A four-body Mistriotis-Flytzanis-Farantos potential

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Four_Body_Mistriotis_Flytzanis_Farantos__MD_514777050453_000

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Title A single sentence description.	A four-body Mistriotis-Flytzanis-Farantos potential
Description	This is a four-body Mistriotis-Flytzanis-Farantos potential model driver. This is intended to calculate lattice constant, cohesive energy, elastic constants, thermal conductivities and several other material properties. The driver can handle maximum two different species.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Amit K. Singh
Maintainer	Amit K. Singh
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_514777050453_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.	Four_Body_Mistriotis_Flytzanis_Farantos__MD_514777050453_000
Citable Link	https://openkim.org/cite/MD_514777050453_000
KIM Item Type	Model Driver
KIM API Version	1.6
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

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Four_Body_Mistriotis_Flytzanis_Farantos.c
Four_Body_Mistriotis_Flytzanis_Farantos.kim.tpl
LICENSE.CDDL
Makefile
README
kimprovenance.edn
kimspec.edn

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This 4-body potential is a modification of the Stillinger-Weber model originally developed for silicon, where a four-body term has been added, and the angle dependence of the 3-body and 4-body terms have been changed. These modifications result in a qualitative improvement when the model was fit to silicon. More specifically, good values for the ground state energies of clusters were obtained for a large range of the parameters of the 3-body and 4-body terms.

The functional form of this potential is:

$$
\begin{align*}
 & \phi(1,2,...,N) =\sum_{1 \leq i \leq N} V_{1}(\textbf{r}_i)+\sum_{1 \leq i \leq j \leq N} V_{2}(\textbf{r}_i,\textbf{r}_j)+\sum_{1 \leq i \leq j \leq k \leq N} V_{3}(\textbf{r}_i,\textbf{r}_j,\textbf{r}_k)+\sum_{1 \leq i \leq j \leq k \leq l \leq N} V_{4}(\textbf{r}_i,\textbf{r}_j,\textbf{r}_k,\textbf{r}_l)&
\end{align*}
$$

where

$$ 
\begin{align*}
&V_{1}(\textbf{r}_i)=0
\end{align*}
$$

$$ 
\begin{align*}
&V_{2}(\textbf{r}_i,\textbf{r}_j)=v_{2}(r_{ij})
\end{align*}
$$

$$ 
\begin{align*}
&v_{2}(r_{ij})=\left\{
\begin{aligned}
&A\left(B/r_{ij}^4-1\right)\exp\left[\alpha(r_{ij}-R)^{-1}\right] , r_{ij}<R \\
&0 , \text{otherwise} \\
\end{aligned}
\right.
\end{align*}
$$

$$ 
\begin{align*}
&V_{3}(\textbf{r}_i,\textbf{r}_j,\textbf{r}_k)=v_{3}\left(r_{ij},r_{ik},\theta_{jik}\right)+v_{3}\left(r_{ji},r_{jk},\theta_{ijk}\right)+v_{3}\left(r_{ki},r_{kj},\theta_{ikj}\right)
\end{align*}
$$

$$ 
\begin{align*}
&v_{3}\left(r_{ij},r_{ik},\theta_{jik}\right)=v_{3r}\left(r_{ij},r_{ik}\right)\cdot v_{3\theta}\left(\theta_{jik}\right)
\end{align*}
$$

$$ 
\begin{align*}
&v_{3r}\left(r_{ij},r_{ik}\right)=\left\{
\begin{aligned}
&\exp\left[\gamma(r_{ij}-R)^{-1}+\gamma(r_{ik}-R)^{-1}\right] ,  r_{ij}<R \quad   r_{ik}<R\\
&0  ,  \text{otherwise}
\end{aligned}
\right.
\end{align*}
$$

$$ 
\begin{align*}
&v_{3\theta}\left(\theta_{jik}\right)=\lambda_{3}\left\{1-\exp\left[-Q\left(\cos\theta_{jik}+1/3\right)^2\right]\right\}
\end{align*}
$$

$$ 
\begin{align*}
&V_{4}(\textbf{r}_i,\textbf{r}_j,\textbf{r}_k,\textbf{r}_l)=v_{4}\left(r_{ij},r_{ik},r_{il},\theta_{jik},\theta_{jil},\theta_{kil}\right)+v_{4}\left(r_{ji},r_{jk},r_{jl},\theta_{ijk},\theta_{ijl},\theta_{kjl}\right)+v_{4}\left(r_{ki},r_{kj},r_{kl},\theta_{ikj},\theta_{ikl},\theta_{jkl}\right)+v_{4}\left(r_{li},r_{lj},r_{lk},\theta_{ilj},\theta_{ilk},\theta_{jlk}\right)
\end{align*}
$$

$$ 
\begin{align*}
&v_{4}\left(r_{ij},r_{ik},r_{il},\theta_{jik},\theta_{jil},\theta_{kil}\right)=v_{4r}\left(r_{ij},r_{ik},r_{il}\right)\cdot v_{4\theta}\left(\theta_{jik},\theta_{jil},\theta_{kil}\right)
\end{align*}
$$

$$ 
\begin{align*}
&v_{4r}\left(r_{ij},r_{ik},r_{il}\right)=\left\{
\begin{aligned}
&\exp\left[\gamma(r_{ij}-R)^{-1}+\gamma(r_{ik}-R)^{-1}+\gamma(r_{il}-R)^{-1}\right] ,  r_{ij}<R \quad r_{ik}<R\quad r_{il}<R\\
&0  ,  \text{otherwise}
\end{aligned}
\right.
\end{align*}
$$

$$ 
\begin{align*}
&v_{4\theta}\left(\theta_{jik},\theta_{jil},\theta_{kil}\right)=\lambda_{4}\left\{1-\exp\left[-Q\left(\cos\theta_{jik}+1/3\right)^2-Q\left(\cos\theta_{jil}+1/3\right)^2-Q\left(\cos\theta_{kil}+1/3\right)^2\right]\right\}
\end{align*}
$$

Reference:

A. D. Mistriotis, N. Flytzanis, and S. C. Farantos, “Potential model for silicon clusters”, Phys. Rev. B, vol. 39, 1212-1218, 1989

Wiki Contributors

2017-04-16T19:32:22	butnowdevil
2017-04-16T19:28:52	butnowdevil
2017-04-13T17:59:51	tadmor
2017-04-13T17:55:22	tadmor
2017-04-13T17:53:47	tadmor
2017-04-13T17:52:16	tadmor
2017-04-13T17:50:00	tadmor
2017-03-21T20:11:37	butnowdevil
2017-03-21T20:00:55	butnowdevil
2017-03-21T20:00:15	butnowdevil
2017-03-21T19:59:16	butnowdevil
2017-03-21T19:58:00	butnowdevil
2017-03-21T19:48:43	butnowdevil
2017-03-21T19:47:17	butnowdevil
2017-03-21T19:34:41	butnowdevil