Video Lesson

Lesson objective 

At the end of this lesson, you will be able to:

• Name two chemical bond theories.
• Explain the valence bond theory.
• Distinguish the Lewis model and the valence bond model.
• Discuss the overlapping of orbitals in covalent bond formation.
• Explain hybridization show the process of hybridization involved in some covalent molecules.
• Draw hybridization diagrams for the formation of space,sp2,sp3,sp3d and sp3d2 hybrids.
• Suggest the kind of hybrid orbitals on the basis of the electron structure of the central atom
• Predict the geometrical shapes of some simple molecules on the basis of hybridization and the nature of electron pairs
• Discuss the hybridization involved in compounds containing multiple bonds.
• Explain bond length and bond strength
• Explain molecular orbital theory.
• Describe molecular orbital using atomic orbitals.
• Describe bonding and anti bonding molecular orbitals.

Brainstorming Questions

• How does Molecular Orbital Theory differ from Valence Bond Theory in describing chemical bonds?
• What is hybridization, and how does it help explain the geometry of molecules?
• What are the main types of crystal lattices, and how are they classified?

key terms and Concepts

2.4. Chemical Bonding Theories

A. Valance bond Theory (V BT)

B. Molecular bond theory (MOT)

2.4.1 Valance bond Theory (VBT)

Valence Bond Theory (VBT) is a fundamental concept in chemistry that explains how atoms combine to form molecules through the overlap of atomic orbitals. Here’s a comprehensive overview of VBT:

Key Concepts of Valence Bond Theory (VBT)

1. Atomic Orbital Overlap:
   • Bond Formation: According to VBT, a covalent bond forms when atomic orbitals from two atoms overlap. The greater the overlap, the stronger the bond.
   • Orbital Types: The orbitals involved in bonding can be s, p, or d orbitals.
2. Orbital Overlap and Bond Strength:
   • The strength of a covalent bond depends on the extent of the overlap between the orbitals.
   • Over lap of atomic orbitals form either Sigma (σ) Bonds or Pi (π) Bonds.

A. Sigma (σ) Bonds: Formed by the head-on overlap of orbitals. Sigma bonds are characterized by their cylindrical symmetry around the bond axis.

Sigma (σ) Bond is formed when the overlap of orbitals is along the inter nuclear axis. Is also called head to head overlap. Includes the overlap of half filled S-S orbitals, S-P orbitals and P_z − P_z orbitals. Sigma bonds are single bonds

B. Pi (π) Bonds: Formed by the side-to-side overlap of p orbitals. Pi bonds are found above and below the bond axis and are usually present in double and triple bonds alongside sigma bonds.

Pi (π) Bond is formed when orbitals overlap not along the inter nuclear axis but rather above and below and parallel to the sigma (σ − 𝒃𝒐𝒏𝒅).

Pi (π) Bond is also called sideways overlap or parallel overlap. It is the P- orbitals that participate

Pi (π) Bonds explains the formation of double and Triple bonds.

Pi (π) Bond has two regions of electron density, one above and one below the sigma bond axis.

• A double bond consists of one σ− bond and one 𝜋 −bond; A triple bond contains one σ −bond and two 𝜋- bonds.

Example:- The figure given below shows the overlap of the two 1s orbitals in the hydrogen molecule:

• Electron density is higher in the overlap region than anywhere else and the atoms are held together due to the attraction between the
  positive nuclei of the atoms and the negative electrons in the overlap region.
• Such an overlap is not restricted only to S atomic orbitals and there are overlaps between 1s orbitals and half filled 2P orbitals.
• The S-orbital is spherical, but p and d- orbitals have particular orientations where there is more electron density in one direction than in another, therefore, a bond involving P or d orbitals will tend to be oriented in the direction that maximizes overlap.

Example 1 : Identify the overlapping orbital’s in molecules of

a. HCl

b. F₂

solution; a. The outer shell electron configuration of Cl is:

The outer shell electron configuration of H is ;

• b. The outer electron configuration of F:

• F + F → F₂

Example 2 : Consider the over lapping in O₂ molecule.

The outer electron configuration of O is ;

• The extent of overlap influences bond strength however, many factors, such as lone pair repulsion, bond polarities and other electrostatic contributions affect overlap and the relative strength of σ and 𝜋 bonds between other pairs of atoms.

