Notes-Part-3-Class-11-Science-Chemistry-Chapter-5-Chemical Bonding-Maharashtra Board

Topics to be Learn : Part-1 Introduction Kossel and Lewis approach to chemical bonding Lewis structures (Lewis representations of simple molecules) Topics to be Learn : Part-2 Valence bond theory Topics to be Learn : Part-3 Molecular orbital theory Parameters of covalent bond Dipole moment Covalent character of ionic bond

Molecular orbital theory :

In some cases valence bond theory gives to incorrect electronic description. Therefore another bonding description called Molecular Orbital Theory (MO) has been introduced.

Features of molecular orbital theory (MOT):

• In a molecule, the electrons are present in various molecular orbitals similar to the electrons in atoms which are present in various atomic orbitals.
• The atomic orbitals of proper symmetry and comparable energies combine to form the molecular orbitals.
• An electron in an atomic orbital is influenced by one nucleus hence atomic orbital is monocentric. While the electron in a molecular orbital is influenced by two or more nuclei depending upon the number of atoms in the molecule, hence, the molecular orbital is polycentric.
• The number of molecular orbitals formed is equal to the number of combining atomic orbitals.
• Two combining atomic orbitals result in the formation of two molecular orbitals, of which one is known as bonding orbital having higher energy and the other is known as antibonding orbital having lower energy.
• The molecular orbitals like atomic orbitals are filled in accordance with the aufbau principle,
• Pauli’s exclusion principle and Hund’s rule of maximum multiplicity.

Formation of molecular orbitals :

According to the MO theory the formation of molecular orbitals from atomic orbitals is expressed in terms of Linear Combination of Atomic Orbitals (LCAO).

Formation of molecular orbitals by a method of linear combination of atomic orbitals (LCAO method) :

• According to wave mechanics, the atomic orbitals can be expressed by wave functions (Ψ).
• The nature of a molecular orbital can be obtained by combining the atomic orbitals of bonding atoms forming a molecule.
• Due to nuclear attraction, the bonding electrons are most likely in the vicinity of the nuclei.
• Consider the atomic orbitals Ψ_A and Ψ_B of comparable energies and same symmetry of two bonding atoms A and B respectively.
• By combining these atomic orbitals, (hence, called linear combination) two molecular orbitals Ψ_a and Ψ_b are obtained.
• Two atomic orbitals combine in two ways to form molecular orbitals. (i) By addition of their wave functions. (ii) By subtraction of their wave functions, mathematically described as follows :

Ψ_b = Ψ_A + Ψ_B

Ψ_a = Ψ_A − Ψ_B

• Where, Ψ_b and Ψ_a are the wave functions of bonding molecular orbital and antibonding molecular orbital respectively.
• For bonding process, two atoms come closer to one another. The atomic orbitals overlap forming two molecular orbitals (M.O.s) one with the lower energy and the other with higher energy than the combining atomic orbitals.

• The molecular orbital with lower energy gives rise to attractive state and more stability and it is called bonding molecular orbital, Ψ_b
• The molecular orbital with higher energy gives rise to a repulsive state, hence decreases the stability and it is called antibonding molecular orbital, Ψ_a.

Formation of Bonding molecular orbital (BMO) :

• Every atomic orbital is represented by a wave function Ψ which may have + ve or −ve sign. Ψ² represents the probability of electron density in the region near nuclei. Ψ² is always positive.
• This molecular orbital (M.O.) is formed by (linear) combination of two atomic orbitals represented by Ψ_A and Ψ_B with the same sign, from two bonding atoms A and B respectively and represented as Ψ_MO or Ψ_b or σ.
• This may be represented mathematically as the addition of two wave functions.

Ψ_MO = σ = Ψ_A + Ψ_B

• In bonding molecular orbital, the overlapping of the atomic orbitals takes place in the region between two nuclei along the internuclear axis.
• The energy of the bonding molecular orbital is lower than that of the parent bonding atoms.

