CRYSTAL FIELD THEORY (CFT):

The Crystal Field Theory (CFT) was originally proposed for explaining the optical properties of crystalline solids. It was applied to the study of coordination compounds in the 1950s. CFT assumes the ligands to be point charges and the interaction between them and the electrons of the central metal to be electrostatic in nature. The five 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 NH₃ and H₂O) in a complex, it becomes asymmetrical and the degeneracy of the d-orbitals is lifted. It results in splitting of the d-orbital energies. The pattern of splitting depends upon the nature of the crystal field. We will first consider:

(1) CRYSTAL FIELD SPLITTING IN OCTAHEDRALCOMPLEXES:

For convenience, let us assume that the six ligands are positioned symmetrically along the Cartesian axes, with the metal atom at the origin. As the ligands approach, first there is an increase in the energy of d orbitals to that of the free ion just as would be the case in a spherical filed. Next, the orbitals lying along the axes (dz²and dx²-y² d) get repelled more strongly than d_xy, d_yz and d_xz orbitals, which have lobes directed between the axes. The d_xy , d_yz , d_xz orbitals are lowered in energy relative to the average energy in the spherical crystal filed. Thus, the degenerate set of d orbitals get split into two sets: the lower energy orbitals set, t₂g and the higher energy, eg set. The energy separation is denoted by del.oct (the subscript o is for octahedral.

CRYSATAL FIELD STABLISATION ENERGY:

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(2) CRYSTAL FIELD SPLITTING IN TETRAHEDRAL COMPLEXES:
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(3) CRYSTAL FIELD SPLITTING IN SQUARE PLANER COMPLEXES:

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LIMITATIONS OF VALENCE BOND THEOTY (VBT):

(1) Although valence bond theory provides a satisfactory representation of the complex compound based upon the concept of orbital hybridisation, it cannot account for the relative stabilities for different shapes and coordination numbers in metal complexes.

(2) VBT cannot explain as to why Cu²⁺ forms only distorted octahedral complexes even when all the six ligands are identical.

(3) The valence bond theory does not provide any satisfactory explanation for the existence of inner orbital and outer orbital complexes.

(4) Sometimes the theory requires the transfer of electron from lower energy to the higher energy level, which is very much unrealistic in absence of any energy supplier (for example, this happens in the case of [CuX₄]^2- .

(5) The changes in the properties of the metal ion along with the ligands and the simple metal ions cannot be explained. For example, the colour changes associated with electronic transition within d orbitals are affected on formation of complex, but the valence bond theory does not offer any explanation.

(6) Sometimes the same metal acquires different geometry when formation of complex takes place with different ligands. The theory does not explain as to why at one time the electrons must be rearranged against the Hund’s rule while, at other times the electronic configuration is not disturbed.

(7) The energy change of the metal orbitals on formation of complex is difficult to be calculated mathematically.

(8) VBT fails to explain the finer details of magnetic properties including the magnitude of the orbital contribution to the magnetic moments.

(9) The VBT does not explain why certain complexes are more labile than the others.

(10) It does not give quantitative interpretation of thermodynamic or kinetic stabilities of coordination compounds.

(11) It does not make exact predictions regarding the tetrahedral and square planar structure of 4-coordinate complexes.

(12) It does not tell about the spectral properties of coordination compounds.

Related Question:

(1) Although both [Mn(H2O)6]2+ and [FeF6]3- have a d5 configuration and high-spin complexes. But the dilute solutions of Mn2+ and Fe +3 complexes are therefore colorless. Why?

(2) Which of the Complex of the following pairs has the highest value of CFSE?

(3) Colour of Complexes due to charge transfer:

(4) Why violet colour of [Ti(H2O)6]Cl3 disapear (colourless) on heating heating ? 

(5) Why [Ni(CN)4]-2 is colourless while [Ni(H2O)4]-2 although both have +2 oxidation state and 3d*8 configuration ?

(6) Why [FeF6]3– is colourless whereas [CoF6]3– is coloured ? 

(7) Why Fe(CO)5 is colourless while Fe(bipy)(CO)3 is intensely purple in colour ?

(8) Why all the tetrahedral Complexes are high spin Complexes ?

CRYSTAL FIELD EFFECTS IN SQUARE PLANAR COMPLEXES:

The square planar arrangement of ligands may be considered to be one derived from the octahedral field by removing two trans-ligands located along the Z-axis. In the process, the eg and t₂g sets of orbitals is lifted i.e., these orbitals will no longer be degenerate.

The four ligands in square planar arrangement around the central metal ion are shown in Fig. As the ligands approach through the axes, they would have greatest influence on dx²-y² orbital, so the energy of this orbital, will be raised most. The d_xy orbital, lying in the same plane, but between the ligands will also have a greater energy though the effect will be less than that on the dx²-y² orbitals. On the other hand, due to absence of ligands along Z-axis, the z²d orbital becomes stable and has energy lower than that of d_xy orbital.

Similarly d_yz and d_xz become more stable. The energy level diagram may be represented as Fig. along with tetrahedral and octahedral fields.

The value of del.sp has been found larger than del.oct because of the reason that d_xz and d_yz orbitals interact with only two ligands in the square planar complexes, while in octahedral complexes the interaction takes place only with four ligands. del.sp has been found equal to 1.3 del.oct

FACTORS FAVOURING SQUARE PLANAR:

(1) Metals (atom/ion) with configuration 4d⁸ or 5d⁸ always form square planar complexes irrespective of natureof the liqand. Such metal atom or ions are as

[PtCl₄ ]^1-although Cl^1- are W.L.yet is is square planar complex

(2) But with the metal atom or the ion with 3d⁸ configuration, for example Ni(II)) complex will be square planar only with the strong field ligands. (tetrahedral with weak ligand).

