The $n$th component of the force acting on atom $i$ is
\begin{eqnarray}
F_n^i & = & - \frac{\partial}{\partial x_n} \sum_{j \neq i} V_{ij} \nonumber\\
The $n$th component of the force acting on atom $i$ is
\begin{eqnarray}
F_n^i & = & - \frac{\partial}{\partial x_n} \sum_{j \neq i} V_{ij} \nonumber\\
& & + f_C(r_{ij}) \big[ \partial_{x_n^i} f_R(r_{ij}) + b_{ij} \partial_{x_n^i} f_A(r_{ij}) + f_A(r_{ij}) \partial_{x_n^i} b_{ij} \big] \Big)
\end{eqnarray}
The cutoff function $f_C$ derivated with repect to $x^i_n$ is
\begin{equation}
\partial_{x^i_n} f_C(r_{ij}) =
& & + f_C(r_{ij}) \big[ \partial_{x_n^i} f_R(r_{ij}) + b_{ij} \partial_{x_n^i} f_A(r_{ij}) + f_A(r_{ij}) \partial_{x_n^i} b_{ij} \big] \Big)
\end{eqnarray}
The cutoff function $f_C$ derivated with repect to $x^i_n$ is
\begin{equation}
\partial_{x^i_n} f_C(r_{ij}) =
\label{eq:d_cutoff}
\end{equation}
for $R_{ij} < r_{ij} < S_{ij}$ and otherwise zero.
The derivations of the repulsive and attractive part are:
\begin{eqnarray}
\label{eq:d_cutoff}
\end{equation}
for $R_{ij} < r_{ij} < S_{ij}$ and otherwise zero.
The derivations of the repulsive and attractive part are:
\begin{eqnarray}
-\partial_{x_n^i} f_R(r_{ij}) & = & - \lambda_{ij} A_{ij} \exp (-\lambda_{ij} r_{ij})\\
-\partial_{x_n^i} f_A(r_{ij}) & = & \mu_{ij} B_{ij} \exp (-\mu_{ij} r_{ij}) \textrm{ .}
+\partial_{x_n^i} f_R(r_{ij}) & = & - \lambda_{ij} \frac{x_n^i - x_n^j}{r_{ij}} A_{ij} \exp (-\lambda_{ij} r_{ij})\\
+\partial_{x_n^i} f_A(r_{ij}) & = & \mu_{ij} \frac{x_n^i - x_n^j}{r_{ij}} B_{ij} \exp (-\mu_{ij} r_{ij}) \textrm{ .}