Chemical Bonding and Molecular Structure

In 1916, Kössel and Lewis independently explained chemical bond formation in terms of valence electrons. Lewis represented the valence electrons of an atom as dots placed around its symbol (a Lewis symbol); the number of dots equals the number of valence electrons. Kössel linked the electronic configurations of noble gases (ns²np⁶, except He which is 1s²) with their chemical inertness, and proposed that atoms combine so as to achieve the stable, completely filled outer-shell configuration of the nearest noble gas.

This idea developed into the octet rule: atoms tend to lose, gain, or share electrons so as to have eight electrons (an octet) in their valence shell, resembling the nearest noble gas; hydrogen and helium instead attain a duet (2 electrons). Bonds form in two main ways: an electrovalent (ionic) bond, formed by complete transfer of one or more electrons from one atom to another, and a covalent bond, formed by mutual sharing of electron pairs between atoms.

Worked example: Consider the formation of magnesium chloride, MgCl₂. Magnesium (electronic configuration 2, 8, 2) loses its two valence electrons to attain the stable configuration of neon (2, 8), forming Mg²⁺. Each chlorine atom (2, 8, 7) gains one electron to attain the stable configuration of argon (2, 8, 8), forming Cl^-. Since one Mg atom releases two electrons but each Cl atom accepts only one, two Cl atoms are needed per Mg atom, giving the formula MgCl₂, i.e. Mg²⁺(Cl^-)₂. Both Mg²⁺ and Cl^- now have complete octets.

The octet rule has important limitations. Some stable molecules have an incomplete octet on the central atom, for example BeCl₂ (only 4 electrons around Be) and BF₃ (only 6 electrons around B). Elements of period 3 and beyond can have an expanded octet using d-orbitals, as in PCl₅ (10 electrons around P) and SF₆ (12 electrons around S). A few molecules with an odd number of valence electrons, such as NO and NO₂, cannot obey the octet rule at all. The rule also does not explain the shapes of molecules or the relative energies of different structures.

An ionic (electrovalent) bond is formed by complete transfer of one or more electrons from a metal atom (which forms a cation) to a non-metal atom (which forms an anion), followed by electrostatic (Coulombic) attraction between the oppositely charged ions. Formation of a stable ionic compound is favoured by: low ionisation enthalpy of the metal (cation forms easily), highly negative (favourable) electron gain enthalpy of the non-metal (anion forms easily), and high lattice enthalpy of the resulting crystal (the solid is very stable).

Lattice enthalpy is the energy required to completely separate one mole of a solid ionic compound into its gaseous constituent ions. It cannot be measured directly, so it is obtained indirectly using an energy cycle based on Hess's law, called the Born–Haber cycle, which connects the enthalpy of formation of the ionic solid to the enthalpies of sublimation, ionisation, bond dissociation, electron gain, and lattice formation.

Worked example: Calculate the lattice enthalpy of NaCl from the following data: sublimation enthalpy of Na(s) = +108.4 kJ mol^-1; ionisation enthalpy of Na(g) = +496 kJ mol^-1; bond dissociation enthalpy of Cl₂(g) = +242 kJ mol^-1; electron gain enthalpy of Cl(g) = -348 kJ mol^-1; enthalpy of formation of NaCl(s) = -411 kJ mol^-1.

By Hess's law: ΔfH° = ΔsubH(Na) + IE₁(Na) + ½ΔdissH(Cl₂) + ΔegH(Cl) − ΔlatticeH(NaCl).

Substituting: -411 = 108.4 + 496 + (½ × 242) + (-348) − ΔlatticeH(NaCl) = 108.4 + 496 + 121 − 348 − ΔlatticeH(NaCl) = 377.4 − ΔlatticeH(NaCl).

Therefore ΔlatticeH(NaCl) = 377.4 + 411 = 788.4 kJ mol^-1. This large positive value shows the NaCl lattice is very stable, consistent with its high melting point.

Lattice enthalpy increases with increasing charge on the ions and decreases with increasing ionic size (inter-ionic distance); thus MgO (doubly charged, smaller ions) has a much higher lattice enthalpy than NaCl.

