\documentclass[preview]{standalone}
\usepackage{varwidth}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath,amssymb,amsthm,bm}
\begin{document}
\begin{varwidth}{50in}
  \begin{equation}
    \vec{F}^{i} = \sum_{j}^{Neighbor} \frac{\partial {J} \left(r_{ij} \right)}{
    \partial r_{ij}} \left( \vec{s}_{i}\cdot \vec{s}_{j} \right) \vec{r}_{ij}  
    ~~{\rm and}~~ \vec{\omega}^{i} = \frac{1}{\hbar} \sum_{j}^{Neighbor} {J} 
    \left(r_{ij} \right)\,\vec{s}_{j} \nonumber
  \end{equation}
\end{varwidth}
\end{document}