B.Sc. 2nd Semester Chemistry Notes

Molecular Orbital Theory (MOT)

Molecular Orbital Theory, proposed by Hund and Mulliken, explains the bonding in molecules by considering that atomic orbitals (AOs) combine to form molecular orbitals (MOs) that belong to the entire molecule rather than individual atoms.

1. Fundamental Principles

• LCAO Approximation: Linear Combination of Atomic Orbitals. When two AOs ($\psi_A$ and $\psi_B$) overlap, they form two MOs:
  • Bonding MO ($\sigma, \pi$): Lower energy, formed by additive overlap ($\psi_A + \psi_B$).
  • Anti-bonding MO ($\sigma^*, \pi^*$): Higher energy, formed by subtractive overlap ($\psi_A - \psi_B$).
• Bond Order: Defines the stability and number of bonds.
  Bond Order (B.O.) = 1/2 (N_b - N_a)
  Where N_b = electrons in bonding orbitals and N_a = electrons in anti-bonding orbitals.

2. Homonuclear Diatomic Molecules

These molecules consist of two identical atoms (e.g., $N_2, O_2, F_2$).

Case A: Up to Nitrogen ($Z \le 7$)

Due to s-p mixing, the $\sigma_{2p_z}$ orbital is higher in energy than the $\pi_{2p_x}$ and $\pi_{2p_y}$ orbitals.

Sequence: $\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < (\pi_{2p_x} = \pi_{2p_y}) < \sigma_{2p_z} < (\pi^*_{2p_x} = \pi^*_{2p_y}) < \sigma^*_{2p_z}$

Case B: Oxygen and Fluorine ($Z > 7$)

No significant s-p mixing occurs. The $\sigma_{2p_z}$ orbital is lower in energy than the $\pi$ orbitals.

Sequence: $\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < (\pi_{2p_x} = \pi_{2p_y}) < (\pi^*_{2p_x} = \pi^*_{2p_y}) < \sigma^*_{2p_z}$

3. Heteronuclear Diatomic Molecules

These molecules consist of two different atoms (e.g., $CO, NO, HF$). The MO diagram becomes asymmetrical because the more electronegative atom has lower energy atomic orbitals.

Example: Nitric Oxide (NO)

• Total electrons: 15 ($7$ from N, $8$ from O).
• The MO diagram follows the Oxygen pattern.
• Configuration: $KK \sigma_{2s}^2 {\sigma^*_{2s}}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 {\pi^*_{2p_{x,y}}}^1$.
• B.O.: $1/2 (10 - 5) = 2.5$.
• Nature: Paramagnetic (due to 1 unpaired electron).

Example: Carbon Monoxide (CO)

• Total electrons: 14.
• Significant s-p mixing occurs. The HOMO (Highest Occupied Molecular Orbital) is a $\sigma$ orbital which is slightly anti-bonding or non-bonding in nature.
• B.O.: $3.0$.
• Nature: Diamagnetic.

4. Summary of Key Molecular Data

Molecule	Total Electrons	Bond Order	Magnetic Property
$H_2$	2	1.0	Diamagnetic
$N_2$	14	3.0	Diamagnetic
$O_2$	16	2.0	Paramagnetic
$He_2$	4	0	Does not exist

Difference Between valence bond theory (VBT) and Molecular orbital theory (MOT)

The main difference between valence bond theory and the molecular orbital theory is that the valence bond theory explains the hybridization of orbitals whereas the molecular orbital theory does not give details about the hybridization of orbitals.

Basis of Comparision	VBT	MOT
Proposed By	Heitler and London in 1927	Hund and Mulliken in 1932
Description	Used to explain the chemical bonding of atoms in a molecule.	Explains the chemical bonding of molecule using hypothetical molecular orbitals.
Hybridization of Molecular Orbitals	Defines the hybridization of molecular orbitals.	Does not define anything about hybridization of orbitals.
Application	Can only be applied for diatomic molecules.	Can be applied on polyatomic molecules.
What The Theory Explains	Bonding of atomic orbitals.	About the mixing of atomic orbitals when forming molecules.
Atom's individual Characteristics	Atoms which are involved in the bond formation, retains their individual characteristic nature.	Atomic orbitals which form molecular orbitals, do not retain their individual characteristic nature.
Bonds Localization	Bonds are localized to two atoms and not molecules	Bonds are localized to both two atoms and molecules.
Electrons	Some of the valence electrons are represented as not shared and not involved in the formation of the molecule.	All the electrons of the valence shell are represented as having taken part in the bonding.
Method Of Obtaining Molecular Orbital	Resulting molecular orbital is obtained by the combination of two wave functions of two unpaired electrons.	Formation of the molecular orbitals is based on the LCAO approximation method, whereby each molecular orbital is constructed from a superposition of atomic orbitals belonging to the atoms in the molecule.
Paramagnetic Nature Of Oxygen	There is no explanation of paramagnetic nature of oxygen	There is an complete explanation of paramagnetic nature of oxygen.
Resonance	Resonance plays an important role.	Resonance does not play any role.

