Chemical Bonding: Shape, Overlap and Molecular Orbitals

Lewis structures are genuinely useful for tracking valence electrons and predicting a molecule's connectivity, but they say nothing at all about why bonds form in the first place, nor why H2's bond enthalpy (435.8 kJ/mol) differs so drastically from F2's (155 kJ/mol) despite both being simple single bonds. The Valence Shell Electron Pair Repulsion model, covered next, fills the shape gap admirably but offers no real theoretical explanation for why it works, and its own applications remain somewhat limited. To close both gaps at once, two quantum-mechanical theories were developed: Valence Bond (VB) theory, introduced by Heitler and London in 1927 and extended by Pauling, and Molecular Orbital (MO) theory, developed by Hund and Mulliken in 1932. Together, these explain not just what shape a molecule takes, but why bonds form, how strong they genuinely are, and even predict subtle physical properties like magnetism that simpler pictures completely miss.

Sidgwick and Powell proposed in 1940, later refined by Nyholm and Gillespie in 1957, that a molecule's shape can be predicted almost entirely from a simple geometric idea: every valence shell electron pair around a central atom, whether bonding or lone, repels every other pair, and the pairs arrange themselves in space to minimise that repulsion, maximising the distance between them. A multiple bond counts as a single repelling unit for this purpose, treated exactly like a single electron pair. Crucially, not all repulsions are equal: lone pair-lone pair repulsion is strongest, since lone pairs are localised entirely on the central atom and occupy more space than a bonding pair, which is shared between two atoms and pulled somewhat away from the centre; lone pair-bond pair repulsion is next; and bond pair-bond pair repulsion is weakest. This single ranking, lp-lp greater than lp-bp greater than bp-bp, is what lets VSEPR predict not just a molecule's rough shape but its precise bond angle distortions too.

Valence Bond Theory starts from the simplest possible case: two isolated hydrogen atoms, far apart, feeling no interaction at all. 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. Experimentally, the attractive forces win out at first, so the atoms draw closer and the system's potential energy drops, reaching a genuine minimum at exactly 74 pm, the hydrogen molecule's actual bond length, before repulsion takes over and energy rises sharply if the atoms are pushed any closer. The energy released at that minimum, 435.8 kJ/mol, is the bond enthalpy, and it directly explains why H2 is more stable than two separate hydrogen atoms. At this minimum-energy distance, the two atoms' orbitals overlap, their electron clouds partially merging, and this overlapping is what Valence Bond Theory identifies as the covalent bond itself: greater overlap means a stronger bond.

Covalent bonds split into two distinct types based purely on how their orbitals overlap. A sigma bond forms from head-on, end-to-end overlap directly along the internuclear axis, achievable through s-s, s-p, or p-p overlap, and this direct, axial arrangement gives sigma bonds their maximal possible overlap and, correspondingly, their greatest strength. A pi bond instead forms from sideways overlap, with the two contributing orbitals' axes running parallel to each other but perpendicular to the bond axis, producing two lobe-shaped regions of electron density, one above and one below the plane connecting the atoms. Because this sideways arrangement achieves less overlap than a direct head-on approach, pi bonds are consistently weaker than sigma bonds. Every single covalent bond contains exactly one sigma bond; any additional bonds in a double or triple bond are always pi bonds layered on top of that one sigma bond, never a second or third sigma bond.

Simple orbital overlap alone cannot explain methane's real 109.5-degree tetrahedral bond angles; carbon's own unhybridised 2p orbitals sit at 90 degrees to each other, predicting the wrong geometry entirely. Pauling's solution was hybridisation: mixing atomic orbitals of similar energy into an entirely new set of equivalent orbitals, matching the molecule's actual observed geometry rather than the plain, unmixed atomic orbitals' own natural directions. One s orbital mixed with one p orbital gives two sp hybrids, oriented 180 degrees apart, producing linear geometry, as in BeCl2. One s mixed with two p orbitals gives three sp2 hybrids at 120 degrees, trigonal planar, as in BCl3. One s mixed with three p orbitals gives four sp3 hybrids at 109.5 degrees, tetrahedral, as in CH4, and this same sp3 hybridisation, applied to nitrogen and oxygen with their lone pairs included, correctly predicts ammonia's pyramidal shape and water's bent shape, once the extra lone pair-bond pair repulsion is accounted for.

Third-period elements and beyond have accessible d orbitals, letting them hybridise beyond the four-orbital sp3 limit. Phosphorus in PCl5 promotes an electron and hybridises one s, three p, and one d orbital into five equivalent sp3d orbitals, pointing toward the corners of a trigonal bipyramid, though the resulting bond angles aren't all identical: three equatorial P-Cl bonds sit in one plane at 120 degrees, while two axial bonds sit perpendicular to that plane at 90 degrees, and because the axial bonds suffer more repulsion from the equatorial ones, they end up slightly longer and weaker, making PCl5 measurably more reactive at those axial positions. Sulphur in SF6 goes further still, hybridising one s, three p, and two d orbitals into six sp3d2 orbitals pointing toward a perfect, fully symmetric octahedron's six corners, giving SF6 the genuinely uniform geometry and remarkable chemical inertness it's known for.

