Crystal Field Theory: H. Bethe and V. Bleck proposed the CFT Theory to explain bonding, electronic spectra, magnetism, etc. The ions or molecules which donate a pair of electrons to the central metal atom or ion and form coordinate bonds are called ligands.

What happens when these ligands approach the central metal atom? Do five degenerate d-orbitals of metal remain the same, or do they split into different energy levels? In this article, we will discuss Crystal field theory and the Crystal field effect in detail; scroll down to learn more. 

What is Crystal Field Theory?

The crystal field theory (CFT) was proposed by H. Bethe and V. Bleck. This theory explains the bonding, properties, electronic spectra, and magnetism of metal complexes more clearly.

The conversion of five degenerate d-orbitals of the metal ion into different sets of orbitals having different energies in the presence of a crystal field of ligands is called crystal field splitting. Crystal field splitting forms the basis of crystal field theory.

Postulates of Crystal Field Theory

The postulates of CFT Theory is mentioned below:

1. The crystal field theory considers that the metal ion is situated in an electric field caused by the surrounding ligands.
2. The attraction between the central metal and the ligand in a complex is purely electrostatic. The negative end of the dipole of the neutral molecule ligand is directed towards the metal ion.
3. The transition metal or ion is considered as a positive ion of charge equal to the oxidation state.
4. The transition metal atom or ion is surrounded by a definite number of ligands, it may be negative ion or neutral molecules having lone pairs of electrons.
5. The ligands are considered as point charges and produce an electric field. This electric field changes the energy of the orbitals on the metal atom or ions.
6. Due to the repulsive force between the central metal ion and ligand, the electrons on the metal ion occupy the \({\rm{d}}\)-orbitals as far as possible from the direction of approach of the ligand.
7. There is no interaction between the metal orbital and ligand orbitals.
8. In an isolated metal atom or ion, all the orbitals have the same energy, i.e., all five d orbitals \(\left( {{{\rm{d}}_{{\rm{xy}}}},{\mkern 1mu} {{\rm{d}}_{{\rm{xz}}}},{\mkern 1mu} {{\rm{d}}_{{\rm{yz}}}},{\mkern 1mu} {{\rm{d}}_{{{\rm{x}}^{\rm{2}}}{\rm{ – }}{{\rm{y}}^{\rm{2}}}}}} \right.{\rm{and}}\left. {{{\rm{d}}_{{{\rm{z}}^2}}}} \right)\) are degenerate.

9. If the central metal atom or ion is surrounded by the spherical symmetrical field of negative charges, the \({\rm{d}}\)-orbitals remain degenerate. However, the energy of the orbitals is raised due to the repulsion between the field and the electron on the metal atom or ion.
10. In most transition metal complexes, the \({\rm{d}}\)-orbitals are affected differently, and their degeneracy gets lost due to the field produced by the unsymmetrical ligand.

Spectrochemical Series

The crystal field splitting depends upon the nature of the ligand. The ligands which cause only a small crystal field splitting are called weak field ligands. The ligands which cause a large crystal field splitting are called strong field ligands.

The arrangement of common ligands in the ascending order of crystal field splitting \(\left( \Delta \right)\) is called spectrochemical series. The spectrochemical series in the increasing order of crystal field splitting is:

\(\begin{array}{l}
{{\rm{I}}^{\rm{ – }}} < {\rm{B}}{{\rm{r}}^{\rm{ – }}} < {{\rm{S}}^{{\rm{2 – }}}} < {\rm{C}}{{\rm{l}}^{\rm{ – }}} < {\rm{NO}}_3^ –  < {{\rm{F}}^{\rm{ – }}} < {\rm{O}}{{\rm{H}}^{\rm{ – }}} < {\rm{EtO}}{{\rm{H}}^{\rm{ – }}} < {{\rm{C}}_2}{\rm{O}}_4^{2 – } < {{\rm{H}}_2}{\rm{O}} <  < {\rm{EDTA}}\\
< {\rm{N}}{{\rm{H}}_3} < {\rm{Py}} < {\rm{Ethylenediamine}} < {\rm{dipyridyl}} < {\rm{0 – phenanthroline}} < {\rm{NO}}_2^ –  < {\rm{C}}{{\rm{N}}^ – } < {\rm{CO}}
\end{array}\)

Crystal Field Theory for Octahedral Complexes

In the octahedral complex ion, the ligand is represented by small negative charges and the metal ion by positive change.

