Types of hybridisation and geometry of molecules

Hybridisation

Bonding in simple molecules such as hydrogen and fluorine can easily be explained on the basis of overlap of the respective atomic orbitals of the combining atoms. But the observed properties of polyatomic molecules such as methane, ammonia, beryllium chloride etc... cannot be explained on the basis of simple overlap of atomic orbitals. For example, it was experimentally proved that methane has a tetrahedral structure and the four C-H bonds are equivalent. This fact cannot be explained on the basis of overlap of atomic orbitals of hydrogen (1s) and the atomic orbitals of carbon with different energies (2s² 2p_x² 2p_y 2p_z).

In order to explain these observed facts, Linus Pauling proposed that the valence atomic orbitals in the molecules are different from those in isolated atom and he introduced the concept of hybridisation. Hybridisation is the process of mixing of atomic orbitals of the same atom with comparable energy to form equal number of new equivalent orbitals with same energy. The resultant orbitals are called hybridised orbitals and they posses maximum symmetry and definite orientation in space so as to minimize the force of repulsion between their electrons .

Types of hybridisation and geometry of molecules

sp Hybridisation:

Let us consider the bond formation in beryllium chloride. The valence shell electronic configuration of beryllium in the ground state is shown in the figure.

In BeCl₂ both the Be-Cl bonds are equivalent and it was observed that the molecule is linear. VB theory explain this observed behaviour by sp hybridisation. One of the paired electrons in the 2s orbital gets excited to 2p orbital and the electronic configuration at the excited state is shown.

Now, the 2s and 2p orbitals hybridise and produce two equivalent sp hybridised orbitals which have 50 % s-character and 50 % p-character. These sp hybridised orbitals are oriented in opposite direction as shown in the figure. 

Overlap with orbital of chlorine

Each of the sp hybridized orbitals linearly overlap with p_z orbital of the chlorine to form a covalent bond between Be and Cl as shown in the Figure.

sp2 Hybridisation:

Consider boron trifluoride molecule. The valence shell electronic configuration of boron atom is [He]2s²2p¹.

In the ground state boron has only one unpaired electron in the valence shell. In order to form three covalent bonds with fluorine atoms, three unpaired electrons are required. To achieve this, one of the paired electrons in the 2s orbital is promoted to the 2p_y orbital in the excite state.

In boron, the s orbital and two p orbitals (p_x and p_y) in the valence shell hybridses, to generate three equivalent sp² orbitals as shown in the Figure. These three orbitals lie in the same xy plane and the angle between any two orbitals is equal to 120º

Overlap with 2pz orbitals of fluorine:

The three sp² hybridised orbitals of boron now overlap with the 2p_z orbitals of fluorine (3 atoms). This overlap takes place along the axis as shown below.

sp3 Hybridisation:

sp³ hybridisation can be explained by considering methane as an example. In methane molecule the central carbon atom bound to four hydrogen atoms. The ground state valence shell electronic configuration of carbon is [He]2s² 2p_x¹ 2p_y¹ 2p_z⁰.

In order to form four covalent bonds with the four hydrogen atoms, one of the paired electrons in the 2s orbital of carbon is promoted to its 2p_z orbital in the excite state. The one 2s orbital and the three 2p orbitals of carbon mixes to give four equivalent sp3 hybridised orbitals. The angle between any two sp3 hybridised orbitals is 109⁰ 28'

Overlap with 1s orbitals of hydrogen:

 The 1s orbitals of the four hydrogen atoms overlap linearly with the four sp³ hybridised orbitals of carbon to form four C-H σ-bonds in the methane molecule, as shown below.

sp3d Hybridisation:

In the molecules such as PCl₅, the  central  atom  phosphorus  is  covalently bound to five chlorine atoms. Here the atomic orbitals of phosphorous undergoes sp³d hybridisation which involves its one 3s orbital, three 3p orbitals and one vacant 3d orbital (d_z2). The ground state electronic configuration of phosphorous is [Ne]3s² 3p¹_x3p_y¹3p_z¹ as shown below.

