The magnitude of Δo dictates whether a complex with four, five, six, or seven d electrons is high spin or low spin, which affects its magnetic properties, structure, and reactivity. Large values of Δo (i.e., Δo > P) yield a low-spin complex, whereas small values of Δo (i.e., Δo < P) produce a high-spin complex. The magnitude of Δo depends on three factors: the valence of the metal, the principal quantum number of the metal (and thus its location in the periodic table), and the nature of the ligand(s). Values of Δo for some representative transition-metal complexes are given in Table \(\PageIndex{1}\).
Table \(\PageIndex{1}\): Crystal Field Splitting Energies for Some Octahedral (Δo)* and Tetrahedral (Δt) Transition-Metal Complexes
| Octahedral Complexes |
Δo (cm−1) |
Octahedral Complexes |
Δo (cm−1) |
Tetrahedral Complexes |
Δt (cm−1) |
| *Energies obtained by spectroscopic measurements are often given in units of wave numbers (cm−1); the wave number is the reciprocal of the wavelength of the corresponding electromagnetic radiation expressed in centimeters: 1 cm−1 = 11.96 J/mol. |
| [Ti(H2O)6]3+ |
20,300 |
[Fe(CN)6]4− |
32,800 |
VCl4 |
9010 |
| [V(H2O)6]2+ |
12,600 |
[Fe(CN)6]3− |
35,000 |
[CoCl4]2− |
3300 |
| [V(H2O)6]3+ |
18,900 |
[CoF6]3− |
13,000 |
[CoBr4]2− |
2900 |
| [CrCl6]3− |
13,000 |
[Co(H2O)6]2+ |
9300 |
[CoI4]2− |
2700 |
| [Cr(H2O)6]2+ |
13,900 |
[Co(H2O)6]3+ |
27,000 |
|
|
| [Cr(H2O)6]3+ |
17,400 |
[Co(NH3)6]3+ |
22,900 |
|
|
| [Cr(NH3)6]3+ |
21,500 |
[Co(CN)6]3− |
34,800 |
|
|
| [Cr(CN)6]3− |
26,600 |
[Ni(H2O)6]2+ |
8500 |
|
|
| Cr(CO)6 |
34,150 |
[Ni(NH3)6]2+ |
10,800 |
|
|
| [MnCl6]4− |
7500 |
[RhCl6]3− |
20,400 |
|
|
| [Mn(H2O)6]2+ |
8500 |
[Rh(H2O)6]3+ |
27,000 |
|
|
| [MnCl6]3− |
20,000 |
[Rh(NH3)6]3+ |
34,000 |
|
|
| [Mn(H2O)6]3+ |
21,000 |
[Rh(CN)6]3− |
45,500 |
|
|
| [Fe(H2O)6]2+ |
10,400 |
[IrCl6]3− |
25,000 |
|
|
| [Fe(H2O)6]3+ |
14,300 |
[Ir(NH3)6]3+ |
41,000 |
|
|
Source of data: Duward F. Shriver, Peter W. Atkins, and Cooper H. Langford, Inorganic Chemistry, 2nd ed. (New York: W. H. Freeman and Company, 1994).
Increasing the valence of a metal ion has two effects: the radius of the metal decreases, and ligands are more strongly attracted to it. Both factors decrease the metal–ligand distance, which in turn causes the ligands to interact more strongly with the d-orbitals. Consequently, the magnitude of Δo increases as the valence of the metal increases. Typically, Δo for a M(III) is about 50% greater than for the M(II) of the same metal; for example, for [V(H2O)6]2+, Δo = 11,800 cm−1; for [V(H2O)6]3+, Δo = 17,850 cm−1.
For a series of complexes of metals from the same group in the periodic table with the same charge and the same ligands, the magnitude of Δo increases with increasing principal quantum number: Δo (3d) < Δo (4d) < Δo (5d). The data for hexaammine complexes of the trivalent Group 9 metals illustrate this point:
[Co(NH3)6]3+: Δo = 22,900 cm−1
[Rh(NH3)6]3+: Δo = 34,100 cm−1
[Ir(NH3)6]3+: Δo = 40,000 cm−1
The increase in Δo with increasing principal quantum number is due to the larger radius of valence orbitals down a column. In addition, repulsive ligand–ligand interactions are most important for smaller metal ions. Relatively speaking, this results in shorter M–L distances and stronger d orbital–ligand interactions.
Factor 3: The Nature of the Ligands
Experimentally, it is found that the Δo observed for a series of complexes of the same metal ion depends strongly on the nature of the ligands. For a series of chemically similar ligands, the magnitude of Δo decreases as the size of the donor atom increases. For example, Δo values for halide complexes generally decrease in the order F > Cl > Br > I because smaller, more localized charges, such as we see for F, interact more strongly with the d-orbitals of the metal. In addition, a small neutral ligand with a highly localized lone pair, such as NH3, results in significantly larger Δo values than might be expected. Because the lone pair points directly at the metal ion, the electron density along the M–L axis is greater than for a spherical anion such as F. The experimentally observed order of the crystal field splitting energies produced by different ligands is called the spectrochemical series which was presented in a previous section.