In octahedral complexes, as the ligands approach metal ions, there is repulsion between the ligands and the \({\rm{d}}\)-orbitals, thereby raising their energy relative to that of the ion. In five \({\rm{d}}\)-orbitals, \({{\rm{d}}_{{{\rm{x}}^{\rm{2}}}{\rm{ – }}{{\rm{y}}^{\rm{2}}}}}\) and \({{\rm{d}}_{{{\rm{z}}^{\rm{2}}}}}\) orbitals have greater repulsion with the ligands as compared to remaining three \({\rm{d}}\)-orbitals, i.e., \({{\rm{d}}_{{\rm{xy}}}},{\mkern 1mu} {{\rm{d}}_{{\rm{xz}}}}\) and \({{\rm{d}}_{{\rm{yz}}}}.\)

Therefore, the energies of \({{\rm{d}}_{{\rm{xy}}}},{\mkern 1mu} {{\rm{d}}_{{\rm{xz}}}}\) and \({{\rm{d}}_{{\rm{yz}}}}\) are lower than those of \({{\rm{d}}_{{{\rm{x}}^{\rm{2}}}{\rm{ – }}{{\rm{y}}^{\rm{2}}}}}\) and \({{\rm{d}}_{{{\rm{z}}^{\rm{2}}}}}\) orbitals.

The \({{\rm{d}}_{{\rm{xy}}}},{\mkern 1mu} {{\rm{d}}_{{\rm{xz}}}}\) and \({{\rm{d}}_{{\rm{yz}}}}\) orbitals of lower energy are called \({{\rm{t}}_{{\rm{2g}}}}\) orbitals and \({{\rm{d}}_{{{\rm{x}}^{\rm{2}}}{\rm{ – }}{{\rm{y}}^{\rm{2}}}}},{\mkern 1mu} \,{{\rm{d}}_{{{\rm{z}}^{\rm{2}}}}}\) orbitals of higher energy are called \({{\rm{e}}_{\rm{g}}}\) orbitals.

The difference of energy between the two sets of d- orbitals is called crystal field splitting energy or crystal field stabilisation energy (CFSE). It is represented as \({{\rm{\Delta }}_{\rm{O}}}\), where ‘\({\rm{O}}\)’ stands for the octahedral complex.

The \({{\rm{e}}_{\rm{g}}}\) orbitals have \({\rm{ + 0}}{\rm{.6}}{{\rm{\Delta }}_{\rm{0}}}\) or \(\frac{{\rm{3}}}{{\rm{5}}}{{\rm{\Delta }}_{\rm{0}}}\) above the average energy level and \({{\rm{t}}_{{\rm{2g}}}}\) orbitals are \({\rm{ – 0}}{\rm{.4}}{{\rm{\Delta }}_{\rm{0}}}\) or \({\rm{ – }}\frac{{\rm{2}}}{{\rm{5}}}{{\rm{\Delta }}_{\rm{0}}}\) below the average.

In octahedral complexes, strong field ligands have high \({{\rm{\Delta }}_{\rm{0}}}\) value and they are low spin complexes. Example: \({\left[ {{\rm{Fe}}{{({\rm{CN}})}_6}} \right]^{4 – }}\) and \({\left[ {{\rm{Co}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_6}} \right]^{3 + }}\)

The weak field ligands have low \({{\rm{\Delta }}_{\rm{0}}}\) value and they are high spin complexes.

