Short Notes: Chemical Bonding

4.1 Types of Bonds

• Chemical bond - an attractive force that holds atoms together in molecules or solids; arises from interactions of valence electrons.
• Ionic bond - formed by electrostatic attraction between oppositely charged ions created by transfer of electrons. Example: NaCl. Characteristic features: high melting/boiling points, electrical conductivity in molten/aqueous state, crystalline solids.
• Covalent bond - formed by sharing of electron pairs between atoms. Example: H2, Cl2, CH4. Can be single, double or triple bonds depending on number of shared electron pairs.
• Polar covalent bond - covalent bond with unequal sharing of electrons due to difference in electronegativity; produces partial charges and bond dipole. Example: HCl.
• Coordinate (dative) covalent bond - a shared pair of electrons contributed by one atom only. Example: formation of NH4+ from NH3 and H+ (lone pair on N donated to H+).
• Metallic bond - metal atoms contribute valence electrons to a delocalised "electron sea" that binds positive metal ions. Features: electrical and thermal conductivity, malleability, ductility.
• Hydrogen bond - a special strong dipole-dipole attraction where H is bonded to a highly electronegative atom (F, O, N) and attracted to a lone pair on another electronegative atom. Example: hydrogen bonding in water causes high boiling point and surface tension.
• van der Waals forces - weak intermolecular attractions including London dispersion forces (present in all molecules), dipole-dipole interactions, and induced dipole interactions; important in physical properties of molecular substances.
• Bond characteristics - bond length (distance between nuclei), bond energy (strength), bond order (number of shared electron pairs). Higher bond order → shorter and stronger bond.

4.2 Lewis Structures and Octet Rule

• Octet Rule - atoms tend to gain, lose or share electrons so as to attain eight valence electrons (noble-gas configuration). Exceptions: hydrogen (stable with 2 electrons), beryllium (often 4), boron (often 6), odd-electron species (e.g., NO), and elements of the third period and beyond that can have expanded octets (e.g., P, S, Cl).
• Formal charge - a bookkeeping device to evaluate the best Lewis structure.
  Formula: \( \text{Formal charge} = V - N - \dfrac{B}{2} \)
  where V = number of valence electrons of the isolated atom, N = number of non-bonding (lone pair) electrons on the atom in the structure, B = number of electrons shared in bonds (bonding electrons) on that atom.
• Resonance - when two or more valid Lewis structures can be drawn for a molecule, the true structure is a resonance hybrid (delocalisation of electrons). Examples: ozone (O3), nitrate ion (NO3-), benzene (C6H6).
• Rules / steps to draw Lewis structures -
  • Count total valence electrons for the molecule/ion (add electrons for negative charge, subtract for positive charge).
  • Choose a skeletal arrangement of atoms (usually the least electronegative atom at centre, hydrogen terminal).
  • Place single bonds between central and peripheral atoms, then distribute remaining electrons as lone pairs to satisfy octets (or duet for H).
  • If octet is not complete for central atom, form multiple bonds (double/triple) as needed.
  • Calculate formal charges to select the most appropriate structure: best structure minimises formal charges and places negative formal charges on more electronegative atoms.
• Worked example (CO2) -
  Carbon: V = 4, nonbonding electrons on C = 0, bonding electrons on C = 8 (two double bonds). Using formula: \( \text{FC}_\text{C} = 4 - 0 - \dfrac{8}{2} = 0 \). Oxygen atoms also have formal charge 0 in the best Lewis structure (O=C=O).
• Worked example (NO3-) -
  Nitrate shows resonance among three equivalent structures; formal charge distribution places +1 on N and -1 spread over O atoms in resonance forms; actual structure has delocalised negative charge and equal N-O bond lengths.