Formation of Antibonding molecular orbital (AMO) :

• This molecular orbital is formed by (linear) combination of two atomic orbitals represented by Ψ_A and Ψ_B with opposite signs from two bonding atoms A and B respectively and represented as Ψ_AMO or Ψ_a or σ*.
• This is mathematically represented as the subtraction of two wave functions.

Ψ_AMO = σ* = Ψ_A + Ψ_B

• This molecular orbital splits into two lobes with a nodal plane at the centre.
• The electrons lie in the region in space where they are not under attraction of both nuclei.
• The energy of the antibonding molecular orbital is higher than that of parent bonding atoms.

Energy levels and electronic configuration :

• We know on combination of two 1s orbitals; two molecular orbitals σ1s and σ*1s are formed. Similarly two 2s orbitals yield σ*2s and σ2s molecular orbitals.
• The three 2p orbitals on one atom combine with three 2p orbitals on another atom forming six molecular orbitals, designated as σ2p_z, πp_x, πp_y and σ*2p_z, π*p_x, π*p_y

Variation in energy levels for molecular orbitals in homonuclear diatomic molecules :

The molecular orbitals in homonuclear diatomic molecules have been determined experimentally.

• For diatomic molecules of second row elements except O₂ and F₂ the rank order of energies is : σ1s < σ*1s < σ2s < σ*2s < π2p_x = π2p_y > < σ2pz < (π*2py = π*2px) < σ*2pz
• For O₂ and F₂ increasing order of energies was found to be : σ1s < σ*1s < σ2s < σ*2s < σ2pz < (π 2px = π2py) < (π*2px = π*2py) < σ*2pz

The sequence of filling the molecular orbitals (MO) give electronic configuration of molecules. The electronic configuration of molecules provides the following information.

• Stability of molecules
• Magnetic nature of molecules
• Bond order of a molecule.

(i) Stability of molecules : If in a molecule the number of electrons in bonding MOs is greater than the number of electrons in antibonding MOs, then the molecule is stable.

(ii) Magnetic nature of molecules : If all MOs in a molecule are completely filled with two electrons each with opposite spins, then their spin moments are cancelled and the molecule is diamagnetic and repelled by magnetic field. However if one or more MOs are half filled with one electron, then the molecule is paramagnetic and attracted by magnetic field.

(iii) Bond order of a molecule : Bond order is defined as one half the difference between the number of electrons present in the bonding (Nb) and the antibonding (Na) molecular orbitals.

Bond order = \(\frac{N_b-N_a}{2}\)

A positive value of bond order indicates a stable molecule while zero or negative bond order indicates an unstable molecule.

Key ideas of MO theory :

• Molecular orbitals (MOs) are formed by combining AOs of different atoms of comparable energies and proper symmetry.
• Molecular orbital describes the region of space in the molecule representing the probability of an electron.
• MOs those are lower in energy than AOs are bonding (σ) MOs while those higher in energy are antibonding (σ*) MOs.
• Only two electrons with opposite spins occupy each MO.
• The electrons are filled in increasing order in MOs beginning with the lowest energy.
• The bond order of the molecule can be calculated from the number of bonding and antibonding electrons.
• The stability of the molecule can be explained.

MO description of simple diatomic Molecules :

*Q. Helium is always monoatomic. Explain on the basis of MOT.

Stability of Li₂ molecule and its diamagnetic character :

• Li atom has electronic configuration, Li(3) = 1 s², 2s².
• Each Li atom has 3 electrons, hence, Liz molecule has 6 electrons.
• Formation of molecular orbitals (MOS) : Linear combination of two atomic orbitals give two molecular orbitals namely bonding σ and antibonding σ* :
• Linear combination of atomic orbitals gives four molecular orbitals σ1s, σ*1s, σ2s, σ*2s

• σ1s and σ*1s being inner MOs, do not contribute towards net chemical bonding hence they are also designated as KK shells. Therefore, the electronic configuration of Li₂ molecule is represented as Li₂ σ1s². σ*1s² σ2s² OR KK σ2s²

• Bond order=(4-2)÷2=1,
• This means in Li₂ molecule there is one bond between the two Lithium atoms.
• Such Li² molecules are found in the vapour state. As there are no unpaired electrons the molecule is diamagnetic.

