Chemical Bonding and Molecular Structure

Inorganic Chemistry Weightage: 7 Marks CBSE Unit 4

1. Kössel-Lewis Approach, Octet Rule & Lewis Structures

A chemical bond is the attractive force which holds various constituents (atoms, ions) together in a chemical species. Kössel and Lewis (1916) gave the first systematic electronic explanation, based on the special stability of noble gas configurations ( $ns^2np^6$ , or a duplet $1s^2$ for He).

Kössel-Lewis approach: an ionic bond forms by complete electron transfer between atoms (each ends up with a noble-gas octet as an ion), while a covalent bond forms by sharing a pair of electrons between two neutral atoms so both attain an octet without transferring charge.

Lewis symbols show only the valence electrons of an atom as dots around its symbol. The number of dots equals the group valence (or 8 minus that number).
Octet rule: atoms tend to combine, by either transferring electrons (ionic bond) or sharing electrons (covalent bond), so as to acquire eight electrons in their outermost shell — the stable configuration of the nearest noble gas.
Writing a Lewis structure: (i) count total valence electrons of all atoms (adjust for ionic charge: add for each negative charge, subtract for each positive charge); (ii) write the skeletal structure, with the least electronegative atom usually central (H and halogens are always terminal); (iii) place a single bond (shared pair) between each pair of bonded atoms, then distribute remaining electrons as lone pairs to complete octets, resorting to double or triple bonds where a single bond leaves an atom's octet incomplete.
Bond order in Lewis terms: a single covalent bond shares one electron pair; a double bond shares two pairs (e.g. O=O in O₂, both C=O bonds in CO₂); a triple bond shares three pairs (e.g. N≡N in N₂, HC≡CH in ethyne).

2. Formal Charge & Limitations of the Octet Rule

When more than one Lewis structure is possible for a species, formal charge helps select the most reasonable one — generally the structure with the smallest formal charges on its atoms.

\text{F.C.} = \left(\text{valence electrons in free atom}\right) - \left(\text{lone-pair electrons}\right) - \frac{1}{2}\left(\text{bonding electrons}\right)

Formal charges are a bookkeeping device (assuming perfectly equal sharing of every bond pair) and do not indicate real charge separation within the molecule.

The octet rule is not universal. Three recognised classes of exceptions:

Incomplete octet of the central atom: central atoms with fewer than four valence electrons cannot complete an octet. Examples: LiCl, BeH₂, BCl₃ (only 6 electrons around B).
Odd-electron molecules: a molecule with an odd total electron count can never have every atom paired into an octet. Examples: nitric oxide (NO), nitrogen dioxide (NO₂).
Expanded octet: elements from Period 3 onward have accessible $d$ orbitals, allowing more than eight electrons around the central atom. Examples: PF₅, SF₆, H₂SO₄.

Other drawbacks: the octet rule cannot account for the shape of molecules, says nothing about relative stability (energy), and does not explain why certain noble gases (Xe, Kr) still form real compounds (XeF₂, KrF₂) despite their supposedly stable configuration.

3. Ionic Bond & Lattice Enthalpy

An ionic (electrovalent) bond forms most readily between an element with low ionization enthalpy (easily forms a cation) and an element with a highly negative electron gain enthalpy (easily forms an anion). Formation involves two separate steps followed by lattice assembly:

\text{M(g)} \rightarrow \text{M}^+\text{(g)} + e^- \quad (\text{ionization enthalpy})

\text{X(g)} + e^- \rightarrow \text{X}^-\text{(g)} \quad (\text{electron gain enthalpy})

\text{M}^+\text{(g)} + \text{X}^-\text{(g)} \rightarrow \text{MX(s)}

Lattice enthalpy is the energy required to completely separate one mole of a solid ionic compound into its gaseous constituent ions (e.g. lattice enthalpy of NaCl = 788 kJ mol⁻¹). Even when the sum of ionization enthalpy and electron gain enthalpy for a pair of elements is net positive (energy-costly), the compound still forms and is stable, because the large negative lattice enthalpy released on crystallisation more than compensates — this is the real thermodynamic reason ionic compounds are stable, not simply "octet achieved."

4. Bond Parameters: Length, Angle, Enthalpy & Order

Bond length: the equilibrium distance between the nuclei of two bonded atoms, $R = r_A + r_B$ (sum of covalent radii). Measured by spectroscopic, X-ray, or electron-diffraction methods.
Bond angle: the angle between two bonding orbitals around a central atom (e.g. 104.5° in H₂O).
Bond enthalpy: the energy required to break one mole of bonds of a particular type in the gaseous state (e.g. H–H bond enthalpy in H₂ = 435.8 kJ mol⁻¹). For polyatomic molecules with more than one bond of the same type, an average (mean) bond enthalpy is used, since successive bonds of the same type don't require identical energy (e.g. the two O–H bonds in water require 502 and 427 kJ mol⁻¹ respectively, averaging to 464.5 kJ mol⁻¹).
Bond order: the number of bonds between two atoms in a molecule (1 for single, 2 for double, 3 for triple), as read directly off the Lewis structure. Higher bond order correlates with greater bond enthalpy and shorter bond length.

