Ligand Field Splitting Calculator
Compute ligand field splitting using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
delta = hc/lambda = 1/lambda (cm-1)
Ligand field splitting delta can be measured from absorption spectra: delta = 1/lambda (in cm-1 when lambda is in cm). Conversion factors: 1 cm-1 = 0.01196 kJ/mol = 1.2398e-4 eV. For different geometries: delta_tet = (4/9) delta_oct, and delta_sq.planar is approximately 1.3 delta_oct. The color observed is complementary to the wavelength absorbed.
Worked Examples
Example 1: Ti3+ Aqua Complex Color
Problem: The [Ti(H2O)6]3+ ion absorbs at 493 nm. Calculate the ligand field splitting.
Solution: Wavelength = 493 nm\nDelta = 1/lambda = 10,000,000/493 = 20,284 cm-1\nDelta in kJ/mol = 20,284 x 0.01196 = 242.6 kJ/mol\nAbsorbed: blue-green (493 nm)\nObserved color: red-purple (complementary)
Result: Delta = 20,284 cm-1 | 242.6 kJ/mol | Purple-red complex
Example 2: Comparing Octahedral and Tetrahedral
Problem: For Co2+ with delta_oct = 9,300 cm-1, find the tetrahedral and square planar splitting values.
Solution: Delta_oct = 9,300 cm-1\nDelta_tet = (4/9) x 9,300 = 4,133 cm-1\nDelta_sq planar = 1.3 x 9,300 = 12,090 cm-1\nWavelength (oct) = 10^7/9,300 = 1,075 nm (infrared)\nOctahedral Co2+ complexes are often pink-red
Result: Oct = 9,300 | Tet = 4,133 | Sq. Planar = 12,090 cm-1
Frequently Asked Questions
What is ligand field splitting?
Ligand field splitting is the separation of d-orbital energies that occurs when ligands surround a transition metal ion, breaking the degeneracy of the five d orbitals. In a free ion, all five d orbitals have the same energy, but in a coordination complex, the electrostatic field of the ligands raises the energy of orbitals pointing toward the ligands and lowers the energy of those pointing between them. In octahedral complexes, this creates two groups: the lower-energy t2g set (dxy, dxz, dyz) and the higher-energy eg set (dx2-y2, dz2). The energy gap between these groups, called delta (or 10Dq), determines the complex color, magnetic properties, and thermodynamic stability.
How does the spectrochemical series rank ligand field strength?
The spectrochemical series arranges ligands from weakest to strongest field strength based on the magnitude of delta they produce. The approximate order is: I- < Br- < S2- < Cl- < N3- < F- < OH- < ox2- < H2O < NCS- < CH3CN < py < NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO < NO+. Weak field ligands like halides produce small splitting and tend to form high-spin complexes, while strong field ligands like cyanide and carbon monoxide produce large splitting and low-spin complexes. The position of a ligand depends on its sigma-donating ability, pi-donating or pi-accepting character, and the overlap between ligand and metal orbitals.
How does ligand field splitting determine the color of transition metal complexes?
The color of a transition metal complex arises from d-d electronic transitions where an electron absorbs visible light to jump from a lower to higher energy d orbital. The energy of the absorbed photon equals the ligand field splitting energy delta. Since delta corresponds to a specific wavelength, the complex absorbs that color and appears as the complementary color. For example, [Ti(H2O)6]3+ absorbs at about 500 nm (blue-green light) and appears purple-red. The relationship is delta = hc/lambda, where h is Planck constant, c is the speed of light, and lambda is the absorbed wavelength. Complexes with delta outside the visible range (380-740 nm) appear colorless.
Why does tetrahedral splitting differ from octahedral splitting?
Tetrahedral splitting differs from octahedral splitting in both magnitude and orbital ordering. In a tetrahedral field, ligands approach between the axes rather than along them, so the orbital energies are inverted: the e set (dx2-y2, dz2) is lower and the t2 set (dxy, dxz, dyz) is higher. The magnitude of tetrahedral splitting (delta-tet) is only about 4/9 of the octahedral value (delta-oct) for the same metal and ligands because there are fewer ligands (4 vs 6) and they interact less directly with the d orbitals. This smaller splitting means tetrahedral complexes are almost always high spin, since delta-tet is rarely large enough to force electron pairing.
What is the relationship between ligand field theory and crystal field theory?
Crystal field theory (CFT) and ligand field theory (LFT) both explain d-orbital splitting but differ in their treatment of metal-ligand bonding. CFT uses a purely electrostatic model where ligands are treated as point charges or dipoles, successfully predicting orbital splitting patterns and magnetic properties. However, CFT fails to explain the spectrochemical series order since uncharged ligands like CO should not produce stronger fields than charged ones like F-. Ligand field theory incorporates molecular orbital concepts, treating metal-ligand bonds as having both sigma and pi components. LFT explains why pi-acceptor ligands like CO are strong field (they stabilize t2g through backbonding) and why pi-donor ligands like halides are weak field.
What formula does Ligand Field Splitting Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.