Three-body Stillinger-Weber (SW) Model Driver

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Three_Body_Stillinger_Weber__MD_335816936951_002

There is a newer version of this item. See SW__MD_335816936951_005

Title A single sentence description.	Three-body Stillinger-Weber (SW) Model Driver
Description	This is a model driver for the generalized Stillinger-Weber (SW) three-body potential supporting multiple species. It is consistent with 'pair_style sw' in the LAMMPS package, but the parameter file has a different format and the driver is less general than the LAMMPS implementation. Specifically, in the KIM parameter file, only independent pairwise parameters are read in and the three-body parameters are generated through geometric averaging. In addition, the costheta_0 parameter is assumed to be the same for all three-body interactions and the tolerance parameter introduced in LAMMPS for efficiency is not supported. See the README file for details. A Python utility "lammps_sw_2_kim_sw.py" is provided to translate LAMMPS pair_style sw parameter files to the KIM model driver format.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Mingjian Wen
Maintainer	Mingjian Wen
Published on KIM	2016
How to Cite	Click here to download this citation in BibTeX format.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MD_335816936951_002
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.	Three_Body_Stillinger_Weber__MD_335816936951_002
Citable Link	https://openkim.org/cite/MD_335816936951_002
KIM Item Type	Model Driver
KIM API Version	1.6
Simulator Potential Compatibility	LAMMPS : — partial This driver is consistent with 'pair_style sw' in the LAMMPS package, but the parameter file has a different format and the driver is less general than the LAMMPS implementation. Specifically, in the KIM parameter file, only independent pairwise parameters are read in and the three-body parameters are generated through geometric averaging. In addition, the costheta_0 parameter is assumed to be the same for all three-body interactions and the tolerance parameter introduced in LAMMPS for efficiency is not supported. See the README file for details. A Python utility "lammps_sw_2_kim_sw.py" is provided to translate LAMMPS 'pair_style sw' parameter files to the KIM model driver format.
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one.	80.75% C 19.25% Python

Previous Version	Three_Body_Stillinger_Weber__MD_335816936951_001

Models using this Model Driver

Files

LICENSE.CDDL
Makefile
README
Three_Body_Stillinger_Weber.c
Three_Body_Stillinger_Weber.kim.tpl
kimprovenance.edn
kimspec.edn
lammps_sw_2_kim_sw.py

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Wiki

## Description
This **Model Driver** implements the Stillinger-Weber three-body potential

## Parameters
Symbols:

$$ a, A, B, p, q, \sigma, \lambda, \gamma$$

Corresponding variables in code:
a, A, B,p, q, sigma, lamda, gamma

## Details

The total potential energy function $$ \phi $$ for Si crystal is approximated by a combination of a pair and three-body potential $$v_2$$ and $$v_3$$ respectively. It takes the following form:

$$ \phi =  \sum_{i,j; i<j} v_2(i,j) + \sum_{i,j,k; i<j<k} v_3(i,j,k) $$

Where

$$ v_2(r_{ij}) = \epsilon f_2(r_{ij}/\sigma) $$

$$ v_3(\mathbf{r}_i ,\mathbf{r}_j, \mathbf{r}_k) = \epsilon f_3(\mathbf{r}_i/\sigma, \mathbf{r}_j/\sigma, \mathbf{r}_k/\sigma) $$

The function $$f_2$$ has the following form:

$$ f_2(r) = \begin{cases}
      A(Br^{-p} - r^{-q})\exp[(r-a)^{-1}] &  \text{if  } r < a\\
     0 & \text{if  }r >=a\\
      
    \end{cases} $$

The function $$f_3$$ takes the form:

$$ f_3(\mathbf{r}_i, \mathbf{r}_j, \mathbf{r}_k) =  h(r_{ij},r_{ik},\theta_{jik}) + h(r_{ji},r_{jk},\theta_{ijk}) + h(r_{ki},r_{kj},\theta_{ikj}) $$

where

$$  h(r_{ij},r_{ik},\theta_{jik}) = \lambda \exp[\gamma(r_{ij}-a)^{-1} + \gamma(r_{ik}-a)^{-1}](\cos\theta_{jik} + 1/3)^2 $$

The term $$ (\cos\theta_{jik} + 1/3)^2 $$ is a penalty term which makes $$h$$ vanish for the ideal tetrahedral angle i.e. $$ \cos\theta = -1/3 $$.

Wiki Contributors

2017-04-13T21:49:53	taru4uce
2017-04-13T17:41:40	tadmor
2017-04-13T17:40:05	tadmor
2017-04-13T17:38:58	tadmor
2017-04-13T17:38:17	tadmor
2017-04-13T17:36:03	tadmor
2017-04-13T17:35:04	tadmor
2017-04-13T17:33:55	tadmor
2017-04-13T17:31:14	tadmor
2017-04-13T17:28:39	tadmor
2017-04-13T17:27:16	tadmor
2017-03-22T12:40:51	taru4uce
2017-03-22T12:37:23	taru4uce
2017-03-22T10:52:42	taru4uce
2017-03-22T10:50:03	taru4uce
2017-03-22T10:40:42	taru4uce
2017-03-22T10:37:32	taru4uce
2017-03-22T10:24:57	taru4uce
2017-03-22T03:04:05	taru4uce
2017-03-22T02:59:18	taru4uce