Chemical Bonding and Molecular Structure

Notes

• Ionic vs covalent: Ionic bonds form by electron transfer (low IE metal + high electron affinity non-metal); covalent character in ionic bonds is predicted by Fajans' rules (small cation, large anion, high charge).
• VSEPR: Electron pairs orient to minimise repulsion (lp-lp > lp-bp > bp-bp), giving CH_4 tetrahedral 109.5^\circ, NH_3 pyramidal 107^\circ, and H_2O bent 104.5^\circ.
• Hybridisation: mixing atomic orbitals gives sp (linear 180^\circ), sp^2 (trigonal 120^\circ), sp^3 (tetrahedral), sp^3d (trigonal bipyramidal), and sp^3d^2 (octahedral) shapes.
• Molecular Orbital Theory: electrons fill bonding and antibonding MOs; bond order =\frac{1}{2}(N_b-N_a); MOT explains the paramagnetism of O_2 (two unpaired \pi^* electrons).
• Hydrogen bonding: intermolecular H-bonds (HF, H_2O, NH_3) raise boiling points, whereas intramolecular H-bonding (o-nitrophenol) lowers them.
• Molecular orbital theory (MOT) correctly predicts paramagnetism of O2 (two unpaired electrons in pi* antibonding), which valence bond theory fails to explain. For diatomics up to N2 the (sigma)2p lies above (pi)2p (s-p mixing); from O2 onward the order reverses.
• Bond order = (Nb - Na)/2 governs bond length, bond energy and magnetic behaviour. Removing an electron from a bonding MO (e.g., N2 -> N2+) decreases bond order and increases bond length; removing from antibonding (e.g., O2 -> O2+) increases bond order.
• Formal charge and resonance: the most stable resonance contributor has minimal formal charges, negative formal charge on the most electronegative atom, and satisfies the octet. Fajans' rules quantify covalent character in ionic bonds: high charge, small cation, large polarisable anion increase covalency (e.g., AgI is more covalent than AgF).
• VSEPR predicts geometry from steric number and lone pairs; lone-pair-bond-pair repulsions distort ideal angles (H2O 104.5, NH3 107). Bent's rule states that atomic s character concentrates in orbitals directed toward electropositive substituents, rationalising angle variations in fluorinated species.
• Back-bonding (p(pi)-d(pi) or p(pi)-p(pi)) explains anomalies: BF3 is a weaker Lewis acid than BCl3 despite F being more electronegative, because efficient B-F back-bonding (good 2p-2p overlap) satisfies boron's electron deficiency; larger Cl 3p overlaps B 2p poorly.

Formulas

• Bond order =\frac{1}{2}(N_b-N_a)
• Formal charge =V-\frac{1}{2}B-L (V = valence e⁻, B = bonding e⁻, L = lone-pair e⁻)
• Dipole moment \mu=q\times d (1\,D=3.336\times10^{-30} C·m)
• % ionic character \approx\frac{\mu_{obs}}{\mu_{ionic}}\times100
• MO order (\leq N_2): \sigma1s<\sigma^*1s<\sigma2s<\sigma^*2s<\pi2p_x=\pi2p_y<\sigma2p_z<\pi^*2p<\sigma^*2p
• \text{Bond order} = \dfrac{N_b - N_a}{2}
• \mu = q \times d\;(\text{Debye}), \quad \%\text{ionic character} = \dfrac{\mu_{obs}}{\mu_{ionic}}\times 100
• \text{Dipole: } \mu_{net} = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2\cos\theta}
• \text{Hybridisation (steric no.)} = \tfrac{1}{2}(V + M - c + a) where V=valence e-, M=monovalent atoms

Exam traps & shortcuts

• Steric number = (bonded atoms + lone pairs): 2→sp, 3→sp^2, 4→sp^3, 5→sp^3d, 6→sp^3d^2.
• For O_2, F_2 the \sigma2p_z lies below the \pi2p; for \leq N_2 the order flips (\pi below \sigma).
• Bent's rule: more electronegative substituents prefer hybrid orbitals with greater p-character.
• For the counterintuitive BF3 < BCl3 < BBr3 Lewis acidity order, the deciding factor is decreasing p(pi)-p(pi) back-donation down the group, not electronegativity.
• Paramagnetism check: species with odd electrons or with degenerate antibonding orbitals half-filled (O2, B2) are paramagnetic; C2 and N2 are diamagnetic.
• Use Bent's rule: in molecules like PCl3F2 (trigonal bipyramidal), more electronegative F occupies axial positions where bonding orbitals have more p character.

Reference tables