Unit 3: Chemical Bonding-I

Covalent Bond (VBT) & Hybridization

Covalent Bond: Lewis Structure

A Lewis structure is a 2D representation of a molecule showing how valence electrons are distributed as shared pairs (bonds) and lone pairs. The goal is usually to satisfy the octet rule (8 electrons) for each atom (or duet rule for H).

Formal Charge (FC): A "bookkeeping" charge to determine the most plausible Lewis structure.

Formula: FC = (Valence e^-) - (Non-bonding e^-) - (1) / (2)(Bonding e^-)

The best structure has FCs closest to zero and any negative FC on the most electronegative atom.

Valence Bond Theory (VBT)

VBT describes a covalent bond as the overlap of half-filled atomic orbitals. The electrons in the overlapping orbitals must have opposite spins.

• Heitler-London Approach (for H₂): As two H atoms approach, new forces arise:
  • Attractive: (Nucleus A - Electron B) and (Nucleus B - Electron A)
  • Repulsive: (Nucleus A - Nucleus B) and (Electron A - Electron B)
  A bond forms at an optimal distance (bond length) where the attractive forces are maximized and the system's potential energy is at a minimum.
• σ (Sigma) Bond: Formed by head-on (axial) overlap of orbitals (e.g., s-s, s-p, p-p). Electron density is on the internuclear axis.
• π (Pi) Bond: Formed by sideways (parallel) overlap of p-orbitals. Electron density is above and below the internuclear axis. A π-bond only forms *after* a σ-bond.

Multiple Bonding: A double bond is (1 σ + 1 π). A triple bond is (1 σ + 2 π).

Hybridization

Hybridization (proposed by Pauling) is the concept of mixing atomic orbitals of slightly different energies to form a new set of degenerate (equal energy) hybrid orbitals. These new orbitals are better suited for bonding and explain observed molecular geometries.

Energetics of Hybridization

Hybridization is an "energy-neutral" process in theory. Energy is "spent" to promote electrons (e.g., 2s → 2p in Carbon), but this energy is more than "repaid" by the formation of more, stronger, and more stable bonds (e.g., 4 C-H bonds in CH₄ vs. the 2 expected for C 2p²).

Equivalent and Non-equivalent Hybrid Orbitals

• Equivalent: All hybrid orbitals are identical.
  • sp: 2 orbitals, 180° (Linear)
  • sp²: 3 orbitals, 120° (Trigonal Planar)
  • sp³: 4 orbitals, 109.5° (Tetrahedral)
• Non-equivalent: Arises in sp³d and sp³d² hybridization.
  • sp³d (Trigonal Bipyramidal): The 3 equatorial orbitals (120°) are different from the 2 axial orbitals (90° to the plane). Axial bonds are longer and weaker.
  • sp³d² (Octahedral): All 6 orbitals are equivalent.

Resonance & Molecular Orbital Theory (MOT)

Resonance

Resonance is used when a single Lewis structure cannot adequately describe the bonding in a molecule. The actual structure is an average or "hybrid" of two or more resonance structures (or canonical forms), which differ only in the placement of π-electrons and lone pairs.

Example: Ozone (O₃). We can draw two valid Lewis structures. The real O₃ molecule is a hybrid of these, with both O-O bonds being identical (length of 1.5) and a charge of -0.5 on each outer oxygen.

Resonance Energy

Definition: The difference in energy between the actual resonance hybrid and the most stable of its contributing resonance structures.

Resonance leads to delocalization of electrons, which stabilizes the molecule. The larger the resonance energy, the more stable the molecule.

Molecular Orbital Theory (MOT)

MOT is a more advanced model where all atomic orbitals (AOs) from all atoms combine to form an equal number of molecular orbitals (MOs) that are delocalized over the *entire* molecule.

• LCAO: Linear Combination of Atomic Orbitals.
  • Bonding MO (BMO): Formed by constructive interference (ψ_A + ψ_B). Lower in energy than the AOs. Stabilizing.
  • Antibonding MO (ABMO): Formed by destructive interference (ψ_A - ψ_B). Higher in energy. Destabilizing. Has a node between nuclei.
• Bond Order (BO):

  Formula: BO = (1) / (2) × (No. of Bonding e^- - No. of Antibonding e^-)

  • BO = 1 (Single bond), 2 (Double bond), 3 (Triple bond)
  • BO > 0: Molecule is stable.
  • BO = 0: Molecule does not exist.
• Magnetic Property: If all electrons are paired → Diamagnetic. If one or more unpaired electrons exist → Paramagnetic.

MO Diagrams of Diatomic Molecules

s-p Mixing

For homonuclear diatomics B₂, C₂, and N₂ (and their ions), the 2s and 2p_z orbitals are close enough in energy to interact (mix). This mixing raises the energy of the σ_2pz MO above that of the π_{2p_{x,y}} MOs.

For O₂, F₂, and Ne₂, the 2s-2p energy gap is too large for mixing, so the "normal" order is followed.

