Chemical Bonding and Molecular Structure

Kössel and Lewis (1916) explained bonding with the octet rule: atoms combine so that each ends up with eight electrons in its valence shell, the configuration of the nearest noble gas (hydrogen settles for a duplet of two). The octet can be reached by transferring electrons from one atom to another, giving ions that attract each other electrostatically (an electrovalent or ionic bond), or by sharing electron pairs between atoms (a covalent bond, Lewis's idea).

A Lewis symbol shows the valence electrons of an atom as dots around its symbol; the number of dots equals the group valence electrons, and the number needed to complete the octet is the usual valency. To draw a Lewis structure: add up the valence electrons of all atoms (add one for each negative charge, subtract one for each positive charge), put the least electronegative atom in the centre, join atoms with single bonds, complete the octets of the outer atoms with lone pairs, place any electrons left over on the central atom, and convert lone pairs into double or triple bonds if the central atom still lacks an octet.

Formal charge on an atom = (valence electrons in the free atom) − (non-bonding electrons) − ½(bonding electrons). In ozone the central O has formal charge 6 − 2 − 3 = +1, the doubly bonded O has 6 − 4 − 2 = 0 and the singly bonded O has 6 − 6 − 1 = −1. Formal charge picks the best of several possible structures: the one with the smallest charges, and with negative charge on the more electronegative atom, is preferred.

Limitations of the octet rule, which examiners like: incomplete octets in LiCl, BeH₂, BF₃ and AlCl₃; odd-electron molecules NO and NO₂, which can never satisfy it; expanded octets in PF₅, SF₆ and H₂SO₄, where the central atom holds more than eight electrons; the rule says nothing about shape or bond energy; and it cannot explain why noble gases form compounds such as XeF₂ and XeF₄.

An ionic bond forms when a metal atom of low ionisation enthalpy loses electrons to a non-metal atom of high (very negative) electron gain enthalpy, and the cations and anions pack into a lattice held together by electrostatic attraction. NCERT's example is NaCl: Na(g) → Na⁺(g) + e⁻ costs 495.8 kJ mol⁻¹, and Cl(g) + e⁻ → Cl⁻(g) releases only 348.7 kJ mol⁻¹, so forming the free ions is endothermic. The compound is stable anyway because arranging the ions into the crystal releases 788 kJ mol⁻¹, the lattice enthalpy, which more than covers the deficit.

NCERT defines lattice enthalpy as the energy required to completely separate one mole of a solid ionic compound into its gaseous constituent ions; for NaCl, Δ_latticeH = +788 kJ mol⁻¹. It rises with the charges on the ions and falls as the ions get bigger, so MgO, with 2+ and 2− ions, has a far larger lattice enthalpy than NaCl. The three favourable factors, in the wording the examiner expects: low ionisation enthalpy of the metal, high negative electron gain enthalpy of the non-metal, and high lattice enthalpy of the solid.

Ionic compounds are crystalline solids with high melting and boiling points, hard but brittle, insulators when solid but conductors when molten or dissolved because the ions become mobile, and soluble mainly in polar solvents such as water.

No bond is purely ionic. Fajans' rule (not spelt out in NCERT but asked in school exams): a small, highly charged cation polarises a large, easily deformable anion, pulling electron density into the region between the nuclei and giving the bond covalent character. This is why LiCl is more covalent than NaCl or KCl, and why AlCl₃ behaves as a covalent compound.

Bond length is the equilibrium distance between the nuclei of two bonded atoms, in picometres. Each atom contributes its covalent radius, so the length of A–B is r_A + r_B. It falls as bond order rises: C–C 154 pm, C=C 134 pm, C≡C 120 pm.

Bond angle is the angle between the orbitals holding the bonding pairs on a central atom, 104.5° for H–O–H in water; it fixes the shape of the molecule.

Bond enthalpy is the energy needed to break one mole of a particular bond in the gaseous state. For a diatomic molecule it is the bond dissociation enthalpy: 435.8 kJ mol⁻¹ for H–H, 498 kJ mol⁻¹ for O=O. In a polyatomic molecule successive bonds cost different amounts: H₂O(g) → H(g) + OH(g) needs 502 kJ mol⁻¹ but OH(g) → H(g) + O(g) needs 427 kJ mol⁻¹, so NCERT quotes the mean bond enthalpy, (502 + 427)/2 = 464.5 kJ mol⁻¹ for O–H.

