Matter is composed of atoms and molecules. Whenever atoms combine together, molecules are formed due to chemical bonding. A ''Chemical bond" is the force that holds the atoms together to form a molecule. Different types of chemical bonding are ionic, covalent, metallic, Hydrogen bonding. These bonds are explained on the basis of Kossel - Lewis approach, VSEPR theory, valence bond theory and molecular orbital theory. Kossel explained the formation of ionic bond, Lewis explained the formation of covalent bond.
            According to them, the chemical reactivity and the valency of the elements depend on the number of electrons present in the outer most (valence) shell. Valency exhibited by elements either by losing or by gaining electrons is called ''Electrovalency" and the valency exhibited by elements by sharing of electrons is called ''Covalency". Atoms of elements tend to attain nearest stable noble gas configuration of 8 electrons in the outer most shell either by losing or by gaining or by sharing electrons is called "octet rule".
Octet rule is obeyed by maximum number of molecules, where as stable molecules which contain either less than (BF3, AlCl3) or more than (PCl5, SF6) octet disobey octet rule.
              A strong electrostatic force of attraction between cations and anions due to transfer of one or more electrons from the valence shell of an atom is called ''Ionic bond". Species with octet configuration are more stable (e.g.: Ca+2) than that of pseudo octet configuration (e.g.: Zn+2). Factors favourable for the formation of ionic bond are the sum of the factors favourable for the formation of cations and anions as well.
              Factors favourable for the formation of cations are low ionization potential of the metal atom, large atomic size, low charge on the ion and the formation of cation with octet configuration.
              Factors favourable for the formation of anion are high electro negativity and high electron affinity of the non metal atom, small atomic size and low charge on the ion. Fajan's rules are useful in predicting the nature of the bond formed between two atoms. Large cationic size, small anionic size, low charge on the ion favours the formation of more ionic bond. Small cationic size, large anionic size, more charge on the ion favours the formation of more covalent bond. Cations with octet configuration are more ionic and with pseudo octet configuration are less ionic (i.e. covalent).
 

Ionic compounds exhibit properties like: Hard, high melting and boiling points; conduct electricity only in fused state or in aqueous solution, highly soluble in polar solvents, do not exhibit isomerism, reaction rates are instantaneous in solution. 
        Crystal lattice energy influences the formation of ionic bond. In order to understand crystal lattice, one must known about coordination number and limiting radius ratio (radius of cation/radius of anion). This ratio is 0.52 for NaCl. This suggests octa hedral arrangement of Na⁺ and Cl^- ions. Ratio 0.93 for CsCl, suggests body centred cubic arrangement The number of oppositely charged ions at equal distance around an ion in ionic crystal is called "Coordination number". Coordination number of Na⁺ in NaCl is 6 and that of Cs⁺ in CsCl is 8.

Crystal structure of NaCl:
In NaCl crystal each Na⁺ is surrounded by 6 Cl^- ions, each
Cl^- is surrounded by 6 Na⁺ions.  radius ratio is 0.52. So coordination number is 6. NaCl is face centred cubic lattice. 

0 - Chloride ion      
• - Sodium ion

Crystal Structure of CsCl:
        In CsCl crystal each Cs+ is surrounded by 8 Cl- ions, each Cl- ion is surrounded by 8 Cs+ ions.  rCs+/ rCl- radius ratio is 0.93. So coordination number is 8. CsCl is body centred cubic lattice.
Unit Cell:
  The smallest basic three dimensional repeated unit from which a crystal lattice is built.    

     structure of CsCl.
 • -  Cs+ ion   0 -  Cl-  ion

        Ions present in crystal lattice are shown by points are called lattice points. These points are located at the corners, edges, faces and the centre of the body. The contribution of the ion to one unit cell at body centre is 1, face centre is

 , edge centre is  and corner is  . Utilising this knowledge one can calculate the number of cations, anions present per unit cell. Number of Na⁺ ions in one unit cell of NaCl are 4 [At body centre 1⁺ at edges 12 ×   ], Cl^- ions are 4 [At face centres 6 ×  + At corners 8 ×  ].
Number of Cs⁺[At body centre 1] and Cl^- [At corners 8 × ] ions in one unit cell of CsCl are 1 & 1.
        "The bond formed due to equal contribution and equal sharing of electrons between two atoms (in order to complete octet) in a molecule (homo atomic or hetero atomic)" is called "covalent bond".
Covalent compounds exhibit properties like... Low melting and boiling points, do not conduct electricity, soluble only in non polar solvents, exhibit isomerism, reaction rates are slow, generally exist as gases or liquids but some polar covalent compounds exist in solid state.
            Even different atoms in a ion or molecule do not carry any charge, to select stable structure (of lowest energy), formal charge on an atom is useful. The structure with lowest formal charges on the atoms is more stable. Same atoms of the same molecule can have different formal charges in different structures. For example in ozone formal charges on O¹, O², O³ are 0, +1, -1 respectively.

