This is a simple task. This matrix element is part of the operator \( \overline{H}_{ab}^{ij}a^\dagger_ia^\dagger_ja_ba_a \), i.e. particles are annihilated and holes are created. Thus, no contraction of the Hamiltonian \( H \) with any cluster operator \( T \) (remember that \( T \) annihilates holes and creates particles) can happen, and we simply have \( \overline{H}_{ab}^{ij} = \langle ij\vert V\vert ab\rangle \).