Chemical Bonding And Molecular Structure

Chemical bonding is the single most "leveraged" chapter in Physical–Inorganic chemistry: it decides molecular shapes, polarity, magnetic behaviour and stability, and its ideas resurface in coordination compounds, p-block, organic reaction mechanisms and even in solid state. NEET typically pulls 2–4 questions directly from here, and many more indirectly.

Why Atoms Combine: The Ionic Bond and Lattice Enthalpy

Isolated atoms (except noble gases) are energetically restless. When two or more atoms come together, they rearrange their valence electrons in whatever way lowers the total energy of the system — that rearrangement, once stable, is what we call a chemical bond. Kössel and Lewis explained the simplest route: one atom hands over electrons, another accepts them, and both end up with a noble-gas-like electron count. The resulting oppositely charged ions are held by electrostatic attraction — the ionic (electrovalent) bond.

Ionic bonding is favoured when the donor has low ionisation enthalpy (alkali/alkaline earth metals) and the acceptor has high negative electron gain enthalpy (halogens, oxygen). But neither of these decides stability by itself. The decisive quantity is lattice enthalpy — the energy released when one mole of an ionic crystal forms from its gaseous ions (or, equivalently, the energy needed to pull the crystal apart into gaseous ions). Note carefully: an ionic "molecule" like NaCl does not exist as a discrete unit in the solid; the crystal is a three-dimensional array in which each Na⁺ is surrounded by six Cl⁻ and vice versa. Formulae like NaCl only give the ratio of ions.

Lattice enthalpy rises when:

• Charges on the ions increase (MgO ≫ NaCl, since 2+/2− beats 1+/1−)
• Ionic radii decrease (LiF > LiI), because the ions can approach more closely

A purely ionic bond is an idealisation. Every cation distorts (polarises) the electron cloud of the anion, giving the bond partial covalent character. Fajans' rules summarise when this covalent character becomes significant: a small, highly charged cation, a large anion, and a cation with a pseudo-noble-gas (18-electron, e.g. Ag⁺, Cu⁺) configuration all increase covalency. This is why LiCl is more covalent than KCl, and AlCl₃ is largely covalent while NaCl is not.

The Covalent Bond: Lewis Structures, Formal Charge and Resonance

When neither atom can afford to lose electrons outright, they share pairs instead. Each shared pair is one covalent bond (a line in a Lewis structure); two shared pairs make a double bond, three a triple bond. Electrons left over on an atom are lone pairs, and they matter enormously for shape and reactivity. If both electrons of the shared pair come from one atom, the bond is coordinate (dative), as in NH₃ → BF₃ or in H₃O⁺.

A working procedure for Lewis structures:

1. Add up all valence electrons of the atoms (add one per unit of negative charge, subtract one per unit of positive charge).
2. Place the least electronegative atom at the centre; join the terminal atoms with single bonds.
3. Distribute the remaining electrons as lone pairs, completing octets on the outer atoms first.
4. If the central atom is short of an octet, convert lone pairs on neighbours into multiple bonds.

To judge between competing structures, compute the formal charge on each atom:

Formal charge = (valence electrons in the free atom) − (lone-pair electrons) − ½(bonding electrons)

The preferred structure is the one with formal charges closest to zero, and with any negative formal charge sitting on the more electronegative atom. In O₃, for instance, the terminal oxygens carry 0 and −1, and the central one +1 — showing that formal charges are bookkeeping devices, not real charges.

Often a single Lewis structure is inadequate. For CO₃²⁻ we can write three equivalent structures differing only in the placement of the double bond, yet experiment shows all three C–O bonds are identical (about 129 pm, intermediate between C=O and C–O). The real molecule is a resonance hybrid — a single structure that cannot be drawn, approximated by a set of canonical forms. Key points: the canonical forms do not exist individually, the molecule does not oscillate between them, and resonance always lowers energy (resonance energy), increasing stability. Greater resonance stabilisation comes from more canonical forms of comparable, low energy.

