Complexes with metal–ligand π-bonding

   The metal d_xy, d_yz and d_xz atomic orbitals (the t_2g set) are nonbonding in an [ML₆]^n‏+, σ-bonded complex (Figure 1.1) and these orbitals may overlap with ligand orbitals of the correct symmetry to give π-interactions (Figure 1.2). Although π-bonding between metal and ligand d orbitals is sometimes considered for interactions between metals and phosphine ligands (e.g. PR₃ or PF₃), it is more realistic to consider the roles of ligand σ^*-orbitals as the acceptor orbitals.  Two types of ligand must be differentiated: π-donor and π-acceptor ligands.   A π-donor ligand donates electrons to the metal centre in an interaction that involves a filled ligand orbital and an empty metal orbital; a π-acceptor ligand accepts electrons from the metal centre in an interaction that involves a filled metal orbital and an empty ligand orbital. π-Donor ligands include Cl^-, Br^- and I^- and the metal– ligand π-interaction involves transfer of electrons from filled ligand p orbitals to the metal centre (Figure 1.2a). Examples of π-acceptor ligands are CO, N₂, NO and alkenes, and the metal–ligand π-bonds arise from the back donation of electrons from the metal centre to vacant antibonding orbitals on the ligand (for example, Figure 1.2b).

Fig. 1.1 An approximate MO diagram for the formation of [ML₆]^n‏+ (where M is a first row metal) using the ligand group orbital approach; the orbitals are shown pictorially in Figure 1.1. The bonding only involves M^_L π-interactions.

Fig. 1.2 π-Bond formation in a linear L^_M^_L unit in which the metal and ligand donor atoms lie on the x axis: (a) between metal d_xz and ligand p_z orbitals as for L = I^-, an example of a π-donor ligand; and (b) between metal d_xz and ligand π^*-orbitals as for L = CO, an example of a π-acceptor ligand.

π-Acceptor ligands can stabilize low oxidation state metal complexes. Figure 1.3 shows partial MO diagrams which describe metal–ligand π- interactions in octahedral complexes; the metal s and p orbitals which are involved in σ-bonding (see Figure 1.1) have been omitted. Figure 1.3a shows the interaction between a metal ion and six π-donor ligands; electrons are omitted from the diagram, and we return to them later. The ligand group π-orbitals are filled and lie above, but relatively close to, the ligand σ-orbitals, and interaction with the metal d_xy, d_yz and d_xz atomic orbitals leads to bonding (t_2g) and antibonding (t_2g^*) MOs. The energy separation between the t_2g^* and e_g^* levels corresponds to Δ_oct. Figure 1.3b shows the interaction between a metal ion and six π-acceptor ligands. The vacant ligand π^* orbitals lie significantly higher in energy than the ligand σ-orbitals. Orbital interaction leads to bonding (t_2g) and antibonding (t_2g^*) MOs as before, but now the t_2g^* MOs are at high energy and Δ_oct is identified as the energy separation between the t_2g and e_g^* levels (Figure 1.3b).

Fig. 1.3 Approximate partial MO diagrams for metal–ligand π-bonding in an octahedral complex: (a) with π-donor ligands and (b) with π-acceptor ligands. In addition to the MOs shown, σ-bonding in the complex involves the a_1g and t_1u MOs (see Figure 1.1). Electrons are omitted from the diagram, because we are dealing with a general Mⁿ⁺‏ ion. Compared with Figure 1.1, the energy scale is expanded.

    Although Figures 1.1 and 1.3 are qualitative, they reveal important differences between octahedral [ML₆]ⁿ⁺‏ complexes containing σ-donor, π-donor and π-acceptor ligands:

• for a complex with π-donor ligands, increased π-donation stabilizes the t_2g level and destabilizes the t_2g^*, thus decreasing Δ_oct;
• for a complex with π-acceptor ligands, increased π-acceptance stabilizes the t_2g level, increasing Δ_oct.

   The above points are consistent with the positions of the ligands in the spectrochemical series; π-donors such as I^- and Br^- are weak-field, while π-acceptor ligands such as CO and [CN]^- are strong-field ligands.   Let us complete this section by considering the occupancies of the MOs in Figures Figure 1.3a and Figure 1.3b. Six π-donor ligands provide 18 electrons (12 σ- and six π-electrons) and these can notionally be considered to occupy the a1g, t_1u, e_g and t_2g orbitals of the complex. The occupancy of the t_2g^* and e_g^* levels corresponds to the number of valence electrons of the metal ion. Six π-acceptor ligands provide 12 electrons (the π-ligand orbitals are empty) and, formally, we can place these in the a1g, t1u and eg orbitals of the complex. The number of electrons supplied by the metal centre then corresponds to the occupancy of the t2g and e_g^* levels. Since occupying antibonding MOs is detrimental to metal–ligand bond formation, it follows that, for example, octahedral complexes with π-accepting ligands will not be favoured for metal centres with d⁷, d⁸, d⁹ or d¹⁰ configurations.  

   This last point brings us to back to some fundamental observations in experimental inorganic chemistry: d-block metal organometallic and related complexes tend to obey the effective atomic number rule or 18-electron rule.

    A low oxidation state organometallic complex contains π-acceptor ligands and the metal centre tends to acquire 18 electrons in its valence shell (the 18 electron rule), thus filling the valence orbitals, e.g. Cr in Cr(CO)₆, Fe in Fe(CO)₅, and Ni in Ni(CO)₄.