An Efficient Saddle Point Search Method Using Kriging Metamodels

2015 ◽  
Author(s):  
Lijuan He ◽  
Yan Wang
Keyword(s):  
Potential Energy ◽  
Saddle Point ◽  
Density Functional ◽  
Search Algorithm ◽  
Saddle Points ◽  
Surrogate Models ◽  
Functional Theory ◽  
Search Results ◽  
Point Search ◽  
Large Systems

Simulating phase transformation of materials at the atomistic scale requires the knowledge of saddle points on the potential energy surface (PES). In the existing first-principles saddle point search methods, the requirement of a large number of expensive evaluations of potential energy, e.g. using density functional theory (DFT), limits the application of such algorithms to large systems. Thus, it is meaningful to minimize the number of functional evaluations as DFT simulations during the search process. Furthermore, model-form uncertainty and numerical errors are inherent in DFT and search algorithms. Robustness of the search results should be considered. In this paper, a new search algorithm based on Kriging is presented to search local minima and saddle points on a PES efficiently and robustly. Different from existing searching methods, the algorithm keeps a memory of searching history by constructing surrogate models and uses the search results on the surrogate models to provide the guidance of future search on the PES. The surrogate model is also updated with more DFT simulation results. The algorithm is demonstrated by the examples of Rastrigin and Schwefel functions with a multitude of minima and saddle points.

Topological studies of the charge density of some group 2 metallocenes M(η5-C5H5)2 (M = Mg or Ca)

1996 ◽  
Vol 74 (6) ◽  
pp. 1059-1071 ◽  
Author(s):  
Ian Bytheway ◽  
Paul L.A. Popelier ◽  
Ronald J. Gillespie
Keyword(s):  
Charge Density ◽  
Density Functional ◽  
Search Algorithm ◽  
Functional Theory ◽  
Cyclopentadienyl Ligands ◽  
Hartree Fock ◽  
The Core ◽  
Point Search ◽  
Charge Concentration ◽  
Group 2

Ab initio quantum chemical calculations using both the Hartree–Fock and the B3LYP density functional theory methods have been performed for the group 2 metallocenes M (η5-C5-C5H5)2 (M = Mg or Ca). The topology of the calculated charge density (ρ) and its Laplacian [Formula: see text] have been analysed using a new critical point search algorithm in order to understand why Mg(η5-C5-H5)2 is linear while Ca(η-C5H5)2 is bent. The Laplacian of the core of the Ca atom in Ca(η5-C5H5)2 is perturbed by the polarizing field of the cyclopentadienyl ligands and the bent geometry is a consequence of the interactions between the distorted core and the ligand atoms. In the case of Mg(η5-C5H5)2, charge concentration maxima in the Mg core occur along the vectors connecting the metal to the centroids of the cyclopentadienyl ligands irrespective of whether or not the molecule is linear, and the preferred geometry is linear as expected. The results of these calculations demonstrate that the geometries of the group 2 metallocenes can be understood in terms of the repulsive interactions between the ligands and between the ligands and the distorted core of the metal atom. Key words: atoms in molecules, group 2 metallocenes, VSEPR, charge density, Laplacian of ρ.

scholarly journals An Efficient First-Principles Saddle Point Searching Method Based on Distributed Kriging Metamodels

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Anh Tran ◽  
Lijuan He ◽  
Yan Wang
Keyword(s):  
Potential Energy ◽  
Saddle Point ◽  
Density Functional ◽  
Materials Science ◽  
Mean Squared Error ◽  
Dimensional Space ◽  
Minimum Energy ◽  
Saddle Points ◽  
Computational Materials ◽  
Searching Method

Searching for local minima, saddle points, and minimum energy paths (MEPs) on the potential energy surface (PES) is challenging in computational materials science because of the complexity of PES in high-dimensional space and the numerical approximation errors in calculating the potential energy. In this work, a local minimum and saddle point searching method is developed based on kriging metamodels of PES. The searching algorithm is performed on both kriging metamodels as the approximated PES and the calculated one from density functional theory (DFT). As the searching advances, the kriging metamodels are further refined to include new data points. To overcome the dimensionality problem in classical kriging, a distributed kriging approach is proposed, where clusters of data are formed and one metamodel is constructed within each cluster. When the approximated PES is used during the searching, each predicted potential energy value is an aggregation of the ones from those metamodels. The dimension of each metamodel is further reduced based on the observed symmetry in materials systems. The uncertainty associated with the ground-state potential energy is quantified using the statistical mean-squared error in kriging to improve the robustness of the searching method.

