 \nonumber \\    & = & \mathcal{C}^{\mathrm{ss},(0)}_{ij}          + 0 \big<\mathrm{\hat n}_{i\sigma}^{\vphantom{\dagger}}\big> \big<\mathrm{\hat n}_{j\sigma}^{\vphantom{\dagger}}\big>          - 0 \big<\mathrm{\hat c}_{i\sigma}^\dagger \mathrm{\hat c}_{j\sigma}^{\vphantom{\dagger}}\big>            \big<\mathrm{\hat c}_{j\sigma}^\dagger \mathrm{\hat c}_{i\sigma}^{\vphantom{\dagger}}\big> 