Chemical Bonding and Molecular Geometry

This is Unit Six of Chemistry, Part Three: the bonding models, and the last part of the unit. Part Two predicted molecular shapes from VSEPR, and noted that VSEPR explains where atoms sit without explaining why a bond forms at all. This part is that explanation — twice over, because chemistry uses two models for it. The through-line is that they are not rivals to be judged true or false. Each predicts something the other misses, and the unit closes by putting both on the same molecule to show exactly where they diverge. By the end you will be able to say what makes a bond sigma rather than pi; say how an atom's hybridization is predicted; say why a double bond resists rotation; calculate a bond order from a molecular orbital diagram; and say what each model predicts that the other cannot.

Four entries. The first model's account of what a bond is, the two ways two orbitals can overlap, and then the model's own statement of where it works and the one thing it cannot explain.

Orbitals overlapping.

Chem 1080 Valence Bond Theory's Core Claim

Valence bond theory explains a covalent bond as the overlap of two atomic orbitals, each contributing one electron, into a single shared region. Two hydrogen 1s orbitals overlap end to end, concentrating the bonding pair between the nuclei. The model ties each electron's orbital to overlap between two specific atoms — which is where the rival model later in this part departs from it.

End to end.

Chem 1083 Sigma Bond

A sigma bond forms from end-to-end orbital overlap along the axis connecting two bonded nuclei, and every single bond has exactly one. Two chlorine 3p orbitals overlap end to end along that axis to form the single bond in Cl2. Sigma bonds are not limited to s orbitals — it is the end-to-end geometry, not the orbital type, that makes a bond sigma.

Side by side.

Chem 1085 Pi Bond

A pi bond forms from side-by-side overlap of two parallel p orbitals, above and below the internuclear axis, alongside an existing sigma bond. Two adjacent p orbitals on double-bonded carbons overlap side by side to form it. A pi bond never occurs alone — it always forms in addition to a sigma bond between the same two atoms.

Where it works.

Chem 1090 Valence Bond Theory's Domain

Valence bond theory correctly predicts bond formation, sigma and pi character, and — with hybridization — most molecular shapes, but it does not predict some molecules' magnetism. It predicts nitrogen's stable triple bond while giving no structural reason for oxygen's attraction to a magnet. The shape and bond-order predictions hold broadly; the magnetism gap is a specific named exception, not a general failure.

Six entries. Valence bond theory alone predicts the wrong shapes, so it is extended: an atom's orbitals mix into a new equivalent set oriented to match the geometry VSEPR already gave. Five schemes follow, and then the shortcut that reads any of them off a domain count.

Mixed into a new set.

Chem 1095 Orbital Hybridization, Defined

Orbital hybridization mixes an atom's s and p orbitals into a new set of equivalent hybrid orbitals, oriented to match its VSEPR geometry. Mixing one 2s and three 2p orbitals on carbon produces four identical hybrids replacing the originals. Only the orbitals entering the mix are replaced — sp and sp squared hybridization each leave some p orbitals unhybridized, unlike sp cubed.

Two hybrids.

Chem 1098 sp Hybridization

sp hybridization mixes one s and one p orbital into two hybrid orbitals oriented a hundred and eighty degrees apart, matching a two-domain linear geometry. Beryllium in beryllium fluoride is sp hybridized, its two hybrids pointing opposite ways toward each fluorine. Hybridization matches the electron-domain count VSEPR sets, not the element alone — the same element hybridises differently in a different molecule.

Three hybrids, one spare.

Chem 1101 sp² Hybridization

sp squared hybridization mixes one s and two p orbitals into three hybrids oriented a hundred and twenty degrees apart in one plane, matching trigonal planar geometry. Boron in boron trifluoride is sp squared hybridized, its three hybrids pointing toward each fluorine in a flat triangle. It leaves one unhybridized p orbital untouched, and that leftover orbital forms a pi bond later in this part.

Four hybrids.

