium Distance

Domains in GaAs can exist which are related to one another by the inversion symmetry, i.e., the sites of gallium and arsenic in one domain are interchanged in the other domain. The boundary between these two different domains is known as an antiphase boundary [1], In the terminology used to describe grain boundaries, the grains on either side of this boundary can be regarded as being Σ=1-related. For the {110} interface plane, in particular, there are equal numbers of GaGa and As-As anti-site bonds across the interface. The equilibrium distance between two atoms of the same kind crossing the boundary is expected to be different from the length of normal GaAs bonds in the bulk. Therefore, the relative position of each grain on either side of an APB may be translated such that the boundary can have a lower energy situation. This translation does not affect the perfect Σ=1 coincidence site relationship. Such a lattice translation is expected for all high-angle grain boundaries as a way of relaxation of the boundary structure.

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