The octet rule has genuine exceptions you must recognise:

• Incomplete octet: LiCl, BeH₂, BCl₃ (boron has only 6 electrons)
• Expanded octet: PF₅ (10), SF₆ (12), H₂SO₄ — possible only for elements from period 3 onwards
• Odd-electron species: NO (11 valence electrons), NO₂ — these are paramagnetic
• It says nothing about shape and nothing about why noble gas configurations are stable; also fails to explain the existence of xenon compounds

Bond Parameters and Bond Polarity

Four numbers describe a bond quantitatively:

• Bond length — equilibrium internuclear distance. It decreases as bond order increases (C–C 154 pm > C=C 134 pm > C≡C 120 pm) and as atomic radii decrease.
• Bond enthalpy — energy needed to break one mole of bonds in the gas phase. Higher bond order and shorter bonds generally mean higher bond enthalpy (N≡N, 946 kJ mol⁻¹, is exceptionally strong). For polyatomic molecules like H₂O, successive O–H bonds have different enthalpies, so we quote a mean bond enthalpy.
• Bond angle — angle between two adjacent bonds at the central atom; fixed by the electron-pair geometry.
• Bond order — number of shared pairs. Isoelectronic species have the same bond order (CO, NO⁺, CN⁻ all have bond order 3).

When two different atoms bond, the more electronegative one pulls the shared cloud towards itself, producing a polar covalent bond with partial charges δ⁺ and δ⁻. This creates a bond dipole moment, μ = q × d, measured in debye (D); by convention the arrow points from positive to negative end (in the Lewis-structure convention, the crossed arrow tail sits on the δ⁺ atom).

The molecular dipole moment is the vector sum of bond dipoles (lone-pair contributions included). Hence:

• CO₂ (linear, O=C=O): two equal, opposite bond dipoles cancel → μ = 0
• H₂O (bent, 104.5°): dipoles don't cancel → μ = 1.85 D
• BF₃ (trigonal planar) and CCl₄ (tetrahedral) → μ = 0, despite polar bonds
• NH₃ (1.47 D) > NF₃ (0.24 D): in NF₃ the lone-pair dipole opposes the resultant N–F bond dipole, while in NH₃ they reinforce each other
• CHCl₃ is polar, CCl₄ is not; cis-1,2-dichloroethene is polar, the trans isomer is not

Molecular Shapes: VSEPR Theory

Lewis structures give connectivity, not geometry. VSEPR (Valence Shell Electron Pair Repulsion) theory supplies shapes using one idea: electron pairs in the valence shell of the central atom repel one another and arrange themselves as far apart as possible. Its main postulates:

1. Geometry is fixed by the total number of electron pairs (bond pairs + lone pairs) around the central atom.
2. Repulsion order: lone pair–lone pair > lone pair–bond pair > bond pair–bond pair, because a lone pair is held by only one nucleus and so spreads out more.
3. Multiple bonds are treated as single "super" bond pairs but exert greater repulsion than single bonds.
4. Lone pairs therefore compress bond angles below the ideal values.

Standard results:

In trigonal bipyramidal systems, lone pairs always occupy equatorial positions, since an axial lone pair would face three 90° repulsions instead of two. Note the angle trend CH₄ (109.5°) > NH₃ (107°) > H₂O (104.5°) as lone pairs increase, and that increasing electronegativity of the surrounding atoms pulls bond pairs away from the centre, reducing repulsion and hence the angle (H₂O > H₂S; NH₃ > NF₃).

Valence Bond Theory and Hybridisation

VSEPR predicts shapes but says nothing about the orbitals involved or bond energies. Valence bond theory (VBT) describes a covalent bond as the overlap of two half-filled atomic orbitals with electrons of opposite spin; the greater the overlap, the stronger the bond. As two H atoms approach, potential energy falls to a minimum at 74 pm (the bond length), releasing 435.8 kJ mol⁻¹ (the bond enthalpy) — the bond forms because the system reaches lower energy.

• σ bond: head-on (axial) overlap — s–s, s–p, p–p, or overlap involving hybrid orbitals. Cylindrically symmetric about the bond axis; permits rotation.
• π bond: sideways (lateral) overlap of parallel p orbitals; electron density above and below the axis; weaker than σ (less effective overlap) and restricts rotation.

Plain atomic orbitals cannot explain CH₄'s four identical bonds at 109.5°, so we invoke hybridisation: mixing of atomic orbitals of comparable energy on the same atom to form an equal number of new, equivalent hybrid orbitals with definite geometry and lower energy. Only orbitals of comparable energy on the same atom can mix, and the number of hybrid orbitals formed always equals the number of atomic orbitals mixed. Common types:

• sp — one s + one p orbital mix to give two orbitals at 180°; linear geometry (BeCl₂, C in HC≡CH).
• sp² — one s + two p orbitals give three orbitals at 120° in a plane; trigonal planar geometry (BF₃, C in C₂H₄).
• sp³ — one s + three p orbitals give four orbitals at 109.5°; tetrahedral geometry (CH₄, C in C₂H₆); lone pairs occupy hybrid orbitals too, so NH₃ (one lone pair) and H₂O (two lone pairs) are also sp³ at the central atom even though their observed shapes are pyramidal and bent.
• sp³d — five orbitals, trigonal bipyramidal (PCl₅).
• sp³d² — six orbitals, octahedral (SF₆).