 
   Formal charge of an atom = Group number of atom - total
   no. of non bonding electrons -

 total no. of bonding electrons.
   To explain the shapes of simple covalent molecules. Sidgwick and Powell, proposed a simple theory " Valency shell electron pair repulsion theory [VSEPR].  

The main postulates of this theory are:
1) Central atom may have lone pairs or bond pairs in its valency shell.
2) Lone pairs occupy more space and bond pairs occupy less space.
3) Electron pairs around the central atom orient themselves, so that the repulsive forces are minimum between them.
4) The magnitude of repulsions between bond pairs depend on the electronegativity difference between central atom and other atoms (Bonded).
5) Order of repulsive forces: L.P. - L.P. > L.P. - B.P. > B.P. - B.P. 
6) The shape of the molecule depends on the number of electron pairs present in the valence shell of the central atom.
7) If the no. of bond pairs are 2, 3, 4 5, 6, the shapes of the molecules are linear, plane triangle, tetrahedral, trigonal bipyramidal, octa hedral respectively.
        Due to presence of one lone pair in N in NH3, the shape of the molecule is pyramidal instead of tetrahedral. The bond angle is 107° instead of 109° 28' due to lone pair - bond pair repulsion. Due to presence of two lone pairs in O in H₂O, the shape of the molecule is angular instead of tetrahedral. The bond angle is 104° 30' instead of 109°28', due to lone pair - lone pair repulsion.
 VSEPR theory could not explain the shapes of all the molecules, direction of the bonds as well. To over come these limitations, Heitler and London proposed "Valence bond theory" on the basis of quantum mechanics. 

The important postulates of  V.B.T.

A Covalent bond is formed due to overlapping of atomic orbitals of two different atoms. The direction of the bond is in the same direction in which atomic orbitals overlap and gives shape of the molecule. Greater the extent of overlap, greater is the strength of the bond (p - p > s - p > s - s). The overlapping atomic orbitals contains unpaired electrons of opposite spins.
          Depending on the type of overlapping of orbitals, two types of covalent bonds (σ & π) are formed. The axial overlapping of pure atomic or hybrid orbitals give sigma bond. Sidewise overlapping of atomic orbitals (p or d) give pi bond. A special case of a covalent bond is called "Coordinate covalent" or "dative bond". This bond was explained by Sidgwick. "The bond formed by the sharing of electron pairs by both the atoms (Electron pair donor and acceptor) but contributed by one of the bonded atoms". H₃O⁺, NH₄⁺, BF₃^- NH₃, O₃, SO₂ have dative bonds. Properties of the compounds with dative bonds are similar to covalent compounds.
To rectify the defects in valence bond theory, Linus Pauling introduced the concept 'hybridisation". Atomic orbitals having nearly same energies undergo hybridisation. The shape, energy of hybrid orbitals are same. Pauli's, Hund's rules are applicable to hybrid orbitals. Depending on the no. of orbitals, nature of orbitals involved in hybridisation, it is classified as follows.

sp hybridisation:
   The hybridisation in which one 's' and one 'p' orbitals of same valence shell of an atom intermix together to give two identical sp hybrid orbitals.
         e.g.: BeCl₂
                       
              Be = 1s² 2s¹ 2p_x1 (1^st excited state)
      One 2s and one 2p orbitals of Be intermix together to give two identical sp hybrid orbitals. These two H.O'S overlap with p orbitals of 2 Cl atoms. The shape of the molecule is linear so its bond angle is 180°. % of s & p characters are 50% each.

