Artist’s Colour Wheel

The observed color of a compound from the color of absorbed light can be determined by using the Artist’s color wheel diagram. Here complementary colors are shown on opposite sides of the color wheel.

  • If a compound absorbs light of one color(say orange), then it reflects(transmit) light of blue color. The transmitted or reflected light of blue color attacks on the retina of our eyes and the compound is seen to be blue colored. The color of the transmitted light is called the complementary color of absorbed light.
  • At the heart of color theory, complementary color are the opposite hues on the color wheel.
  • In their most basic form, they are one primary color and that is created by mixing the other two primary color. For example, the complementary color of yellow is purple which is a mix of blue and red.
  • With that knowledge, it is rather easy to remember the first set of complementary color i.e.         yellow and purple, blue and orange, red and green as shown in the above diagram.
  • If we add the tertiary color, those are made up of one primary and one secondary color, we will find that that color are also complementary i.e.  yellow-orange  and  blue-purple(indigo)                                                                                       orange-red  and  blue-green(aqua)                                                                                                 red-purple(pink) and  green-yellow

    Limitations of Crystal Field Theory

    Crystal Field Theory was given by Hans Bethe and Van Vleck. This theory is based on the assumption that the interaction between metal ion and ligands is purely electrostatic in nature. When the ligands approach the central metal atom or ion, the five degenerate  d-orbital of the central atom become different i.e.they split into the different energy level under the influence of the electrostatic field of ligands.

    Limitations of Crystal Field Theory:

    Crystal field theory explains successfully the structure of complex, magnetic properties, color, and electronic spectra, thermodynamic and kinetic aspects of the complexes. However, this theory has some serious limitations.
    • In CFT only d-electrons of the metal ion are considered, the other orbitals such as s, are not taken into consideration.
    • This theory has not considered the covalent character in transition metal complexes. It treats the metal-ligand as purely ionic.
    • CFT cannot explain the relative strength of ligands as given in spectrochemical series, i.e. it cannot explain why H2 is a stronger ligand as compared to OH ion.
    • CFT has also not considered the Pi bonding in complexes either it is metal to ligand or ligand to metal.
    • This theory has no significance to the orbits of the ligands. Therefore it cannot explain any properties related to ligand orbitals and their interaction with metal orbitals.
    • It don’t explain the effect of π bond on Δ0.
    • The compounds like in which metal is in zero oxidation states and the ligand is neutral have no electrostatic attraction between the metal and the ligands.

    Evidence of metal-ligand covalent bonding in complexes

    1.Cr(CO)6 is a volatile compound and Ni(CO)4 is a liquid. This indicates that there is a covalent bonding between metal and ligand instead of the ionic. If there would be an ionic bond, then Cr(CO)should be non-volatile and  Ni(CO)4 is solid.

    2. Electron Spin Resonance(ESR):

    • The ESR spectrum of [IrCl6]2- suggests that the single unpaired electron is only 70% localized on the metal atom, and 30% is localized on the chloride ion. This indicates that there is sharing of electron and hence some covalency between metal and ligands.

    3. The Nuclear Magnetic Resonance(NMR):

    • The fluoride NMR has detected the delocalization of electron in the fluoro complexes, of the paramagnetic metal ion. It is possible only when an unpaired electron spends more than negligible time on  19F nucleus.

    4. The Nephelauxetic Effect:

    • The electronic repulsion in d-orbitals of transition metal cations gives rise to a number of energy levels depending upon the arrangement of electrons in d-orbitals.
    • The energy difference between two energy states can be expressed in terms of interelectronic repulsion parameters, called Racah parameters B and C. The difference in energy between two levels having same spin multiplicity can be expressed in terms of  only B, and the difference in energy between  two  energy levels having different spin multiplicities can be expressed in terms of B and C.
    • It is observed experimentally(i.e. from electronic spectra of complexes)that the magnitude of B and C decreases when the complex is formed. The reduced value of B and C indicates that electron density is reduced on metal cation i.e. electron cloud is delocalized over both the metal cation and the ligands. This suggests that there is some covalency between metal cation and ligands.
    • The more the value of B and C is reduced, the greater the delocalization of electron cloud and greater the covalency. The delocalization of the electron cloud over the metal cation and the ligand is called the nephelauxetic effect.

