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Crystal Field Theory Versus Valence Bond Theory Engineering Essay


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Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck van VlecK in the 1930s. CFT was subsequently combined with molecular orbital theory to form the more realistic and complex ligand field theory (LFT), which delivers insight into the process of chemical bonding in transition metal complexes.

In the ionic CFT, it is assumed that the ions are simple point charges. When applied to alkali metal ions containing a symmetric sphere of charge, calculations of energies are generally quite successful. The approach taken uses classical potential energy equations that take into account the attractive and repulsive interactions between charged particles (that is, Coulomb's Law interactions).

Electrostatic Potential is proportional to q1 * q2/r

where q1 and q2 are the charges of the interacting ions and r is the distance separating them. This leads to the correct prediction that large cations of low charge, such as K+ and Na+, should form few coordination compounds.

For transition metal cations that contain varying numbers of d electrons in orbitals that are NOT spherically symmetric, however, the situation is quite different. The shape and occupation of these d-orbitals then becomes important in an accurate description of the bond energy and properties of the transition metal compound

According to CFT, the interaction between a transition metal and ligands arises from the attraction between the positively charged metal cation and negative charge on the non-bonding electrons of the ligand. The theory is developed by considering energy changes of the five degenerate d-orbitals upon being surrounded by an array of point charges consisting of the ligands. As a ligand approaches the metal ion, the electrons from the ligand will be closer to some of the d-orbitals and farther away from others causing a loss of degeneracy. The electrons in the d-orbitals and those in the ligand repel each other due to repulsion between like charges. Thus the d-electrons closer to the ligands will have a higher energy than those further away which results in the d-orbitals splitting in energy.

This splitting is affected by the following factors:-

1. The nature of the metal ion.

2. The metal's oxidation state. A higher oxidation state leads to a larger splitting.

3. The arrangement of the ligands around the metal ion.

4. The nature of the ligands surrounding the metal ion. The stronger the effect of the ligands then the greater the difference between the high and low energy 3d groups.

The most common type of complex is octahedral; here six ligands form an octahedron around the metal ion. In octahedral symmetry the d-orbitals split into two sets with an energy difference, Δoct (the crystal-field splitting parameter) where the dxy, dxz and dyz orbitals will be lower in energy than the dz2 and dx2-y2, which will have higher energy, because the former group are farther from the ligands than the latter and therefore experience less repulsion. The three lower-energy orbitals are collectively referred to as t2g, and the two higher-energy orbitals as eg. (These labels are based on the theory of molecular symmetry). Typical orbital energy diagrams are given below in the section High-spin and low-spin.

Tetrahedral complexes are the second most common type; here four ligands form a tetrahedron around the metal ion. In a tetrahedral crystal field splitting the d-orbitals again split into two groups, with an energy difference of Δtet where the lower energy orbitals will be dz2 and dx2-y2, and the higher energy orbitals will be dxy, dxz and dyz - opposite to the octahedral case. Furthermore, since the ligand electrons in tetrahedral symmetry are not oriented directly towards the d-orbitals, the energy splitting will be lower than in the octahedral case. Square planar and other complex geometries can also be described by CFT.

The size of the gap Δ between the two or more sets of orbitals depends on several factors, including the ligands and geometry of the complex. Some ligands always produce a small value of Δ, while others always give a large splitting. The reasons behind this can be explained by ligand field theory. The spectrochemical series is an empirically-derived list of ligands ordered by the size of the splitting Δ that they produce (small Δ to large Δ; see also this table):

I− < Br− < S2− < SCN− < Cl− < NO3− < N3− < F− < OH− < C2O42− < H2O < NCS− < CH3CN < py < NH3 < en < 2,2'-bipyridine < phen < NO2− < PPh3 < CN− < CO

The oxidation state of the metal also contributes to the size of Δ between the high and low energy levels. As the oxidation state increases for a given metal, the magnitude of Δ increases. A V3+ complex will have a larger Δ than a V2+ complex for a given set of ligands, as the difference in charge density allows the ligands to be closer to a V3+ ion than to a V2+ ion. The smaller distance between the ligand and the metal ion results in a larger Δ, because the ligand and metal electrons are closer together and therefore repel more.