Hybridization of Orbitals

• Hybridization is an imaginary mixing process in which the orbitals of an atom rearrange themselves to form new atomic orbital’s called Hybrid orbitals. Hybrid orbitals are identical, have the same energy and contain unpaired electrons.
• In the formation of hybrid orbitals, electrons jump from the lower orbital to a higher orbital, i.e. from “s” to “P” or from “P” to “d”, and this process is known as Excitation.
• The symbols used for hybrid orbitals identify the kinds and numbers of atomic orbitals used to form the hybrids.

Types of Hybrid Orbitals

A. Sp Hybrid orbitals.
 Combines one S and one P orbitals
 Possesses 50% S and 50% P- characters.
 Valance Bond theory proposes that mixing two non-equivalent orbitals of a central atom one S and one P, gives rise to two equivalent SP Hybrid orbitals that lie 180⁰ a part.
Consider the hybridization in BeCl₂

B. SP² Hybrid Orbitals
Combines one S and two P-orbitals.
Possesses 33% S and 67% P- character
Are distributed geometrically with in a plane at 1200 angles.

• Consider the hybridization in C₂H₄

C.   SP³ Hybrid orbitals

• Combines one S and three P- orbitals
• Contains 25% S and 75% P- character
• They represent a tetrahedral electron set geometry

Consider the hybridization in CH₄

D.   SP³d  Hybridization

• Expanded octets must include additional orbitals and these extra orbitals can come from a d-sub shell.
• Combines one S, three P and one d orbitals.

• Contains 20% S, 60% P and 20% d- character.
• Five orbitals are used in SP³d hybridization, giving a trigonal bipyramidal electron set geometry.
• Three of the orbitals are directed in the plane of the central atom at 120⁰ angles with one another.
• The other two orbitals are perpendicular to the plane of the other three.
• The three positions in the central plan are called the equatorial positions, and the two positions perpendicular to the plane are called axial positions.  

                                Consider the hybridization in PCl₅

E. SP³d²– Hybridization

• Combines one S, three P and two d orbitals. Involves 16.7% S-character, 50% P- character and 33.3% d- character
• Results in octahedral electron arrangement

consider the hybridization in SF₆. 

EXAMPLES

1. From the Lewis structure of the following molecules predict the hybridization of their central atom.

a. O₃                                         b.   ClO₄^–               c. XeF₄

Solution;

Strengths and Limitations of Valence Bond Theory

Strengths:

• Provides a clear explanation of bonding through orbital overlap and hybridization.
• Accounts for molecular shapes and bond angles using hybridization.

Limitations:

• Does not explain the concept of delocalized electrons well, which is covered by Molecular Orbital Theory.
• Struggles to explain the magnetic properties of molecules or the electronic structure of molecules with significant resonance.

2.4.2 Molecular Orbitals Theory (MOT)

1. Molecular Orbital Theory( MOT)

• Is a method of accounting for covalent bonds that depends on quantum theory and mathematical principles.
• Quantized electron distribution as atomic orbitals ( AO), which are capable of combining, or over lapping, to produce new electron distributions called molecular orbitals (MO). There is one M.O for every A.O.
• When two atomic orbitals from different atoms interact, two new molecular orbitals are generated, one additive and one subtractive.
• The additive orbital (bonding molecular orbital) has high electron density between the nuclei, and is denoted by σ or 𝝅.
• The subtractive orbital (Anti bonding molecular orbital) has low electron density between the nuclei .
• It places a high electron charge density away from the region between the two nuclei.
• It is denoted by 𝜹∗ 𝒐𝒓 𝝅∗

Electrons in bonding orbitals contribute to bond formation and electrons in anti-bonding orbitals detract from bond formation.

Electron Configuration of Diatomic Molecules Is based on the rules that apply for filling orbital’s, these are, The Aufbau, The hunds, and pauli- exclusion principles.

Consider the molecular diagram for H₂

There are no more electrons in H2 so that the σ1𝑠∗ orbital remains empty in the ground state.
N.b: The number of molecular orbitals formed must equal the number of atomic orbitals available for combination.

• Unfilled molecular orbitals are considered to be there, even when there are no electrons in them.

Orbitals and their Respective Bonds

1. σ- orbital and σ- bonds
   − σ molecular orbital’s are cylindrically symmetrical about the inter nuclear axis, so that the whole area of electron probability completely surrounds that axis.
   − 𝐴𝑛𝑦 bond in which the distribution of electron is density cylindrical symmetrical around the inter nuclear axis is σ−bond.

