Ligand Field Splitting Calculator

Ligand field splitting energy, written delta or 10Dq, is the energy separation between the two sets of d orbitals created when ligands surround a transition metal ion. In octahedral geometry the eg pair points directly at the ligands and rises by 6Dq, while the t2g set points between them and falls by 4Dq, preserving the barycentre. Because the gap is usually crossed by a d-d absorption band, delta is read straight off a UV-visible spectrum: in wavenumbers, delta equals 10,000,000 divided by the band maximum in nanometres. Practical ranges are wide. First-row aqua ions sit near 8,000 to 14,000 cm-1, with [Ni(H2O)6]2+ close to 8,500 cm-1, while strong-field ligands push much higher, [Fe(CN)6]3- reaching roughly 35,000 cm-1. Delta grows with metal oxidation state, rises by about half again on moving from 3d to 4d and again to 5d, and follows the spectrochemical series across ligands. Whether a d4 to d7 ion is high or low spin depends on delta against the mean pairing energy, typically 15,000 to 25,000 cm-1 for first-row ions. Useful conversions are 1 cm-1 equals 0.01196 kJ/mol and 1.2398e-4 eV, and delta for a tetrahedral field is about four ninths of the octahedral value, which is why tetrahedral complexes are almost always high spin. Caveats matter: only for d1 and d9 ions does the band maximum equal delta directly, since interelectron repulsion means other configurations require Tanabe-Sugano analysis. Intense charge-transfer bands can also mask weak d-d absorptions, and Jahn-Teller distortion broadens or splits them.

Hans Bethe laid the foundation in 1929 with his paper on term splitting in crystals, applying group theory to show how the symmetry of a surrounding electrostatic field lifts the degeneracy of atomic d and f levels. John Hasbrouck Van Vleck extended the treatment through the early and mid 1930s, connecting it to magnetic susceptibility measurements and pointing out that a purely electrostatic picture was incomplete, since covalent overlap between metal and ligand orbitals had to be included. That correction became ligand field theory, essentially crystal field theory embedded in a molecular orbital framework, and it explained why neutral pi-acceptor ligands like carbon monoxide produce far larger splittings than charged pi-donors such as fluoride. The empirical ordering of ligands came from spectroscopy rather than theory. Ryutaro Tsuchida, working in Japan, arranged ligands by the absorption shifts they produced in cobalt and chromium complexes and published the spectrochemical series in 1938. Analysis of the resulting spectra was systematized by Yukito Tanabe and Satoru Sugano, whose 1954 energy-level diagrams plot term energies against delta and remain the standard tool for extracting splitting parameters from multi-band spectra. Leslie Orgel produced simplified correlation diagrams in the mid 1950s, and Christian Klixbull Jorgensen introduced the nephelauxetic series to quantify how much metal-ligand covalency reduces interelectron repulsion below the free-ion value.