High-spin and low-spin

[Fe(NO2)6]3− crystal field diagram Ligands which cause a large splitting Δ of the d- orbitals are referred to as strong-field ligands, such as CN− and CO from the spectrochemical series. In complexes with these ligands, it is unfavourable to put electrons into the high energy orbitals. Therefore, the lower energy orbitals are completely filled before population of the upper sets starts according to the Aufbau principle. Complexes such as this are called "low spin". For example, NO2− is a strong-field ligand and produces a large Δ. The octahedral ion [Fe(NO2)6]3−, which has 5 d-electrons, would have the octahedral splitting diagram shown at right with all five electrons in the t2g level.

[FeBr6]3− crystal field diagram Conversely, ligands (like I− and Br−) which cause a small splitting Δ of the d-orbitals are referred to as weak-field ligands. In this case, it is easier to put electrons into the higher energy set of orbitals than it is to put two into the same low-energy orbital, because two electrons in the same orbital repel each other. So, one electron is put into each of the five d-orbitals before any pairing occurs in accord with Hund's rule and "high spin" complexes are formed. For example, Br− is a weak-field ligand and produces a small Δoct. So, the ion [FeBr6]3−, again with five d-electrons, would have an octahedral splitting diagram where all five orbitals are singly occupied.

In order for low spin splitting to occur, the energy cost of placing an electron into an already singly occupied orbital must be less than the cost of placing the additional electron into an eg orbital at an energy cost of Δ. As noted above, eg refers to the dz2 and dx2-y2 which are higher in energy than the t2g in octahedral complexes. If the energy required to pair two electrons is greater than the energy cost of placing an electron in an eg, Δ, high spin splitting occurs.

The crystal field splitting energy for tetrahedral metal complexes (four ligands) is referred to as Δtet, and is roughly equal to 4/9Δoct (for the same metal and same ligands). Therefore, the energy required to pair two electrons is typically higher than the energy required for placing electrons in the higher energy orbitals. Thus, tetrahedral complexes are usually high-spin.

The use of these splitting diagrams can aid in the prediction of the magnetic properties of coordination compounds. A compound that has unpaired electrons in its splitting diagram will be paramagnetic and will be attracted by magnetic fields, while a compound that lacks unpaired electrons in its splitting diagram will be diamagnetic and will be weakly repelled by a magnetic field.

Crystal field stabilization energy

The crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands. It arises due to the fact that when the d-orbitals are split in a ligand field (as described above), some of them become lower in energy than before with respect to a spherical field known as the barycenter in which all five d-orbitals are degenerate. For example, in an octahedral case, the t2g set becomes lower in energy than the orbitals in the barycenter. As a result of this, if there are any electrons occupying these orbitals, the metal ion is more stable in the ligand field relative to the barycenter by an amount known as the CFSE. Conversely, the eg orbitals (in the octahedral case) are higher in energy than in the barycenter, so putting electrons in these reduces the amount of CFSE.

Octahedral crystal field stabilization energyIf the splitting of the d-orbitals in an octahedral field is Δoct, the three t2g orbitals are stabilized relative to the barycenter by 2/5 Δoct, and the eg orbitals are destabilized by 3/5 Δoct. As examples, consider the two d5 configurations shown further up the page. The low-spin (top) example has five electrons in the t2g orbitals, so the total CFSE is 5 x 2/5 Δoct = 2Δoct. In the high-spin (lower) example, the CFSE is (3 x 2/5 Δoct) - (2 x 3/5 Δoct) = 0 - in this case, the stabilization generated by the electrons in the lower orbitals is canceled out by the destabilizing effect of the electrons in the upper orbitals.

Crystal Field stabilization is applicable to transition-metal complexes of all geometries. Indeed, the reason that many d8 complexes are square-planar is the very large amount of crystal field stabilization that this geometry produces with this number of electrons.

