Low-order moment expansions to tight binding for interatomic potentials: Successes and failures

1995 ◽  
Vol 52 (12) ◽  
pp. 8766-8775 ◽  
Author(s):  
Joel D. Kress ◽  
Arthur F. Voter
Keyword(s):  
Tight Binding ◽  
Order Moment ◽  
Interatomic Potentials ◽  
Successes And Failures ◽  
Low Order

Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression

2019 ◽  
Author(s):  
Chiara Panosetti ◽  
Artur Engelmann ◽  
Lydia Nemec ◽  
Karsten Reuter ◽  
Johannes T. Margraf
Keyword(s):  
Gaussian Process ◽  
Density Functional ◽  
Functional Form ◽  
Tight Binding ◽  
Gaussian Process Regression ◽  
Direct Access ◽  
Interatomic Potentials ◽  
Global Parameter ◽  
Repulsive Potentials ◽  
The Cost

The Density-Functional Tight Binding (DFTB) method is a popular semiempirical approximation to Density Functional Theory (DFT). In many cases, DFTB can provide comparable accuracy to DFT at a fraction of the cost, enabling simulations on length- and time-scales that are unfeasible with first principles DFT. At the same time (and in contrast to empirical interatomic potentials and force-fields), DFTB still offers direct access to electronic properties such as the band-structure. These advantages come at the cost of introducing empirical parameters to the method, leading to a reduced transferability compared to true first-principle approaches. Consequently, it would be very useful if the parameter-sets could be routinely adjusted for a given project. While fairly robust and transferable parameterization workflows exist for the electronic structure part of DFTB, the so-called repulsive potential Vrep poses a major challenge. In this paper we propose a machine-learning (ML) approach to fitting Vrep, using Gaussian Process Regression (GPR). The use of GPR circumvents the need for non-linear or global parameter optimization, while at the same time offering arbitrary flexibility in terms of the functional form. We also show that the proposed method can be applied to multiple elements at once, by fitting repulsive potentials for organic molecules containing carbon, hydrogen and oxygen. Overall, the new approach removes focus from the choice of functional form and parameterization procedure, in favour of a data-driven philosophy.

Interatomic Interactions for BCC Metals Based on the Low Order Moments of the Density of States

1992 ◽  
Vol 278 ◽  
Author(s):  
Stephen M. Foiles
Keyword(s):  
Large Deviations ◽  
Density Of States ◽  
Fourth Moment ◽  
Interatomic Potentials ◽  
Energy Term ◽  
Additional Energy ◽  
Electronic Density ◽  
Bcc Metals ◽  
New Feature ◽  
Low Order

AbstractA model of the energetics of bcc transition metals based on the low-order moments of the electronic density of states is presented. The new feature of the model is an additional energy term related to the fourth moment of the density of states. This term reflects the coarse shape of the density of states. The model is tested by the computation of point defect properties, phonon dispersions, structural energy differences and surface properties. The results are compared to experiment, ab-initio calculations and other model interatomic potentials. The results indicate that the inclusion of the fourth moment term in the energy does not significantly improve the description of properties of the bulk bcc metals. However, the fourth moment term substantially improves the description of large deviations from the bcc bulk such as surfaces and alternative crystal structures.

scholarly journals Charge redistribution at Pd surfaces:Ab initiogrounds for tight-binding interatomic potentials

1997 ◽  
Vol 56 (19) ◽  
pp. 12161-12166 ◽  
Author(s):  
S. Sawaya ◽  
J. Goniakowski ◽  
C. Mottet ◽  
A. Saúl ◽  
G. Tréglia
Keyword(s):  
Tight Binding ◽  
Interatomic Potentials ◽  
Charge Redistribution

Formation and Binding Energies of Vacancy Clusters in Silicon

1997 ◽  
Vol 469 ◽  
Author(s):  
L. Colombo ◽  
A. Bongiorno ◽  
T. Diaz De La Rubia
Keyword(s):  
Molecular Dynamics ◽  
Large Scale ◽  
Tight Binding ◽  
Model Potential ◽  
Binding Energies ◽  
Quantum Mechanical ◽  
Interatomic Potentials ◽  
Mechanical Approach ◽  
Dynamics Simulations ◽  
Quantum Mechanical Approach

ABSTRACTWe critically readdress the problem of vacancy clustering in silicon by perform large-scale tight-binding molecular dynamics simulations. We also compare the results of this quantum-mechanical approach to the widely used model-potential molecular dynamics scheme based on the Tersoff and Stillinger-Weber interatomic potentials.

On the geometry of d-orbitals: W (001) surface

1988 ◽  
Vol 53 (4) ◽  
pp. 661-664 ◽  
Author(s):  
Štěpán Pick
Keyword(s):  
Surface Reconstruction ◽  
Moment Analysis ◽  
Order Moment ◽  
Additional Mechanism ◽  
D Orbitals ◽  
Surface Coupling ◽  
Low Order

Low-order moment analysis of the W (001) surface reconstruction leads to the following conclusions: 1) The d-orbitals participate in the reconstruction-induced surface-surface coupling, the effect being most pronounced for the x2 - y2 orbital. 2) A non-negligible surface-bulk coupling exists and it is due to the (x - y) z orbital. An additional mechanism favouring the zig-zag mode is suggested.

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