Others Examples:

CRYSTAL FIELD STABILISATION ENERGY (CFSE):

The difference in energy of eg and t₂g Orbitals are called crystal field stabilisation energy (CFSE):

Where m and n = are number of electrons in t₂g and eg orbitals respectively and del.oct is crystal field splitting energy in octahedral Complexes.

l = represents the number of extra electron pair formed because of the ligands in comparison to normal degenerate configuration.
P= (Pairing energy) the energy required for electron pairing in a single orbital. The actual configuration of complex adopted is decided by the relative values of delta and P
Case (1): If del.oct is less than P :
We have so called weak field or high spin situation, the fourth electron entered one of the eg orbitals giving configuration (t₂g³ and eg¹)
If now 5th electron is added to a weak field the configuration become  (t₂g³ and eg²).
Case (2): If del.oct  is more than P: we have the strong field , low spin situation and pairing will occur in the t₂g level with eg level remaining unoccupied in entities of d¹ and d⁶ ions .

Calculation shows that coordination entities with four to seven d electron are more stable for strong field as compared to weak field cases.

(A)For configuration (d⁰, d¹, d², d³, d⁸, d⁹, d¹⁰):

SN	METAL ION	EXAMPLE	CONF IN L.F	CFSE(del.oct)
1	d0	Sc3+	t2g 0,0,0  eg 0	=0.0
2	d1	Ti3+	t2g 1,0,0 eg 0	=-0.4
3	d2	V3+	t2g 1,1,0 eg 0	=-0.8
4	d3	Cr3+ , V2+	t2g1,1,1  eg 0	=-1.2
5	d8	Ni2+	t2g 2,2,2  eg1,1	= -2.4 +1.2+ 3P =-1.2+3P
6	d9	Cu2+	t2g2,2,2  eg 2,1	=-2.4 +1.8+4P =-0.6+ 4P
7	d10	Zn2+	t2g2,2,2  eg 2,2	=-2.4 +2.4+ 5P =  5P

Therefore, for the above configurations, there is no effect of the nature of ligand. They may be strong or weak; the formula for CFSE will remain the same.

(A)For configuration (d⁴, d⁵, d⁶, d⁷):

SN	METAL ION	EXAMPLE	CONF IN L.F	CFSE(del.oct)
1	d4	Cr2+ (S.L.) Cr2+ (W.L.)	t2g 2,1,1  eg 0,0 t2g 1,1,1  eg 1,0	=-1.6  +1P =-1.6
2	d5	Mn2+,Fe3+(S.L.)                  (W.L)	t2g 2,2,1  eg 0,0 t2g 1,1,1  eg 1,1	=-2.0+2P =0.0
3	d6	Co3+,Fe2+(S.L.)                 (W.L.)	t2g 2,2,2 eg 0,0 t2g 2,1,1 eg 1,1	=-2.4 +3P =-0.4+ 1P
4	d7	Co2+ (S.L.)          (W.L.)	t2g2,2,2  eg 1,0 t2g2,2,1  eg 1,1	=-1.8+3 P -0.8+2P

Crystal field stabilisation energy (CFSE) in Tetrahedral:

The difference in energy of eg and t₂g Orbitals are called crystal field stabilisation energy (CFSE) in tetrahedral complexes:

Where m and n = are number of electrons in t₂g and eg orbitals respectively and del.oct is crystal field splitting energy in octahedral Complexes.
l = represents the number of extra electron pair formed because of the ligands in comparison to normal degenerate configuration.
P= (Pairing energy) the energy required for electron pairing in a single orbital. The actual configuration of complex adopted is decided by the relative values of delta and P

HYBRIDISATION AND GEOMETRY:

SN	CN	Hybridisation	Geometry	Bond angle	Examples
1	2	Sp	Linear	180	[Cu(CN)2]-, [Ag(CN)2]-, [Au(CN)2]-, [Ag(Cl)2]-, [Ag(NH3)2]+,
2	3	Sp2	Trigonal planer	120	[Hg(I3)2]2-,
3	4	Sp3	Tetrahedral	109. 28	[Ni(Cl)4]2-,[Zn(NH3)4]2+, [Cd(CN)4]2-,[Hg(I)4]2-, [Ag(S2O3)2]2,[Co(SCN)4]2
4	4	d3S                    /dxy,dyz,dzx,S	tetrahedral	109.28	CrO42-, MnO41-, MnO42- VO43-, Cr2O72-
5	4	dsp2             /dx2-y2Sp3	Square planer	90	[Ni(en)2]2+,[Cu(NH3)4]2+, [Ag(F)4]1-,[Pt(Cl)4]2-, [Au(F)4]1-,[Pd(H2O)4]2+, [Ni(dmg)2]
6	5	dz2Sp3                       / Sp3dz2	TBP	120, 90	[Fe(CO)5] , [Mn(CO)5] , [Cu(Cl)5]3
7	5	dx2-y2Sp3	Square pyramidal	90, 90	[Ni(CN)5] 3-
8	6	d2Sp3               /dx2-y2,dz2Sp3	Octahedral	90, 90	[Cr(NH3)6] 3+ , [NiF6] 2- , [Co(H2O)6] 3+ , [IrF6] 3-, [Rh(H2O)6] 3+ , [Ptcl6] 2- , [Pd(H2O)6] 4+,[Co(NH3)6] 3+
9	6	Sp3d2                          / Sp3 dx2y2,dz2	Octahedral	90, 90	[Fe(NH3)6] 2 ,[Fe(H2O)6] 3+   [Cr(H2O)6]2,[Ni(en)3]2+ [Mn(NH3)6] 2+