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# Crystal Field Theory

Crystal field theory is a model that describes how the electrons fill in the outer energy levels or orbital in the presence of ligands. Crystal field theory also describes the strength of the bond, but it cannot attempt to describe the actual bonding.

The magnetic properties, hydration enthalpies, and color are changed according to the strength of ligands, which are the molecular compounds are ions that attach to the central transition metal to form a co-ordination complex. In particular optical colors, crystal field theory to describe various spectroscopic of transition metal co-ordination complex.

Crystal field theory was developed in 1929 by the physicist Hans Bethe. He describes the magnetic and electronic structure of crystal solid. Further developed of crystal field theory was done by John Hasbrouck Van Vleck, in 1930’s. He describes that the interaction between the central metal ions that is surrounded by the anions. Crystal field theory along with the molecular orbital theory form the ligand field theory, which gives an insight into the various method of chemical bonding within an transition metal complex.

Bonding in a complex ion is due to electrostatic interactions between the positively charged nucleus of the central metal ion and electrons in the ligands i.e., attractive as well as repulsive interactions.

1. The attractive forces will arrive due to the positive metal ion and the negatively charged ligand.
2. The repulsive forces arise between the lone pairs on the ligand and the electrons in the d-orbital of the metal.

 Related Calculators Electric Field Calculator

## Crystal Field Splitting Theory

Crystal field splitting theory was developed to describe the complexes important properties such as magnetism, oxidation states, absorption spectra & coordination. The interaction of the d-orbital is entirely dependent on the central atom with ligands, which are nothing but considered as the point charges, is the basis of these model.

According to crystal field theory, the attractive force between the central positively charged metal cation and the Ligand's negatively charged non-bonding electrons spread in a complex is nothing but electrostatic in nature. Crystal field theory is developed by basically keeping in context of the changes in the energy level of the 05 degenerate d-orbital’s being surrounded by an series of point charges involving the ligands.

The loss of degeneracy is because of the approaching ligand towards the metal ion and then the ligand electrons getting close to few d-orbitals and move away from other d-orbital. The repelling in between the electrons which are present in the d-orbital and those in the ligand is because of the like charges repulsion and hence the electrons closer to ligands will have a high energy compared with the ones which are far away resulting in d-orbital’s split in energy.

The following are the important factors that can be affecting the splitting in energy.
1. The characteristics of the ligands surrounding the metal ions. If the ligand is stronger which resulting the greater in the splitting.
2. The nature of metal ions.
3. Oxidation state of the central metals, as a elevated oxidation state results in larger splitting.
4. The arrangement of the ligands surrounding the metal ions.
5. Orbital size.
6. Complex geometry.

### Orbital Splitting

dxy , dzx, dyz, dx2-y2 and dz2 are five symbol of d-orbital’s. In a complex they are aligned differently in comparison to the incoming charge. Basically now depending completely upon the geometry of the complex, some of the d-orbital point towards the ligands directly and while some of them point between the ligands. Those pointing at the ligands would come across more repulsion in-between the same species of electrons and the ones coming from ligands, compared to those which do not point directly at the respective ligands. Thus, the orbital facing towards the ligands will have higher energy level but at the same time the stability will be less. Now all the d-orbital’s are found to be no longer equivalent and thus giving rise to the orbital splitting phenomenon, and the energy difference(D) between the more repelled and the less repelled orbital’s are better known as the crystal field splitting parameter.

Based upon the overall crystal field splitting energy magnitude, the electrons can either go in high or low spin arrangement.

## Crystal Field Stabilization Energy

• Crystal field stabilization energy is the stability, which basically occurs by placing a transition group metallic ion within the crystal field, generated by a set of ligands.
• Crystal filed stabilization energy arises only because of the d-orbital split in a ligand field.
• A few of these become lower in energy in comparison than before in respect to a spherical field better known as bary center which has all the 05 d-orbitals degenerated.
• Like in the case of octahedral, the t2g set becomes lower in energy in comparison with the orbitals in the bary center.
• The system gains high stability due to the rearrangement of the d electron filling in the d-orbital’s of lower energy level.
• The consequent gain in bonding energy is called as crystal field stabilization energy.
Conversely, in an octahedral case, the ‘eg’ orbitals are higher in energy compared with the bary center, and so placing the electrons in these results in the reduction of the crystal field stabilization energy amount.

If ∆oct is the splitting of the d-orbital in an octahedral field, the three t2g orbitals are stabilized relative to the bary center by 2/5 ∆oct, and the ‘eg’ orbital’s are destabilized by 3/5 ∆oct.

Crystal field stabilization is applicable to all geometries of transition metal complexes. Many of the d8 complexes are shaped square planar and the reason behind this is the very large amount of crystal field stabilization that this geometry provides with respect to the number of electrons.

Crystal field stabilization energy for an octahedral complex is,

CSFE = - 0.4 x n(t2g) + 0.6 x n(eg) ∆o

Where,

n(t2g) and n(eg) – number of electrons occupying the respective energy levels

The magnitude of the tetrahedral splitting energy only 4/9 of the octahedral splitting energy, which may represented by

∆t = 4/9 ∆o
CSFE = 0.4 x n(t2g) - 0.6 x n(eg) ∆t

## Crystal Field Theory Color

Crystal field theory color can explain the bright colors exhibited by many co-ordination compounds. If the d-orbital’s complex have been split in to two sets with an energy difference, when the molecules absorbs the photon of visible light the it results in one or more than one electrons can jump from lower energy level of d-orbital’s to higher energy level of d-orbital’s ones to form an excited atom.

The energy contained within the observed photon is equivalent to the difference in energy between the ground state atom with that of the excited state. The energy difference (D) is also related inversely to the wave length of the light. Because only certain wavelength (λ) of lights are absorbed that will matching or struck exactly the energy difference, the compound appears the appropriate complementary color, since the complex absorbs light of that frequency and reflects the rest.

We can see the different color of complexes, which is due to the different ligands, generates different strength of crystal field and different effect on the magnitude of the splitting of d-orbital, ∆. There is a formation of a complex between the weaker field ligands with smaller ∆, which will absorb light of longer wave length λ and thus lower frequency ν.

On the other hand a stronger field ligand creates a complex with larger ∆, which will absorb light of shorter wave length λ and thus higher frequency ν. The absorbed photon energy relates exactly to the gap size ∆, there are things like the electron-electron repulsion and the Jahn teller effect also affect the energy difference (D) between the ground and exited states.

From the above shown figure, we can get the complement of a color. First find which color they absorbed and move across the wheel to the other side to get the complement.

For example, the complex [CO[NH3]6]+3 absorbs light with a wave length of 437nm which is in the blue violet region spectrum. If we look directly across the color wheel from blue violet region spectrum, these complexes will appear as yellow in color.

 Color of light absorbed Approx λ (nm) Color of light transmitted Red 700- 620 Green Orange 620- 580 Blue Yellow 580- 560 Violet Green 560- 490 Red Blue 490- 430 Orange Violet 430- 380 Yellow

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