Chemical Bonding and Molecular Structure

In this chapter: Kössel-Lewis approach and the octet rule, Lewis structures and formal charge, limitations of the octet rule, ionic bond and lattice enthalpy, bond length, bond angle, bond enthalpy and bond order, resonance, dipole moment and Fajans' rules, VSEPR theory, valence bond theory, σ and π bonds, hybridisation, molecular orbital theory of homonuclear diatomic molecules, and hydrogen bonding.

Kössel-Lewis approach and the octet rule

Atoms combine to reach a stable noble gas configuration, usually eight electrons in the valence shell (two for hydrogen and helium). Kössel explained ionic (electrovalent) bonds by transfer of electrons: Na gives one electron to Cl, and Na⁺ and Cl⁻ are held by electrostatic attraction. Lewis and Langmuir explained covalent bonds by sharing: each shared pair counts towards the octet of both atoms. Sharing two pairs gives a double bond (O=O, CO₂) and three pairs a triple bond (N≡N, HC≡CH).

Formal charge

When several Lewis structures are possible, the one with the lowest formal charges on the atoms is usually the most stable.

Worked example: Find the formal charges on the three oxygen atoms in the Lewis structure of ozone, O=O−O (central O has one lone pair; the double-bonded end O has two lone pairs; the single-bonded end O has three).
Solution: Central O: 6 − 2 − ½(6) = +1. Double-bonded end O: 6 − 4 − ½(4) = 0. Single-bonded end O: 6 − 6 − ½(2) = −1. The charges add up to zero, as they must for a neutral molecule.

Limitations of the octet rule

• Incomplete octet: the central atom has fewer than eight electrons, as in LiCl, BeH₂ and BCl₃.
• Odd-electron molecules: NO and NO₂ cannot give every atom an octet.
• Expanded octet: elements of period 3 onwards can use d orbitals and have more than eight electrons: PF₅ (10), SF₆ (12), H₂SO₄ (12 around S).
• Noble gases also form compounds such as XeF₂, XeF₄ and XeOF₂. The octet rule says nothing about the shape of a molecule or the energy of its bonds.

Ionic bond and lattice enthalpy

Ionic bonds form easily between a metal of low ionisation enthalpy and a non-metal with a large negative electron gain enthalpy. The crystal is held together by lattice enthalpy, the energy needed to completely separate one mole of a solid ionic compound into gaseous ions. For NaCl it is 788 kJ mol⁻¹.

Bond parameters

• Bond length: equilibrium distance between the nuclei of two bonded atoms. The covalent radius is half the distance between two identical bonded atoms.
• Bond angle: angle between the orbitals containing bonding electron pairs around the central atom, for example 104.5° in water.
• Bond enthalpy: energy needed to break one mole of bonds of a particular type in the gaseous state: H−H 435.8, O=O 498, N≡N 946.0 kJ mol⁻¹.
• Bond order: number of bonds between two atoms (H₂ 1, O₂ 2, N₂ 3). Higher bond order means greater bond enthalpy and shorter bond length. Isoelectronic species have the same bond order: F₂ and O₂²⁻ have 1; N₂, CO and NO⁺ have 3.

Resonance

When one Lewis structure cannot describe a molecule, it is shown as a resonance hybrid of two or more canonical structures. In O₃ both O−O bonds are 128 pm, between the single bond (148 pm) and the double bond (121 pm). In CO₃²⁻ all three C−O bonds are identical. The canonical forms have no real existence; the molecule does not flip between them. Resonance lowers the energy of the molecule and so stabilises it.

Polarity and dipole moment

In a bond between atoms of different electronegativity the shared pair shifts towards the more electronegative atom, giving a polar covalent bond. Dipole moment μ = charge × distance; its unit is the debye, 1 D = 3.33564 × 10⁻³⁰ C m. It is a vector, and the molecular dipole moment is the vector sum of bond moments.

• CO₂ (linear), BF₃ (trigonal planar) and CH₄ (tetrahedral) have zero dipole moment because the bond moments cancel. H₂O is bent and has μ = 1.85 D.
• NH₃ has a larger dipole moment than NF₃. In NH₃ the lone pair moment is in the same direction as the resultant of the N−H bond moments; in NF₃ it opposes the N−F bond moments.

Fajans' rules: an ionic bond gains covalent character when the cation is small, the anion is large and the charges on the ions are high. A cation with an (n−1)dⁿns⁰ configuration polarises an anion more than one of similar size and charge with a noble gas configuration.

VSEPR theory

The shape of a molecule depends on the number of electron pairs, bonded and lone, around the central atom. The pairs repel each other and take up positions as far apart as possible. A multiple bond is treated as a single super pair. Repulsion falls in the order lone pair-lone pair > lone pair-bond pair > bond pair-bond pair, so lone pairs squeeze bond angles.

