Semiempirical tight-binding interatomic potentials based on the Hubbard model

1997 ◽  
Vol 56 (9) ◽  
pp. 5235-5242 ◽  
Author(s):  
Qian Xie ◽  
Peng Chen
Keyword(s):  
Hubbard Model ◽  
Tight Binding ◽  
Interatomic Potentials

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.

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

Tight-binding treatment of the Hubbard model in infinite dimensions

1996 ◽  
Vol 54 (3) ◽  
pp. 1629-1636 ◽  
Author(s):  
L. Craco ◽  
M. A. Gusmão
Keyword(s):  
Hubbard Model ◽  
Tight Binding ◽  
Infinite Dimensions

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.

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.

Simulation of the Diffusion Features of Point Defects in bcc Metals

2006 ◽  
Vol 249 ◽  
pp. 41-46
Author(s):  
Andrey S. Chirkov ◽  
Andrei V. Nazarov
Keyword(s):  
Point Defects ◽  
Density Functional ◽  
Tight Binding ◽  
Interatomic Potentials ◽  
Binding Theory ◽  
Many Body ◽  
Functional Theory ◽  
Bcc Metals ◽  
Diffusion Characteristics ◽  
The Density Functional Theory

This work is devoted to simulation of the diffusion features of point defects in bcc metals. The properties of point defects have been investigated with the usage of many-body interatomic potentials. This approach, based on the density-functional theory, permitted us to derive more adequate diffusion features of solids. This investigation is carried out within the framework of the Finnis-Sinclair formalism, developed for an assembly of N atoms and represents the secondmoment approximation of the tight-binding theory. We used a new model, based on the molecular static method for simulating the atomic structure near the defect and vacancy migration in pure metals. This approach gives the opportunity to simulate the formation and the migration volumes of the point defects, taking into consideration the influence of pressure on structure and consequently on energy. The diffusion characteristics of bcc α-Fe and anomalous β-Zr have been investigated.

Interatomic Potentials for Al and Ni From Experimental Data and AB Initio Calculations

1998 ◽  
Vol 538 ◽  
Author(s):  
Y. Mishin ◽  
D. Farkas ◽  
M. J. Mehl ◽  
D. A. Papaconstantopoulos
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Phonon Dispersion ◽  
Tight Binding ◽  
Interatomic Potentials ◽  
Alternative Structures ◽  
Embedded Atom ◽  
Local Environments ◽  
Basic Equilibrium ◽  
And Migration

AbstractNew embedded-atom potentials for Al and Ni have been developed by fitting to both experimental data and the results of ab initio calculations. The ab initio data were obtained in the form of energies of different alternative computer-generated crystalline structures of these metals. The potentials accurately reproduce basic equilibrium properties of Al and Ni such as the elastic constants, phonon dispersion curves, vacancy formation and migration energies, stacking fault energies, and surface energies. The equilibrium energies of various alternative structures not included in the fitting database are calculated with these potentials. The results are compared with predictions of total-energy tight-binding calculations for the same structures. The embedded-atom potentials correctly reproduce the structural stability trends, which suggests that they are transferable to different local environments encountered in atomistic simulations of lattice defects.

Effects of the interplay between electron–electron interaction and intrinsic spin–orbit interaction on the indirect RKKY coupling in graphene nanoflakes

2019 ◽  
Vol 21 (3) ◽  
pp. 1324-1335 ◽  
Author(s):  
Akram Mirehi ◽  
Ebrahim Heidari-Semiromi
Keyword(s):  
Hubbard Model ◽  
Tight Binding ◽  
Mean Field ◽  
Orbit Interaction ◽  
Electron Interaction ◽  
Magnetic Impurities ◽  
Spin Orbit ◽  
Spin Orbit Interaction ◽  
Graphene Nanoflakes ◽  
The Mean

The effects of electron–electron (e–e) interaction and intrinsic spin–orbit interaction (ISOI) on the maximum of the magnetization and the indirect RKKY (Ruderman–Kittel–Kasuya–Yosida) coupling between the magnetic impurities embedded in zig-zag graphene nanoflakes are investigated using the tight-binding Hamiltonian and the mean-field Hubbard model.

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