2. 𝝅- orbitals and 𝝅- bonds
    When two Atomic orbitals overlap from parallel positions, they form two pi molecular orbitals (π M. Os).
    Any two parallel Atomic orbitals (e.g. two Py Atomic orbitals ) can overlap to produce 𝝅 molecular orbitals , i.e. one bonding 𝛑 molecular orbitals and another Anti-bonding molecular orbital, 𝝅 ∗molecular orbitals that is separated by the inter nuclear axis.
    A bond in which the distribution of electron density is separated by inter- nuclear axis is called a 𝝅- bond

Fig 2.4 Energy pattern for homo nuclear diatomic molecules.

• 2P_y* and P_z* are degenerate Anti- bonding molecular orbitals.
   The order of energy of molecular orbitals has been determined mainly from spectroscopic data.
  i. In simple homonuclear diatomic molecules where the total electron is 14 or less, the order is:

ii. For simple homonuclear diatomic molecules where the total electron is greater than 14, the order is:

• Write the molecular electron configurations of
•     a. C₂^–                     b. C₂                                       C. C₂⁺

                       Bond order

 Is used to indicate the type of bond in a covalent bond, or is the number of covalent bonds that exists, between a pair of atoms.
 The net bond order in a molecule is given by:

• A substance is stable if the stabilization energy is greater than that of the destabilization energy, or if the net bond order is greater than zero.
• When the bond order is exactly zero the molecule doesn’t exist.

Magnetic Properties

• Species which are attracted by an external magnetic field exhibit paramagnetic property.
• Paramagnetic species have unpaired electrons.
• Species which are not attracted by an external magnet exhibit diamagnetism.
• Diamagnetic species are in fact, slightly repelled by a magnetic field.

EXAMPLES

1. What are the bond orders for
   • a. CN^– ,
   • b. CN
   • c. CN⁺
   • d. O₂^2- ?

Solution:- The molecular electron configurations are:
a. CN^– Has (6+7+1= 14 ) electrons : σ1s²σ1s² ∗σ2s², σ2s² ∗{ π2Py², π2Py², σ2Px²
Bond order =1/2[ B. 0 − (ABe−)]
B. O =1/2[10 − 4] =1/2× 6 = 3 …..triple bond
b. CN Has (6+7=13 ) electrons : σ1s²σ1s² ∗σ2s², σ2s² ∗{ π2Py², π2Py², σ2Px¹
Bond order =1/2[9 − 4] =5/2= 2.5
c. CN⁺ ; Has (6+7-1=12 ) electrons : σ1s²σ1s² ∗σ2s², σ2s² ∗{ π2Py², π2Py²,

Bond order =1/2[8 − 4] =4/2= 2…………….. double bond

d. O₂^2- Has (2×8+2=18 ) electrons : σ1s² , σ1s^2∗ , σ2s², σ2s^2∗ , σ2Px² , { π2Py², π2Py², π2Py^1∗, π2Py^1∗ , σ2Px⁰

B. O =1/2[10 − 6] =4/2 = 2……………double bond

Types Of Solids

• Depending On the arrangement of atoms, there are two types of solids
• Crystalline
• Amorphous

Types of crystals

1. Ionic Crystals

• Ionic crystals consist of ions held together by ionic bonds
• The structure of an ionic crystal depends on the charges on the cation, anion and on their radii.
• Thepropertiesofionicsolidsaredirectconsequencesofthestronginterionic forces, which create a high lattice energy.
• Ionic solids have high melting points, an indication of the strong attraction force holding the ions together.

2.Molecular crystals

• Contains molecules
• Molecular solids are made up of discrete molecules that interact via intermolecular forces.
• Various combinations of dipole-dipole, dispersion and hydrogen-bonding forces

3. Covalent network crystals

• In This Type Of Crystalline Solids, separate particles are not present. Instead ,strong covalent bonds link the atoms together throughout the network of covalent solid.
• As a consequence of the strong bonding, all these substances have extremely high melting and boiling points, but their conductivity and hardness depend on the nature of their bonding.
• Eg. graphite and diamond

4. Metallic crystals

• The strong metallic bonding forces hold individual atoms together in metallic solids.
• Bonding in metals can be explained as a network of positive ions immersed in a sea of electrons. That is, the electrons in the valence shell of the metal atoms are highly delocalized. For this Reason, metals are very good conductors of electricity.
• Metallic bonding forces are stronger than those arising from intermolecular forces, so metallic solids have higher melting points than molecular solids