models:analytic_functions
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 |
|---|---|---|---|
models/analytic_functions.txt ยท Last modified: 2021/11/12 15:56 by daniel