VSEPR Theory and Linear/Trigonal Geometries
VSEPR theory (valence shell electron pair repulsion) predicts the shape of a molecule by assuming that the electron domains around a central atom arrange themselves as far apart as possible; two domains give a linear shape and three domains give a trigonal planar shape. In brief: CO2 has two electron domains and is linear (180°), BF3 has three and is trigonal planar (120°), and SO2 has three domains but one is a lone pair, so it is bent (about 119°).
The three-dimensional shape of a molecule governs its polarity, reactivity and physical properties. VSEPR is a simple method for predicting shape from a Lewis structure, and it works well for most main-group compounds. This article explains the idea, applies it to molecules with two and three electron domains, and gives a summary table and examples.
What is the basic idea of VSEPR?
Electrons repel each other. The regions of electron density around a central atom, called electron domains, therefore adopt positions that minimize repulsion. A domain is a single bond, a double bond, a triple bond or a lone pair. A multiple bond counts as one domain, since all of its electrons occupy the same region of space between two atoms.
The arrangement of all domains is the electron geometry. The arrangement of the atoms only, which ignores lone pairs, is the molecular geometry, commonly called the shape of the molecule. Chemists use the notation AXnEm, where A is the central atom, X is a bonded atom and E is a lone pair.
How do you predict a molecular shape?
- Draw the Lewis structure of the molecule.
- Count the electron domains around the central atom (bonds of any order plus lone pairs).
- Choose the electron geometry for this number of domains.
- Place the atoms on the domains, and the lone pairs on the rest, to find the molecular geometry.
- Adjust the bond angles slightly: lone pairs and multiple bonds take up more space than single bonds.
Why are two-domain molecules linear?
With two domains, the largest separation is achieved when the domains are on opposite sides of the atom, at 180°. This is the case in AX2 molecules without lone pairs on the central atom:
- CO2: O=C=O has two double bonds around carbon.
- BeCl2 (gas): Cl–Be–Cl has two single bonds and an incomplete octet around beryllium.
- HCN: H–C≡N has a single and a triple bond around carbon.
The central atom uses sp hybrid orbitals. Diatomic molecules such as HCl and O2 are linear by definition, since two atoms always lie on a line.
What shapes do three electron domains give?
With three domains, the best arrangement is a flat triangle with 120° angles, the trigonal planar electron geometry (sp2 hybridization).
Trigonal planar: AX3
When all three domains are bonds, the shape is trigonal planar. Examples are BF3 (F–B–F angle 120°), SO3, the nitrate ion NO3−, the carbonate ion CO32− and formaldehyde, H2C=O. In formaldehyde the C=O double bond takes up more space than a C–H bond, so the H–C–H angle is about 116° and the H–C=O angle about 122°.
Bent: AX2E
When one of the three domains is a lone pair, the atoms form a bent (V-shaped) molecule. The lone pair repels the bonding pairs more strongly, so the angle is a little smaller than 120°. In SO2 the O–S–O angle is about 119°, and in ozone the angle is 117°. Nitrite, NO2−, has an angle of about 115°.
Summary table
| Domains | Notation | Electron geometry | Molecular shape | Ideal angle | Examples |
|---|---|---|---|---|---|
| 2 | AX2 | Linear | Linear | 180° | CO2, BeCl2, HCN |
| 3 | AX3 | Trigonal planar | Trigonal planar | 120° | BF3, SO3, NO3− |
| 3 | AX2E | Trigonal planar | Bent | < 120° | SO2, O3, NO2− |
Worked examples
Example 1: carbon dioxide
The Lewis structure is O=C=O. Carbon has two domains and no lone pairs, so the notation is AX2, the shape is linear and the O=C=O angle is 180°. Although each C=O bond is polar, the molecule is nonpolar since the two dipoles cancel.
Example 2: sulfur dioxide
Sulfur has 6 valence electrons. In the structure O=S–O (with resonance), sulfur has one double bond, one single bond and one lone pair: three domains. The notation is AX2E, the electron geometry is trigonal planar and the shape is bent, with an angle of about 119°. The molecule is polar.
Example 3: the carbonate ion
CO32− has 4 + 18 + 2 = 24 valence electrons. Carbon has three domains (one C=O and two C–O in each resonance form) and no lone pairs, so the shape is trigonal planar with O–C–O angles of 120°, and all three C–O bonds are equal in length (about 129 pm).
Example 4: formaldehyde
H2C=O has three domains around carbon with no lone pairs, so it is trigonal planar. The H–C–H angle is about 116°, smaller than 120°, since the double bond repels the other domains more strongly.
How was VSEPR developed?
The idea that electron pairs repel each other and determine the shape of a molecule was suggested by Nevil Sidgwick and Herbert Powell in 1940. Ronald Gillespie and Ronald Nyholm expanded it into a full theory in 1957, and Gillespie promoted it for decades afterwards, notably in his teaching at McMaster University in Canada. Today the model is part of nearly all introductory chemistry courses. Its predictions are often checked by spectroscopy and diffraction, and more sophisticated quantum-chemical calculations give the same shapes in most cases.
Which mistakes are common?
- Counting each bond of a multiple bond as a separate domain: a double or triple bond is one domain.
- Forgetting the lone pairs: SO2 is bent, not linear, because of its lone pair.
- Confusing electron geometry with molecular geometry: a bent molecule can have a trigonal planar electron geometry.
- Assuming that the shape implies polarity: that depends on the bond dipoles as well.
- Using the ideal angle without correction: compare with measured angles where they are known.