    \Gamma_{\alpha\beta\gamma\delta} \delta({\mathrm{i}}\omega_0 + {\mathrm{i}}\omega_0 - {\mathrm{i}}\omega_0 - {\mathrm{i}}\omega_0)  \times \nonumber \\ & & \hspace{0em}    V^{\mathrm{in},-0}_{\gamma\tilde\rho} V^{\mathrm{in},-0}_{\delta\tilde\sigma}    \mathcal{G}_{\tilde\rho\tilde\rho}({\mathrm{i}}\omega_0) \mathcal{G}_{\tilde\sigma\tilde\sigma}({\mathrm{i}}\omega_0)    V^{\mathrm{ri},-0}_{\tilde\rho i} V^{\mathrm{ri},-0}_{\tilde\sigma j}.    \label{eq:TwoParticleGF:connected:frequency:i