Editing Ligand field theory (section)

===σ-bonding (sigma bonding)===

In an octahedral complex, the molecular orbitals created by coordination can be seen as resulting from the donation of two [[electron]]s by each of six σ-donor ligands to the ''d''-orbitals on the [[metal]]. In octahedral complexes, ligands approach along the ''x''-, ''y''- and ''z''-axes, so their σ-symmetry orbitals form bonding and anti-bonding combinations with the ''d''<sub>''z''<sup>2</sup></sub> and ''d''<sub>''x''<sup>2</sup>&minus;''y''<sup>2</sup></sub> orbitals. The ''d''<sub>''xy''</sub>, ''d''<sub>''xz''</sub> and ''d''<sub>''yz''</sub> orbitals remain non-bonding orbitals. Some weak bonding (and anti-bonding) interactions with the ''s'' and ''p'' orbitals of the metal also occur, to make a total of 6 bonding (and 6 anti-bonding) molecular orbitals<ref>{{Cite web |date=2021-09-03 |title=10.3.1: Ligand Field Theory - Molecular Orbitals for an Octahedral Complex |url=https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Inorganic_Chemistry_(LibreTexts)/10%3A_Coordination_Chemistry_II_-_Bonding/10.03%3A_Ligand_Field_Theory/10.3.01%3A__Ligand_Field_Theory_-_Molecular_Orbitals_for_an_Octahedral_Complex |access-date=2023-12-07 |website=Chemistry LibreTexts |language=en}}</ref>

[[Image:LFTi(III).png|center|thumb|400px|Ligand-Field scheme summarizing σ-bonding in the octahedral complex [Ti(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup>.]]

In [[molecular symmetry]] terms, the six lone-pair orbitals from the ligands (one from each ligand) form six symmetry-adapted linear combinations (SALCs) of orbitals, also sometimes called ligand group orbitals (LGOs). The [[irreducible representation]]s that these span are ''a<sub>1g</sub>'', ''t<sub>1u</sub>'' and ''e<sub>g</sub>''. The metal also has six valence orbitals that span these [[irreducible representation]]s - the s orbital is labeled ''a<sub>1g</sub>'', a set of three p-orbitals is labeled ''t<sub>1u</sub>'', and the ''d''<sub>''z''<sup>2</sup></sub> and ''d''<sub>''x''<sup>2</sup>&minus;''y''<sup>2</sup></sub> orbitals are labeled ''e<sub>g</sub>''.  The six σ-bonding molecular orbitals result from the combinations of ligand SALCs with metal orbitals of the same symmetry.<ref>{{Cite web |date=2021-09-03 |title=10.3.1: Ligand Field Theory - Molecular Orbitals for an Octahedral Complex |url=https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Inorganic_Chemistry_(LibreTexts)/10%3A_Coordination_Chemistry_II_-_Bonding/10.03%3A_Ligand_Field_Theory/10.3.01%3A__Ligand_Field_Theory_-_Molecular_Orbitals_for_an_Octahedral_Complex |access-date=2023-12-07 |website=Chemistry LibreTexts |language=en}}</ref>