Molecular Shapes - VSEPR Theory

A Lewis structure, built across the previous two chapters, tells you which atoms are bonded, how many bonding pairs connect them, and how many lone pairs each atom carries — but it says nothing about the molecule's actual three-dimensional shape, since it is drawn flat on a page. This chapter supplies that missing piece: Valence Shell Electron Pair Repulsion (VSEPR) theory, a remarkably simple model that predicts molecular geometry directly from the electron-pair count a completed Lewis structure already provides.

You should bring forward fluent Lewis-structure construction, including the exceptions from the previous chapter (incomplete and expanded octets in particular, since they introduce genuinely new shape categories here). Nothing in this chapter yet explains bond polarity quantitatively or orbital hybridization — those follow in the next two chapters, built directly on the shapes established here.

1. The VSEPR Principle

VSEPR theory rests on a single physical idea: regions of electron density around a central atom — whether bonding pairs (shared with another atom) or lone pairs (belonging only to the central atom) — are all negatively charged and therefore repel one another. The molecule adopts whatever three-dimensional arrangement keeps these electron pairs, collectively called electron domains, as far apart as possible, minimizing their mutual repulsion.

A double or triple bond, recall from two chapters ago, is treated as a single electron domain for VSEPR purposes — it occupies one region of space pointing towards one neighbouring atom, regardless of whether one, two, or three electron pairs are shared along that direction. Counting electron domains therefore means counting bonded atoms plus lone pairs on the central atom, never the number of individual shared electron pairs.

Key distinction. Electron-domain geometry describes the arrangement of all electron domains (bonding and lone pairs together); molecular geometry describes only the positions of the atoms, ignoring lone pairs (which are real but invisible to any shape-measuring technique that detects nuclei). The two coincide only when no lone pairs are present on the central atom.

2. Two Electron Domains: Linear

With exactly two electron domains and no lone pairs (notation $\text{AX}_2$), the domains repel into the arrangement that maximizes their separation in three dimensions: directly opposite each other, at $180^\circ$.

Worked example. Predict the shape of $\text{CO}_2$.

The Lewis structure (Chapter 2) has carbon at the centre with two C=O double bonds and no lone pairs — two electron domains, each a double bond. VSEPR places them at $180^\circ$, giving a linear molecule, $\text{O}=\text{C}=\text{O}$ in a straight line. $\text{BeCl}_2$ (incomplete octet, two single bonds, no lone pairs on beryllium) is linear by identical reasoning.

3. Three Electron Domains: Trigonal Planar and Bent

With three electron domains, the domains spread into a single plane, $120^\circ$ apart, whenever no lone pairs are present ($\text{AX}_3$). When one of the three domains is a lone pair instead ($\text{AX}_2\text{E}$, where $\text{E}$ denotes a lone pair), the molecular geometry — the positions of the atoms alone — becomes bent, with a bond angle slightly less than $120^\circ$.

Worked example. Predict the shapes of $\text{BF}_3$ and $\text{SO}_2$.

$\text{BF}_3$ (incomplete octet, previous chapter) has boron with three single bonds and no lone pairs: electron-domain geometry and molecular geometry coincide, giving a trigonal planar shape, bond angles of exactly $120^\circ$.

$\text{SO}_2$ has sulfur as the central atom with one S=O double bond, one S-O single bond (via a minor resonance adjustment covered in the previous chapter), and one lone pair — three electron domains overall ($\text{AX}_2\text{E}$). The electron-domain geometry is trigonal planar, but since one "corner" is an invisible lone pair, the molecular geometry (the shape traced out by the three atoms, O-S-O) is bent, with a bond angle of about $119^\circ$ — slightly compressed from $120^\circ$ by the extra repulsion of the lone pair, developed quantitatively in Section 7.

4. Four Electron Domains: Tetrahedral, Trigonal Pyramidal and Bent

Four electron domains spread into three dimensions, $109.5^\circ$ apart — the tetrahedral electron-domain geometry, found whenever a central atom has four bonding/lone pairs combined. The molecular geometry, however, depends on how many of those four domains are lone pairs:

• Zero lone pairs ($\text{AX}_4$): tetrahedral molecular geometry, bond angle $109.5^\circ$. Example: $\text{CH}_4$.
• One lone pair ($\text{AX}_3\text{E}$): trigonal pyramidal molecular geometry, bond angle compressed to about $107^\circ$. Example: $\text{NH}_3$.
• Two lone pairs ($\text{AX}_2\text{E}_2$): bent molecular geometry, bond angle further compressed to about $104.5^\circ$. Example: $\text{H}_2\text{O}$.

