VALENCE BOND THEORY

      It is the simplest of the three theories and was developed mainly by Pauling. It describes the bonding in terms of hybridized orbitals of the central metal atom or ion. The theory mainly deals withe the geometry and magnetic properties of the complexes. The salient features of the theory are:

(i) The central metal loses a requisite number of electrons to form the ion. The number of electrons lost is the valency of the resulting cation. In some cases, the metal atom does not lose electrons.

(ii) The central metal ion or atom (as the case may be) makes available a number of empty s-, p- and d-atomic orbitals equal to its coordination number. These vacant orbitals hybridize together to form hybrid orbitals which are same in the number as the atomic orbitals hybridizing together. They are vacant, equivalent in energy and have definite geometry.

Some of the common hybridized orbitals met in the coordination compounds are listed below:

Coordination number	Type of hybridization	Geometry	Examples
2	sp	Linear	[Ag(NH3)2]+ ; [Ag(CN)2]-
3	sp2	Trigonal planar	[HgI3]-
4	sp3 dsp2	Tetrahedral Square planar	Ni(CO)4, [Ni(X4]2- [ZnCl4]2-, [CuX4]2- Where X= Cl-, B- , I- [Ni(CN)4]2- , [Cu(NH3)4]2- [Ni(NH3)4]2=
5	dsp3 sp3d	Trigonal bipyramidal Square pyramidal	Fe(CO)5, [CuCl5]3- [SbF5]2-
6	d2sp3 or sp3d2	Octahedral (Inner orbital) (Outer orbital)	[Cr(NH3)6]3+ ; [Fe(CN)6]3- [Fe(H2O)6]2+ ; [Ni(NH3)6]2+ [FeF6]3-

(iii) The non-bonding electrons of the metal occupy the inner orbitals. These ate grouped in accordance with Hund's rule, however, under the influence of some strong ligands, there may be some re-arrangement of electrons in the atomic orbitals the d-orbitals participating in this process of hybridization may be either (n-1)d2sp3 or nsp3d2. The complexes thus formed are referred to as inner or low spin and outer or high spin complexes, respectively.

(iv) The ligands have at least one o-orbital containing a lone pair of electrons. Vacant hybrid orbitals of the metal atom or ion overlap with the o-orbitals containing lone pair or electrons of the ligands to form M<- ligand o-bond.This bond is called coordinate bond and possesses a considerable amount of polarity.

(v) It is  possible to predict the magnetic properties of the complex if the geometry of the complex ion is known. If the complex contains unpaired electrons, it is paramagnetic in nature whereas if it does not contain unpaired electrons all re paired, the complex is diamagnetic in nature.
the number of unpaired electrons and the geometries of the complex ions having central metal ion with configurations d1 to d9 are related to each other as shown below:

dx Configuration	Number of unpaired electrons for different geometries
				Octahedral
				Inner orbitals (d2sp3)	Outer orbitals (sp3d2)
d1	1		1	1	1
d2	2		2	2	2
d3	3		3	3	3
d4	4		4	2	4
d5	5		3	1	5
d6	4		2	0	4
d7	3		1	1 (Shifted to higher orbits)	3
d8	2		0	0 (2 electrons shifted)	2
d9	1		1 (Shifted)	1 (3 electrons shifted)	1

           

        Limitation of valence bond theory:

The valence bond theory was fairly successful in explaining qualitatively the geometry and magnetic properties of complexes. However, it has a number of limitations.

(i) The theory does not offer any explanation about the spectra of complex (why most of the complexes are coloured).

(ii) Sometimes the same metal ion assumes different geometry when formation of complex ion takes place.The theory is unable to explain why at one time the electrons are rearranged against the Hund's rule while at other times the electronic configuration is not disturbed.

(iii) The theory does not offer an explanation for the existence of inner-orbital and outer-orbital complexes.

(iv) The theory does not explain why certain complexes are labile while others are inert.

(v) In the formation of [Cu(NH3)4]2+, one electron is shifted from 3d to 4p-orbital. The theory is silent about the energy availability for shifting such an electron. Such an electron can be easily lost, then why [Cu(NH3)4]2+ complex does not show reducing properties.

