T2G

t2g is a term used in inorganic chemistry and solid-state chemistry to describe a set of three d orbitals of a transition-metal ion that are degenerate under octahedral symmetry. The notation comes from group theory: t2g denotes a triply degenerate representation that is symmetric with respect to inversion (gerade) in the Oh point group, corresponding to the attribution of the d orbitals under the ligand field. In an octahedral ligand field, the five d orbitals of a transition metal ion split into two groups: a lower-energy t2g set, consisting of dxy, dxz, and dyz, and a higher-energy eg set, consisting of dz2 and dx2−y2. The energy difference between these sets is denoted Δo (the octahedral crystal-field splitting). The t2g set is lower in energy because its orbitals point between the ligand axes and thus interact less strongly with the ligands than the eg set.

Electrons fill the t2g orbitals before the eg orbitals, subject to spin pairing and the overall d-electron count. Depending on the magnitude of Δo relative to the spin-pairing energy, a complex may be low-spin (paired in t2g) or high-spin (electrons occupy eg as needed). In a tetrahedral field, the splitting is reversed, with the e set lower in energy than t2g, and the magnitude is typically smaller (about 4/9 of Δo). The t2g designation remains useful for describing ligand-field effects in distorted octahedral environments and in modern computational models.

Beyond spectroscopy and magnetism, the concept of t2g helps explain color in many transition-metal complexes, as t2g → eg electronic transitions can be allowed or spin-forbidden depending on the system.