Three-body cluster potential by Biswas and Hamann (1987) v000

Dipanjan Ghosh; Daniel S. Karls; Rajesh Biswas; Donald. R. Hamann

doi:10.25950/972369ee

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ThreeBodyCluster_BH__MD_043141570610_000

Title A single sentence description.	Three-body cluster potential by Biswas and Hamann (1987) v000
Description	A theory of classical two- and three-body interatomic potentials is developed. The ability of the classical potentials to model quantum-mechanical local-density-functional calculations for a wide range of silicon structures is explored. In developing classical models it was found to be necessary to perform new local-density-functional calculations for self-interstitial and layered silicon structures. Two different potentials are derived from fits and tests to energies of bulk, surface, layered, and self-interstitial structures. One potential models bulk energies and high-pressure properties well; the other is more appropriate for properties of the tetrahedral structure. Simulated annealing is used to find low-energy structures for silicon-atom clusters.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Dipanjan Ghosh
Maintainer	Dipanjan Ghosh
Implementer	Dipanjan Ghosh Daniel S. Karls
Developer	Rajesh Biswas Donald. R. Hamann
Published on KIM	2019
How to Cite	This Model Driver originally published in [1] is archived in OpenKIM [2-4]. [1] Biswas R, Hamann DR. New classical models for silicon structural energies. Phys Rev B. 1987;36(12):6434–45. doi:10.1103/PhysRevB.36.6434 [2] Ghosh D, Karls DS, Biswas R, Hamann DR. Three-body cluster potential by Biswas and Hamann (1987) v000. OpenKIM; 2019. doi:10.25950/972369ee [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_043141570610_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_BH__MD_043141570610_000
DOI	10.25950/972369ee https://doi.org/10.25950/972369ee https://commons.datacite.org/doi.org/10.25950/972369ee
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_BH_BiswasHamann_1987_Si__MO_019616213550_000

Files

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

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### Introduction
In an attempt to explore the ability of classical mechanics to replicate quantum-mechanical calculations, R. Biswas and D. R. Hamann developed a three body cluster potential for Si in 1987. In their article “New classical models for silicon structural energies” (*Physical Review B*, 36(12): 6434, 1987), Biswas and Hamann discuss two different potentials, referred to as ‘old’ and ‘new’ potentials in their original article. To address the shortcomings of their ‘old’ potential, namely its inability to capture properties of tetrahedral structure of Si, they introduce their ‘new’ potential, which is attractive for molecular-dynamics simulations given its short range. However, as a trade-off, the ‘new’ potential is not as efficient as the ‘old’ model in describing high-pressure transitions and bulk metallic Si structures. The authors discuss how their ‘new’ potential is able to model the formation energies of interstitials and vacancies, and can also give reasonable account of thermal properties and melting of Si. Our model driver implements this ‘new’ potential of Biswas and Hamann.

#### Functional form
The functional form of the two-body potential is

$$\phi^{\rm BH}_2(r_{ij}) = (A_1 \exp[-\lambda_1 r_{ij}^2] + A_2 \exp[-\lambda_2 r_{ij}^2]) f_{\rm 2c}^{\rm BH}(r_{ij}) $$

$$ f_{\rm 2c}^{\rm BH} = \{1+\exp[(r-r_c)/\mu]\}^{-1} $$

The functional form of the three body potential is

$$ \phi^{\rm BH}_3(r_{ij},r_{ik},\theta_{jik})  = [B_1 \exp[-\alpha_1 r_{ij}^2] \exp[-\alpha_1 r_{ik}^2] (\cos\theta_{jik}+\tfrac{1}{3})^2 +  B_2 \exp[-\alpha_2 r_{ij}^2] \exp[-\alpha_2 r_{ik}^2] (\cos\theta_{jik}+\tfrac{1}{3})^3] f_{\rm 2c}^{\rm BH}(r_{ij}) f_{\rm 2c}^{\rm BH}(r_{ik})$$

Wiki Contributors

2019-05-10T08:51:41.361133	tadmor
2019-05-09T20:58:09.455384	tadmor
2019-05-09T18:24:01.727405	dipghosh