5. Resonance & Bond Polarity

When a single Lewis structure cannot accurately represent a molecule's actual (experimentally measured) bond lengths, several structures of similar energy — called canonical (resonance) forms — are combined into a resonance hybrid, which alone describes the real molecule. Classic example: ozone (O₃), whose two O–O bonds are experimentally identical (128 pm each, between a single-bond 148 pm and double-bond 121 pm), impossible to draw with one Lewis structure. The same reasoning applies to the carbonate ion (CO₃²⁻) and CO₂. Canonical forms have no independent real existence — the molecule does not oscillate between them; it simply has one single, averaged, resonance-hybrid structure at all times.

Bond polarity: no real bond is 100% ionic or 100% covalent. In a covalent bond between two different atoms, the shared pair shifts toward the more electronegative atom, creating a polar covalent bond with a dipole moment, $\mu = Q \times r$ (charge magnitude × separation distance), measured in Debye (1 D = $3.336 \times 10^{-30}$ C m). For a polyatomic molecule, the net dipole moment is the vector sum of individual bond dipoles — this is why BeF₂ (linear, opposing dipoles) and BF₃ (trigonal planar, three dipoles summing to zero by symmetry) are both net non-polar despite having polar bonds.

NH₃ vs NF₃ paradox: although F is more electronegative than H, NH₃ has a larger dipole moment (4.90 × 10⁻³⁰ C m) than NF₃ (0.8 × 10⁻³⁰ C m). In NH₃, the lone pair's orbital dipole points the same direction as the resultant N–H bond dipoles (reinforcing); in NF₃, the lone pair's dipole points opposite to the resultant N–F bond dipoles (partially cancelling), lowering the net value.

6. VSEPR Theory & Molecular Shapes

The Valence Shell Electron Pair Repulsion (VSEPR) theory (Sidgwick & Powell; refined by Nyholm & Gillespie) predicts molecular geometry from a simple idea: electron pairs around a central atom repel each other and arrange themselves to be as far apart as possible.

The five base geometries VSEPR predicts for a central atom with no lone pairs, by electron-pair count: 2 → linear, 3 → trigonal planar, 4 → tetrahedral, 5 → trigonal bipyramidal, 6 → octahedral. A lone pair on the central atom distorts these further (e.g. NH₃ and H₂O below).

Repulsion strength decreases in the order: lone pair–lone pair (lp–lp) $>$ lone pair–bond pair (lp–bp) $>$ bond pair–bond pair (bp–bp). This single ranking explains every distortion from an "ideal" geometry:

Molecule	Ideal angle (no lone pair)	Actual angle	Reason
NH₃ (1 lone pair)	109.5°	107°	one lp–bp repulsion compresses the H–N–H angle
H₂O (2 lone pairs)	109.5°	104.5°	two lp–bp repulsions (plus lp–lp) compress it further

A multiple bond is treated as a single "super pair" for VSEPR counting purposes, and where resonance structures exist, VSEPR applies to any one of them equally.

7. Valence Bond Theory & Orbital Overlap

Valence Bond (VB) theory (Heitler-London, extended by Pauling) explains covalent bond formation via the overlap of atomic orbitals, each singly occupied and with opposite electron spins. As two atoms approach, attractive forces (nucleus–other atom's electron) and repulsive forces (electron–electron, nucleus–nucleus) both grow, but attraction dominates until a minimum-energy, equilibrium bond length is reached (e.g. 74 pm for H₂, releasing 435.8 kJ mol⁻¹ as bond enthalpy).

Types of overlap:

Sigma (σ) bond: head-on (axial) overlap along the internuclear axis — from $s$ - $s$ , $s$ - $p$ , or $p$ - $p$ (end-on) combinations. Sigma bonds involve greater overlap and are therefore stronger.
Pi (π) bond: sidewise (lateral) overlap of $p$ orbitals whose axes stay parallel to each other but perpendicular to the internuclear axis, producing electron density above and below the bond axis. Pi bonds involve less overlap and are weaker than sigma bonds. A double bond = 1 σ + 1 π; a triple bond = 1 σ + 2 π.

Simple, unhybridised orbital overlap fails to explain the actual bond angles of polyatomic molecules like CH₄ (would predict 90° HCH angles from pure $p$ orbitals, but the real angle is 109.5°) — this gap is exactly what hybridisation resolves.

8. Hybridisation (sp, sp², sp³, sp³d, sp³d²)

Hybridisation is the intermixing of atomic orbitals of similar energy to produce an equal number of new, equivalent hybrid orbitals with a definite geometry — introduced by Pauling to explain the real shapes of polyatomic molecules.