A covalent bond forms when two atoms share one or more electron pairs so both attain a stable noble-gas configuration. One shared pair gives a single bond (e.g. H–H); two shared pairs give a double bond (e.g. O=O); three shared pairs give a triple bond (e.g. N≡N). A Lewis (dot) structure shows all bonding pairs and all non-bonding lone pairs on every atom, consistent with the total valence electrons available.

To judge which of several valid Lewis structures is more reasonable, chemists calculate the formal charge on each atom: Formal charge = (valence electrons of the free atom) − (non-bonding/lone-pair electrons) − ½ (bonding electrons).

Worked example (formal charges in ozone, O₃): Ozone is bent, with a central O bonded to two terminal O atoms; one O–O bond is drawn as a double bond and the other as a single bond. For the central O (1 lone pair = 2 non-bonding electrons; bonding electrons = 4 from the double bond + 2 from the single bond = 6): formal charge = 6 − 2 − 3 = +1. For the double-bonded terminal O (2 lone pairs = 4 non-bonding electrons; 4 bonding electrons): formal charge = 6 − 4 − 2 = 0. For the single-bonded terminal O (3 lone pairs = 6 non-bonding electrons; 2 bonding electrons): formal charge = 6 − 6 − 1 = −1. The charges (+1, 0, −1) sum to zero, matching the neutral molecule; since an identical structure can be drawn with the double bond on the other side, O₃ is a resonance hybrid with both O–O bonds equal and of intermediate length.

Every covalent bond has three key bond parameters. Bond length, the equilibrium internuclear distance, decreases in the order single > double > triple bond for the same pair of atoms. Bond angle is the angle between two adjacent bonds at a central atom. Bond enthalpy is the energy needed to break one mole of a bond in the gaseous state; for several identical bonds in a molecule, an average (mean) bond enthalpy is used. For methane, the four successive C–H bond dissociation enthalpies are 427, 439, 452 and 347 kJ mol^-1; summing gives 1665 kJ mol^-1, so the mean C–H bond enthalpy = 1665/4 = 416.25 kJ mol^-1.

The Valence Shell Electron Pair Repulsion (VSEPR) theory predicts a molecule's 3-D shape on the idea that electron pairs (bond pairs and lone pairs) around a central atom arrange as far apart as possible to minimise repulsion. Key postulates: shape depends on the total number of electron pairs around the central atom; both bond pairs (bp) and lone pairs (lp) repel each other but the repulsion strength decreases in the order lp-lp > lp-bp > bp-bp (a lone pair is held closer to the nucleus and occupies more space); and a multiple bond is treated as a single electron-pair position for shape prediction.

With only bond pairs on the central atom: 2 bp give a linear shape (180°, e.g. BeCl₂); 3 bp give a trigonal planar shape (120°, e.g. BF₃); 4 bp give a tetrahedral shape (109.5°, e.g. CH₄); 5 bp give a trigonal bipyramidal shape (120° and 90°, e.g. PCl₅); 6 bp give an octahedral shape (90°, e.g. SF₆).

Lone pairs distort these regular shapes and reduce bond angles below the ideal value. In NH₃ (3 bp + 1 lp on N), the underlying arrangement is tetrahedral, but the lone pair compresses the H–N–H angle to about 107°, giving a pyramidal shape. In H₂O (2 bp + 2 lp on O), the two lone pairs compress the angle further to about 104.5°, giving a bent (angular) shape.

Worked example: Predict the shape of SF₄. Sulphur forms 4 bonds to F and retains 1 lone pair, giving 5 electron pairs (AX₄E) that adopt an underlying trigonal bipyramidal arrangement; the lone pair occupies an equatorial position (to minimise the stronger 90° lp-bp repulsions with axial atoms), giving the distorted-tetrahedron shape known as see-saw.

