Three-body cluster potential by Kaxiras and Pandey (1988) v000

Joshua Vievering; Daniel S. Karls; Efthimios Kaxiras; K C Pandey

doi:10.25950/477dbd2b

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ThreeBodyCluster_KP__MD_527786671773_000

Title A single sentence description.	Three-body cluster potential by Kaxiras and Pandey (1988) v000
Description	A three-body cluster potential which is especially suited to simulate processes in the diamond lattice rather than in high-energy bulk structures of Si. The potential is based on a very large quantum-mechanical data base. It consists of two- and three-body terms with short-range separable forms, and reproduces accurately the energy surface for atomic exchange in Si. Thus, it is ideally suited for molecular dynamics simulations of atomic processes in Si.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Joshua Vievering
Maintainer	Joshua Vievering
Implementer	Joshua Vievering Daniel S. Karls
Developer	Efthimios Kaxiras K C Pandey
Published on KIM	2019
How to Cite	This Model Driver originally published in [1] is archived in OpenKIM [2-4]. [1] Kaxiras E, Pandey KC. New classical potential for accurate simulation of atomic processes in Si. Phys Rev B. 1988;38(17):12736–9. doi:10.1103/PhysRevB.38.12736 [2] Vievering J, Karls DS, Kaxiras E, Pandey KC. Three-body cluster potential by Kaxiras and Pandey (1988) v000. OpenKIM; 2019. doi:10.25950/477dbd2b [3] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [4] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MD_527786671773_000
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	ThreeBodyCluster_KP__MD_527786671773_000
DOI	10.25950/477dbd2b https://doi.org/10.25950/477dbd2b https://commons.datacite.org/doi.org/10.25950/477dbd2b
KIM Item Type	Model Driver
KIM API Version	2.0
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one.	100.00% C

Models using this Model Driver

ThreeBodyCluster_KP_KaxirasPandey_1988_Si__MO_072486242437_000

Files

CMakeLists.txt
LICENSE
README
ThreeBodyCluster.c
cluster.inc
kimprovenance.edn
kimspec.edn

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This potential was developed by Efthimios Kaxiras and K. C. Pandey and published in December 1988.  It was developed for calculating the energy of realistic atomic processes in Si, particularly for simulating processes in the diamond lattice as opposed to high-energy bulk structures of Si.  It is difficult to construct a potential that accurately describes both high-energy crystal structures and local distortions of the diamond lattice.  This potential is meant to accurately reproduce energy costs for various local distortions from the tetrahedral coordination, including the breaking and formation of bonds, cohesive energy, and bulk modulus of the diamond lattice, which is the lowest-energy crystal structure for Si.  This potential encompasses most of the low-energy, physically accessible configurations.  Previous attempts at constructing Si potentials relied on quantum-mechanical calculations for high-coordination bulk structures of Si, which has been proven to be insufficient.  For instance, previous classical potentials exhibited unrealistic structure, incorrect curvature, and an inability to reproduce activation energy for the concerted exchange (CE) phase-space path for Si, when compared to reliable quantum-mechanical local-density-functional calculations.  To construct the potential, Kaxiras and Pandey utilized the energy surface of atomic exchange, which is a large quantum-mechanical data base.  The potential has a simple, transparent functional form, and it uses a small set of parameters, namely seven.  It reproduces the CE path within an accuracy of $$ 0.1\ eV $$, which is a significant improvement over previous potentials.

The Kaxiras and Pandey potential is a three-body potential.  The two-body term is the difference of two Gaussians and is as follows:

$$ V_{ij}=A_1\exp(-\alpha_1r_{ij}^2\ )-A_2\exp(-\alpha_2r_{ij}^2\ ) $$

where $$ r_{ij} $$ is the distance between atoms $$ i $$ and $$ j $$.  The full three-body term is a symmetrized sum over all atom triplets, as shown below:

$$ V_3=V_{ijk}+V_{jki}+V_{kij} $$

$$ V_{ijk}=\exp[-\beta(r_{ij}^2+r_{ik}^2\ )] [Bg^2 (θ)+Dg^4 (θ)] $$

$$ g(\theta)=(cos\theta+1/3) $$

where $$ \theta $$ is the angle at the $$ i $$ vertex of the $$ ijk $$ triangle, subtended by the bonds $$ r_{ij} $$ and $$ r_{ik} $$.  The radial dependence of the three-body term is a Gaussian, and the angular dependence is of the generalized Keating-form.  The two-body and three-body terms both vanish at $$ r_c = 5.5\ Å. $$

Wiki Contributors

2019-05-08T16:26:00.513389	tadmor
2019-05-08T13:47:03.262905	jvievering
2019-05-08T13:39:07.361936	jvievering