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  LENNARD-JONES LINES


 
  • Definition:
    Consider two lines of finite length $L$ containing a homogeneous density of LJ centers. Let $\vec{e}_{1,2}$ be the direction vectors, $\vec{r}_{12}$ the vector between the centers of the two line segments, and $\lambda, \, \mu$ parameters giving the positions of the interacting points along $1$ and $2$. The squared distance between any two such points is given by $r^{2}= \left| r_{12}+\mu \vec{e}_{2}-\lambda \vec{e}_{1} \right|^{2}$. The total interaction energy between the two lines is then

    $ u(\vec{r}_{12},\vec{e}_{1},\vec{e}_{2}) = \frac{\textstyle 1}{\textstyle L^{2}} \int \limits_{1} d\lambda \int \limits_{2} d\mu \, \, u_{LJ} ( r ) $

    with $u_{LJ}(r)=4 \,(r^{-12}-r^{-6})$.
 
  Cannot be integrated in closed form, but: LJ Lines Paper (JCP 2006)



vesely apr-2007