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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.

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
$$V(r)=D_e\left[\exp\left(a\left(1-\frac{r}{r_0}\right)\right)-2\exp\left(\frac{a}{2}\left(1-\frac{r}{r_0}\right)\right)\right]$$

`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

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