Bond order is the number of bonds between two atoms: 1 in H₂, 2 in O₂, 3 in N₂. Isoelectronic species share a bond order (N₂, CO and NO⁺ all have 3; F₂ and O₂²⁻ both have 1). As bond order rises, bond enthalpy rises and bond length falls.

Resonance: when a single Lewis structure cannot describe a molecule, it is represented as a hybrid of two or more canonical structures that differ only in the positions of electrons. In O₃ the two structures put the double bond on either O–O bond; the real molecule has two identical bonds of 128 pm, between a single (148 pm) and a double (121 pm) bond, and is more stable than any one canonical form (resonance stabilisation). CO₃²⁻ and NO₃⁻ have three equivalent structures each.

Polarity: a bond between atoms of different electronegativity is polar, with partial charges δ+ and δ−. The dipole moment μ = charge × distance is measured in debye (1 D = 3.33564 × 10⁻³⁰ C m) and is a vector, drawn as an arrow from δ+ to δ−. In a polyatomic molecule the net dipole is the vector sum of the bond dipoles, so shape decides polarity: linear CO₂ and trigonal planar BF₃ have μ = 0 because their bond dipoles cancel, while bent H₂O has μ = 1.85 D. In NH₃ the lone-pair moment adds to the N–H dipoles (1.47 D); in NF₃ it opposes the N–F dipoles (0.24 D).

VSEPR theory (Sidgwick and Powell, refined by Nyholm and Gillespie) predicts shape from the repulsion between electron pairs on the central atom. Postulates: the shape depends on the number of valence-shell electron pairs, bonding and non-bonding; the pairs stay as far apart as possible to minimise repulsion; a lone pair, held by one nucleus only, spreads out more than a bond pair, so repulsion decreases in the order lone pair–lone pair > lone pair–bond pair > bond pair–bond pair; a multiple bond is treated as a single super pair; and lone pairs squeeze the angles between neighbouring bond pairs.

Shapes with no lone pairs: 2 pairs linear 180° (BeCl₂, CO₂); 3 pairs trigonal planar 120° (BF₃); 4 pairs tetrahedral 109.5° (CH₄); 5 pairs trigonal bipyramidal 120° and 90° (PCl₅); 6 pairs octahedral 90° (SF₆). With lone pairs (bp, lp): (2,1) bent, SO₂; (3,1) trigonal pyramidal 107°, NH₃; (2,2) bent 104.5°, H₂O; (4,1) see-saw, SF₄; (3,2) T-shaped, ClF₃; (2,3) linear, XeF₂; (5,1) square pyramidal, BrF₅; (4,2) square planar, XeF₄. In a trigonal bipyramid lone pairs always take equatorial positions, because there they suffer only two 90° repulsions instead of three; in an octahedron two lone pairs go opposite each other.

The standard question is the fall in bond angle from CH₄ (109.5°) to NH₃ (107°) to H₂O (104.5°): each extra lone pair adds stronger lp–bp repulsion, and in water lp–lp repulsion as well, pushing the bond pairs closer together. Always name both the electron-pair geometry (tetrahedral for NH₃) and the molecular shape (trigonal pyramidal).

Valence bond theory (Heitler and London, 1927, developed by Pauling) describes a covalent bond as the overlap of half-filled atomic orbitals. Take two hydrogen atoms far apart. As they approach, new forces appear: attraction between each nucleus and the other atom's electron, and repulsion between the two electrons and between the two nuclei. Attraction wins, the potential energy falls, and it reaches a minimum at an internuclear distance of 74 pm, the bond length of H₂; the energy released, 435.8 kJ mol⁻¹, is the bond enthalpy. Push the atoms closer and repulsion takes over, so the curve rises steeply. This energy–distance curve is a common diagram question.

Overlap can be positive (lobes of the same sign add and build electron density between the nuclei), negative (opposite signs cancel) or zero (an s orbital with a p orbital lying perpendicular to the axis). Only positive overlap bonds. Because p orbitals overlap best along their own axis, bonds have direction, which is why molecules have definite shapes.