Example: \({\left[ {{\rm{Fe}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_6}} \right]^{2 + }}\) and \({\left[ {{\rm{Co}}{{\rm{F}}_6}} \right]^{3 – }}\)

Crystal Field Theory for Tetrahedral Complexes

The splitting pattern of tetrahedral complexes is the reverse of the splitting pattern of octahedral complexes. In tetrahedral complexes, \({{\rm{d}}_{{{\rm{x}}^{\rm{2}}}{\rm{ – }}{{\rm{y}}^{\rm{2}}}}}\) and \({{\rm{d}}_{{{\rm{z}}^{\rm{2}}}}}\) orbitals have lower energy than \({{\rm{d}}_{{\rm{xy}}}},{\mkern 1mu} {{\rm{d}}_{{\rm{xz}}}}\) and \({{\rm{d}}_{{\rm{yz}}}}\) orbitals.

The difference of energy between two energy levels is \({{\rm{\Delta }}{\rm{t}}}\left( {{{\rm{\Delta }}{\rm{t}}}{\rm{ = }}\frac{{\rm{4}}}{{\rm{9}}}{{\rm{\Delta }}_{\rm{0}}}} \right)\). Due to this small energy gap, electrons do not pair. Therefore, tetrahedral complexes have a high spin configuration.

Crystal Field Stabilisation Energy

The difference of energy between the two sets of \({\rm{d}}\)-orbitals is called crystal field splitting energy or crystal field stabilisation energy (CFSE). It is represented as \({\rm{\Delta }}\).

Crystal Field Stabilization Energy Table

Crystal field stabilisation energy (CFSE) of tetrahedral complex is as follow:

Number of \({\rm{d}}\)-electrons	Tetrahedral CFSE
\(1\) or \(6\)	\({\rm{ – 0}}{\rm{.6}}{{\rm{\Delta }}_{\rm{t}}}\)
\(2\) or \(7\)	\({\rm{ – 1}}{\rm{.2}}{{\rm{\Delta }}_{\rm{t}}}\)
\(3\) or \(9\)	\({\rm{ – 0}}{\rm{.8}}{{\rm{\Delta }}_{\rm{t}}}\)
\(4\) or \(9\)	\({\rm{ – 0}}{\rm{.4}}{{\rm{\Delta }}_{\rm{t}}}\)
\(5\) or \(10\)	zero

Crystal field stabilisation energy (CFSE) of octahedral complex is as follow:

Configuration	Strong field (low spin)	CFSE	Weak field (high spin)	CFSE
\({{\rm{d}}^1}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{1}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 0}}{\rm{.4}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{1}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 0}}{\rm{.4}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^2}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{2}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 0}}{\rm{.8}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{2}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 0}}{\rm{.8}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^3}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{3}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 1}}{\rm{.2}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{3}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 1}}{\rm{.2}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^4}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{4}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 1}}{\rm{.6}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{3}}}{\rm{e}}{{\rm{g}}^{\rm{1}}}\)	\({\rm{ – 0}}{\rm{.6}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^5}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{5}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 2}}{\rm{.0}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{3}}}{\rm{e}}{{\rm{g}}^{\rm{2}}}\)	\({\rm{0}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^6}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{0}}}\)	\({\rm{ – 2}}{\rm{.4}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{4}}}{\rm{e}}{{\rm{g}}^{\rm{2}}}\)	\({\rm{ – 0}}{\rm{.4}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^7}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{1}}}\)	\({\rm{ – 1}}{\rm{.8}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{5}}}{\rm{e}}{{\rm{g}}^{\rm{2}}}\)	\({\rm{ – 0}}{\rm{.8}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^8}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{2}}}\)	\({\rm{ – 1}}{\rm{.2}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{2}}}\)	\({\rm{ – 1}}{\rm{.2}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^9}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{3}}}\)	\({\rm{ – 0}}{\rm{.6}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{3}}}\)	\({\rm{ – 0}}{\rm{.6}}{{\rm{\Delta }}_{\rm{0}}}\)
\({{\rm{d}}^10}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{4}}}\)	\({\rm{0}}{{\rm{\Delta }}_{\rm{0}}}\)	\({{\rm{t}}_{\rm{2}}}{{\rm{g}}^{\rm{6}}}{\rm{e}}{{\rm{g}}^{\rm{4}}}\)	\({\rm{0}}{{\rm{\Delta }}_{\rm{0}}}\)

