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models:analytic_functions

# Analytic potential functions

The following analytic functions are currently implemented in potfit.

For details see the functions.h and functions.c files.

If you want to add other analytic potentials see this guide.

Each function is given in the following form:

 identifier # of parameters order of parameters reference functional form

## General potentials

Most of these potentials do not have any special properties. They may be used as regular pair potentials as well as for advanced potentials like EAM, ADP or MEAM.

##### Basic potentials
 const 1 $c$ [none] $$V(r)=c$$
 lj 2 $\varepsilon, \sigma$ Link $$V(r)=4\varepsilon\left[\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6}\right]$$
 morse 3 $D_e, a, r_e$ Link $$V(r)=D_e \left( \left[ 1-\exp\left(-a(r-r_e)\right) \right]^2 - 1 \right)$$
 power 2 $\alpha,\,\beta$ [none] $$V(r)=\alpha r^\beta$$
 softshell 2 $\alpha, \beta$ [none] $$V(r)=\left(\frac{\alpha}{r}\right)^\beta$$
 power_decay 2 $\alpha,\,\beta$ [none] $$V(r)=\alpha\left(\frac{1}{r}\right)^\beta$$
 exp_decay 2 $\alpha,\,\beta$ [none] $$V(r)=\alpha \exp\left(-\beta r\right)$$
 mexp_decay 3 $\alpha,\,\beta,\,r_0$ [none] $$V(r)=\alpha\exp\left(-\beta(r-r_0)\right)$$
 exp_plus 3 $\alpha,\,\beta,\,c$ [none] $$V(r)=\alpha\exp\left(-\beta r\right)+c$$
 sqrt 2 $\alpha,\,\beta$ Link $$V(r)=\alpha\sqrt{r/\beta}$$
 born 5 $\alpha,\beta,\gamma,\delta,r_0$ Link $$V(r)=\alpha\exp(\frac{r_0 - r}{\beta})-\frac{\gamma}{r^6}+\frac{\delta}{r^8}$$
 harmonic 2 $\alpha,r_0$ [none] $$V(r)=\alpha(r-r_0)^2$$
 acosharmonic 2 $\alpha,r_0$ [none] $$V(r)=\alpha(\arccos(r)-r_0)^2$$
 eopp 6 $C_1,\,\eta_1,\,C_2,\,\eta_2,k,\,\varphi$ Link $$V(r)=\frac{C_1}{r^{\eta_1}}+\frac{C_2}{r^{\eta_2}}\cos\left(kr+\varphi\right)$$
 meopp 7 $C_1,\,\eta_1,\,C_2,\,\eta_2,\,k,\,\varphi,\,r_0$ Link $$V(r)=\frac{C_1}{\left(r-r_0\right)^{\eta_1}}+\frac{C_2}{r^{\eta_2}}\cos\left(kr+\varphi\right)$$
 eopp_exp 6 $C_1,\,\eta_1,\,C_2,\,\eta_2,\,k,\,\varphi$ Link $$V(r)=C_1\exp\left(-\eta_1r\right)+\frac{C_2}{r^{\eta_2}}\cos\left(kr+\varphi\right)$$
 ms 3 $D_e,\,a,\,r_0$ Link $$V(r)=D_e\left[\exp\left(a\left(1-\frac{r}{r_0}\right)\right)-2\exp\left(\frac{a}{2}\left(1-\frac{r}{r_0}\right)\right)\right]$$
 strmm 5 $\alpha,\,\beta,\,\gamma,\,\delta,\,r_0$ Link $$V(r)=2\alpha\exp\left(-\beta(r-r_0)/2\right) - \gamma\left[1+\delta(r-r_0)\exp\left(-\delta(r-r_0)\right)\right]$$
 double_morse 7 $E_1,\alpha_1,r_0^{(1)},E_2,\alpha_2,r_0^{(2)},\delta$ Link $$V(r)=E_1M(r,r_0^{(1)},\alpha_1)+E_2M(r,r_0^{(2)},\alpha_2)+\delta$$ $$M(r,r_0,\alpha) = \exp\left(-2\alpha(r-r_0)\right)-2\exp\left(-\alpha(r-r_0)\right)$$
 double_exp 5 $a,\beta_1,r_0^{(1)},\beta_2,r_0^{(2)}$ Link $$V(r)=a\exp\left(-\beta_1(r-r_0^{(1)})^2\right)+\exp\left(-\beta_2(r-r_0^{(2)})\right)$$
 poly_5 5 $F_0,\,F_2,\,q_1,\,q_2,\,q_3$ Link $$V(r)=F_0+\frac{1}{2}F_2(r-1)^2+\sum_{n=1}^3q_n(r-1)^{n+2}$$
 buck 3 $\alpha, \beta, \gamma$ Link $$V(r)=\alpha\exp\left(-\frac{r}{\beta}\right)-\gamma\left(\frac{\beta}{r}\right)^6$$
 kawamura 9 $z_1,z_2,f_0,a_1,a_2,b_1,b_2,$ $c_1,c_2$ Link $$V(r)=\frac{z_1z_2}{r}+f_0(b_1+b_2)\exp\left(\frac{a_1+a_2-r}{b_1+b_2}\right)-\frac{c_1c_2}{r^6}$$
 kawamura_mix 12 $z_1,z_2,f_0,a_1,a_2,b_1,b_2,$ $c_1,c_2,D,\beta,r_0$ Link $$V(r)=\frac{z_1z_2}{r}+f_0(b_1+b_2)\exp\left(\frac{a_1+a_2-r}{b_1+b_2}\right)-\frac{c_1c_2}{r^6}$$ $$+ f_0 D \left[\exp\{-2\beta(r-r_0)\}-2\exp\{-\beta(r-r_0)\}\right]$$
 mishin 6 $A_0,B_0,C_0,r_0,y,\gamma$ Link $$V(r)=A_0(r-r_0)^y\exp\left(-\gamma(r-r_0)\right)\left[1+B_0\exp\left(-\gamma(r-r_0)\right)\right]+C_0$$
 gen_lj 5 $V_0,b_1,b_2,r_1,\delta$ Link $$V(r)=\frac{V_0}{b_2-b_1}\left(\frac{b_2}{(r/r_1)^{b_1}}-\frac{b_1}{(r/r_1)^{b_2}}\right)+\delta$$
 gljm 12 $V_0,b_1,b_2,r_1,\delta,m,A_0,$ $B_0,C_0,r_0,y,\gamma$ Link $$V(r)=\frac{V_0}{b_2-b_1}\left(\frac{b_2}{(r/r_1)^{b_1}}-\frac{b_1}{(r/r_1)^{b_2}}\right)+\delta$$ $$+ m\left[A_0(r-r_0)^y\exp\left(-\gamma(r-r_0)\right)\left[1+B_0\exp\left(-\gamma(r-r_0)\right)\right]+C_0\right]$$
 vas 2 $\alpha, \beta$ Link $$V(r)=\exp\left(\frac{\alpha}{r-\beta}\right)$$
 vpair 7 $\alpha, \beta, \gamma, \delta, a, b, c$ Link $$V(r)=14.4\left[\frac{\alpha}{r^\beta}-\frac{a\delta^2+b\gamma^2}{r^4}\exp\left(-\frac{r}{c}\right)\right]$$

