2.4: σ, π, and δ orbitals

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Inorganic compounds use s, p, and d orbitals (and more rarely f orbitals) to make bonding and antibonding combinations. These combinations result in σ, π, and δ bonds (and antibonds).

You are already familiar with σ and π bonding in organic compounds. In inorganic chemistry, π bonds can be made from p- and/or d-orbitals. δ bonds are more rare and occur by face-to-face overlap of d-orbitals, as in the ion Re₂Cl₈²^-. The fact that the Cl atoms are eclipsed in this anion is evidence of δ bonding.

Figure \(\PageIndex{1}\): The octachlorodirhenate(III) anion, [Re₂Cl₈]²⁻, which has a quadruple Re-Re bond.^[3]

Some possible σ (top row), π (bottom row), and δ bonding combinations (right) of s, p, and d orbitals are sketched below. In each case, we can make bonding or antibonding combinations, depending on the signs of the AO wavefunctions. Because pπ-pπ bonding involves sideways overlap of p-orbitals, it is most commonly observed with second-row elements (C, N, O). π-bonded compounds of heavier elements are rare because the larger cores of the atoms prevent good π-overlap. For this reason, compounds containing C=C double bonds are very common, but those with Si=Si bonds are rare. δ bonds are generally quite weak compared to σ and π bonds. Compounds with metal-metal δ bonds occur in the middle of the transition series.

Sigma bonds are bonds in which orbitals directly overlap, as seen in s-s, s p (z), and p (z) -p (z) orbitals. Pi bonds involve orbitals with sideways overlap as shown with p (y) - p (y) orbitals. Both orbitals point upward and are able to overlap next to each other. Similar overlap occurs in p (y) - d (y z) and d (y z) - d (y z) orbitals.

Transition metal d-orbitals can also form σ bonds, typically with s-p hybrid orbitals of appropriate symmetry on ligands. For example, phosphines (R₃P:) are good σ donors in complexes with transition metals, as shown below.

The s orbital of phosphorus of the phosphine overlaps with the d orbital of a transition metal. The p orbital of phosphorus is also able to overlap with a separate d orbital of the transition metal.

pπ-dπ bonding is also important in transition metal complexes. In metal carbonyl complexes such as Ni(CO)₄ and Mo(CO)₆, there is sideways overlap between filled metal d-orbitals and the empty π-antibonding orbitals (the LUMO) of the CO molecule, as shown in the figure below. This interaction strengthens the metal-carbon bond but weakens the carbon-oxygen bond. The C-O infrared stretching frequency is diagnostic of the strength of the bond and can be used to estimate the degree to which electrons are transferred from the metal d-orbital to the CO π-antibonding orbital.

A metal is bonded to carbon monoxide along an axis of bonding. Electrons are initially donated from the carbon to the metal through direct overlap with signma bonding. The sideways interaction of pi orbitals allows for donation back to the carbon from the metal above and below the axis of bonding.

The same kind of backbonding occurs with phosphine complexes, which have empty π orbitals, as shown at the right. Transition metal complexes containing halide ligands can also have significant pπ-dπ bonding, in which a filled pπ orbital on the ligand donates electron density to an unfilled metal dπ orbital. We will encounter these bonding situations in Chapter 5.