(vi) The changes in energies of the metal orbitals on formation of complex are difficult to calculate mathematically. The properties of the complexes are more satisfactorily explained by other two theories. The approach of ligands towards a metal or ion creates a field which is responsible for the splitting of d-orbitals into different energy levels. The extent of splitting depends on the nature and number of ligands which surround the metal atom or ion and explains the magnetic and spectroscopic properties of the complex. More details about these theories are dealt in higher classes. 

BORN-HABER CYCLE

     There are several important concept to understand before the Born-Haber Cycle can be applied to determine the lattice energy of an ionic solid; ionization energy, electron affinity, dissociation energy, sublimation energy, heat of formation, and Hess's Law.

Ionization Energy is the energy required to remove an electron from a neutral atom or an ion. This process always requires an input of energy, and thus will always have a positive value. In general, ionization energy increases across the periodic table from left to right, and decreases from top to bottom. There are some excepts, usually due to the stability of half-filled and completely filled orbitals.

 Electron Affinity is the energy released when an electron is added to a neutral atom or an ion. Usually, energy released would have a negative value, but due to the definition of electron affinity, it is written as a positive value in most tables. Therefore, when used in calculating the lattice energy, we must remember to subtract the electron affinity, not add it. In general, electron affinity increases from left to right across the periodic table and decreases from top to bottom.

 Dissociation energy is the energy required to break apart a compound. The dissociation of a compound is always an endothermic process, meaning it will always require an input of energy. Therefore, the change in energy is always positive. The magnitude of the dissociation energy depends on the electronegativity of the atoms involved.

Sublimation energy is the energy required to cause a change of phase from solid to gas, bypassing the liquid phase. This is an input of energy, and thus has a positive value. It may also be referred to as the energy of atomization.

The heat of formation is the change in energy when forming a compound from its elements. This may be positive or negative, depending on the atoms involved and how they interact.

 Hess's Law states that the overall change in energy of a process can be determined by breaking the process down into steps, then adding the changes in energy of each step. The Born-Haber Cycle is essentially Hess's Law applied to an ionic solid.

 USING THE BORN-HABER CYCLE

 The values used in the Born-Haber Cycle are all predetermined changes in enthalpy for the processes described in the section above. Hess' Law allows us to add or subtract these values, which allows us to determine the lattice energy.

STEP 1

 Determine the energy of the metal and nonmetal in their elemental forms. (Elements in their natural state have an energy level of zero.) Subtract from this the heat of formation of the ionic solid that would be formed from combining these elements in the appropriate ration. This is the energy of the ionic solid, and will be used at the end of the process to determine the lattice energy.

 STEP 2

 The Born-Haber Cycle requires that the elements involved in the reaction are in their gaseous forms. Add the changes in enthalpy to turn one of the elements into its gaseous state, and then do the same for the other element.

 STEP 3

 Metals exist in nature as single atoms and thus no dissociation energy needs to be added for this element. However, many nonmetals will exist as polyatomic species. For example, Cl exists as Cl in its elemental state. The energy required to change Cl into 2Cl atoms must be added to the value obtained in Step 2. 

STEP 4

 Both the metal and nonmetal now need to be changed into their ionic forms, as they would exist in the ionic solid. To do this, the ionization energy of the metal will be added to the value from Step 3. Next, the electron affinity of the nonmetal will be subtracted from the previous value. It is subtracted because it is a release of energy associated with the addition of an electron. *This is a common error due to confusion caused by the definition of electron affinity, so be careful when doing this calculation. 

STEP 5

 Now the metal and nonmetal will be combined to form the ionic solid. This will cause a release of energy, which is called the lattice energy. The value for the lattice energy is the difference between the value from Step 1 and the value from Step 4.

The diagram below is another representation of the Born-Haber Cycle.

EQUATION

The Born-Haber Cycle can be reduced to a single equation: Heat of formation= Heat of atomization+ Dissociation energy+ (sum of Ionization energies)+ (sum of Electron affinities)+ Lattice energy

*Note: In this general equation, the electron affinity is added. However, when plugging in a value, determine whether energy is released (exothermic reaction) or absorbed (endothermic reaction) for each electron affinity. If energy is released, put a negative sign in front of the value; if energy is absorbed, the value should be positive. Rearrangement to solve for lattice energy gives the equation: Lattice energy= Heat of formation- Heat of atomization- Dissociation energy- (sum of Ionization energies)- (sum of Electron Affinities)