Fajan's Rule

Kazimierz Fajans in 1923, gave some important points to predict whether a chemical bond is expected to be predominantly ionic or covalent.They are given below-
1. Size of Cations
2. Size of Anions
3. Charge on ions (Cations and Anions)
4. 18 electron configuration
1. Size of Cations
Smaller the size of cation, greater the covalent character.
Example: LiCl, NaCl, KCl, RbCl, CsCl
LiCl is most covalent among the given IA chlorides as the size of Li⁺ is smaller than that of other IA cations.
The order of covalent character is-
LiCl > NaCl > KCl > RbCl > CsCl
2. Size of Anions
Larger the size of anions, greater the covalent character.
Example: LiF, LiCl, LiBr, LiI
LiI is most covalent among the given IA halides as the sixe of iodide ion is larges.
So, the order of covalent character is-
LiI > LiBr > LiCl > LiF
3. Charge on ions (Cations and Anions)
Higher the charge on ions, greater the covalent character.
Example: NaCl, MgCl₂, AlCl₃
AlCl₃ is most covalent among the given molecules as the chage on Al is +3 highest (charge on Na is +1 and on Mg is +2).
So, the order of covalent character is-
AlCl₃ > MgCl₂ > NaCl
4. 18 electron configuration
Molecules which follows 18 electron configuration is more covalent in nature than those molecules which follows 8 electron configuration.
Example: NaCl and CuCl CuCl is more covalent as it follows 18 electron configuration while NaCl is more ionic because it follows 8 electron configuration.

Polarization And Polarizability

The ability of a cation to polarize the anion is referred to as polarizing power. It is directly proportional to the charge density, which in turn is directly related to the charge on cation, while inversely related to the size of anion.
The polarizing power increases with increase in the size of cation i.e. smaller cations are very effective in the polarization of anion. However, the polarizing power increases with increase in the charge on cation (i.e. smaller cation).
The tendency of an anion to become polarized by the cation is called polarizibility. It indicates the easiness with which an anion undergoes distortion in presence of a cation.
It is directly proportional to the size and the charge on an anion. The larger anions can polarized very easily than the smaller ones.
From the above discussion we can easily say that greater the polarizing power of cation and greater the polarizability of anion, greater is the polarization and hence greater will be the covalent nature.

Multicentered Bonding in Diborane ($B_2H_6$)

Diborane ($B_2H_6$) is the classical example of an electron-deficient molecule. It does not have enough valence electrons to form conventional two-center, two-electron (2c-2e) bonds between all its atoms.

The Electron Count Challenge:

• Each Boron (B) has 3 valence electrons ($2 \times 3 = 6$).
• Each Hydrogen (H) has 1 valence electron ($6 \times 1 = 6$).
• Total Valence Electrons: 12 electrons (6 pairs).
• To form a structure like Ethane ($C_2H_6$), 7 bonds (14 electrons) would be required. Thus, $B_2H_6$ is short by 2 electrons.

1. The Structure of Diborane

Experimental studies (Electron diffraction and NMR) reveal that:

• Four hydrogen atoms are terminal (lie in one plane with the two Boron atoms).
• Two hydrogen atoms are bridging (lie in a plane perpendicular to the rest of the molecule).

2. Three-Center Two-Electron (3c-2e) Bonding

To explain the stability of $B_2H_6$, the concept of multicentered bonding is used. Boron undergoes $sp^3$ hybridization.

A. Terminal Bonds (2c-2e)

Four $sp^3$ hybrid orbitals of the two Boron atoms overlap with the $1s$ orbitals of four terminal Hydrogens. These are four regular 2-center 2-electron bonds, consuming 8 electrons.

B. Bridging Bonds (3c-2e) - "The Banana Bond"

Each Boron is left with one filled $sp^3$ orbital, one empty $sp^3$ orbital, and 1 electron (totaling 4 electrons remaining for the bridge). The overlap occurs between:

• An $sp^3$ orbital from Boron 1.
• An $sp^3$ orbital from Boron 2.
• The $1s$ orbital of a bridging Hydrogen.

This results in a 3-center 2-electron (3c-2e) bond. Because of its curved shape, it is often called a Banana Bond.

3. Comparison of Bond Types in $B_2H_6$

Bond Type	Number of Bonds	Electrons per Bond	Bond Length
Terminal (B-Ht)	4	2	~1.19 Å (Shorter/Stronger)
Bridging (B-Hb-B)	2	2 (shared by 3 atoms)	~1.33 Å (Longer/Weaker)

4. Summary of Hybridization

• Boron Hybridization: $sp^3$
• Geometry: Approximately tetrahedral around each Boron.
• Bonding Logic: The 3c-2e bond allows the molecule to achieve stability despite having fewer electrons than required for localized covalent bonds.

