Crystal Field Theory Versus Valence Bond Theory Engineering Essay

Crystal field theory is a theoretical account that describes the electronic construction of passage metal compounds, all of which can be considered coordination composites. CFT successfully accounts for some magnetic belongingss, colorss, hydration heat contents, and spinel constructions of passage metal composites, but it does non try to depict bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck new wave VlecK in the 1930s. CFT was later combined with molecular orbital theory to organize the more realistic and complex ligand field theory ( LFT ) , which delivers penetration into the procedure of chemical bonding in passage metal composites.

In the ionic CFT, it is assumed that the ions are simple point charges. When applied to alkali metal ions incorporating a symmetric domain of charge, computations of energies are by and large rather successful. The attack taken uses classical possible energy equations that take into history the attractive and abhorrent interactions between charged atoms ( that is, Coulomb ‘s Law interactions ) .

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Electrostatic Potential is relative to q1 * q2/r

where q1 and q2 are the charges of the interacting ions and R is the distance dividing them. This leads to the right anticipation that big cations of low charge, such as K+ and Na+ , should organize few coordination compounds.

For passage metal cations that contain changing Numberss of 500 negatrons in orbitals that are NOT spherically symmetric, nevertheless, the state of affairs is rather different. The form and business of these d-orbitals so becomes of import in an accurate description of the bond energy and belongingss of the passage metal compound

Harmonizing to CFT, the interaction between a passage metal and ligands arises from the attractive force between the positively charged metal cation and negative charge on the non-bonding negatrons of the ligand. The theory is developed by sing energy alterations of the five pervert d-orbitals upon being surrounded by an array of point charges dwelling of the ligands. As a ligand approaches the metal ion, the negatrons from the ligand will be closer to some of the d-orbitals and farther off from others doing a loss of degeneration. The negatrons 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 hold a higher energy than those farther off which consequences in the d-orbitals splitting in energy.

This splitting is affected by the undermentioned factors: –

1. The nature of the metal ion.

2. The metal ‘s oxidization province. A higher oxidization province leads to a larger splitting.

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

4. The nature of the ligands environing the metal ion. The stronger the consequence of the ligands so 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 symmetricalness the d-orbitals split into two sets with an energy difference, I”oct ( the crystal-field splitting parametric quantity ) where the dxy, dxz and dyz orbitals will be lower in energy than the dz2 and dx2-y2, which will hold higher energy, because the former group are further from the ligands than the latter and therefore experience less repulsive force. The three lower-energy orbitals are jointly referred to as t2g, and the two higher-energy orbitals as eg. ( These labels are based on the theory of molecular symmetricalness ) . Typical orbital energy diagrams are given below in the subdivision High-spin and low-spin.

Tetrahedral composites are the 2nd most common type ; here four ligands form a tetrahedron around the metal ion. In a tetrahedral crystal field dividing the d-orbitals once more split into two groups, with an energy difference of I”tet where the lower energy orbitals will be dz2 and dx2-y2, and the higher energy orbitals will be dxy, dxz and dyz – antonym to the octahedral instance. Furthermore, since the ligand negatrons in tetrahedral symmetricalness are non oriented straight towards the d-orbitals, the energy splitting will be lower than in the octahedral instance. Square planar and other complex geometries can besides be described by CFT.

The size of the spread I” between the two or more sets of orbitals depends on several factors, including the ligands and geometry of the composite. Some ligands ever produce a little value of I” , while others ever give a big splitting. The grounds 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 I” that they produce ( little I” to big I” ; see besides this tabular array ) :

Ia?’ & lt ; Bra?’ & lt ; S2a?’ & lt ; SCNa?’ & lt ; Cla?’ & lt ; NO3a?’ & lt ; N3a?’ & lt ; Fa?’ & lt ; OHa?’ & lt ; C2O42a?’ & lt ; H2O & lt ; NCSa?’ & lt ; CH3CN & lt ; py & lt ; NH3 & lt ; en & lt ; 2,2′-bipyridine & lt ; phen & lt ; NO2a?’ & lt ; PPh3 & lt ; CNa?’ & lt ; CO

The oxidization province of the metal besides contributes to the size of I” between the high and low energy degrees. As the oxidization province additions for a given metal, the magnitude of I” additions. A V3+ composite will hold a larger I” than a V2+ composite for a given set of ligands, as the difference in charge denseness 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 consequences in a larger I” , because the ligand and metal negatrons are closer together and hence drive more.

High-spin and low-spin

[ Fe ( NO2 ) 6 ] 3a?’ crystal field diagram Ligands which cause a big dividing I” of the d- orbitals are referred to as strong-field ligands, such as CNa?’ and CO from the spectrochemical series. In composites with these ligands, it is unfavorable to set negatrons into the high energy orbitals. Therefore, the lower energy orbitals are wholly filled before population of the upper sets starts harmonizing to the Aufbau rule. Complexes such as this are called “ low spin ” . For illustration, NO2a?’ is a strong-field ligand and produces a big I” . The octahedral ion [ Fe ( NO2 ) 6 ] 3a?’ , which has 5 d-electrons, would hold the octahedral splitting diagram shown at right with all five negatrons in the t2g degree.

