20,000
cm^-1
2.4797
eV
239.25
kJ/mol
500
nm
2,000
cm^-1
-16,000
cm^-1
-191.4
kJ/mol
20,000
cm^-1
2.4797
eV
239.25
kJ/mol
500
nm
2,000
cm^-1
-16,000
cm^-1
-191.4
kJ/mol
The Crystal Field Splitting Calculator computes the energy of crystal field splitting, the absorption wavelength of d-d transitions, and the crystal field stabilization energy (CFSE) for transition metal complexes. Crystal field theory (CFT), developed by Hans Bethe in 1929 and extended by Van Vleck, explains the colors, magnetism, and thermodynamic stability of coordination compounds.
In an octahedral complex, six ligands approach the metal ion along the x, y, and z axes. The d orbitals pointing directly at the ligands (d_x2-y2 and d_z2, collectively the e_g set) are destabilized relative to the ligands-free ion, while those pointing between ligand approach directions (d_xy, d_xz, d_yz, collectively t_2g) are stabilized. The energy gap between these two sets is Delta_o (or 10Dq in Dq units), the octahedral crystal field splitting parameter.
Delta_o determines the color of the complex: an electron absorbing a photon of energy equal to Delta_o jumps from a t_2g to e_g orbital. The complementary color is observed. [Ti(H2O)6]^3+ (d^1) absorbs at ~493 nm (green) so appears violet-red; [Cr(NH3)6]^3+ (d^3) absorbs at ~465 nm (blue) so appears orange-yellow.
The spectrochemical series orders ligands by their ability to produce large Delta_o: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < CN- < CO. Strong field ligands (CO, CN-) produce large Delta_o and favor low-spin configurations (all paired electrons), while weak field ligands produce small Delta_o and high-spin configurations.
The CFSE (crystal field stabilization energy) is the extra stability a complex gains from d electron occupancy of lower-energy t_2g orbitals. It affects lattice energies, hydration enthalpies, and reaction rates of transition metal compounds.
Delta_o in eV: E = h*c*nu_bar = 6.626e-34 * 3e10 * Delta_o(cm^-1) / 1.602e-19. In kJ/mol: multiply J by Avogadro's number / 1000. Absorption wavelength: lambda = 10^7/Delta_o(cm^-1) nm. CFSE for weak-field octahedral (in Dq): d^1=-4, d^2=-8, d^3=-12, d^4=-6, d^5=0, d^6=-4, d^7=-8, d^8=-12, d^9=-6, d^10=0 (10Dq = Delta_o).
Typical Delta_o values: 7,500-12,000 cm^-1 for weak field halide ligands, 15,000-25,000 cm^-1 for water, 20,000-35,000 cm^-1 for NH3/en, up to 50,000 cm^-1 for CO/CN-. Larger Delta_o produces shorter wavelength (more blue/green) absorption and more stabilized complexes. CFSE values are additional stability beyond the mean energy of the d set.
Inputs
Results
Titanium(III) hexaaquaion absorbs at ~493 nm (green), appearing violet. Delta_o = 20,300 cm^-1 = 2.52 eV. CFSE = -4Dq = -40% of Delta_o = -97 kJ/mol stabilization.
Inputs
Results
Chromium(III) hexaaquaion (d^3) has CFSE = -12Dq, the maximum possible for a d^3 or d^8 configuration. It appears violet due to absorption in the yellow-green region at ~575 nm.
The energy difference between the two sets of d orbitals (t_2g and e_g for octahedral geometry) caused by the electrostatic field of surrounding ligands. It determines the color, magnetism, and stability of transition metal complexes.
The color is the complement of the absorbed wavelength. The absorbed wavelength corresponds to Delta_o: smaller Delta_o absorbs red (complex appears blue/violet), larger Delta_o absorbs blue/UV (complex appears yellow/orange).
An ordering of ligands by their ability to cause crystal field splitting: I- < Br- < Cl- < F- < OH- < H2O < py < NH3 < en < bipy < NO2- < CN- < CO. Strong field ligands (right side) give large Delta_o and low-spin complexes.
When Delta_o > pairing energy (P), electrons prefer to pair in t_2g rather than enter e_g: low-spin complex with fewer unpaired electrons. When Delta_o < P: high-spin complex where Hund's rule dominates. Strong field ligands favor low-spin.
Crystal Field Stabilization Energy — the extra stability arising from d electrons occupying lower-energy t_2g orbitals. For d^3 (t_2g^3): CFSE = -12Dq = -1.2*Delta_o. For d^5 high-spin: CFSE = 0 (symmetric filling of both sets).
High-spin complexes have more unpaired electrons and are paramagnetic; low-spin complexes may be diamagnetic. Measuring the magnetic moment (by Gouy balance or SQUID magnetometer) determines the number of unpaired electrons and hence spin state.
Crystal field theory treats ligands as point charges. Ligand field theory (LFT) includes molecular orbital interactions between metal and ligand, providing a more accurate description of pi-donor and pi-acceptor effects on Delta_o.
CO is a pi-acceptor ligand: it accepts electron density from the metal into its pi* orbitals, stabilizing the t_2g set and increasing Delta_o. This backbonding also weakens the C-O bond (evidenced by a red-shift in the IR CO stretch).
Yes. For tetrahedral geometry, the splitting is reversed (e set below t_2 set) and Delta_tet = (4/9)*Delta_o for the same ligands. Smaller splitting means tetrahedral complexes are almost always high-spin. Square planar geometry has a unique splitting pattern with four energy levels.
For certain d electron configurations (d^9, high-spin d^4 in octahedral) the complex is electronically degenerate and distorts its geometry to lower symmetry and lift the degeneracy. This Jahn-Teller distortion is why Cu(II) complexes are elongated octahedra rather than regular.
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