According to Valence Bond (VB) theory, a covalent bond forms when a half-filled atomic orbital of one atom overlaps with a half-filled atomic orbital of another, and the shared electron pair (opposite spins) concentrates in the overlap region. Head-on (axial) overlap gives a strong sigma (σ) bond (permits free rotation); sideways overlap of parallel p-orbitals gives a weaker pi (π) bond (restricts rotation). A single bond is 1σ; a double bond is 1σ + 1π; a triple bond is 1σ + 2π.

Hybridisation is the mixing of an atom's orbitals of comparable energy (s, p, and sometimes d) into a new set of equivalent hybrid orbitals for maximum overlap and minimum repulsion, fixing the molecular geometry.

• sp: 1 s + 1 p orbital give 2 linear hybrid orbitals at 180° (central Be in BeCl₂; each C in HC≡CH).
• sp²: 1 s + 2 p orbitals give 3 trigonal planar hybrid orbitals at 120° (central B in BF₃; each C in H₂C=CH₂).
• sp³: 1 s + 3 p orbitals give 4 tetrahedral hybrid orbitals at 109.5° (C in CH₄; N in NH₃; O in H₂O, where lone pairs also occupy sp³ orbitals).
• sp³d: 5 hybrid orbitals, trigonal bipyramidal (P in PCl₅).
• sp³d²: 6 hybrid orbitals, octahedral (S in SF₆).

Worked example: Describe the bonding in ethyne, HC≡CH. Each carbon undergoes sp hybridisation, giving two collinear sp orbitals (180° apart) and leaving two unhybridised p orbitals on each carbon, mutually perpendicular and perpendicular to the molecular axis. One sp orbital on each carbon overlaps with an H 1s orbital to form a C–H σ bond; the remaining sp orbital on each carbon overlaps head-on with the sp orbital on the other carbon to form the C–C σ bond. The two unhybridised p orbitals on one carbon overlap sideways with those on the other carbon to form two mutually perpendicular π bonds. The C≡C triple bond is therefore 1σ + 2π, and the molecule is linear, as expected for sp hybridisation.

Molecular Orbital (MO) theory treats electrons in a molecule as occupying molecular orbitals formed by the linear combination of atomic orbitals (LCAO), belonging to the molecule as a whole. Combining two atomic orbitals constructively gives a lower-energy bonding molecular orbital (electron density concentrated between nuclei, stabilising); combining them destructively gives a higher-energy antibonding molecular orbital (a node between nuclei, destabilising). Molecular orbitals fill by the same aufbau, Pauli exclusion, and Hund's rule principles as atomic orbitals, in order of increasing energy.

Stability is expressed as bond order = ½ (electrons in bonding MOs − electrons in antibonding MOs). A positive bond order means a stable molecule; bond order 0 means the species does not exist (e.g. He₂). Higher bond order generally means shorter bond length and higher bond enthalpy. Unpaired electrons in MOs make a species paramagnetic; all electrons paired makes it diamagnetic.

Worked example: For N₂ (14 electrons), the MO configuration is σ1s² σ*1s² σ2s² σ*2s² π2p_x² = π2p_y² σ2p_z². Bonding electrons = 2+2+2+2+2 = 10; antibonding electrons = 2+2 = 4. Bond order = ½(10 − 4) = 3, matching the N≡N triple bond; all electrons are paired, so N₂ is diamagnetic. By contrast, O₂ (16 electrons) has configuration …π2p_x² = π2p_y² π*2p_x¹ = π*2p_y¹, giving bond order = ½(10 − 6) = 2 with two unpaired electrons in the π* orbitals — correctly predicting that O₂ is paramagnetic, a fact that simple Lewis/VB structures cannot explain.

A hydrogen bond is a weak-to-moderate attraction between a hydrogen atom covalently bonded to a small, highly electronegative atom (F, O, or N) and a lone pair on another electronegative atom (F, O, or N), either within the same molecule (intramolecular) or between different molecules (intermolecular, e.g. in water or HF). It is weaker than a covalent bond but stronger than ordinary van der Waals forces, and it explains the anomalously high boiling and melting points of HF, H₂O, and NH₃ compared with other hydrides of their groups, as well as properties such as water's high specific heat and expansion on freezing.