Molecular Shape and Lone-Pair Effects
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You should be comfortable counting electron domains around a central atom and identifying the idealised electron-domain geometries (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral) associated with steric numbers 2 through 6.
Why this matters
Lone pairs are invisible in the final molecular shape but dictate its geometry and reactivity.
While the positions of atoms define the molecular geometry, the positions of all electron domains—including lone pairs—define the electron-domain geometry. Because lone pairs occupy more space than bonding pairs, they compress bond angles and alter the shape of the molecule. Understanding this distinction is critical for predicting molecular polarity, dipole moments, and the stereochemical outcome of reactions, as the spatial arrangement of atoms is a direct consequence of these electronic repulsions.
The Invisible Occupants
Imagine a central atom surrounded by a set of balloons representing electron domains. If all balloons are attached to other atoms, they represent bonding pairs. If some balloons are attached only to the central atom, they represent lone pairs. In both cases, the balloons repel each other and try to get as far apart as possible. However, a balloon attached to only one point (a lone pair) is "looser" and can expand more into the surrounding space than a balloon tethered between two points (a bonding pair). Consequently, lone pairs exert a stronger repulsive force on their neighbours, pushing the bonding pairs closer together and distorting the ideal angles predicted by simple symmetry.
Repulsion Strengths and Angle Compression
The VSEPR model quantifies the relative strength of repulsions between electron domains. The hierarchy of repulsive strength is generally accepted as: lone pair–lone pair (LP–LP) > lone pair–bonding pair (LP–BP) > bonding pair–bonding pair (BP–BP). This ordering arises because lone pairs are held by only one nucleus and are therefore more diffuse, occupying a larger volume of space closer to the central atom than bonding pairs, which are shared between two nuclei and pulled away from the centre.
As a result, the presence of lone pairs reduces the bond angles relative to the idealised geometry. For example, in a tetrahedral electron-domain geometry (steric number 4), the ideal angle is \(109.5^\circ\). In ammonia (\(\mathrm{NH_3}\)), which has one lone pair, the \(\mathrm{H-N-H}\) angle is compressed to approximately \(107^\circ\). In water (\(\mathrm{H_2O}\)), with two lone pairs, the \(\mathrm{H-O-H}\) angle is further compressed to approximately \(104.5^\circ\). The more lone pairs present, the greater the compression of the remaining bond angles.
Stereochemical Consequences in Higher Coordination
In molecules with steric numbers 5 and 6, the distinction between axial and equatorial positions becomes crucial for predicting the placement of lone pairs. In a trigonal bipyramidal geometry, axial positions experience repulsion from three equatorial positions at \(90^\circ\), while equatorial positions experience repulsion from only two axial positions at \(90^\circ\). Therefore, lone pairs preferentially occupy equatorial positions to minimise these \(90^\circ\) repulsions.
Phosphorus pentachloride (\(\mathrm{PCl_5}\)) has no lone pairs and is trigonal bipyramidal. Sulfur tetrafluoride (\(\mathrm{SF_4}\), four bonds and one lone pair) puts its lone pair in an equatorial site and is seesaw-shaped; chlorine trifluoride (\(\mathrm{ClF_3}\), three bonds and two lone pairs) puts both lone pairs equatorial and is T-shaped; and \(\mathrm{XeF_2}\) (three lone pairs) is linear. In octahedral systems (steric number 6), all positions are equivalent with respect to \(90^\circ\) neighbours, so a single lone pair can sit in any position (as in square-pyramidal \(\mathrm{BrF_5}\)), but a second lone pair goes opposite the first, giving the square-planar shape of \(\mathrm{XeF_4}\).
From Electron Domains to Molecular Geometry
The molecular geometry is defined solely by the positions of the atoms, ignoring the lone pairs. However, the lone pairs must be accounted for to determine the correct geometry. The steric number \(SN\) determines the electron-domain geometry. The number of bonding domains determines the molecular geometry.
For instance, a steric number of 4 corresponds to a tetrahedral electron-domain geometry. If there are 4 bonding pairs, the molecular geometry is tetrahedral. If there are 3 bonding pairs and 1 lone pair, the molecular geometry is trigonal pyramidal. If there are 2 bonding pairs and 2 lone pairs, the molecular geometry is bent (or angular). It is essential to distinguish between these terms, as "tetrahedral" refers to the arrangement of electron domains, while "trigonal pyramidal" refers to the arrangement of atoms.
The result
VSEPR and molecular shape
The three-dimensional shape a molecule adopts is set, to good approximation, by the number of electron domains (bonding regions plus lone pairs, treating a multiple bond as one domain) around the central atom, which arrange themselves to maximise their mutual angular separation. The steric number \(SN=(\text{number of }\sigma\text{ bonds})+(\text{number of lone pairs on the central atom})\) determines an idealised electron-domain geometry; removing the lone-pair positions from that geometry (while they still occupy space and distort the remaining angles) gives the observed molecular geometry.
Open the full result →A common misconception is that lone pairs are "invisible" and therefore do not affect the shape. In reality, they are the primary drivers of shape distortion. Another subtle point is that in trigonal bipyramidal systems, the lone pair always occupies an equatorial position, not an axial one, because axial positions have three \(90^\circ\) interactions with equatorial domains, whereas equatorial positions have only two \(90^\circ\) interactions with axial domains. Placing a lone pair in an axial position would result in greater repulsion and a higher energy state. C
Worked example
Problem. Predict the electron-domain geometry, the molecular shape and the F–Xe–F bond angles of xenon tetrafluoride, \(\mathrm{XeF_4}\).
- Valence electrons: \(8\ (\mathrm{Xe}) + 4 \times 7\ (\mathrm{F}) = 36\).
- Four Xe–F bonds use 8 electrons; three lone pairs on each F use \(4 \times 6 = 24\); \(36 - 8 - 24 = 4\) electrons remain, i.e. two lone pairs on Xe.
- Steric number \(4 + 2 = 6\): octahedral electron-domain geometry.
- The two lone pairs go opposite each other (180°) to avoid a 90° lone pair–lone pair contact, so the four F atoms lie in a square.
Units check. The electron count must balance: \(8 + 24 + 4 = 36\). Square-planar \(\mathrm{XeF_4}\) is non-polar, because the four Xe–F dipoles cancel in pairs.
Three quick tests
- What is the molecular geometry of \(\mathrm{ClF_3}\)?
Answer
T-shaped. Steric number 5 (3 bonds, 2 lone pairs). Lone pairs occupy equatorial positions in the trigonal bipyramidal electron-domain geometry. - Why is the \(\mathrm{H-O-H}\) angle in water (\(\approx 104.5^\circ\)) smaller than the \(\mathrm{H-N-H}\) angle in ammonia (\(\approx 107^\circ\))?
Answer
Water has two lone pairs on oxygen, while ammonia has one lone pair on nitrogen. Lone pair–lone pair repulsions are stronger than lone pair–bonding pair repulsions, causing greater compression in water. - In a trigonal bipyramidal electron-domain geometry, do lone pairs prefer axial or equatorial positions?
Answer
Equatorial positions. This minimises the number of \(90^\circ\) repulsive interactions with other electron domains.
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Every lecture and every result in this unit, with prerequisites and threads.
Lecture notes drafted with a local model and checked line by line by the editor; every number in the worked example was recomputed.