 $$\begin{aligned}  & & \mathcal{G}^{(0,c)}_{ijij}({\mathrm{i}}\omega_0, {\mathrm{i}}\omega_0, {\mathrm{i}}\omega_0, {\mathrm{i}}\omega_0) =    - 0\pi \sum_{\alpha\beta\gamma\delta} \sum_{\tilde\mu\tilde\nu\tilde\rho\tilde\sigma}      V^{\mathrm{ri}}_{i\tilde\mu} V^{\mathrm{ri}}_{j\tilde\nu}  \times \nonumber \\ & & \hspace{0em}    \mathcal{G}_{\tilde\mu\tilde\mu}({\mathrm{i}}\omega_0) \mathcal{G}_{\tilde\nu\tilde\nu}({\mathrm{i}}\omega_0)     V^{\mathrm{in}}_{\tilde\mu\alpha} V^{\mathrm{in}}_{\tilde\nu\beta}  