Spectrochemical Series

Ligand Field Splitting Energy

Both Crystal Field Theory and Ligand Field Theory predict a splitting in the normally degenerate valence-shell d orbitals upon complexation of a metal by a ligand. The magnitude of the splitting, Δ, is an important parameter in characterizing coordination compounds.

What factors affect the magnitude of Δ?

• Oxidation State of the Metal

  Complex	[Cr(OH2)6]2+	[Cr(OH2)6]3+	[Co(NH3)6]2+	[Co(NH3)6]3+
  Δo (cm-1)	14100	17400	10200	22900

  For a given metal, Δ_o increases as the oxidation state increases. Part of the interaction between the metal and the ligand is electrostatic. The greater the charge on the metal, the closer the approach of the ligand and the stronger the overlap between the metal and ligand orbitals.

  
  
• Valence Shell of the Metal

  Complex	[Co(NH3)6]3+	[Rh(NH3)6]3+	[Ir(NH3)6]3+
  Δo (cm-1)	22900	34100	41100

  For a given oxidation state, the value of Δ increases as one moves down a group.

  
  
• Number and geometry of the ligands

  The more ligands coordinated to the metal, the larger Δ. The d orbital splitting is greatest when the ligand geometry allows direct overlap between the ligand σ donor orbital and a metal d orbital, such as occurs for linear, square planar, and octahedral geometries. Overlap in tetrahedral complexes is relatively poor, and consequently Δ_t (the splitting for a tetrahedral geometry) is less than Δ_o (the splitting for an octahedral geometry). In most cases Δ_t is approximately 4/9 Δ_o. Even allowing for the smaller number of ligands in the tetrahedral geometry, which accounts for a factor of 2/3, the orbital overlap is appreciable less, as can be visualized using the isosurfaces for the metal and ligand orbitals for Zn(NH₃)₄²⁺ and Co(NH₃)₆³⁺.

  
  
• Nature of the ligand

Exercise

This exercise explores the last item in the list: the impact of the chemistry of the ligand on Δ. A set of eleven ligands are shown below in random order. The goal of this exercise is to arrange the ligands in order of increasing Δ, with the ligand producing the smallest Δ on the far left and the ligand producing the largest Δ on the far right. Click on a ligand to select it, and use the <<< and >>> buttons to shift the position of the selected ligand in the list. The vertical status bar at the far left indicates the accuracy of the current order. Look at each ligand and determine whether it is likely to yield a relatively small or relatively large Δ. Then adjust the order of the ligands accordingly.

What characteristics of a ligand are relevant in determining Δ? Here are some properties to consider.

• size
• basicity
• polarizability
• ability to π bond with metal

If you would like a little help in establishing the correct order, enable the energy diagram. For the sake of simplicity, the energy diagram shows the splitting for this ligand in an octahedral complex. The semi-quantitative energy diagram separates the effects of σ and π bonding. The rightmost pattern shows both effects.

In completing this exercise, bear in mind the following issues.

• Several ligands have comparable influences on Δ and these are separated in the series by the ≤ sign. The order in which these pairs of ligands are listed is unimportant.
• The thiocyanate (SCN^-) ligand can bind via the sulfur or the nitrogen. An underscore denotes the atom that binds to the metal. Thus SCN^- indicates the thiocyanato or thiocyanato-S- ligand while NCS^- indicates the isothiocyanato or thiocyanato-N- ligand. (Why would the atom through which bonding occurs affect the position in this series?)
• The symbol py represents the pyridyl ligand, C₅H₅N or .

Shift Ligand:
100%	Δo d orbitals Ligand is a σ donor. Ligand is a π donor.

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