forked from lijiext/lammps
19 lines
889 B
TeX
19 lines
889 B
TeX
\documentstyle[12pt]{article}
|
|
|
|
\begin{document}
|
|
\begin{eqnarray*}
|
|
E & = & \left[LJ(r) | Morse(r) \right] \qquad \qquad \qquad r < r_{\rm in} \\
|
|
& = & S(r) * \left[LJ(r) | Morse(r) \right] \qquad \qquad r_{\rm in} < r < r_{\rm out} \\
|
|
& = & 0 \qquad \qquad \qquad \qquad \qquad \qquad \qquad r > r_{\rm out} \\
|
|
LJ(r) & = & AR^{-12}-BR^{-10}cos^n\theta=
|
|
\epsilon\left\lbrace 5\left[ \frac{\sigma}{r}\right]^{12}-
|
|
6\left[ \frac{\sigma}{r}\right]^{10} \right\rbrace cos^n\theta\\
|
|
Morse(r) & = & D_0\left\lbrace \chi^2 - 2\chi\right\rbrace cos^n\theta=
|
|
D_{0}\left\lbrace e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)}
|
|
\right\rbrace cos^n\theta \\
|
|
S(r) & = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2
|
|
\left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]}
|
|
{ \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 }
|
|
\end{eqnarray*}
|
|
\end{document}
|