Chem 1104 sp³ Hybridization

sp cubed hybridization mixes one s and three p orbitals into four hybrids oriented toward a tetrahedron's corners, matching four domains. Carbon in methane is sp cubed hybridized, each hybrid overlapping one hydrogen 1s orbital. A hybrid holding a lone pair, as on ammonia's nitrogen, still counts as one of the four.

Bringing in d.

Chem 1107 sp³d and sp³d² Hybridization

sp cubed d hybridization mixes in one d orbital for a five-domain geometry, and sp cubed d squared mixes in two for a six-domain geometry, extending the same pattern past period two. Phosphorus in phosphorus pentachloride is the first; sulfur in sulfur hexafluoride the second. Both are limited to central atoms from period three and below — the same elements capable of an expanded octet.

Read it off the count.

Chem 1110 Predicting Hybridization from VSEPR Domain Count

A central atom's hybridization reads directly from its VSEPR domain count: two domains give sp, three give sp squared, four give sp cubed, and upward from there. Counting sulfur dioxide's three domains — one lone pair and two bonding — predicts sp squared without analysing orbitals separately. It is the domain count from a completed Lewis structure, not the molecule's final named geometry, that predicts hybridization.

Three entries. What the second bond in a double bond actually is, what the third adds, and the consequence that follows for the molecule's freedom to twist — which is where the spare p orbital from sp squared finally does its work.

One of each.

Chem 1115 A Double Bond as Sigma Plus Pi

A double bond consists of exactly one sigma bond from hybrid-orbital overlap plus one pi bond from leftover unhybridized p-orbital overlap. Ethylene's carbon-carbon double bond is one sp-squared sigma bond plus one pi bond from the remaining p orbitals. The second bond is always a pi bond, never a second sigma — two atoms share only one overlap axis.

One and two.

Chem 1117 A Triple Bond as Sigma Plus Two Pi

A triple bond consists of one sigma bond plus two pi bonds, formed from two separate pairs of perpendicular unhybridized p orbitals. Nitrogen's triple bond in N2 is one sp-sp sigma bond plus two pi bonds from two perpendicular p-orbital pairs. Those two pi bonds occupy perpendicular planes around the same sigma axis and do not overlap each other.

Locked flat.

Chem 1120 Pi Bonding Restricts Rotation

Rotating one atom of a double bond relative to the other would break the pi bond's side-by-side overlap, so a double bond strongly resists rotation. The two carbons in ethylene's double bond stay fixed in one plane, unlike the freely rotating single bond in ethane. The restriction comes specifically from the pi bond's overlap geometry — a molecule's single sigma bonds rotate freely.

Four entries introducing the second model, which does not refine the first but replaces its central picture. Orbitals belong to the whole molecule rather than to a pair of atoms, they come in two kinds, they are filled by rules already familiar, and the filling yields a number.

Across the molecule.

Chem 1125 Molecular Orbital Theory's Core Claim

Molecular orbital theory treats bonding electrons as occupying orbitals belonging to the whole molecule, formed by combining every bonded atom's orbitals together. Combining two hydrogen 1s orbitals produces two molecular orbitals spanning the entire H2 molecule rather than one localised bond region. It replaces the localised shared-pair picture — a distinct model, not a refinement of the first.

In phase, or out.

Chem 1128 Bonding Orbital Versus Antibonding Orbital

Combining two atomic orbitals in phase produces a lower-energy bonding orbital that holds nuclei together; combining them out of phase produces a higher-energy antibonding orbital that pulls them apart. Two hydrogen 1s orbitals give a sigma-1s bonding orbital and a sigma-1s-star antibonding one. Antibonding orbitals fill by energy rather than by class — a sigma-2s-star can fill before a higher-energy bonding orbital.

Nothing new to learn.

Chem 1132 Molecular Orbital Diagram

A molecular orbital diagram ranks a molecule's bonding and antibonding orbitals by energy and fills them using the same Aufbau, Pauli and Hund rules from atomic configuration. Nitrogen's ten valence electrons fill the ranked orbitals lowest first, completing bonding and antibonding orbitals in energy order. The three filling rules carry over unchanged — no new procedure applies.

