A molecular orbital study is presented of the magnetic coupling in the one-dimensional vanadium oxide $Ba_2V_3O_9$ with a bridge formed by two different types of $VO_4$ tetrahedra. The concept of complementary versus counter-complementary effect has been used to explain the structural origin of the magnetic behavior of the compound. Namely, the observed antiferromagnetic coupling is dominated by the orbital complementarity of the V(1) tetrahedra sharing only one oxygen corner with two adjacent $VO_6$ octahedra. The second type of V(2) tetrahedra does not provide a noticeable contribution to the magnetic coupling due to the orbital counter-complementarity of the bridging ligand.