    5. Nuclear Quadrupole Resonance(NQR);

    • The NQR spectrum of some of the complexes containing halide ions as ligands like [PtCl4]2- ,  [PdCl4]2-suggests that metal-ligand bond is partly ionic and partly covalent.

    Application of CFSE

    1.Enthalpy of Hydration: 

    • When one mole of an ionic crystal is dissolved in water, water molecules gather from the ion and this process is called hydration. In this process, some amount of energy is released which is called Hydration energy.
    • Hydration energy of a metal cation increases with the increase in effective nuclear charge and decrease in ionic radii because these two factors bring the water molecules closer to the metal cation resulting in the increased electrostatic attraction between the metal cation and the water molecule.
    • For dipositive transition metal cation of 3d-series, the effective nuclear charge increases and ionic radii decrease across a period. So hydration energy should increase regularly from Ca2+ to Zn2+
    • So, Hydration energy  α  charge of the cation  ̸   size of the cation
    • For example, Hydration energy of Co2+ <  Co3+ because here as the size of both the ions are same, the ion having higher charge has greater hydration energy.

    2.lattice Energy:

    • When one mole of an ionic crystal is formed from its constituent gaseous ions, some amount of energy is released which is called lattice energy.
    • Or energy required to break one mole of ionic crystal into its surrounding gaseous ion is called lattice energy.
    • According to Born Lande’s equation lattice energy of an ionic crystal increases with the increase in the product of Z+and Zand decrease in the interionic distance(r0).
    • The lattice energy for the halides of dipositive metal ions of the 3d-series transition element should increase from  Ca2+ to Zn2+ion and a straight line should be observed.

    3.Ionic radii of Divalent Metal ions of 3d-series transition element:

    • The ionic radii of dipositive and tripositive metal cations of  3d-series transition metals in the low spin or high-spin octahedral field might be expected to decrease regularly from Ca2+to Zn2+ . 
    • The reason is that there is an increase of force of attraction between metal cations and ligands due to the increase in effective nuclear charge and the poor shielding effect of d-electrons due to which ligands and metal cation approach each other more closely.

      Pairing Energy

      Pairing Energy:

               The energy required to force the two unpaired electrons in one orbital is called pairing energy. When more than one electrons are paired, P becomes the mean pairing energy. It may be obtained from the analysis of electronic spectra.
      If  ∆0 > P, it favors the low spin complex
      If  ∆0 < P, it favors the low spin complex
      If  ∆0 = P, high spin and low spin complex equally exist
      In general, for 4d and 5d series transition metal complexes, the magnitude of  ∆is greater than that of P. 
      • In weak field octahedral complex of 3d-series transition metal with oxidation number less than equal to +3, the value of is  ∆small and there will be no pairing of electrons. Therefore in weak field complexes of d4, d5, d6, and dconfiguration, there is no pairing of electrons. These complexes have the maximum number of unpaired electrons are called high spin or spin free complexes. The term high spin or spin free is used because these complexes have the same number of spin as in d-orbital of free metal cations.
      • In strong field octahedral complex of 3d-series transition metal with oxidation number, in general, greater than equal to +2, the value of ∆0 is large. In strong field complexes of d4, d5, d6, and dconfigurations, the pairing of d-electrons will take place in according to Hund’s rule. These complexes have the maximum number of paired electrons are called low spin or spin paired complexes. The term low spin or spin paired is used because these complexes have more number of paired electrons(or spin)than that of the free metal cation.
      •  It is to be notated that week field octahedral complexes are always not the high spin complexes. The metal cation of 3d-transition series with the oxidation number of greater than equal to +4 and 4d and 5d series transition metal cations always form low spin complexes with weak ligands.
      • For example, [NiF6]2- ion (oxidation state of Ni is +4) is low spin and diamagnetic, though Fis a weak ligand. [Rh(H2O)6]3+is low spin and diamagnetic, though is a weak ligand.
      • An exception is observed for 3d-series transition metals in which Co3+ form low spin complexes with H2O and O2- though H2O and  O2-are weak ligands.

      Factors Affecting the magnitude of ∆

      There are several factors that affect the magnitude of splitting (0)of d-orbitals by the surrounding ligands.

      1. Oxidation State of the Metal Cation:

      The higher the oxidation state of the metal cation, the greater will be the magnitude of ∆. The higher the oxidation state of the metal causes the ligand to approach more closely to it and, therefore the ligand causes more splitting of metal d-orbitals.
           For example               ∆0 for [Co(H2O)6]2+ = 9200 cm-1
                   and                     ∆0 for [Co(H2O)6]3+ = 20760 cm-1

      2. Same Oxidation State of Metal Cation but the number of d-electrons is                   Different:

      In general, for a given series of transition elements(say 3d-series), in complexes having the metal cation with the same oxidation state but the different number of electrons in the d-orbitals, the magnitude of  decreases with increase in the number of d-electrons. It is due to the fact that the higher number of d-electrons prevents the ligands to come closer to the metal cation.
                                       For example        0 for [Co(H2O)6]2+ = 9200 cm-1(3d7)
                                              and                ∆0 for [Ni(H2O)6]2+ = 8500 cm-1(3d8)

      3. Principal Quantum Number(n) of the d-orbital of the Metal Cation:

      In case of complexes having the metal cation with the same oxidation states and the same number of d-electrons, the magnitude of for analogous complexes within a given group increases about 30% to 50% from 3d to 4d and by about the same amount from 4d to 5d. It is because:
        (1) On moving from 3d to 4d and 4d to 5d, the size of the d-orbital increases and electron density              decreases in them. Therefore the ligands can approach the metal cation with larger d-orbital                more closely.
        (2) There is less steric hindrance around a larger metal cation.
              For example      ∆0 for [Co(NH3)6]2+ = 2300 cm-1 
                                        ∆0 for [Rh( NH3)6]2+= 34100 cm-1 
                                        ∆0 for [Ir( NH3)6]2+= 41200 cm-1 

       4. Nature of Ligands:

      The ligands are classified as a weak and strong ligand. The ligand which causes a small degree of splitting of d-orbitals are called weak ligands and the ligands which cause a large splitting are called strong ligands. The common ligands have been arranged in order of their increasing crystal field splitting power to cause splitting of d-orbitals from a study of their effects on the spectra of transition metal ions.
      (weak end)O22−< I < Br < S2− < SCN (S–bonded) < Cl− < N3 < F< NCO < OH < C2O42− < H2O < NCS (N–bonded) < CH3CN < gly (glycine) < py (pyridine) < NH3 < en (ethylenediamine) < bipy (2,2′-bipyridine) < phen (1,10-phenanthroline) < NO2 < PPh3 < CN < CO < CH2(strong end)
       This order s usually called as Spectrochemical series
      The order of the field strength of common ligands is independent of the nature of the metal cation and the geometry of the complex.

      5. Number of Ligands:

      The magnitude of crystal field splitting(∆)increases with the increase of the number of ligands.For example  > ∆t
       Though the number of ligands in a square planar complex is smaller than that of octahedral complexes, the magnitude of  ∆sp is greater than ∆0. It is because of the fact that square planar complexes are formed by much strong ligands with dmetal cation of 3d-series transition metal cation and 4d and 5d series d8metal cation with either weak or strong ligand. The very strong ligands and 4d or 5d series transition metal cations are responsible for higher crystal field splitting. Also in square planar complexes of dmetal cation, the dZ2 orbital with two electrons is stabilized and the vacant dX2-y2 orbital is destabilized.