4.3 Hybridization and Geometry

• Hybridisation - mixing of atomic orbitals of similar energies on the same atom to produce new equivalent hybrid orbitals that explain observed molecular shapes and bond angles.
• Steric number (SN) method to predict hybridisation - SN = number of sigma bonds + number of lone pairs around the central atom. Common correspondences:
  • SN = 2 → sp hybridisation → linear geometry (bond angle 180°). Example: BeCl2.
  • SN = 3 → sp2 hybridisation → trigonal planar geometry (bond angle ≈ 120°). Example: BF3.
  • SN = 4 → sp3 hybridisation → tetrahedral geometry (bond angle ≈ 109.5°). Example: CH4.
  • SN = 5 → sp3d hybridisation → trigonal bipyramidal geometry (angles 90°, 120°). Example: PCl5.
  • SN = 6 → sp3d2 hybridisation → octahedral geometry (angles 90°). Example: SF6.
• Examples and observations - NH3: central N has SN = 4 (3 bonds + 1 lone pair) → sp3 hybridisation; due to lone pair repulsion, the H-N-H bond angle is ≈ 107°. H2O: O has SN = 4 (2 bonds + 2 lone pairs) → sp3 hybridisation; lone pairs compress bond angle to ≈ 104.5°.
• Limitations - hybridisation is a useful model for covalent bonding and molecular shape but is a simplified picture; in molecules with extensive delocalisation (resonance) or transition metal complexes, pure hybridisation descriptions may be insufficient.
• Expanded octet & d-orbitals - elements in period 3 and beyond can use d-orbitals to form sp3d or sp3d2 hybrids, allowing more than eight electrons around the central atom (e.g., PCl5, SF6).

4.4 VSEPR Theory

• Basic principle - Valence Shell Electron Pair Repulsion (VSEPR) theory: electron pairs (bonding and lone pairs) around a central atom arrange themselves to minimise mutual repulsion, determining molecular shape.
• Electron domains - each lone pair, single bond, multiple bond or lone electron is counted as an electron domain for geometry determination.
• Repulsion order - lone pair-lone pair > lone pair-bond pair > bond pair-bond pair. This causes lone pairs to compress bond angles compared with ideal values.
• Electron geometry vs molecular geometry - electron geometry accounts for all electron domains; molecular geometry describes positions of atoms only (ignoring lone pairs). Example: tetrahedral electron geometry can give trigonal pyramidal molecular geometry (NH3) or bent geometry (H2O) depending on lone pairs.
• Examples of common shapes and angles -
  • Linear - 180° (e.g., CO2, BeCl2).
  • Trigonal planar - ≈120° (e.g., BF3).
  • Tetrahedral - ≈109.5° (e.g., CH4).
  • Trigonal bipyramidal - 90° & 120° (e.g., PCl5).
  • Octahedral - 90° (e.g., SF6).
• Effect of multiple bonds - multiple bonds occupy more space than single bonds and therefore can exert greater repulsion, slightly modifying bond angles.

4.5 Molecular Orbital Theory

• Fundamental idea - molecular orbitals (MOs) are formed by linear combination of atomic orbitals (LCAO). Electrons occupy MOs that extend over the entire molecule rather than being localised between two atoms.
• Bonding and antibonding orbitals - constructive overlap of atomic orbitals produces lower-energy bonding MOs; destructive overlap produces higher-energy antibonding MOs (denoted with an asterisk, e.g., σ*).
• Sigma (σ) and pi (π) MOs - sigma MOs arise from head-on overlap, pi MOs from side-on overlap. σ bonds are generally stronger along the internuclear axis; π bonds restrict rotation around the bond axis.
• Energy ordering (period-2 diatomics) - the relative energies of σ2p and π2p orbitals depend on s-p mixing. For B2, C2, N2 the order places π2p lower than σ2p; for O2, F2 σ2p is lower than π2p. This energy ordering affects electron configurations and magnetic properties.
• Bond order -
  Formula: \( \text{Bond order} = \dfrac{N_b - N_a}{2} \)
  where Nb = number of electrons in bonding MOs and Na = number of electrons in antibonding MOs. Examples: H2 has bond order 1 (stable), He2 has bond order 0 (unstable), O2 has bond order 2 and is paramagnetic due to two unpaired electrons.
• Magnetism - MO theory correctly explains paramagnetism (presence of unpaired electrons) and diamagnetism of molecules; for example, O2 is paramagnetic while N2 is diamagnetic.
• Applications and limitations - MO theory provides quantitative insight into bond order, bond strength, magnetic properties and delocalisation (conjugation). It is more complete than simple Lewis or hybridisation models for molecules with delocalised electrons, but MO diagrams can be more complex to construct for large molecules.

Summary: Chemical bonding covers a range of models - from Lewis structures and the octet rule useful for simple covalent molecules, to VSEPR for molecular shapes, hybridisation for bonding directions, and molecular orbital theory for electronic structure, bond order and magnetic properties. Use the appropriate model based on the problem: Lewis/VSEPR/hybridisation for shapes and simple reactivity; MO theory for bond order and magnetism.