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Analytic potential functions


The following analytic functions are currently implemented in potfit.

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

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
$$V(r)=\alpha\sqrt{r/\beta}$$
Advanced potentials
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 $V_0,b_1,b_2,r_1,m,\delta,A_0,$ $B_0,C_0,r_0,y,\gamma$ 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
analytic_functions.txt ยท Last modified: 2014/07/07 18:09 by daniel