Here, x collects the variables of all electrons. Substitutig Equation (3) into Equation (2), one can rewrite the TDM as an expansion in MO products, and further expressing MOs φ i as linear combinations of atomic orbitals (AOs) η µ , φ i (⃗ r) = µ c µi η µ (⃗ r), as an expansion in AO products: