Chemistry Bonding in Coordination Compounds : CFT
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### Topics Covered :

● Crystal Field theory
● Crystal Field Splitting in Octahedral Complexes
● Crystal Field Splitting in Tetrahedral Complexes
● Colour in Coordination Compounds
● Limitations of Crystal Field Theory

### Crystal Field Theory :

=> The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand.

=> Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules.

=> The five color{red}(d)-orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate.

● This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion.

● However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like color{red}(NH_3) and color{red}(H_2O)) in a complex, it becomes asymmetrical and the degeneracy of the d-orbitals is lifted.

● It results in splitting of the d-orbitals.

● The pattern of splitting depends upon the nature of the crystal field.

### Crystal field splitting in octahedral coordination entities :

=> In an octahedral coordination entity with six ligands surrounding the metal atom/ion, there will be repulsion between the electrons in metal d-orbitals and the electrons (or negative charges) of the ligands.

● Such a repulsion is more when the metal d-orbital is directed towards the ligand than when it is away from the ligand.

=> Therefore, the color{red}(d_(x^2 − y^2)) and color{red}(d_(z^2)) orbitals which point towards the axes along the direction of the ligand will experience more repulsion and will be raised in energy; and the color{red}(d_(xy), d_(yz)) and color{red}(d_(xz)) orbitals which are directed between the axes will be lowered in energy relative to the average energy in the spherical crystal field.

=> Thus, the degeneracy of the d orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, color{red}(t_(2g)) set and two orbitals of higher energy, color{red}(e_g) set.

=> This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by color{red}(Δ_o) (the subscript o is for octahedral) (Fig.9.8).

=> Thus, the energy of the two color{red}(e_g) orbitals will increase by color{red}((3/5) Δ_o) and that of the three color{red}(t_(2g)) will decrease by color{red}((2/5)Δ_o).

=> The crystal field splitting, color{red}(Δ_o), depends upon the field produced by the ligand and charge on the metal ion.

=> Some ligands are able to produce strong fields in which case, the splitting will be large whereas others produce weak fields and consequently result in small splitting of d-orbitals.

● In general, ligands can be arranged in a series in the order of increasing field strength as given below :

color{red}(I^– < Br^– < SCN^– < Cl^– < S2^– < F^– < OH^– < C_2O_4^(2–) < H_2O < NCS^– < edta^(4–) < NH_3 < en < CN^(–) < CO)

● Such a series is termed as color{green}("spectrochemical series").

● It is an experimentally determined series based on the absorption of light by complexes with different ligands.

=> Let us assign electrons in the color{red}(d)-orbitals of metal ion in octahedral coordination entities.

● Obviously, the single color{red}(d) electron occupies one of the lower energy color{red}(t_(2g)) orbitals.

● In color{red}(d^2) and color{red}(d^3) coordination entities, the color{red}(d) electrons occupy the color{red}(t_(2g)) orbitals singly in accordance with the Hund’s rule.

● For color{red}(d^4) ions, two possible patterns of electron distribution arise :

(i) the fourth electron could either enter the color{red}(t_(2g)) level and pair with an existing electron, or

(ii) it could avoid paying the price of the pairing energy by occupying the color{red}(e_g) level.

● Which of these possibilities occurs, depends on the relative magnitude of the crystal field splitting, color{red}(Δ_o) and the pairing energy, P (P represents the energy required for electron pairing in a single orbital).

● The two options are :

(i) If color{red}(Δ_o < P), the fourth electron enters one of the color{red}(e_g) orbitals giving the configuration color{red}(t_(2g)^3 e_(g)^1). Ligands for which color{red}(Δ_o < P) are known as weak field ligands and form high spin complexes.

(ii) If color{red}(Δ_o > P), it becomes more energetically favourable for the fourth electron to occupy a color{red}(t_(2g)) orbital with configuration color{red}(t_(2g)^4 e_(g)^0). Ligand which produce this effect are known as strong field ligands and form low spin complexes.

color{red}("Note ") : Calculations show that color{red}(d^4) to color{red}(d^7) coordination entities are more stable for strong field as compared to weak field cases.