Know This : Among diatomic molecules the bond order and bond enthalpy of N2 is highest. Bond order = 3, Bond enthalpy = 946 kJ mol-1.

Parameters of covalent bond :

A covalent bond is characterised by different parameters.

Polarity of a covalent bond :

• When a covalent bond is formed between two atoms differing in electronegativity, the electron bond pair is pulled towards more electronegative atom resulting in separation of charges.
• The more electronegative atom acquires a partial negative charge and the less electronegative atom or electropositive atom acquires equal partial positive charge developing a polar covalent bond or a dipole.
• More the bond polarity, stronger is the bond.
• When the difference in electronegativities is about 10%, the covalent bond has about 50% ionic character.

The examples of polar molecules include. HF, HCl etc.

H : F  ^δ+H−F^δ- ….H-F (Polar covalent bond)

Dipole moment :

Definition : Dipole moment (μ) is the product of the magnitude of charge and distance between the centres of +ve and -ve charges.

μ = Q × r

Q : charge ; r : distance of separation.

unit of dipole moment is Debye (D)

1 D = 3.33564 × 10-30 Cm

C : coulomb ; m : meter

Dipole moment being a vector quantity is represented by a small arrow with the tail on the positive centre and head pointing towards the negative centre.

The crossed arrow  above the Lewis structural indicates the direction of the shift of electron density towards the more electronegative atom

Dipole moments of polyatomic molecules :

• Each polar bond in a polyatomic molecule, each polar bond has its own dipole and dipole moment.
• Since dipole moment is a vector quantity, the resultant dipole moment of the molecule is decided by (i) shape of the molecule and (ii) contribution of each dipole moment of a polar bond in the molecule.
• Hence the resultant dipole moment of the polyatomic molecule is the vector sum of the dipole moments of various bonds and lone pairs.
• For example, consider BeF₂ molecule. It is a linear molecule ad the bond moments of two Be — F bonds are equal in strength and opposite in direction. Hence the net dipole moment of BeF₂ is zero.

Dipole moment of BF₃ molecule :

BF₃ is a planar, symmetrical trigonal molecule with bond angle 120°.

Since three B-F polar bonds are oriented at 120° with each other, the sum of any two bond moments is equal and opposite to the third, therefore sum of three B—F dipole moments is zero.

Lone pairs and dipole moment :

• In some molecules, the central atom carries an unshared lone pairs of electrons.
• These lone pairs also contribute to the resultant dipole moment of the molecule. For example, NH₃ molecule in which N has one lone pair of electrons.

Covalent character of ionic bond :

Several ionic compounds possess partial covalent character and show properties similar to covalent compounds.

To explain the partial covalent character in ionic bonds Fajans put forth the following rules :

• The smaller the size of a cation and larger the size of an anion, greater is covalent character of an ionic compound. For example, LiCl is more covalent than NaCl.
• Greater the charge on cation, more is covalent character of the ionic compound. For example, covalent character decreases as,

3 + −     2 + −      + −

AlCl₃ > MgCl₂ > NaCl

• A cation with outer electronic configuration s²p⁶d¹⁰ possesses greater polarising power than a cation having outer electronic configuration size and same size and charge, since d-electrons have less screening effect than s, p-electrons.

Phenomenon of resonance :

• Many polyatomic molecules can be represented by more than one lewis structures.
• Each structure differs from the other only in position of electrons without changing the position of atoms.
• None of these individual structures explains the properties adequately.
• For example, CO₃^2-

• The actual structure of CO₃^2- is a combination of three Lewis structures and it is called resonance hybrid.
• Resonance signifies that there is more than one possible arrangement of electrons around the atoms in the molecule or more than one Lewis structures. These are also called canonical structures.

Resonance energy :

• Many polyatomic ions and molecules can be represented by different canonical forms and each form has a different energy.
• The energy of resonating structures is different than the energy of the most stable structure or resonance hybrid.
• The difference in energy of the most stable resonating structure or resonance hybrid and different resonating forms is called resonance energy.