Explaining the colours of transition metal complexes

The bright colours exhibited by many coordination compounds can be explained by Crystal Field Theory. If the d-orbitals of such a complex have been split into two sets as described above, when the molecule absorbs a photon of visible light one or more electrons may momentarily jump from the lower energy d-orbitals to the higher energy ones to transiently create an excited state atom. The difference in energy between the atom in the ground state and in the excited state is equal to the energy of the absorbed photon, and related inversely to the wavelength of the light. Because only certain wavelengths (λ) of light are absorbed - those matching exactly the energy difference - the compounds appears the appropriate complementary colour.

As explained above, because different ligands generate crystal fields of different strengths, different colours can be seen. For a given metal ion, weaker field ligands create a complex with a smaller Δ, which will absorb light of longer λ and thus lower frequency ν. Conversely, stronger field ligands create a larger Δ, absorb light of shorter λ, and thus higher ν. It is, though, rarely the case that the energy of the photon absorbed corresponds exactly to the size of the gap Δ; there are other things (such as electron-electron repulsion and Jahn-Teller effects) that also affect the energy difference between the ground and excited states

Crystal field splitting diagrams

Crystal field splitting diagrams


Pentagonal bipyramidal

Square antiprismatic

Square planar

Square pyramidal


Trigonal bipyramidal


CFT ignores the attractive forces the d-electrons of the metal ion and neuclear charge on the ligand atom. Therefore all the properties are dependent upon the ligand orbitals and their interaction with metal orbitals are not explained.

In CFT model partial covalency of metal -ligand bond is not taken into consideration According to CFT metal-ligand bonding is purely electrostatic.

In CFT only d-electrons of the metal ion are considered .the other metal orbitals such as s,Px,Py,Pz are taken into considerations.

In CFT π-orbitals of ligand are not considered

The theory cant explain the relative strength of the ligands i.e. it cannot explain that why water is stronger than OH according to spectrochemical series .

It does not explain the charge transfer spectra on the intensities of the absorption bands.


In chemistry, valence bond theory is one of two basic theories, along with molecular orbital theory, that developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine on molecular formation to give individual chemical bonds. In contrast, molecular orbital theory has orbitals that cover the whole molecule

According to this theory a covalent bond is formed between the two atoms by the overlap of half filled valence atomic orbitals of each atom containing one unpaired electron. A valence bond structure is similar to a Lewis structure, but where a single Lewis structure cannot be written, several valence bond structures are used. Each of these VB structures represents a specific Lewis structure. This combination of valence bond structures is the main point of resonance theory. Valence bond theory considers that the overlapping atomic orbitals of the participating atoms form a chemical bond. Because of the overlapping, it is most probable that electrons should be in the bond region. Valence bond theory views bonds as weakly coupled orbitals (small overlap). Valence bond theory is typically easier to employ in ground state molecules.


The overlapping atomic orbitals can differ. The two types of overlapping orbitals are sigma and pi. Sigma bonds occur when the orbitals of two shared electrons overlap head-to-head. Pi bonds occur when two orbitals overlap when they are parallel. For example, a bond between two s-orbital electrons is a sigma bond, because two spheres are always coaxial. In terms of bond order, single bonds have one sigma bond, double bonds consist of one sigma bond and one pi bond, and triple bonds contain one sigma bond and two pi bonds. However, the atomic orbitals for bonding may be hybrids. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an atomic orbital with the proper character for the bonding is called hybridization


Valence bond theory now complements Molecular Orbital Theory (MO theory), which does not adhere to the VB idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can extend over the entire molecule. MO theory can predict magnetic properties in a straightforward manner, while valence bond theory gives similar results but is more complicated. Valence bond theory views aromatic properties of molecules as due to resonance between Kekule, Dewar and possibly ionic structures, while molecular orbital theory views it as delocalization of the π-electrons. The underlying mathematics are also more complicated limiting VB treatment to relatively small molecules. On the other hand, VB theory provides a much more accurate picture of the reorganization of electronic charge that takes place when bonds are broken and formed during the course of a chemical reaction. In particular, valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple molecular orbital theory predicts dissociation into a mixture of atoms and ions.