sp² hybridisation:
    The hybridisation in which one 's' and two 'p' orbitals of same valence shell of an atom intermix together to give 3 identical sp2 hybrid orbitals.
              e.g.: BCl₃                    
              B = 1s² 2s¹ 2p_x1 2p_y1( 1^st excited state)
     One 2s and two 2p orbitals of B inter mix together to give three identical sp² hybrid orbitals. Three H.O.  s over lap with p orbitals of 3 Cl atoms. Molecule gets trigonal planar, bond angle is 120°, % of s is 33.33%, p is 66.67%

sp³ hybridisation:
  The hybridisation in which one s and three p orbitals of same valence shell of an atom intermix together to give 4 identical sp3 hybrid orbitals. e.g.: CH₄
              C = 1s² 2s¹ 2p_x1 2p_y1 2p_z1 (1^st excited state) 
   One 2s and three 2p orbitals of valence shell of carbon intermix together to give 4 identical sp3 hybrid orbitals. These 4 Orbitals overlap with s orbitals of 4 H atoms. The shape of the molecule is tetrahedral, bond angle is 109o 28', % of s is 25%, p is 75%.

sp3d hybridisation: One s, three p, one d orbitals of same valence shell of an atom intermix together to give 5 identical sp³d H.O.'S is known as sp³d hybridisation. e.g.: PCl₅
         P = 1s² 2s² 2p⁶ 3s¹ 3p_x1 3p_y1 3p_z1 3d¹ (1^st excited state)    
One 3s, three 3p and one 3d atomic orbitals of valence shell of Phosphorous overlap to give 5 identical sp3 d hybrid orbitals. These 5 H.O's overlap with p orbitals of 5 Cl atoms. The shape of the molecule is trigonal bipyramidal, bond angle in the plane is 120°, perpendicular to plane is 90°. % of s & d is 20% each, % of p is 60%.

sp³d² hybridisation:
 One s, three p, two d orbitals of same valence shell of an atom intermix together to give 6 identical sp³d² H.O's is known as sp³d² hybridisation.
                                 e.g.: SF₆
        S = 1s² 2s² 2p⁶ 3s¹ 3p_x1 3p_y1 3pz1 3d¹ 3d¹ (2^nd excited state)     

         One 3s, three 3p, one 3d orbitals of same valence shell of 's' intermix to give 6 identical sp³d² hybrid orbitals. The shape of the molecule is octa hedral, bond angles are 90°, 90°. % of s character is 16.66%, d is 33.33%, p is 50%.

 It is easy to predict the shape of the molecule and hybridisation by calculating the no.of hybrid orbitals formed by the central atom by using the formula. 
      No.of H.O's =  [Group no. of central atom + no.of mono valent atoms - charge on the cation + charge on the anion]        e.g.: SF₆
     For SF6 H.O's     =      [6 + 6 - 0 + 0] = 6               sp³d², octa hedral
     For NH4+ H.O's  =     [5 + 4 -1 + 0] =   4                   sp³, tetrahedral
     For ClO4- H.O's   =     [7 + 0 - 0 + 1] = 4                    sp3, tetrahedral.
     If the no. of H.O's are 2, 3, 4, 5, 6, 7; the type of hybridisation is sp, sp², sp³, sp³d, sp³d² , sp³d³ respectively.
     To explain properties such as paramagnetic diamagnetic nature, bond length, bond strength, bond order of molecules, ions Hund and Mullikan proposed "Molecular Orbital Theory (MOT)". The main postulates of this theory are: When two atomic orbitals (AO's) combine, they give 2 new molecular orbitals (MO's); one of which is bonding MO(BMO) and the other is antibonding MO (ABMO). Bonding MO's are represented as a σ*, Π*, ABMO's are represented as σ*, Π*. Filling of electrons in MO's follow Hund, Pauli, Aufbau principles. The no. of molecular orbitals formed are equal to the no. of AO's Combining.
Order of energies: BO' s < Non BO' s < Anti BO' s. There are 2 types of energy level diagrams. The order of filling of orbitals for the molecules.
         1) After N2 : σ (1s) σ* (1s) σ (2s) σ* (2s) Π (2p_y) = Π (2p_z) σ (2p_x) Π*(2p_y) =  Π* (2p_z) σ* (2p_x)
         2) Up to N2: σ (1s) σ* (1s) σ (2s) σ(2s) σ* (2p_x) Π (2p_y) = Π (2p_z) Π* (2p_y) =  Π* (2p_z) σ* (2p_x)