A sigma (σ) bond comes from head-on overlap along the internuclear axis: s–s (H₂), s–p (HCl), p–p end to end (Cl₂). It is cylindrically symmetric about the axis and allows free rotation. A pi (π) bond comes from sideways overlap of two parallel p orbitals perpendicular to the axis; the electron cloud sits above and below the axis, with a nodal plane through the nuclei, and rotation about the bond would break it. Sideways overlap is smaller than head-on overlap, so a π bond is weaker than a σ bond between the same atoms. A single bond is one σ, a double bond one σ + one π, a triple bond one σ + two π.

Hybridisation is the mixing of atomic orbitals of nearly equal energy on the same atom to give the same number of new, equivalent hybrid orbitals of identical energy and shape, pointing in fixed directions. The hybrid orbitals overlap more effectively than pure orbitals and so form stronger bonds. Orbitals need not be half-filled to hybridise: promotion of an electron (2s²2p² → 2s¹2p³ in carbon) is imagined first, and a hybrid orbital can hold a lone pair.

sp (one s + one p, two orbitals at 180°, linear): BeCl₂; the carbons of ethyne, HC≡CH. Each carbon uses one sp orbital for the C–H σ bond and one for the C–C σ bond, and its two unhybridised p orbitals overlap sideways with those of the other carbon to give two π bonds. Ethyne: 3 σ + 2 π, linear.

sp² (one s + two p, three orbitals at 120°, planar): BF₃; the carbons of ethene, H₂C=CH₂. Three sp² orbitals form two C–H σ bonds and the C–C σ bond; the leftover p orbital on each carbon, perpendicular to the plane, forms the π bond. Ethene: 5 σ + 1 π, planar, C–C 134 pm.

sp³ (one s + three p, four orbitals at 109.5°, tetrahedral): CH₄, ethane (7 σ, free rotation about C–C, 154 pm), NH₃ (one hybrid holds the lone pair, 107°), H₂O (two lone pairs, 104.5°).

sp³d (one s, three p, one d; trigonal bipyramidal): PCl₅. Three equatorial P–Cl bonds lie in a plane at 120°; two axial bonds at 90° to it are slightly longer and weaker, because each axial pair suffers three 90° repulsions while an equatorial pair suffers only two. PCl₅ is therefore reactive. sp³d² (octahedral, 90°): SF₆, all bonds equivalent.

Quick method: count σ bonds plus lone pairs on the central atom (the steric number): 2 sp, 3 sp², 4 sp³, 5 sp³d, 6 sp³d². So carbon in CH₃–CHO is sp³ then sp², and in BF₃ + NH₃ → F₃B·NH₃ boron changes from sp² to sp³ while nitrogen stays sp³.

Molecular orbital theory (Hund and Mulliken, 1932) says electrons in a molecule belong to the molecule as a whole and occupy molecular orbitals that spread over all the nuclei. Molecular orbitals are built by the linear combination of atomic orbitals (LCAO). Adding two 1s wave functions, ψ_A + ψ_B, gives a bonding orbital σ1s with more electron density between the nuclei and lower energy than the atomic orbitals; subtracting them, ψ_A − ψ_B, gives an antibonding orbital σ*1s with a node between the nuclei and higher energy. The bonding orbital is lowered by as much as the antibonding orbital is raised.

Conditions for combination: the atomic orbitals must have nearly the same energy, the same symmetry about the molecular axis, and must overlap as much as possible. So 2s combines with 2s, 2p_z (taken along the axis) with 2p_z to give σ2p_z and σ*2p_z, and 2p_x, 2p_y sideways to give the degenerate pairs π2p_x, π2p_y and π*2p_x, π*2p_y. Electrons fill the molecular orbitals by the aufbau principle, the Pauli principle and Hund's rule.

Energy order for O₂ and F₂: σ1s < σ*1s < σ2s < σ*2s < σ2p_z < (π2p_x = π2p_y) < (π*2p_x = π*2p_y) < σ*2p_z. For Li₂, Be₂, B₂, C₂ and N₂ the σ2p_z orbital lies above the π2p pair because of mixing between 2s and 2p, so the order is σ1s < σ*1s < σ2s < σ*2s < (π2p_x = π2p_y) < σ2p_z < (π*2p_x = π*2p_y) < σ*2p_z.