A quick way to assign hybridisation from a Lewis structure is to count the steric number (σ-bonds + lone pairs) around the central atom: steric numbers 2, 3, 4, 5, 6 correspond to sp, sp², sp³, sp³d, sp³d² respectively — this shortcut reproduces the VSEPR table directly, because hybridisation is really just VSEPR's electron-pair count dressed in orbital language.

Molecular Orbital Theory

VBT treats bonding electrons as localised between two atoms, but it cannot explain the paramagnetism of O₂ (which has two unpaired electrons despite a perfectly reasonable Lewis structure with all electrons paired) or give a clean account of species like He₂⁺. Molecular orbital theory (MOT) instead treats electrons as delocalised over the whole molecule: atomic orbitals combine (Linear Combination of Atomic Orbitals, LCAO) to give an equal number of molecular orbitals — a lower-energy bonding MO (constructive overlap, electron density concentrated between nuclei) and a higher-energy antibonding MO (destructive overlap, a node between nuclei), marked with an asterisk (σ*, π*).

For homonuclear diatomics of period 2, the energy order of MOs is:

σ1s < σ1s < σ2s < σ2s < (π2px = π2py) < σ2pz < (π2px = π2py) < σ*2pz (for O₂, F₂, Ne₂)

with σ2pz and the π2p pair swapped in order for Li₂ through N₂, because of s–p mixing at lower atomic number.

Electrons fill MOs following the same Aufbau, Pauli and Hund's rules used for atomic orbitals. Bond order is then:

Bond order = ½ (number of bonding electrons − number of antibonding electrons)

A bond order of zero means the species cannot exist (He₂); higher bond order means shorter, stronger bonds. MOT's signature success is predicting that O₂ has bond order 2 with two unpaired electrons in the π*2p orbitals, correctly accounting for its paramagnetism — something VBT's simple Lewis structure misses entirely. Similarly, removing an electron to form O₂⁺ raises bond order (to 2.5) and shortens the bond, since the electron removed comes from an antibonding orbital, while forming O₂⁻ or O₂²⁻ progressively lowers bond order and weakens the bond.

Hydrogen bonding, though not covalent, is the last bonding interaction NEET expects you to place correctly: an unusually strong dipole–dipole attraction that occurs when hydrogen is bonded to a small, highly electronegative atom (F, O, N) and interacts with a lone pair on a similar atom nearby. It explains the anomalously high boiling points of HF, H₂O and NH₃ relative to their heavier hydride analogues, and it is classified as intermolecular (linking separate molecules, as in water) or intramolecular (within one molecule, forming a ring, as in ortho-nitrophenol, which is why ortho-nitrophenol is more volatile and less water-soluble than its para isomer that hydrogen-bonds intermolecularly instead).

Common Mistakes and Exam Traps

1. Assuming hybridisation always matches observed molecular shape. NH₃ and H₂O are both sp³ hybridised at the central atom, but their observed shapes (pyramidal, bent) look different from CH₄'s tetrahedron only because lone pairs are invisible in the final shape though they still occupy hybrid orbitals and compress bond angles.
2. Ignoring lone-pair placement in trigonal bipyramidal geometries. Lone pairs always go equatorial (not axial) in sp³d systems, because an equatorial lone pair experiences only two 90° repulsions instead of three — students who place lone pairs axially get see-saw/T-shaped/linear shapes wrong.
3. Believing a molecule with polar bonds must have a net dipole. CO₂, BF₃ and CCl₄ all have polar bonds but zero net dipole because of symmetric geometry — the vector sum, not the presence of polar bonds, decides molecular polarity.
4. Forgetting that MOT bond order changes on ionisation depend on which orbital loses the electron. Removing an electron from a bonding MO lowers bond order (weakens the bond), but removing one from an antibonding MO raises it (strengthens the bond) — O₂ → O₂⁺ is the classic example examiners use to test this.