To be able to calculate the first-order exchange energy using equation (40) it is necessary to derive its explicit form expressed by one-and two-electron integrals. To achieve this, the formalism of second quantization is used, accompanied by diagrammatic techniques. Explicit expression for the V P2n L term consists of all possible linked-diagrams that have exactly 2n overlap matrix elements and have either vertices corresponding to (ω A ) s b , (ω B ) r a or v rs ab integrals on top. Due to the form of the P2n permutation operator, given in equation ( ), all S overlap matrix elements appearing in diagrams must have exactly one index belonging to monomer A and one belonging to monomer B. Furthermore, it is worth noting that the P2n operator cannot introduce extra particle-type lines into the diagram. These two properties greatly limit the number of possible diagrams contributing to the V P2n L term.