Outer orbital complexes involve transition metal ions that have d-orbitals available in their outermost electron shell. These complexes are typically formed by transition metals that can utilize d-orbitals beyond the \( 3d \) shell (e.g., \( 4d \) or \( 5d \) orbitals) to bond with ligands.
- Option (A): \( [Co(NH_3)_6]^{3+} \) is a low-spin inner orbital complex, where the \( 3d \) orbitals are involved, so it is not an outer orbital complex.
- Option (B): \( [Mn(CN)_6]^{3-} \) involves inner orbital bonding as well, where the \( 3d \) orbitals are involved.
- Option (C): \( [Co(C_2O_4)_3]^{3-} \) is also an inner orbital complex.
- Option (D): \( [MnCl_6]^{3-} \) is an outer orbital complex because Mn(III) uses its \( 4d \) orbitals to form bonds with the chloride ligands.
- Option (E): \( [Fe(CN)_6]^{3-} \) is another inner orbital complex, as Fe(III) uses its \( 3d \) orbitals for bonding.
Thus, the correct answer is (D) \([MnCl_6]^{3-}\), which is an outer orbital complex.