[ FeBr6 ] 3a?’ crystal field diagram Conversely, ligands ( like Ia?’ and Bra?’ ) which cause a little splitting I” of the d-orbitals are referred to as weak-field ligands. In this instance, it is easier to set negatrons into the higher energy set of orbitals than it is to set two into the same low-energy orbital, because two negatrons in the same orbital repel each other. So, one negatron is put into each of the five d-orbitals before any coupling occurs in agreement with Hund ‘s regulation and “ high spin ” composites are formed. For illustration, Bra?’ is a weak-field ligand and produces a little I”oct. So, the ion [ FeBr6 ] 3a?’ , once more with five d-electrons, would hold an octahedral splitting diagram where all five orbitals are singly occupied.

In order for low spin splitting to happen, the energy cost of puting an negatron into an already singly occupied orbital must be less than the cost of puting the extra negatron into an eg orbital at an energy cost of I” . As celebrated above, eg refers to the dz2 and dx2-y2 which are higher in energy than the t2g in octahedral composites. If the energy required to partner off two negatrons is greater than the energy cost of puting an negatron in an eg, I” , high spin splitting occurs.

The crystal field dividing energy for tetrahedral metal composites ( four ligands ) is referred to as I”tet, and is approximately equal to 4/9I”oct ( for the same metal and same ligands ) . Therefore, the energy required to partner off two negatrons is typically higher than the energy required for puting negatrons in the higher energy orbitals. Therefore, tetrahedral composites are normally high-spin.

The usage of these dividing diagrams can help in the anticipation of the magnetic belongingss of coordination compounds. A compound that has unpaired negatrons in its splitting diagram will be paramagnetic and will be attracted by magnetic Fieldss, while a compound that lacks odd negatrons in its splitting diagram will be diamagnetic and will be weakly repelled by a magnetic field.

Crystal field stabilisation energy

The crystal field stabilisation energy ( CFSE ) is the stableness that consequences from puting a passage 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 regard to a spherical field known as the barycenter in which all five d-orbitals are debauched. For illustration, in an octahedral instance, the t2g set becomes lower in energy than the orbitals in the barycenter. As a consequence of this, if there are any negatrons busying these orbitals, the metal ion is more stable in the ligand field relation to the barycenter by an sum known as the CFSE. Conversely, the eg orbitals ( in the octahedral instance ) are higher in energy than in the barycenter, so seting negatrons in these reduces the sum of CFSE.

Octahedral crystal field stabilisation energyIf the splitting of the d-orbitals in an octahedral field is I”oct, the three t2g orbitals are stabilized comparative to the barycenter by 2/5 I”oct, and the eg orbitals are destabilized by 3/5 I”oct. As illustrations, see the two d5 constellations shown farther up the page. The low-spin ( top ) illustration has five negatrons in the t2g orbitals, so the entire CFSE is 5 ten 2/5 I”oct = 2I”oct. In the high-spin ( lower ) illustration, the CFSE is ( 3 x 2/5 I”oct ) – ( 2 x 3/5 I”oct ) = 0 – in this instance, the stabilisation generated by the negatrons in the lower orbitals is canceled out by the destabilizing consequence of the negatrons in the upper orbitals.

Crystal Field stabilisation is applicable to transition-metal composites of all geometries. Indeed, the ground that many d8 composites are square-planar is the really big sum of crystal field stabilisation that this geometry produces with this figure of negatrons.

Explaining the colors of passage metal composites

The bright colorss 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 seeable light one or more negatrons may momently leap from the lower energy d-orbitals to the higher energy 1s to transiently make an aroused province atom. The difference in energy between the atom in the land province and in the aroused province is equal to the energy of the captive photon, and related reciprocally to the wavelength of the visible radiation. Because merely certain wavelengths ( I» ) of visible radiation are absorbed – those fiting precisely the energy difference – the compounds appears the appropriate complementary coloring material.

As explained above, because different ligands generate crystal Fieldss of different strengths, different colorss can be seen. For a given metal ion, weaker field ligands create a complex with a smaller I” , which will absorb visible radiation of longer I» and therefore lower frequence I? . Conversely, stronger field ligands create a larger I” , absorb visible radiation of shorter I» , and therefore higher I? . It is, though, seldom the instance that the energy of the photon absorbed corresponds precisely to the size of the spread I” ; there are other things ( such as electron-electron repulsive force and Jahn-Teller effects ) that besides affect the energy difference between the land and aroused provinces

Crystal field dividing diagrams

Crystal field dividing 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 belongingss are dependent upon the ligand orbitals and their interaction with metal orbitals are non explained.

In CFT theoretical account partial covalence of metal -ligand bond is non taken into consideration Harmonizing to CFT metal-ligand bonding is strictly electrostatic.