      Splitting of d-orbital in octahedral complex

      Crystal field splitting in Octahedral complex:

      •  In a free metal cation all the five d-orbitals are degenerate(i.e.these have the same energy.In octahedral complex say [ML6]n+the metal cation is placed at the center of the octahedron and the six ligands are at the six corners. These six corners are directed along the cartesian coordinates i.e. along the x, y, and z-axis. When all the ligands are at an infinite distance from the metal cation, the five d-orbital of the metal cation will not be affected by the ligand electrostatic field and will remain degenerate. When the ligands move towards the metal cation, there are two electrostatic forces i.e. 

                      (1)The attraction between metal cation and ligand
                      (2)Electrostatic repulsion between d-electrons of the metal cation and lone pairs of ligands

      • Greater the repulsion between metal cation and ligands, ligands will be more closer to the metal cation and hence more will be the repulsion between the metal d-electrons and the lone pair of electrons on the ligand. When the ligands are closer to the metal cation an electrostatic force of repulsion also exists among the ligands.These two repulsion cause to adopt the octahedral geometry that locates the ligand at the internuclear distance from the metal cation and as far apart from one another as possible.
      • The force of repulsion between metal d-electron and the ligand electrons cause to increase in potential energy of metal d-electrons. Remember that greater the force of repulsion higher will be the potential energy. If all the six ligands approaching the metal cation surrounds it spherically symmetric i.e. all the six ligands are at equal distance from each of the d-orbitals.
      • The energy of each d-orbital will raised by the same amount and all the five d-orbital will remain degenerate. This is a hypothetical situation and has the average energy of a set of d-orbitals.In an actual octahedral complex, a spherically symmetric field is never obtained. Therefore all the five d-orbitals are not affected by the same extent.
      • Since the two d-orbitals( dx2-y2 and  dz2 ) points directly towards the ligands and the three d- orbitals(  dxy ,dyz and dzx ) point in between the path of the approaching ligand. Therefore the  dx2-y2 and  dz2 orbitals will be more strongly repelled than the  dxy ,dyz and dzx orbitals. Therefore the energy of the dx2-y2 and  dz2 orbitals will be raised and that of the other three orbitals which lie far away from the ligand will be decreased relative to the hypothetical energy state.
      • The five d-orbital which were degenerate in a free metal cation is now split into two sets of d-orbitals of different energies, a higher energy level with two orbitals(dx2-y2 and  dz2)having the same energy and a lower level with three equal energy orbitals(dxy,dyz, and dzx). The set of   dx2-y2 and dz2orbitals are referred to as eset which is doubly degenerate and the set of dxy,dyz, and dzx is referred to as t2g set which is triply degenerate.
      • Since the distance between metal cation and the ligands has remained the same, the net potential energy(or average energy) of the system must remain the same as that of the spherical field before splitting. This state of average energy is called the barycentre.
      • The separation of five d-orbitals of metal cation into two sets of different energies is called crystal field splitting. The energy difference between two sets of orbitals which arise from an octahedral field is measured in terms of the parameter ∆0 or 10Dq where o in ∆0 stands for octahedral. 
      • Since the energy of barycentre remains constant, the total energy decrease of the t2g set must be equal to the total energy increase of the eg set. Therefore since there are two eg orbitals, they must increase by 0.6∆0 or 6Dq and the three t2g orbitals must decrease by 0.4∆0 or 4Dq per electron. The decreased energy t2g of orbitals stabilizes the complex by 0.4∆0 and the increase in energy of eorbitals destabilizes the complex by 0.6∆0.