### Crystal field splitting in tetrahedral coordination entities :

=> In tetrahedral coordination entity formation, the color{red}(d)-orbital splitting (Fig. 9.9) is inverted and is smaller as compared to the octahedral field splitting.

=> For the same metal, the same ligands and metal-ligand distances, it can be shown that color{red}(Δ_t = (4/9) Δ_o).

=> Consequently, the orbital splitting energies are not sufficiently large for forcing pairing and, therefore, low spin configurations are rarely observed.

### Colour in Coordination Compounds

=> We know that one of the most distinctive properties of transition metal complexes is their wide range of colours.

=> This means that some of the visible spectrum is being removed from white light as it passes through the sample, so the light that emerges is no longer white.

=> The colour of the complex is complementary to that which is absorbed.

=> The complementary colour is the colour generated from the wavelength left over; if green light is absorbed by the complex, it appears red.

=> Table 9.3 gives the relationship of the different wavelength absorbed and the colour observed.

=> The colour in the coordination compounds can be readily explained in terms of the crystal field theory.

color{red}("Example ") : Consider the complex color{red}([Ti(H_2O)_6]^(3+)), which is violet in colour.

● This is an octahedral complex where the single electron (color{red}(Ti^(3+)) is a color{red}(3d^1) system) in the metal color{red}(d)-orbital is in the color{red}(t_(2g)) level in the ground state of the complex.

● The next higher state available for the electron is the empty color{red}(e_g) level.

● If light corresponding to the energy of yellow-green region is absorbed by the complex, it would excite the electron from color{red}(t_(2g)) level to the color{red}(e_g) level (color{red}(t_(2g)^1 e_(g)^0 → t_(2g)^0 e_g^1)).

● As a result, the complex appears violet in colour (Fig. 9.10).

● The crystal field theory attributes the colour of the coordination compounds to d-d transition of the electron.

color{red}("Note ") : In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.

● For example, removal of water from color{red}([Ti(H_2O)_6]Cl_3) on heating renders it colourless.

● Similarly, anhydrous color{red}(CuSO_4) is white, but color{red}(CuSO_4 .5H_2O) is blue in colour.

=> The influence of the ligand on the colour of a complex may be illustrated by considering the color{red}([Ni(H_2O)_6]^(2+)) complex, which forms when nickel(II) chloride is dissolved in water.

● If the didentate ligand, ethane-1,2-diamine(en) is progressively added in the molar ratios color{red}(en : Ni, 1:1, 2:1, 3:1), the following series of reactions and their associated colour changes occur :

color{red}(underset (text (green) ) ( [Ni (H_2O)_6]^(2+) (aq)) + en (aq) = underset (text (pale blue) ) ( [Ni (H_2O)_4 (en) ]^(2+) (aq) ) + 2H_2O)

color{red}([Ni (H_2O)_4 (en)^(2+) (aq) ]^(2+) + en (aq) = underset (text (blue /purple) ) ( [Ni (H_2O)_2 (en)_2 ]^(2+) (aq) ) + 2H_2O)

color{red}([Ni (H_2O)_2 (en)_2 ]^(2+) (aq) + en (aq) = underset (text (violet) ) [Ni (en)_3]^(2+) (aq) + 2H_2O)

### Limitations of Crystal Field Theory :

=> The crystal field model is successful in explaining the formation, structures, colour and magnetic properties of coordination compounds to a large extent.

=> However, from the assumptions that the ligands are point charges, it follows that anionic ligands should exert the greatest splitting effect. The anionic ligands actually are found at the low end of the spectrochemical series.

=> Further, it does not take into account the covalent character of bonding between the ligand and the central atom.

=> These are some of the weaknesses of CFT, which are explained by ligand field theory (LFT) and molecular orbital theory.