\sum_{\substack{(\mathbf{k}',\mathbf{l}')\in \mathcal{C}\\\mathbf{k}'\neq \mathbf{k},\mathbf{l}'\neq \mathbf{l}}}\mathcal{H}_{\alpha_0,c_0}(\mathbf{k}'-\mathbf{k})\mathcal{H}_{\alpha_0,c_0}(\mathbf{l}'-\mathbf{l})\