Bonding minus antibonding.

Chem 1135 Bond Order from a Molecular Orbital Diagram

Calculating bond order from a molecular orbital diagram means subtracting the antibonding electrons from the bonding electrons, then dividing by two. Dihydrogen has two electrons in its sigma-1s bonding orbital and none antibonding, so two minus zero over two gives a bond order of one — matching its known single bond. The division by two accounts for two electrons per bond, and omitting it doubles every calculated bond order.

Four entries closing the unit. The magnetic property that separates the two models, the molecule where valence bond theory visibly fails and molecular orbital theory succeeds, each model's own declared domain, and then the capstone putting both on one molecule.

Drawn in, or pushed out.

Chem 1138 Paramagnetism and Diamagnetism

A molecule with unpaired electrons in its molecular orbitals is paramagnetic, weakly drawn into a magnetic field; one with every electron paired is diamagnetic, weakly repelled. A molecule whose highest filled orbitals hold two unpaired electrons is drawn slightly into an external field. The behaviour is set by unpaired electrons in molecular orbitals specifically, and is unrelated to the molecule's overall charge.

Where the first model fails.

Chem 1141 O2's Paramagnetism, Predicted by Molecular Orbital Theory

Oxygen's Lewis structure shows only paired lone pairs and gives no reason for magnetism. Its molecular orbital diagram does: twelve valence electrons fill in energy order, and the final two occupy two separate degenerate antibonding pi orbitals singly, by Hund's rule. The same count gives a bond order of two, matching O2's known double bond, and those two unpaired electrons are what correctly predict liquid oxygen being drawn into a magnet. A correct Lewis structure and a correct valence-bond picture both miss this entirely — the gap is in what those models track.

Where the second works.

Chem 1145 Molecular Orbital Theory's Domain

Molecular orbital theory correctly predicts magnetic behaviour and fractional bond order that valence bond theory misses, at the cost of a more demanding diagram. It predicts oxygen's paramagnetism where valence bond theory's localised picture gives no such signal. Neither model is the better one: valence bond theory stays the tool for shape in large molecules, and this one for magnetism.

Nitrogen monoxide, twice.

Chem 1200 Capstone: Two Bonding Models Applied to One Molecule

Nitrogen monoxide has eleven valence electrons — an odd number that strains any Lewis structure. Valence bond theory, through the best available structure, gives a double bond with one unpaired electron on nitrogen: bond order two, and correctly paramagnetic. Molecular orbital theory fills the diagram and gives eight bonding electrons against three antibonding, so a bond order of two and a half — a fractional value no whole-number Lewis structure can represent. Both models agree on the paramagnetism. They diverge on precision: NO's measured bond length sits between a double and a triple bond, matching two and a half. Concluding one model is flatly right and the other wrong misses the point.

Five things to carry out of this part, and out of the unit. What makes a bond sigma is end-to-end overlap along the axis joining two nuclei, and what makes one pi is side-by-side overlap of parallel p orbitals above and below that axis — it is the geometry of the overlap rather than the type of orbital, which is why a p-p overlap can be sigma. An atom's hybridization reads straight off its VSEPR domain count: two domains give sp, three sp squared, four sp cubed, and five and six bring in d orbitals for period-three atoms and below. A double bond resists rotation because its second bond is a pi bond, and twisting the two atoms relative to each other would break that side-by-side overlap — whereas a single sigma bond rotates freely. Bond order from a molecular orbital diagram is the bonding electrons minus the antibonding electrons, divided by two, and forgetting the division doubles every answer. And each model predicts what the other misses: valence bond theory gives bond formation, sigma and pi character and most shapes but no account of magnetism, while molecular orbital theory predicts magnetic behaviour and fractional bond orders at the cost of a harder diagram. Nitrogen monoxide shows both at once — bond order two by one model, two and a half by the other, and a measured bond length that matches the fraction. Unit Seven takes up gases.