-- \frac{1}{2n_i} \chi_{ij} \Bigg( 1 + \beta_i^{n_i} \Bigg[ \sum_{k \ne i,j} \bigg( f_C(r_{ij}) \omega_{ik} \Big( 1 + \frac{c_i^2}{d_i^2} - \frac{c_i^2}{d_i^2 + (h_i - \cos \theta_{ijk})^2} \Big) \bigg)^{n_i} \Bigg] \Bigg)^{-\frac{1}{2n_i} - 1} \times \nonumber\\
-&& \times n_i \beta_i^{n_i} \Bigg[ \sum_{k \ne i,j} f_C(r_{ik}) \omega_{ik} \Big( 1 \frac{c_i^2}{d_i^2} - \frac{c_i^2}{d_i^2 + (h_i - \cos \theta_{ijk})^2} \Big) \Bigg]^{n_i -1} \times \nonumber\\
-&& \times \sum_{k \ne i,j} \Bigg( \omega_{ik} \Big( 1 + \frac{c_i^2}{d_i^2} - \frac{c_i^2}{d_i^2 + (h_i - \cos \theta_{ijk})^2} \Big) \partial_{x^i_n} f_C(r_{ik}) + \nonumber\\
-&& + f_C(r_{ik}) \omega_{ik} (-1) \frac{c_i^2}{(d_i^2 + (h_i - \cos \theta_{ijk})^2)^2} \times \nonumber\\
-&& \times 2 \Big( h_i - \cos \theta_{ijk} \Big) \sin \theta_{ijk} \partial_{x^i_n} \theta_{ijk} \Bigg)
+- \frac{1}{2n_i} \chi_{ij} \Bigg( 1 + \beta_i^{n_i} \Bigg[ \sum_{k \ne i,j} \bigg( f_C(r_{ik}) \omega_{ik} \Big( 1 + \frac{c_i^2}{d_i^2} - \frac{c_i^2}{d_i^2 + (h_i - \cos \theta_{ijk})^2} \Big) \bigg)^{n_i} \Bigg] \Bigg)^{-\frac{1}{2n_i} - 1} \times \nonumber\\
+&& \times n_i \beta_i^{n_i} \sum_{k \ne i,j} \Bigg( \Bigg[ f_C(r_{ik}) \omega_{ik} \Big( 1 + \frac{c_i^2}{d_i^2} - \frac{c_i^2}{d_i^2 + (h_i - \cos \theta_{ijk})^2} \Big) \Bigg]^{n_i -1} \times \nonumber\\
+&& \times \Bigg[ \omega_{ik} \Big( 1 + \frac{c_i^2}{d_i^2} - \frac{c_i^2}{d_i^2 + (h_i - \cos \theta_{ijk})^2} \Big) \partial_{x^i_n} f_C(r_{ik}) + \nonumber\\
+&& + f_C(r_{ik}) \omega_{ik} \frac{c_i^2}{(d_i^2 + (h_i - \cos \theta_{ijk})^2)^2} \times \nonumber\\
+&& \times 2 \Big( h_i - \cos \theta_{ijk} \Big) \sin \theta_{ijk} \partial_{x^i_n} \theta_{ijk} \Bigg] \Bigg)