The one-body operator is defined as $$ \hat{F} = \sum_{pq} \langle p|\hat{f}|q\rangle a_p^\dagger a_q $$ while the two-body opreator is defined as $$ \hat{V} = \frac{1}{4} \sum_{pqrs} \langle pq|\hat{v}|rs\rangle_{AS} a_p^\dagger a_q^\dagger a_s a_r $$ where we have defined the antisymmetric matrix elements $$ \langle pq|\hat{v}|rs\rangle_{AS} = \langle pq|\hat{v}|rs\rangle - \langle pq|\hat{v}|sr\rangle. $$