Factors Affecting the Magnitude of Orbital Splitting Energy \(\left( {\rm{\Delta }} \right)\)

1. Higher the oxidation state of the central ion, the larger the value of orbital splitting energy.
2. In d-block (transition) elements, \({\rm{\Delta }}\) value increases from \({\rm{3d}}\) to \({\rm{4d}}\) to \({\rm{5d}}\) elements. Therefore, the elements of the second series \({\rm{4d}}\) and third series \({\rm{5d}}\) have a greater tendency to form low spin complexes than the first \(\left( {{\rm{3d}}} \right)\) transition series.
3. The \({\rm{\Delta }}\) value of the coordination entity helps in the determination of the type of complex. The \({\rm{\Delta }}\) value of the tetrahedral complex is nearly \({\rm{50\% }}\) of the octahedral complex.

For the same metal ion, different ligands have different splitting amounts.

What are the Limitations of Crystal Field Theory?

The crystal field theory could explain the formation, structure, optical, and magnetic properties of the coordination compound quite satisfactorily. But the crystal field theory could not explain the following factors.

1. The existence of covalent bonding in some transition metal complexes.
2. The order of ligands in the spectrochemical series. As ligands are considered as point charges, the anionic ligands should exert a greater splitting effect. However, the anionic ligands are placed at the lower end of the spectrochemical series.

Summary About CFT Theory

The crystal field theory explains the bonding, electronic spectra, properties, and magnetism of metal complexes. It was proposed by H. Bethe and V. Bleck. Furthermore, crystal field splitting is the basis of crystal field theory. The crystal field splitting is dependent on the nature of the ligand. Furthermore, we also learned that the crystal field stabilisation energy is described as the difference of energy between the two sets of \({\rm{d}}\)-orbitals.

It is important to note that the CFT was able to explain bonding, electronic spectra, etc., however, it failed to explain some of the factors. The crystal field theory failed to explain the presence of covalent bonding in certain transition metal complexes.

FAQs on Crystal Field Theory

Q What is crystal field theory?
Ans: The conversion of five degenerate d-orbitals of the metal ion into different sets of orbitals having different energies in the presence of a crystal field of ligands is called crystal field splitting. Crystal field splitting forms the basis of crystal field theory.

Q What are the main features of crystal field theory?
Ans: The crystal field theory considers that the metal ion is situated in an electric field caused by the surrounding ligands. The attraction between the central metal and the ligand in a complex is purely electrostatic. The negative end of the dipole of the neutral molecule ligand is directed towards the metal ion. The transition metal or ion is considered as a positive ion of charge equal to the oxidation state. The transition metal atom or ion is surrounded by a definite number of ligands, it may be negative ion or neutral molecules having lone pairs of electrons.

Q Define crystal field stabilisation energy.
Ans: The Crystal field stabilisation energy is defined as the difference of energy between the two sets of \({\rm{d}}\)-orbitals. It is represented as \({\rm{\Delta }}\).

Q How do you use crystal field theory?
Ans: Crystal field theory explains bonding properties, electronic spectra and magnetism of metal complexes. In octahedral complexes, strong field ligands have high \({{\rm{\Delta }}_{\rm{0}}}\) value and they are low spin complexes. The weak field ligands have low \({{\rm{\Delta }}_{\rm{0}}}\) value and they are high spin complexes.

Q What are the factors affecting crystal field splitting?
Ans: The nature of the ligand and oxidation state of the central atom affects the crystal field splitting. Higher the oxidation state of the central ion, the larger the value of orbital splitting energy. For the same metal ion, different ligands have different splitting magnitudes.