More recently, several groups have developed what is often called modern valence bond theory. This replaces the overlapping atomic orbitals by overlapping valence bond orbitals that are expanded over a large number of basis functions, either centered each on one atom to give a classical valence bond picture, or centered on all atoms in the molecule. The resulting energies are more competitive with energies from calculations where electron correlation is introduced based on a Hartree-Fock reference wavefunction.

Applications of VB theory

An important aspect of the VB theory is the condition of maximum overlap which leads to the formation of the strongest possible bonds. This theory is used to explain the covalent bond formation in many molecules.

For Example in the case of F2 molecule the F - F bond is formed by the overlap of pz orbitals of the two F atoms each containing an unpaired electron. Since the nature of the overlapping orbitals are different in H2 and F2 molecules, the bond strength and bond lengths differ between H 2 and F2 molecules.

In a HF molecule the covalent bond is formed by the overlap of 1s orbital of H and 2pz orbital of F each containing an unpaired electron. Mutual sharing of electrons between H and F results in a covalent bond between HF


Some of the properties of complexes which could not be explained on the basis of valence bond theory are satisfactorily explained by crystal field theory.CFT is thus definitely an improvement over vbt these are the following merits of cft over vbt will prove that statement:

CFT predicts a gradual change in magnetic properties of complexes rather than the abrupt change predicted by VBT .

In some complexes ,when Δ is very close to P, simple temperature changes may affect the magnetic properties of complexes .Thus the CFT provides theoretical basis for understanding and predicting the variations of magnetic moments with temperature as well as detailed magnetic properties of complexes ,this is just in contrast of VBT which can not predict or explain magnetic behaviour beyond the level of specifying the number of unpaired electrons.

Though the assumptions inherent in VBT and CFT are vastly different , the main difference lies in their description of the orbitals not occupied in the low spin states .VBT forbids their use as they are involved in forming hybrid orbitals, while they are involved in forming hybrid orbitals, while CFT strongly discourages their use as they are repelled by the ligands.

According to VBT, the bond between the metal and the ligand is covalent,,while according to CFT it is purely ionic. The bond is now considered to have both ionic and covalent charachter .Unlike valence bond theory

CFT provides a framework for the ready interpretation of such phenomenon as tretagonal distortions.

CFT provides satisfactory explanation for the colour of transition metal complexes , i.e. spectral properties ofcomplexes, i.e. spectral properties of complexes.

CFT can semiquantitatevily explain certain thermodynamic and kinetic properties.

CFT makes possible a clear understanding of stereochemical properties of complexes.


J. H. Van Vleck, "Theory of the Variations in Paramagnetic Anisotropy Among Different Salts of the Iron Group", Phys. Rev. 41, 208 - 215 (1932)[1]

Zumdahl, Steven S. Chemical Principles Fifth Edition. Boston: Houghton Mifflin Company, 2005. 550-551,957-964.

3) Silberberg, Martin S. Chemistry: The Molecular Nature of Matter and Change, Fourth Edition. New York: McGraw Hill Company, 2006. 1028 -1034.

4 )D. F. Shriver and P. W. Atkins Inorganic Chemistry 3rd edition, Oxford University Press, 2001. Pages: 227-236.

5) http://wwwchem.uwimona.edu.jm:1104/courses/CFT.html

Murrel, J. N.; S. F. Tedder (1985). The Chemical Bond. John Wiley & Sons. ISBN 0-471-90759-6

6) I. Hargittai, When Resonance Made Waves, The Chemical Intelligencer 1, 34 (1995))

7) Shaik, Sason S.; Phillipe C. Hiberty (2008). A Chemist's Guide to Valence Bond Theory. New Jersey: Wiley-Interscience.

8)text book of cordination chemistry by dr.R.K. sharma pg 61,62

9)engineering chemistry by A.K.pahari,B.S.chauhan.

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