Molecular Orbital Theory takes a genuinely different starting view from Valence Bond Theory: rather than treating a bond as two atoms' orbitals overlapping while each electron still, in some sense, belongs to its original atom, MO theory treats every electron as occupying a molecular orbital spanning the entire molecule, influenced by every nucleus present at once, exactly as an atomic orbital is influenced by just one nucleus in an isolated atom. These molecular orbitals are built mathematically through the linear combination of atomic orbitals (LCAO): adding two atomic wave functions together produces a lower-energy bonding molecular orbital, with electron density concentrated between the two nuclei, holding them together, while subtracting them produces a higher-energy antibonding molecular orbital instead, with a genuine node, zero electron density, between the nuclei, actively working against the bond. Exactly as many molecular orbitals form as atomic orbitals combined: two atomic orbitals always yield exactly one bonding and one antibonding molecular orbital.

Not every pair of atomic orbitals is free to combine into molecular orbitals; three specific conditions must hold. First, the combining orbitals must be similar in energy, which is why a 1s orbital combines readily with another 1s but not with a much higher-energy 2s orbital. Second, they must share the same symmetry about the molecular axis, which is why a 2pz orbital on one atom combines only with a 2pz orbital on the other, never with a differently-oriented 2px or 2py orbital. Third, they must overlap to the maximum extent possible, since greater overlap produces more electron density concentrated between the nuclei. Molecular orbitals formed this way are named for their symmetry: sigma molecular orbitals are symmetric all the way around the bond axis, as formed by 1s-1s or 2pz-2pz combinations, while pi molecular orbitals are not, since they carry positive lobes above and negative lobes below the molecular plane, exactly as formed by 2px-2px or 2py-2py combinations.

Filling molecular orbitals follows the same Aufbau, Pauli exclusion, and Hund's rule logic used for atomic orbitals, filling from lowest energy up, at most two opposite-spin electrons per orbital, singly before pairing within a degenerate set. From this filled configuration, bond order is defined as half the difference between the number of electrons in bonding orbitals (Nb) and antibonding orbitals (Na): a positive bond order predicts a stable molecule, while a zero or negative bond order predicts an unstable one that simply won't form. Oxygen's Lewis structure shows every electron neatly paired, predicting no magnetism at all, yet oxygen gas is genuinely, measurably paramagnetic, attracted into a magnetic field. Building O2's actual molecular orbital configuration resolves this instantly: its last two electrons end up in separate, degenerate pi* antibonding orbitals, occupying them singly by Hund's rule rather than pairing up, giving two genuinely unpaired electrons and correctly predicting the paramagnetism that stumped simpler theories for decades.

Applying molecular orbital theory across the periodic table's simplest diatomic molecules reveals real, testable predictions. Hydrogen molecule H2 places its two electrons in the bonding sigma1s orbital, giving configuration (sigma1s)^2 and a bond order of 1, matching its known stable existence. Helium, with two electrons per atom, would need to fill both the bonding sigma1s and the antibonding sigma*1s orbitals in He2, giving (sigma1s)^2 (sigma*1s)^2 and a bond order of exactly zero, correctly predicting that He2 simply doesn't exist as a stable molecule, exactly matching observation, since helium only ever appears as single, unbonded atoms. Lithium's Li2, building on a filled inner (sigma1s)^2(sigma*1s)^2 core, adds two more electrons into the bonding sigma2s orbital, giving a bond order of 1, correctly predicting genuine, if weak, stability, and diamagnetic Li2 molecules have indeed been detected in the vapour phase, exactly as this theory predicts.

When hydrogen bonds to a strongly electronegative atom, fluorine, oxygen, or nitrogen, the shared electron pair shifts heavily toward that atom, leaving hydrogen carrying a genuine partial positive charge. This partially positive hydrogen can then form a further, weaker attraction to another nearby electronegative atom's lone pair, called a hydrogen bond, conventionally drawn as a dotted line to distinguish it from an ordinary solid-line covalent bond, and always weaker than a true covalent bond. Hydrogen bonds come in two forms: intermolecular, formed between separate molecules, as the chain of hydrogen bonds linking one HF molecule's hydrogen to the next molecule's fluorine, or between water or alcohol molecules; and intramolecular, formed within a single molecule between two electronegative atoms already present in it, as in ortho-nitrophenol, where hydrogen bridges between an oxygen on one part of the molecule and a nearby oxygen on another. Hydrogen bonding is strongest in the solid state and weakest in the gas phase, and despite being far weaker than a covalent bond, it has a genuinely powerful influence on structure and properties, from water's unusually high boiling point to the double helix shape of DNA.