To find the number of lone pairs quickly: lone pairs on the central atom = (valence electrons of central atom − electrons used in bonds)/2. For NH₃, (5 − 3)/2 = 1.

Valence bond theory and hybridisation

When two hydrogen atoms approach, attraction between each nucleus and the other electron competes with nucleus-nucleus and electron-electron repulsion. Energy falls to a minimum at 74 pm, the bond length of H₂, and 435.8 kJ mol⁻¹ is released. A covalent bond forms by overlap of half-filled atomic orbitals; the greater the overlap, the stronger the bond.

• σ bond: end-to-end (head-on) overlap along the internuclear axis: s-s, s-p or p-p.
• π bond: sideways overlap of p orbitals, above and below the internuclear axis. It is weaker than a σ bond. A double bond is one σ + one π; a triple bond is one σ + two π.

Hybridisation is the mixing of atomic orbitals of slightly different energies on the same atom to give an equal number of identical hybrid orbitals, which then form σ bonds (or hold lone pairs).

In PCl₅ the two axial bonds are longer than the three equatorial bonds, because axial pairs suffer more repulsion. This is why PCl₅ is reactive. In ethene each carbon is sp²; the C=C bond is one sp²-sp² σ bond and one π bond from the unhybridised 2p orbitals. In ethyne each carbon is sp, and the C≡C bond is one σ and two π bonds.

Molecular orbital theory

Atomic orbitals of comparable energy and the same symmetry about the molecular axis combine (linear combination of atomic orbitals) to form the same number of molecular orbitals. Addition gives a bonding MO (lower energy, electron density between the nuclei); subtraction gives an antibonding MO (higher energy, a node between the nuclei, marked *). Electrons fill MOs by the Aufbau principle, Pauli principle and Hund's rule.

The order of MO energies differs for light and heavy second-period molecules:

• Up to N₂ (B₂, C₂, N₂): σ1s < σ*1s < σ2s < σ*2s < (π2p_x = π2p_y) < σ2p_z < (π*2p_x = π*2p_y) < σ*2p_z
• O₂ and F₂: σ2p_z lies below the π2p pair; the rest of the order is the same.

N₂ (14 electrons) has bond order ½(10 − 4) = 3 and all electrons paired, so it is diamagnetic. O₂ (16 electrons) has bond order ½(10 − 6) = 2 and two unpaired electrons in the π* orbitals, so it is paramagnetic. Valence bond theory cannot explain this.

Worked example: Compare the bond order and magnetic behaviour of O₂⁺, O₂, O₂⁻ and O₂²⁻.
Solution: Start from O₂ (N_b = 10, N_a = 6) and change only the π* electrons. O₂⁺: ½(10 − 5) = 2.5, one unpaired electron. O₂: 2, two unpaired. O₂⁻: ½(10 − 7) = 1.5, one unpaired. O₂²⁻: ½(10 − 8) = 1, no unpaired electron, so only the peroxide ion is diamagnetic. Bond length increases as bond order falls: O₂⁺ < O₂ < O₂⁻ < O₂²⁻.

Hydrogen bonding

When hydrogen is bonded to a highly electronegative atom (F, O or N), it carries a partial positive charge and is attracted to a lone pair on an electronegative atom of another molecule or of the same molecule. This attraction is much weaker than a covalent bond.

• Intermolecular: between different molecules, as in HF and H₂O. It raises boiling points, which is why water is a liquid while H₂S is a gas at room temperature.
• Intramolecular: within the same molecule, as in o-nitrophenol, where the −OH hydrogen bonds to an oxygen of the neighbouring −NO₂ group.

Common mistakes: (1) Using the O₂ order of MO energies for N₂, or the other way round. (2) Forgetting lone pairs when naming the shape: NH₃ is pyramidal and H₂O is bent, even though both are sp³. (3) Assuming every molecule with polar bonds has a dipole moment; symmetrical CO₂ and BF₃ have none. (4) Counting a double bond as two σ bonds. (5) Treating resonance structures as real forms that interconvert.

JEE and NEET focus

• Shapes and bond angles from VSEPR, including molecules with lone pairs (SF₄, ClF₃, XeF₄, BrF₅).
• Hybridisation of the central atom and counting σ and π bonds in organic and inorganic molecules.
• MO configuration, bond order and magnetic character of H₂, He₂, N₂, O₂ and their ions; bond length order.
• Dipole moment comparisons (NH₃ vs NF₃, cis vs trans isomers, symmetrical molecules).
• Formal charge, resonance structures and Fajans' rules.
• Effect of hydrogen bonding on boiling point and solubility.

Practice questions