          Crystal Field Theory

          Crystal Field Theory:

                    Valence bond theory is useful to visualize the bonding in complexes, but it fails to explain the nature of ligands, colour and electronic spectra, effect of temperature on magnetic moment and magnetic susceptibilities, why some complexes are high spin and others are low spin, stability of complexes.
          To explain these properties Bethe and van Vleck proposed the crystal field theory.This theory was originally applied to ionic crystals and is therefore called crystal field theory.
          This theory is based on the following assumptions:
          • Ionic ligands such as Cl,OH,CN are regarded as negative point charges(or simply point charges) and the neutral ligands such as  H20,NH3,Py are regarded as dipole(or simply dipoles) because these ligands are dipolar.If the ligand is neutral molecule like the negative end of the dipole is directed towards the metal ion.
          • Metal-ligand bond is not covalent i.e. there is no overlapping of orbitals.Instead of bonding in complexes is purely electrostatic in nature.In complexes two types of  electrostatic forces come into account,

                       (1)One is the attraction between metal cation and the negatively charged ligand or the                                negative end of the polar ligand(i.e. dipole)

                       (2)The second type of electrostatic interaction is the electrostatic repulsion between the                            lone pairs of electrons on the ligands and the electrons in the d-orbital of the metal cation                    and the repulsion between nuclei of metal cation and the ligands but to a small extent.
          • Another repulsion also come into account that occurs among the ligands.
          • the five d-orbital in a free metal ion are degenerate(i.e.have same energy).When a complex is formed, the electrostatic field of ligands destroy the degeneracy of these d-orbitals i.e. these orbitals now have same energies.
          • The orbital lying in the direction of the lidands are raised in energy more than those lying away from the ligands because of the repulsion between the d-electrons and the ligands.
          • In order to understand CFT, it is necessary to know the geometry and orientation of the five d-orbitals.      

          Hybridisation in outer orbital octahedral complex

          Outer orbital octahedral complex:

                  Let’s take an example   [Fe(H2O)5(NO)]2+
          • In this complex ion oxidation state of Fe is +1, because NO exists in +1 oxidation state in a complex of Fe and it is valence shell electronic configuration is 3d6, 4s1
          • Magnetic moment measurement indicates that its experimental magnetic moment is 3.89 B.M. which corresponds to three unpaired electrons in the d-orbital of complexion.
          • The single NOstrong ligand has little tendency to pair up only two unpaired electrons. Since  H2O is a weak ligand, therefore, it has no tendency to pair up electrons and none of the five 3d orbitals is vacant. 
          • Therefore the  4s, 4p and two of the five 4d orbitals (i.e.4dx2-y2  and  4dz)combine to give six sp3d2 hybrid orbitals.
          • These hybrid orbital form bonds with six ligands by accepting six pairs of electrons, one pair from each of the six ligands.

          • Here as outer d-orbital is involved in hybridization it gives outer orbital octahedral geometry.


          • The octahedral complex of  d1, d2, and d3 metal cation are always inner orbital octahedral complexes whether the ligands are strong or weak.
          • The octahedral complex of d8, d9, and d10 metal cation are always outer orbital complexes either the ligands are strong or weak. 
          • The complexes of d4, d5,d6, and d7 metal cation are outer orbital complex if the ligands are weak.

          Inner orbital octahedral complex

          Let’s discuss inner orbital complexing taking an example, [Co(CN)6]3-  ion

          • In this complex oxidation state of cobalt is +3

                       Valence shell electronic configuration is

          • Magnetic moment measurement indicates that  [Co(CN)6]3-C ion is diamagnetic(given). So that all the d-electrons arranged in such a way, that no unpaired electron is left in the d-orbital. 
          • In other words as CN  ion is a strong ligand, it causes the pairing of 3d-electrons.


          •  Here two vacant 3d-orbital combine with the vacant 4s and 4p orbital to form six  d2sp3

             hybrid orbital. 

          • Then six hybrid orbital overlap with six filled orbital of  CN ligand, one on each of the ligand and thus six coordinate covalent bonds are formed which gives d2sp3  hybridization.
          • As inner d-orbitals are involved in hybridization, it gives inner orbital octahedral geometry.

          Test your understanding:

              Explain hybridisation in, 
               [Co(NO2)6]4-   (one unpaired electron) 
               [Mn(CN)6]3-    (two unpaired electron)
               [Cr(CN)6]3-C   (paramagnetic corresponding to three unpaired electron)