## EAM embedding functions

 universal 4 $F_0,\,p,\,q,\,F_1$ Link $$F(n)=F_0\left[\frac{q}{q-p}n^p-\frac{p}{q-p}n^q\right]+F_1n$$
 bjs 3 $F_0,\,\gamma,\,F_1$ Link $$F(n)=F_0\left[1-\gamma\ln n\right]n^\gamma+F_1n$$

## EAM transfer functions

 parabola 3 $a,\,b,\,c$ [none] $$\rho(r)=ar^2+br+c$$
 csw 4 $a_1,\,a_2,\,\alpha,\,\beta$ Link $$\rho(r)=\frac{1+a_1\cos\left(\alpha r\right)+a_2\sin\left(\alpha r\right)}{r^\beta}$$
 csw2 4 $a_1,\,\alpha,\,\varphi,\,\beta$ Link $$\rho(r)=\frac{1+a_1\cos\left(\alpha r+\varphi\right)}{r^\beta}$$

## Tersoff functions

These functions do not correspond directly to the Tersoff potential. They only hold the parameters for the potentials.

 tersoff_pot 11 $A, B, \lambda, \mu, \gamma, n,c, d, h, S, R$ Link
 tersoff_mix 2 $\chi, \omega$ Link

## modified Tersoff function

This dummy function holds all 16 parameters required to defined a modified Tersoff potential.

 tersoff_mod_pot 16 $A, B, \lambda, \mu, \eta, \delta, \alpha, \beta, c_1, c_2, c_3, c_4, c_5, h, R_1, R_2$ Link

## Stillinger-Weber functions

The stiweb_2 functions is equvalent to the $V_2$ potential in the Stillinger-Weber potential model. The stiweb_3 function, however, only accounts for the exponential function in $V_3$.

 stiweb_2 6 $A, B, p, q, \delta, a$ Link $$V_2(r) = \left(\frac{A}{r^p}-\frac{B}{r^q}\right)\exp\left(\frac{\delta}{r-a}\right)$$
 stiweb_3 2 $\gamma, b$ Link $$V_3^\text{part} = \exp\left(\frac{\gamma}{r-b}\right)$$
 stiweb_lambda $N^2(N+1)/2$ $\lambda_{ijk}$ Link