Table of Contents

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]
$$V(r)=\alpha(\arccos(r)-r_0)^2$$
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
$$V(r)=D_e\left[\exp\left(a\left(1-\frac{r}{r_0}\right)\right)-2\exp\left(\frac{a}{2}\left(1-\frac{r}{r_0}\right)\right)\right]$$ When using electrostatic interactions this function is defined differently! See section 2. Shifting in Coulomb Interactions for details. This definition is available under the new name ms_non_es.
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
$$V(r)=\alpha\exp\left(-\frac{r}{\beta}\right)-\gamma\left(\frac{\beta}{r}\right)^6$$ When using electrostatic interactions this function is defined differently! See section 2. Shifting in Coulomb Interactions for details. This definition is available under the new name buck_non_es.
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