A Review of Recent Phase Transition Simulation Methods: Saddle Point Search

2008 ◽  
Author(s):  
Devendra Alhat ◽  
Vernet Lasrado ◽  
Yan Wang
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Saddle Point ◽  
Energy Surface ◽  
Kinetic Monte Carlo ◽  
Saddle Points ◽  
Transition Process ◽  
Point Search ◽  
Recent Phase ◽  
First Order Phase

A review of saddle point search methods on a potential energy surface is presented in this paper. Finding saddle points on a complex potential energy surface is the major challenge in modeling and simulating the kinetics of first-order phase transitions. Once the saddle points have been identified and the activation energy for the transition is known, one can apply the kinetic Monte Carlo method to simulate the transition process. We consider some factors while reviewing the methods, such as whether the solution is global, the knowledge of the Hessian during the search, the capability to locate multiple saddle points and higher order saddle points, the kind of approximations used for potential energy surface, if any; and the convergence of the methods.

THE H2NO POTENTIAL ENERGY SURFACE EXPLORED WITH HIGH LEVEL AB INITIO AND DENSITY FUNCTIONAL THEORY METHODS

2007 ◽  
Vol 06 (03) ◽  
pp. 549-562
Author(s):  
ABRAHAM F. JALBOUT
Keyword(s):  
Density Functional Theory ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Density Functional ◽  
Energy Surface ◽  
Hybrid Methods ◽  
Transition States ◽  
Basis Set ◽  
Functional Theory ◽  
High Level

The transition states for the H 2 NO decomposition and rearrangements mechanisms have been explored by the CBS-Q method or by density functional theory. Six transition states were located on the potential energy surface, which were explored with the Quadratic Complete Basis Set (CBS-Q) and Becke's one-parameter density functional hybrid methods. Interesting deviations between the CBS-Q results and the B1LYP density functional theory lead us to believe that further study into this system is necessary. In the efforts to further assess the stabilities of the transition states, bond order calculations were performed to measure the strength of the bonds in the transition state.

Elimination of AgR (R = H, CH3, C6H5) from Collisionally-Activated Argentinated Amines

2000 ◽  
Vol 6 (2) ◽  
pp. 187-192 ◽  
Author(s):  
R. Natasha Grewal ◽  
Christopher F. Rodriquez ◽  
Tamer Shoeib ◽  
Ivan K. Chu ◽  
Ya-Ping Tu ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Potential Energy ◽  
Density Functional ◽  
Amino Nitrogen ◽  
Functional Theory ◽  
Immonium Ions

Fragmentation of collisionally-activated argentinated amines results in the formation of Ag+ and non-silver-containing ions. The latter are likely immonium ions that are formed after elimination of AgH and, when the ion structures permit, AgCH3 or AgC6H5. The H, CH3 and C6H5 groups are attached to the carbon alpha to the amino nitrogen, and are believed to be cleaved with the Ag in a 1,2-elimination. This hypothesis is supported by potential energy hypersurfaces calculated using density functional theory for the reactions involving methanamine and ethanamine.

scholarly journals Double-well potential energy surface in the interaction between h-BN and Ni(111)

2019 ◽  
Vol 21 (21) ◽  
pp. 10888-10894
Author(s):  
Jorge Ontaneda ◽  
Francesc Viñes ◽  
Francesc Illas ◽  
Ricardo Grau-Crespo
Keyword(s):  
Density Functional Theory ◽  
Potential Energy ◽  
Density Functional ◽  
Energy Surface ◽  
Density Functional Theory Calculations ◽  
Dispersion Forces ◽  
Local Correlation ◽  
Functional Theory ◽  
Non Local ◽  
Double Well Potential

Density functional theory calculations with non-local correlation functionals, properly accounting for dispersion forces, predict the presence of two minima in the interaction energy between h-BN and Ni(111).

The Variediene-Forming Carbocation Cyclization/Rearrangement Cascade

2017 ◽  
Vol 70 (4) ◽  
pp. 362 ◽  
Author(s):  
Young J. Hong ◽  
Dean J. Tantillo
Keyword(s):  
Density Functional Theory ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Density Functional ◽  
Energy Surface ◽  
Functional Theory ◽  
Density Functional Theory Computations

An energetically viable (on the basis of results from density functional theory computations) pathway to the diterpene variediene is described. Only one of the three secondary carbocations along this pathway is predicted to be a minimum on the potential energy surface.

Sign in / Sign up

Export Citation Format

Share Document