Crystal Field Theory for Coordination Complexes

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This Demonstration introduces crystal-field theory, which describes the geometry and energetics of coordination complexes. According to this model, ligands bonded to transition metal cause splitting of the -orbitals by electrostatic repulsion between the electrons in the -orbitals and the negatively charged ligands.


It is possible to understand this splitting by observing how the spatial displacement of the -orbitals influences the geometry of the complex: orbitals pointing directly toward the ligand will increase in energy; otherwise, energy will decrease for orbitals distant from the ligands. However, the charge barycenter is always preserved. The common complexes considered are octahedral, tetrahedral, trigonal bipyramidal, pentagonal and bipyramidal, as well as complexes that result from distortions of the octahedral complexes (square pyramidal, square planar) [1]. The "complex" menu allows you to select the spatial geometry.

By varying the ligand distance, it is possible to observe the splitting of the -orbitals. Initially degenerate, their splitting increases as the ligands get closer. The dashed line represents the charge barycenter. In the last two cases, the slider pushes away one or two ligands into axial positions of the octahedral complex.

To visualize the -orbitals, uncheck the "hide/show -orbital" checkbox and use the "-orbital" control is to select one out of the five -orbitals.


Contributed by: D. Meliga and S. Z. Lavagnino (May 2018)
Open content licensed under CC BY-NC-SA



Snapshot 1: the splitting caused by the tetragonal field is shown; three orbitals increase their energy, while two decrease it

Snapshot 2: the splitting caused by the octagonal field is shown; three orbitals decrease their energy, while two increase it

Snapshot 3: planar complex derived from the octagonal field; starting levels are represented in red, while the final situation is black


[1] C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 3rd ed., London: Pearson Education, Ltd., 2008.

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