Bond order = ½(N_b − N_a), the bonding electrons minus the antibonding electrons, halved. A positive bond order means the molecule can exist; zero or negative means it cannot. Higher bond order means a shorter, stronger bond. If every electron is paired the molecule is diamagnetic; any unpaired electron makes it paramagnetic. This is where MOT beats the Lewis picture: it predicts that O₂, with two unpaired electrons in its π* orbitals, is paramagnetic, which experiment confirms.

H₂ (2 electrons): σ1s²; bond order ½(2 − 0) = 1; diamagnetic; bond length 74 pm, bond enthalpy 435.8 kJ mol⁻¹.

He₂ (4): σ1s² σ*1s²; bond order ½(2 − 2) = 0, so He₂ does not exist. He₂⁺ (3 electrons, σ1s² σ*1s¹) has bond order 0.5 and is known.

Li₂ (6): σ1s² σ*1s² σ2s², often written KK σ2s²; bond order 1; diamagnetic; exists in the vapour phase. Be₂ (8): KK σ2s² σ*2s²; bond order 0; does not exist. B₂ (10): KK σ2s² σ*2s² π2p_x¹ π2p_y¹; bond order 1; paramagnetic. C₂ (12): KK σ2s² σ*2s² π2p_x² π2p_y²; bond order 2, both bonds are π; diamagnetic.

N₂ (14): KK σ2s² σ*2s² π2p_x² π2p_y² σ2p_z²; bond order ½(10 − 4) = 3; diamagnetic; bond length 110 pm, bond enthalpy about 945 kJ mol⁻¹, which is why N₂ is so unreactive.

O₂ (16): KK σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x¹ π*2p_y¹; bond order ½(10 − 6) = 2; paramagnetic with two unpaired electrons; 121 pm, 498 kJ mol⁻¹. Remove an electron from π* and you get O₂⁺, bond order 2.5, one unpaired electron, shorter bond. Add one for the superoxide O₂⁻, bond order 1.5, one unpaired electron; add two for the peroxide O₂²⁻, bond order 1, diamagnetic. Stability and bond strength: O₂⁺ > O₂ > O₂⁻ > O₂²⁻; bond length runs the opposite way.

F₂ (18): KK σ2s² σ*2s² σ2p_z² π2p_x² π2p_y² π*2p_x² π*2p_y²; bond order 1; diamagnetic. Ne₂ (20) fills σ*2p_z as well, bond order 0, does not exist.

When hydrogen is covalently bonded to a small, highly electronegative atom (F, O or N) the shared pair is pulled away from it, leaving the hydrogen with a large partial positive charge. That hydrogen is then attracted to the lone pair of an electronegative atom in a neighbouring molecule, or elsewhere in the same molecule. This attraction is a hydrogen bond, written as a dotted line: H^δ+–F^δ− ··· H^δ+–F^δ−. It is much weaker than a covalent bond (about 10 to 40 kJ mol⁻¹) but stronger than van der Waals forces, and it needs F, O or N because only they are electronegative enough and small enough.

Intermolecular hydrogen bonding acts between molecules, of the same or different compounds: the zig-zag chains of HF, the network in water and ice, alcohols, carboxylic acids, and water–ethanol mixtures. Intramolecular hydrogen bonding acts within one molecule when the geometry allows a five- or six-membered ring, as in o-nitrophenol and salicylaldehyde.

Consequences the exam asks for: NH₃, H₂O and HF boil far higher than the other hydrides of their groups (water at 100 °C against −60 °C for H₂S); water has a high viscosity, surface tension and specific heat; ice has an open hexagonal lattice in which each molecule is hydrogen-bonded to four neighbours, so it is less dense than liquid water and floats; o-nitrophenol is steam-volatile and lower boiling than p-nitrophenol, whose intermolecular hydrogen bonds hold the molecules together; ethanol and acetic acid dissolve in water because they hydrogen-bond with it; and the two strands of DNA are held together by hydrogen bonds between base pairs.