Three-body cluster potential by Gong (1993) v000

X G Gong

doi:10.25950/e549e4b7

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ThreeBodyCluster_Gong__MD_065419309200_000

Title A single sentence description.	Three-body cluster potential by Gong (1993) v000
Description	A model driver for a three-body potential implementation of a similar form to the Stillinger-Weber potential for silicon with an amended angular potential. The driver was originally developed to study silicon clusters.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Kevin Schmalbach
Maintainer	Kevin Schmalbach
Developer	X G Gong
Published on KIM	2019
How to Cite	This Model Driver originally published in [1] is archived in OpenKIM [2-4]. [1] Gong XG. Empirical-potential studies on the structural properties of small silicon clusters. Physical Review B. 1993;47(4):2329–32. doi:10.1103/PhysRevB.47.2329 [2] Gong XG. Three-body cluster potential by Gong (1993) v000. OpenKIM; 2019. doi:10.25950/e549e4b7 [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_065419309200_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_Gong__MD_065419309200_000
DOI	10.25950/e549e4b7 https://doi.org/10.25950/e549e4b7 https://commons.datacite.org/doi.org/10.25950/e549e4b7
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_Gong_Gong_1993_Si__MO_407755720412_000

Files

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

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ThreeBodyCluster_Gong__MD_065419309200_000.txz	Tar+XZ	Linux and OS X archive
ThreeBodyCluster_Gong__MD_065419309200_000.zip	Zip	Windows archive

### Background
This potential was published by X. G. Gong in *Physical Review B* in 1993$$^1$$; it was developed to study small clusters of silicon atoms which are not effectively modeled by interatomic potentials developed for bulk silicon crystals. Although the author proposed that *ab initio* molecular dynamics with local-density approximation would be suitable for studying small silicon clusters, such methods were very computationally expensive at the time, so an empirical potential was suggested. Other available potentials such the those by Stillinger & Weber (SW)$$^2$$ and Tersoff$$^3$$ were effective for bulk silicon and silicon surfaces, but not for silicon clusters with only tens of atoms. The results from the potential were used to analyze the stability of very small ($$\leq$$ 11 atoms) clusters.

### Functional form of the potential
#### Pair term:
$$
\begin{align}
\phi^{\rm G}_2(r_{ij}) &= A(B r_{ij}^{-p} - r_{ij}^{-q})f_{\rm 2c}^{\rm G}(r_{ij})\\
f_{\rm 2c}^{\rm G} &= \exp[(r_{ij}-a)^{-1}] 
\end{align}
$$
#### Three-body term:
$$
\begin{align}
\phi^{\rm G}_3(r_{ij},r_{ik},r_{jk}) &= h^{\rm G}(r_{ij},r_{ik},\theta_{jik}) + h^{\rm G}(r_{ij},r_{kj},\theta_{ijk}) + h^{\rm G}(r_{ik},r_{kj},\theta_{ikj}) \\
h^{\rm G}(r,s,\theta) &= \lambda_1 (\cos\theta+\tfrac{1}{3})^2 [(\cos\theta+c_0)^2+c_1] f_{\rm 3c}^{\rm G}(r,s)  \\
f_{\rm 3c}^{\rm G}(r,s) &= \exp\{\gamma[(r-a)^{-1}+(s-a)^{-1}]\} 
\end{align}
$$

### References
1.) X. G. Gong, Phys. Rev. B **47**, 2329 (1993).
2.) F. H. Stillinger and T. A. Weber, Phys. Rev. B **31**, 5262 (1985).
3.) J. Tersoff, Phys. Rev. B **37**, 6991 (1988).

Wiki Contributors

2019-05-13T20:33:39.366046	tadmor
2019-05-09T08:29:18.091810	Schma174
2019-05-05T20:30:18.470361	Schma174