Each hybridisation type mixes a fixed count of s, p (and sometimes d) orbitals of nearly equal energy into that same number of new, equivalent hybrid orbitals, oriented to keep electron pairs as far apart as possible.

Type	Orbitals mixed	Geometry (angle)	Examples
$sp$	1 $s$ + 1 $p$	Linear (180°)	BeCl₂, CO₂, C₂H₂
$sp^2$	1 $s$ + 2 $p$	Trigonal planar (120°)	BCl₃, C₂H₄
$sp^3$	1 $s$ + 3 $p$	Tetrahedral (109.5°)	CH₄, NH₃, H₂O
$sp^3d$	1 $s$ + 3 $p$ + 1 $d$	Trigonal bipyramidal	PCl₅
$sp^3d^2$	1 $s$ + 3 $p$ + 2 $d$	Octahedral	SF₆

Salient features: the number of hybrid orbitals always equals the number of atomic orbitals mixed; hybrid orbitals are equivalent in energy and shape, and are more effective at forming stable bonds than pure atomic orbitals because they concentrate electron density more directionally toward the bonded atom. Promotion of an electron to an empty orbital (e.g. one 2s electron of Be promoted to 2p) is a common but not compulsory precondition.

Axial vs equatorial bonds in PCl₅ ( $sp^3d$ ): the three equatorial P–Cl bonds (120° to each other) experience less repulsion than the two axial bonds (90° to the equatorial plane), so axial bonds are slightly longer and weaker than equatorial bonds — making PCl₅'s axial chlorines more reactive.

9. Molecular Orbital Theory & Homonuclear Diatomics

Molecular Orbital (MO) theory (Hund & Mulliken) treats electrons in a molecule as belonging to the molecule as a whole (polycentric), not to individual atoms. Atomic orbitals of comparable energy and matching symmetry combine, via Linear Combination of Atomic Orbitals (LCAO), to form molecular orbitals:

\sigma = \psi_A + \psi_B \quad (\text{bonding MO, lower energy})

\sigma^* = \psi_A - \psi_B \quad (\text{antibonding MO, higher energy})

Each box is one molecular orbital holding at most 2 electrons (Pauli), and degenerate π orbitals fill singly first (Hund's rule) — exactly why O₂ ends up with one unpaired electron in each π*2p orbital, correctly predicting its experimentally observed paramagnetism, something the simple Lewis structure O=O cannot explain.

Electrons fill molecular orbitals following the same rules as atomic orbitals: Aufbau (lowest energy first), Pauli exclusion, and Hund's rule (degenerate orbitals like the two π2p fill singly before pairing).

Bond order (MO definition): $\text{B.O.} = \frac{1}{2}(N_b - N_a)$ , where $N_b$ and $N_a$ are the number of electrons in bonding and antibonding MOs respectively. A positive bond order means a stable molecule; zero or negative means the molecule does not exist.

H₂: $(\sigma1s)^2$ , bond order $= \frac{1}{2}(2-0) = 1$ ; diamagnetic.
He₂: $(\sigma1s)^2(\sigma^*1s)^2$ , bond order $= \frac{1}{2}(2-2) = 0$ — He₂ does not exist.
O₂: bond order 2 (a double bond), but crucially has two unpaired electrons in the degenerate $\pi^*2p$ orbitals — correctly predicting O₂'s experimentally observed paramagnetism, something the simple Lewis structure O=O (all electrons paired) cannot explain. This is MO theory's signature success over the Lewis/VB picture.

10. Hydrogen Bonding

When hydrogen is covalently bonded to a small, highly electronegative atom (F, O, or N), the bond's shared electron pair shifts strongly toward that atom, leaving hydrogen with a significant partial positive charge ( $\delta^+$ ). This exposed proton is then attracted to a lone pair on an electronegative atom (F, O, or N) of a different molecule (or a different part of the same molecule) — this attractive force is the hydrogen bond, weaker than a covalent bond but strong enough to noticeably affect physical properties.

Intermolecular H-bonding links separate molecules into chains or networks, raising boiling point substantially (water); intramolecular H-bonding forms a ring within a single molecule instead, so the molecule stays discrete and volatile (o-nitrophenol boils far lower than its para-isomer, which can only H-bond intermolecularly).

Intermolecular hydrogen bonding: occurs between separate molecules (e.g. in HF, water, alcohols), often forming extended chains or networks. This is why water's boiling point is anomalously high for its molecular weight, and why water shows a density maximum at 277 K, not 273 K (as ice melts, its open, hydrogen-bonded cage collapses, initially increasing density, until thermal expansion of the liquid takes over past 277 K).
Intramolecular hydrogen bonding: occurs within a single molecule, between two suitably positioned electronegative sites (e.g. o-nitrophenol, o-hydroxybenzaldehyde). Because the molecule stays as discrete, non-associated units, intramolecular H-bonding compounds have lower boiling/melting points than their para-isomer counterparts, which can only hydrogen-bond intermolecularly and therefore associate into higher-boiling aggregates.