\documentclass[12pt]{article}
\begin{document}
$$
S_{ab} = - \left[ m v_a v_b +
\frac{1}{2} \sum_{j = 1}^{N_p} (a_i - a_j) F_{p_{ij}} +
\frac{1}{2} \sum_{j = 1}^{N_b} (a_i - a_j) F_{b_{ij}} \right]
\end{document}