Comparative Study of s- and p-Block Elements

1. General Introduction

• s-Block: Elements where the last electron enters the ns orbital. Includes Group 1 (Alkali metals) and Group 2 (Alkaline earth metals).
• p-Block: Elements where the last electron enters the np orbital. Includes Groups 13 to 18. Together with s-block, they are called Representative Elements.

2. Key Periodic Properties

Property	s-Block Characteristics	p-Block Characteristics
Occurrence	Highly reactive; never found free in nature. Occur as halides, carbonates, and sulfates.	Found both in free state (e.g., Noble gases, N, O, Noble metals) and combined states.
Electronic Configuration	ns1-2	ns2 np1-6 (Except Helium)
Atomic & Ionic Radii	Largest in their respective periods. Increases down the group.	Smaller than s-block due to increased nuclear charge. Decreases across a period.
Density	Low density (Li, Na, K float on water) due to large atomic volumes.	Higher density than s-block; increases across the period and down the group.
Ionization Potential (IP)	Very low. Easily lose electrons to form M+ or M+ ions.	Relatively high. Increases across a period; decreases down the group.
Metallic Behaviour	Strongly metallic (Electropositive).	Shows a transition from metals → metalloids → non-metals.
Electronegativity	Very low (Cesium is the least electronegative).	High (Fluorine is the most electronegative). Increases across the period.
Electron Affinity	Almost zero or very low.	High negative values (especially Halogens). Increases across a period.

3. Physical and Chemical Nuances

A. Hydration Energy

s-block ions, especially smaller ones like Li⁺, have high hydration energies. This is why lithium salts are often hydrated (e.g., LiCl.2H⁺O). In p-block, hydration energy decreases as we move down the group with increasing ionic size.

B. Flame Colouration (s-Block Specialty)

s-block elements (except Be and Mg) impart characteristic colours to the Bunsen flame because their outer electrons are easily excited to higher energy levels.

• Li → Crimson red
• Na → Golden yellow
• K → Violet
• Ca → Brick red
• Sr → Crimson red
• Ba → Apple green

p-block elements generally no characteristic flame colour (except some like Tl, In).

C. Photoelectric Effect

Due to extremely low ionization potentials, elements like Cesium (Cs) and Potassium (K) emit electrons when exposed to light. This makes them ideal for use in photoelectric cells.

D. Polarization Power (Fajans' Rule)

Small cations with high charges (like Li⁺ or Be²⁺) have high polarizing power, leading to covalent character in their compounds. In p-block, polarizing power increases across the period as the charge-to-size ratio increases.

E. Melting and Boiling Points

s-block: Generally low due to weak metallic bonding (large atoms, few valence electrons).
p-block: Follows a complex trend. Generally high for giant covalent structures (like Diamond/Boron) and very low for molecular gases (like N₂, O₂, and Noble gases).

Summary Note: The reactivity of s-block elements increases down the group, whereas for p-block (non-metals), reactivity generally decreases down the group (e.g., Fluorine is more reactive than Iodine).

F. Diagonal Relationship

Definition: Similarity in properties between first element of a group and second element of the next group (due to similar charge/radius ratio).

Important Diagonal Pairs:

• Li and Mg
• Be and Al
• B and Si

Reasons: Similar ionic size and charge density.

Examples: Both Li and Mg form nitrides with N₂, both Be and Al form amphoteric oxides, both show covalent character in compounds.

G. Catenation

Definition: Self-linking property of atoms to form long chains or rings.

Maximum in Carbon (p-block) due to small size and high bond energy of C–C bond.

Order of catenation: C >> Si > Ge > Sn > Pb (decreases down the group)

Note: s-block elements show very little or no catenation.

H. Inert Pair Effect

Definition: Reluctance of the valence s-electrons to participate in bonding in heavier p-block elements.

Prominent in: Group 13 (Tl), Group 14 (Pb), Group 15 (Bi)

Consequence: Lower oxidation state becomes more stable than higher one.

Examples:

• Tl⁺ is more stable than Tl³⁺
• Pb²⁺ is more stable than Pb⁴⁺
• Bi³⁺ is more stable than Bi⁵⁺

This effect increases down the group in p-block.

Must Read Inert Pair Effect

I. pπ–pπ Multiple Bonding

Definition: Formation of π-bond by lateral overlap of p-orbitals.

Common in: Second period p-block elements (C, N, O, F).

Examples: C=C, C≡C, C=O, N≡N, O=O, N=O

Note: Effective in small atoms (2p–2p overlap). Weak or absent in heavier elements due to larger size and poor overlap.

J. dπ–pπ Multiple Bonding

Definition: π-bond formed by overlap of p-orbital of one atom and d-orbital of another atom.

Occurs in: Heavier p-block elements (Si, P, S, Cl etc.)

Examples:

• P=O in phosphates
• S=O in sulphates, SO₂, SO₃
• Si–O in silicates

Importance: Explains stability of oxoacids and oxides of third period elements.