One of the paired electrons in the 3s orbital of phosphorous is promoted to one of its vacant 3d orbital (d_z²) in the excite state. One 3s orbital, three 3p orbitals and one 3d_z² orbital of phosphorus atom mixes to give five equivalent sp3d hybridised orbitals. The orbital geometry of sp³_d hybridised orbitals is trigonal bi-pyramidal as shown in the figure 10. x. 

Overlap with 3pz orbitals of chlorine:

The 3p_z orbitals of the five chlorine atoms linearly overlap along the axis with the five sp³d hybridised orbitals of phosphorous to form the five P-Cl σ-bonds, as shown below.

sp³d² Hybridisation:

In sulphur hexafluoride (SF₆) the central atom sulphur extend its octet to undergo sp³d² hybridisation to generate six sp³d²   hybridised orbitals which accounts for six equivalent S-F bonds. The ground state electronic configuration of sulphur is[Ne]3s² 3p_x¹ 3p_y¹ 3p_z¹.

One electron each from 3s orbital and 3p orbital of sulphur is promoted to its two vacant 3d orbitals (d_z2 and d_x2-y2) in the excite state. A total of six valence orbitals from sulphur (one 3s orbital, three 3p orbitals and two 3d orbitals) mixes to give six equivalent sp³d² hybridised orbitals. The orbital geometry is       octahedral as shown in the figure. 

Overlap with 2pz orbitals of fluorine:

The six sp³d²  hybridised orbitals of sulphur overlaps linearly with 2p_z      orbitals of six fluorine atoms to form the six S-F bonds in the sulphur hexafluoride molecule.

Bonding in ethylene:

The bonding in ethylene can be explained using hybridisation concept. The molecular formula of ethylene is C₂H₄. The valency of carbon is 4. The electronic configuration of valence shell of carbon in ground state is [He]2s² 2p_x¹ 2p_y¹ 2p_z⁰. To satisfy the valency of carbon promote an electron from 2s orbital to 2p_z orbital in the excited state.

In ethylene both the carbon atoms undergoes sp² hybridisation involving 2s, 2p_x and 2p_y orbitals, resulting in three equivalent sp2 hybridised orbitals lying in the xy plane at an angle of 120⁰ to each other. The unhybridised 2p_z orbital lies perpendicular to the xy plane.

Formation of sigma bond:

One of the sp² hybridised orbitals of each carbon lying on the molecular axis (x-axis) linearly overlaps with each other resulting in the formation a C-C sigma bond. Other two sp2 hybridised orbitals of both carbons linearly overlap with the four 1s orbitals of four hydrogen atoms leading to the formation of two C-H sigma bonds on each carbon. 

Formation of pi bond:

The unhybridised 2p_z orbital of both carbon atoms can overlap only sideways as they are not in the molecular axis. This lateral overlap results in the formation a pi bond between the two carbon atoms as shown in the figure.

Bonding in acetylene:

Similar to ethylene, the bonding in acetylene can also be explained using hybridization concept. The molecular formula of acetylene is C₂H₂. The electronic configuration of valence shell of carbon in ground state is [He]2s² 2p¹_x 2p¹_y 2p⁰_z. To satisfy the valency of carbon promote an electron from 2s orbital  to 2p_z orbital in the excited state.

In acetylene molecule, both the carbon atoms are in sp hybridised state. The 2s and 2p_x orbitals, resulting in two equivalent sp hybridised orbitals lying in a straight line along the molecular axis (x-axis). The unhybridised 2p_y and 2p_z orbitals lie perpendicular to the ymolecularz axis.

Formation of sigma bond:

One of the two sp hybridised orbitals of each carbon linearly overlaps with each other resulting in the formation a C-C sigma bond. The other sp hybridised orbital of both carbons linearly overlap with the two 1s orbitals of two hydrogen atoms leading to the formation of one C-H sigma bonds on each carbon.

Formation of pi bond:

The unhybridised 2p_y and 2p_z orbitals of each carbon overlap sideways. This lateral overlap results in the formation of two pi bonds ( p_y-p_y  and p_z-p_z) between the two carbon atoms as shown in the figure.