MO Filling Order

For B2, C2, N2 (s-p mixing)	For O2, F2 (no s-p mixing)
σ1s < σ*1s < σ2s < σ*2s < π2p_{x,y} < σ2pz < π*2p_{x,y} < σ*2pz	σ1s < σ*1s < σ2s < σ*2s < σ2pz < π2p_{x,y} < π*2p_{x,y} < σ*2pz

MOs for Simple Polyatomic Molecules

• HCl: H(1s) orbital overlaps with Cl(3p_z) orbital. The Cl(3p_x, 3p_y) orbitals are non-bonding.
• BeF₂: (Linear) The Be(2s) and Be(2p_z) orbitals combine with F(p_z) orbitals to form σ and σ^* MOs.
• CO₂: (Linear) Involves combinations of C(2s, 2p) and O(2s, 2p) to form a set of σ and π MOs delocalized over all three atoms.

Valence Shell Electron Pair Repulsion (VSEPR) Theory

VSEPR is a model used to predict the 3D geometry of molecules based on the idea that electron pairs in the valence shell of a central atom repel each other and will arrange themselves to be as far apart as possible, minimizing repulsion.

Postulates of VSEPR

1. The shape of a molecule depends on the number of valence shell electron pairs (Bonding Pairs, BP, and Lone Pairs, LP) around the central atom.
2. Electron pairs (LP and BP) repel each other.
3. The order of repulsion strength is:

   LP-LP > LP-BP > BP-BP

   Reason: A lone pair is only held by one nucleus, so it is "fatter" and "wider" than a bonding pair, which is held by two nuclei.
4. Multiple bonds (double/triple) are treated as a single "superpair" for determining geometry, but they exert more repulsion than a single bond.

Shapes of Simple Molecules (AXE method)

A = Central Atom, X = Bonded Atom (BP), E = Lone Pair (LP)

VSEPR Geometries

Total Pairs (X+E)	Type	BP (X)	LP (E)	Electron Geometry	Molecular Shape	Angle(s)	Example
2	AX2	2	0	Linear	Linear	180°	BeF2, CO2
3	AX3	3	0	Trigonal Planar	Trigonal Planar	120°	BF3
3	AX2E	2	1	Trigonal Planar	Bent (V-shape)	< 120°	SO2, O3
4	AX4	4	0	Tetrahedral	Tetrahedral	109.5°	CH4, NH4+
4	AX3E	3	1	Tetrahedral	Trigonal Pyramidal	< 109.5° (e.g., 107°)	NH3, PCl3
4	AX2E2	2	2	Tetrahedral	Bent (V-shape)	< 109.5° (e.g., 104.5°)	H2O, SCl2
5	AX5	5	0	Trigonal Bipyramidal	Trigonal Bipyramidal	90°, 120°	PCl5
5	AX4E	4	1	Trigonal Bipyramidal	See-Saw	< 90°, < 120°	SF4
5	AX3E2	3	2	Trigonal Bipyramidal	T-shape	< 90°	ClF3
5	AX2E3	2	3	Trigonal Bipyramidal	Linear	180°	XeF2
6	AX6	6	0	Octahedral	Octahedral	90°	SF6
6	AX5E	5	1	Octahedral	Square Pyramidal	< 90°	BrF5
6	AX4E2	4	2	Octahedral	Square Planar	90°	XeF4

Bond Polarity & Fajan's Rules

Ionic Character in Covalent Compounds

When two different atoms form a covalent bond (e.g., H-Cl), the shared electrons are not shared equally. The more electronegative atom (Cl) pulls the electrons closer, creating a polar covalent bond.

• This creates a partial negative charge (δ^-) on the Cl and a partial positive charge (δ⁺) on the H.
• Bond Moment: The dipole moment of a single bond.
• Dipole Moment (μ): The vector sum of all bond moments in a molecule. It is a measure of the overall polarity of the molecule.

  Formula: μ = q × d
  Where: q = magnitude of charge, d = distance of separation. Unit = Debye (D).

Symmetrical molecules (like CO₂, CCl₄, BF₃) can have polar bonds, but their bond moments cancel out, resulting in a zero dipole moment (μ = 0). They are non-polar.

Asymmetrical molecules (like H₂O, NH₃) have bond moments that do not cancel, resulting in a net dipole moment. They are polar.

Covalent Character in Ionic Compounds

No bond is 100% ionic. An "ionic bond" (e.g., NaCl) always has some covalent character because the cation (Na⁺) pulls on, or polarizes, the electron cloud of the anion (Cl^-).

• Polarizing Power: The ability of a cation to distort an anion's electron cloud.
• Polarizability: The ease with which an anion's electron cloud can be distorted.

Fajan's Rules

Fajan's rules predict the degree of covalent character in an ionic bond. Covalent character is favored by:

1. Small Cation: A small cation has a high charge density and high polarizing power. (e.g., LiCl is more covalent than NaCl).
2. Large Anion: A large anion's electron cloud is loosely held and highly polarizable. (e.g., LiI is more covalent than LiCl).
3. High Charge on Cation or Anion: Higher charges lead to stronger attraction/polarization. (e.g., AlCl₃ is more covalent than MgCl₂, which is more covalent than NaCl).
4. Pseudo-Noble Gas Configuration: A cation with 18 valence electrons (e.g., Cu⁺) has a higher polarizing power than one with 8 electrons (e.g., Na⁺) due to poor shielding by d-electrons. (e.g., CuCl is more covalent than NaCl).

Consequences of Polarization

Increased covalent character leads to:

• Lower melting and boiling points. (e.g., AlCl₃ sublimes, while NaCl melts at 801°C).
• Lower solubility in polar solvents (like water).
• Increased color. (e.g., AgCl is white, AgBr is cream, AgI is yellow, as I^- is more polarized).