Why water is bent and carbon dioxide is straight: the VSEPR model

Regions that push apart

Water is bent and carbon dioxide is straight, although each molecule is three atoms with one in the middle. A Lewis structure cannot tell them apart by shape: it records which atoms are joined, in what order, and carries no geometry beyond that.

The valence shell electron pair repulsion model, VSEPR for short, looks instead at the outer-shell electrons of an atom bonded to two or more others. It sorts them into regions of negative charge, or electron clouds. There is one region for each atom bonded to it, however many pairs that bond holds, and one for each pair it keeps. Those regions repel one another, so they settle as far apart as they can and carry the bonds with them.

The atom whose regions are counted is the central atom, and the number of regions around it is its coordination number. Lone pairs, the pairs that belong to the central atom alone, count as well as bonded atoms. The AXE notation writes X for each bonded atom and E for each lone pair.

Two geometries follow. Coordination geometry is where the regions point; molecular shape is where the atoms sit. When every region is a bond the two are the same, and a lone pair makes the shape simpler than the coordination geometry. Ronald Gillespie and Ronald Nyholm first presented the model in 1957, extending Lewis’s 1916 picture of the shared electron pair.

Two regions and three: straight and flat

With two regions around a central atom, the farthest apart they can get is 180°, on opposite sides. A molecule of the type AX₂ is therefore linear. Beryllium chloride, BeCl₂, is the plain case: beryllium is joined to two chlorines and carries no lone pairs, so the two chlorines sit on opposite sides.

Carbon dioxide has two double bonds, which looks like a complication. It changes nothing in the count, because a double bond is one connection: carbon is still joined to only two atoms, and its two regions lie 180° apart. Carbon dioxide’s model shows those two double bonds leaving one carbon in opposite directions, and from any side its three atoms stay in one straight line.

The evidence for that line is something the model cannot draw. Each carbon–oxygen bond is polar, and bond polarities combine like arrows: in a straight molecule the two point in opposite directions and cancel. Carbon dioxide’s dipole moment, the charge separation that lets a polar molecule respond to an electric field, is zero. That zero is one of the simplest experimental ways of showing the molecule is linear.

Three regions repel least at 120°, an angle that puts the central atom and its three partners in one plane: the trigonal planar shape. Boron trifluoride, BF₃, is flat in this way around boron. The double-bond rule carries over. Each carbon of ethylene is joined to three atoms, one of them by a double bond, and sits in the same flat, trigonal arrangement.

Four regions: the tetrahedron

With four regions, a tempting guess is 360° divided by four, or 90°. It is wrong. That figure would hold only if the atoms were confined to one plane, and nothing confines them. In three dimensions the four regions point to the corners of a tetrahedron, a solid with four triangular faces, and the angle between any two bonds is 109.5°. This is tetrahedral coordination. Methane’s model shows four hydrogens around one carbon, and from any side no three of them lie flat with it.

Methane has four bonding pairs and no lone pairs, so its coordination geometry and its shape are one and the same tetrahedron. Chemistry supplies evidence too. Only one kind of CH₂Cl₂ molecule is known, so all four positions around carbon must be equivalent, and only tetrahedral coordination makes them so. Chloroform is built on the same four-cornered carbon, the coordination carbon has in most of its organic compounds.

Five regions meet a problem: no regular solid has five corners. They take a trigonal bipyramid, two three-sided pyramids joined base to base, with three equatorial positions around the middle and two axial ones above and below it. Six regions point to the corners of an octahedron, which is a pair of square-based pyramids sharing one base. Phosphorus pentachloride, PCl₅, takes the first shape, and sulfur hexafluoride, SF₆, has six regions around sulfur.

One lone pair: ammonia’s pyramid

A lone pair occupies space and repels the other regions just as a bond does, so it counts. Nitrogen has five outer electrons. In ammonia three of them bond to hydrogen and the other two stay on nitrogen as a lone pair. That makes three bonded atoms and one lone pair, a coordination number of four.

The four regions are tetrahedral, but a shape names only the positions of atoms. Three atoms on three corners of a tetrahedron make a trigonal pyramid, a pyramid with a triangular base; in the notation, ammonia is AX₃E. Ammonia’s model shows that pyramid, three hydrogens forming its base and nitrogen at its tip, with the fourth corner of the tetrahedron left empty.

Nothing fills that corner in the model because the lone pair is not drawn, yet its effect shows in the angles. A lone pair has no nucleus at its far end to draw its charge outward. Its charge therefore gathers closer to nitrogen, and the fatter lone-pair region pushes the three bonding regions slightly together. Each H–N–H angle closes to about 107°, a little under the tetrahedral 109.5°.

Two lone pairs: why water is bent

Oxygen has six outer electrons. In water only two of them are used in bonds, and the remaining four form two lone pairs. The count is two bonding pairs and two lone pairs: four regions, or AX₂E₂.

Four regions point to the corners of a tetrahedron, but only two of those corners hold atoms. Oxygen is tetrahedrally coordinated, yet the shape of the molecule is bent. Both lone pairs keep their charge close to oxygen and push the two bonding regions together, closing the angle between the bonds to 104.5° from the tetrahedral 109.5°. Methane at 109.5°, ammonia at about 107° and water at 104.5° make a sequence: each lone pair added closes the angle further. Water’s model shows a V of two hydrogens on the oxygen, with the other two corners of its tetrahedron empty.

That V has a consequence the model cannot draw. Water’s two polar H–O bonds point at 104.5° to each other rather than in opposite directions, so they do not cancel. Water therefore has a dipole moment, where carbon dioxide has none. One rule gives both answers: two regions on carbon make a straight molecule, and four on oxygen, two of them lone pairs, make a bent one.

Where the model stops

VSEPR gets the overall shape of most molecules right, but it cannot give exact angles. It cannot say, for example, why the bonds of hydrogen sulfide close so much more tightly than water’s. Hydrogen sulfide has the same count as water: two bonding pairs and two lone pairs on the central atom. VSEPR therefore predicts the same squeezed tetrahedral angle, yet the two bonds of hydrogen sulfide meet at 92° against water’s 104.5°.

A gap of more than ten degrees between two molecules with identical counts has two accounts. The first lies in the model itself. VSEPR weighs repulsions between regions of charge and leaves out the detailed nature of the orbitals that hold the electrons, and so of the bonds. The second begins from the angle. Repulsion between two lone pairs can hardly be pushing the H–S bonds that close together. Instead, sulfur’s electrons are better described by its atomic p orbitals, which lie 90° apart, than by sp³ hybrid orbitals, four equivalent orbitals aimed at a tetrahedron’s corners.

Neither account removes the count. The count still places two bonds and two lone pairs around sulfur; the angle needs a picture of the orbitals themselves. That is the difference between a model and a law: VSEPR is a tool that works within limits.

Larger molecules raise a different limit, since they have no single central atom. The rule is then applied one central atom at a time. In propane and butane, each carbon has four regions, so the chain is a row of tetrahedra joined end to end, and its carbon backbone is not really straight.