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+

VALENCE BOND THEORY (VBT):

Valence bond theory explains the bonding in co-ordination compounds. VBT proposed by Pauling and The main postulates of valence bond theory are: 

 (1) The central metal ion makes available a number of empty orbitals for accommodating electrons donated by the ligands. The number of empty orbitals is equal to the coordination number of the metal ion for the particular complex.

COORDINATION NUMBER

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(2) These empty atomic orbitals (s, p or d) of the metal ion hybridize to form hybrid orbitals with definite directional properties and give a specific geometry. These hybrid orbitals now axially overlap with the filled orbital of ligand orbitals to form strong coordinate bonds and complex obtained a specific geometry.

HYBRIDASATION AND GEOMETRY

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(3) The d-orbitals involved in the hybridization may be either inner (n–1) d-orbitals or outer ndorbitals. The complexes formed in these two ways are referred to as low spin and high spin complexes, respectively.

(4)  Each ligand contains a lone pair of electrons.

(5) A covalent-bond is formed by the overlap of a vacant hybridized metal orbital and a filled orbital of the ligand. The bond is also sometimes called as a coordinate bond.

(6) If the complex contains unpaired electrons, it is paramagnetic in nature, while if it does not contain unpaired electrons, it is diamagnetic in nature.

(7) The number of unpaired electrons in the complex points out the geometry of the complex and vice-versa. In practice, the number of unpaired electrons in a complex is found from magnetic moment measurements as given as

Magnetic moment  (BM)	0	1.73	2.83	3.87	4.90	5.92
Number of unpaired electron	0	1	2	3	4	5

Thus the knowledge of the magnetic moment can be of great help in ascertaining the type of complex.

(8) Strong field ligands affects electronic configuration of central metal my making unpaired electron to pair up, while weak field ligands does not affect electronic configuration of central metal atom i.e. they does not make unpaired electrons to pair up.

SPECTROCHEMICAL SERIES:

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Under the influence of a strong ligand, the electrons can be forced to pair up against the Hund’s rule of maximum multiplicity.

Important Note:

Above Statement is valid for first transition series however for second and third transition series unpaired electrons, pair up irrespective of nature of ligands provide pairing of electrons is allowed.

LIMITATION OF VALENCE BOND THEORY

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