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

In CFT Iˆ-orbitals of ligand are non considered

The theory buzzword explain the comparative strength of the ligands i.e. it can non explicate that why H2O is stronger than OH harmonizing to spectrochemical series.

It does non explicate the charge transportation spectra on the strengths of the soaking up bands.


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

Harmonizing to this theory a covalent bond is formed between the two atoms by the convergence of half filled valency atomic orbitals of each atom incorporating one odd negatron. A valency bond construction is similar to a Lewis construction, but where a individual Lewis construction can non be written, several valency bond constructions are used. Each of these VB structures represents a specific Lewis construction. This combination of valency bond constructions is the chief point of resonance theory. Valence bond theory considers that the overlapping atomic orbitals of the take parting atoms organize a chemical bond. Because of the imbrication, it is most likely that negatrons should be in the bond part. Valence bond theory positions bonds as weakly coupled orbitals ( little convergence ) . Valence bond theory is typically easier to use in land province 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 negatrons overlap tete-a-tete. Pi bonds occur when two orbitals overlap when they are parallel. For illustration, a bond between two s-orbital negatrons is a sigma bond, because two domains are ever coaxal. In footings of bond order, individual bonds have one sigma bond, dual bonds consist of one sigma bond and one pi bond, and ternary bonds contain one sigma bond and two pi bonds. However, the atomic orbitals for bonding may be loanblends. Often, the adhering atomic orbitals have a character of several possible types of orbitals. The methods to acquire an atomic orbital with the proper character for the bonding is called hybridisation


Valence bond theory now complements Molecular Orbital Theory ( MO theory ) , which does non adhere to the VB thought that electron braces are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can widen over the full molecule. MO theory can foretell magnetic belongingss in a straightforward mode, while valency bond theory gives similar consequences but is more complicated. Valence bond theory positions aromatic belongingss of molecules as due to resonance between Kekule, Dewar and perchance ionic constructions, while molecular orbital theory positions it as delocalization of the Iˆ-electrons. The implicit in mathematics are besides more complicated restricting VB intervention to comparatively little molecules. On the other manus, VB theory provides a much more accurate image of the reorganisation of electronic charge that takes topographic point when bonds are broken and formed during the class of a chemical reaction. In peculiar, valence bond theory right 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 late, several groups have developed what is frequently called modern valency bond theory. This replaces the overlapping atomic orbitals by overlapping valency bond orbitals that are expanded over a big figure of footing maps, either centered each on one atom to give a classical valency bond image, or centered on all atoms in the molecule. The resulting energies are more competitory with energies from computations where negatron correlativity is introduced based on a Hartree-Fock mention wavefunction.

Applications of VB theory

An of import facet of the VB theory is the status of upper limit convergence which leads to the formation of the strongest possible bonds. This theory is used to explicate the covalent bond formation in many molecules.

For Example in the instance of F2 molecule the F – F bond is formed by the convergence of pz orbitals of the two F atoms each incorporating an odd negatron. Since the nature of the imbrication 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 convergence of 1s orbital of H and 2pz orbital of F each incorporating an odd negatron. Common sharing of negatrons between H and F consequences in a covalent bond between HF


Some of the belongingss of composites which could non be explained on the footing of valency bond theory are satisfactorily explained by crystal field theory.CFT is therefore decidedly an betterment over vbt these are the following virtues of cft over vbt will turn out that statement:

CFT predicts a gradual alteration in magnetic belongingss of composites instead than the disconnected alteration predicted by VBT.

In some composites, when I” is really close to P, simple temperature alterations may impact the magnetic belongingss of composites.Thus the CFT provides theoretical footing for understanding and foretelling the fluctuations of magnetic minutes with temperature every bit good as detailed magnetic belongingss of composites, this is merely in contrast of VBT which can non foretell or explicate magnetic behavior beyond the degree of stipulating the figure of odd negatrons.

Though the premises inherent in VBT and CFT are immensely different, the chief difference prevarications in their description of the orbitals non occupied in the low spin provinces.VBT forbids their usage as they are involved in organizing intercrossed orbitals, while they are involved in organizing intercrossed orbitals, while CFT strongly discourages their usage as they are repelled by the ligands.

Harmonizing to VBT, the bond between the metal and the ligand is covalent, ,while harmonizing to CFT it is strictly ionic. The bond is now considered to hold both ionic and covalent charachter.Unlike valency bond theory

CFT provides a model for the ready reading of such phenomenon as tretagonal deformations.

CFT provides satisfactory account for the coloring material of passage metal composites, i.e. spectral belongingss ofcomplexes, i.e. spectral belongingss of composites.

CFT can semiquantitatevily explicate certain thermodynamic and kinetic belongingss.

CFT makes possible a clear apprehension of stereochemical belongingss of composites.


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 ) hypertext transfer protocol: //

Murrel, J. N. ; S. F. Tedder ( 1985 ) . The Chemical Bond. John Wiley & A ; 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 chemical science by dr.R.K. sharma pg 61,62

9 ) technology chemical science by A.K.pahari, B.S.chauhan.



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