Worked example. Predict the shape of ammonia, $\text{NH}_3$.

From the Lewis-structure chapter, nitrogen has three N–H bonding pairs and one lone pair — four electron domains, giving a tetrahedral electron-domain geometry. Since one domain is a lone pair, the molecular geometry (traced by the four atoms N, H, H, H) is trigonal pyramidal: picture a tetrahedron with the lone pair occupying one vertex invisibly, leaving the three hydrogens and the nitrogen forming a pyramid. The H–N–H bond angle, $107^\circ$, is measurably less than the ideal tetrahedral $109.5^\circ$, compressed by the lone pair's stronger repulsion (Section 7).

Warning. A very common error is describing $\text{NH}_3$'s electron-domain geometry (tetrahedral) as if it were the molecule's shape. The molecule's actual shape — what a student is normally asked to name — is trigonal pyramidal; "tetrahedral" describes only the full arrangement of all four domains, lone pair included.

5. Five Electron Domains: Trigonal Bipyramidal and Its Variants

Five electron domains (only possible for an expanded-octet central atom, from Period 3 or below) spread into a trigonal bipyramidal electron-domain geometry: three domains in an equatorial plane at $120^\circ$ to each other, and two further domains axial, perpendicular to that plane, at $90^\circ$ to every equatorial domain. This arrangement, unlike all the previous ones, has two distinct types of position — axial and equatorial — which are not equivalent, so where a lone pair is placed matters.

• Zero lone pairs ($\text{AX}_5$): trigonal bipyramidal. Example: $\text{PCl}_5$.
• One lone pair ($\text{AX}_4\text{E}$): the lone pair occupies an equatorial position (it experiences less repulsion there, with only two neighbours at $90^\circ$ rather than three), giving a see-saw (sawhorse) molecular geometry. Example: $\text{SF}_4$.
• Two lone pairs ($\text{AX}_3\text{E}_2$): both lone pairs occupy equatorial positions, giving a T-shaped molecular geometry. Example: $\text{ClF}_3$.
• Three lone pairs ($\text{AX}_2\text{E}_3$): all three equatorial positions are lone pairs, leaving the two axial bonding domains directly opposite each other — a linear molecular geometry. Example: $\text{XeF}_2$.

Key distinction. Lone pairs preferentially occupy equatorial positions in a trigonal bipyramidal arrangement, since an equatorial position has only two $90^\circ$ neighbours, while an axial position has three. Minimizing the number of $90^\circ$ (strongest) repulsive interactions a lone pair is involved in is the rule governing every one of these variants.

Worked example. Predict the shape of $\text{SF}_4$.

From the previous chapter, sulfur in $\text{SF}_4$ has four bonding pairs and one lone pair — five electron domains, trigonal bipyramidal electron-domain geometry. The lone pair occupies an equatorial position to minimize repulsion, leaving four bonded fluorines in a distorted, asymmetric arrangement: two axial F atoms at $\approx 173^\circ$ to each other (slightly bent from $180^\circ$ by the equatorial lone pair's repulsion) and two equatorial F atoms at $\approx 102^\circ$ to each other (compressed from $120^\circ$). This is the characteristic see-saw shape.

6. Six Electron Domains: Octahedral and Its Variants

Six electron domains (expanded octet) spread into an octahedral electron-domain geometry: every domain is $90^\circ$ from its four nearest neighbours, with every position in this arrangement fully equivalent (unlike the trigonal bipyramidal case).

• Zero lone pairs ($\text{AX}_6$): octahedral. Example: $\text{SF}_6$.
• One lone pair ($\text{AX}_5\text{E}$): since all six positions start out equivalent, the lone pair's exact placement does not matter; the result is a square pyramidal molecular geometry, with the remaining five bonds slightly bent away from the lone pair. Example: $\text{BrF}_5$.
• Two lone pairs ($\text{AX}_4\text{E}_2$): the two lone pairs occupy positions directly opposite each other (minimizing lone-pair/lone-pair repulsion, the strongest kind), leaving the four bonded atoms in a square planar molecular geometry. Example: $\text{XeF}_4$.

Worked example. Predict the shape of $\text{XeF}_4$.

Xenon (expanded octet, previous chapter) has four bonding pairs and two lone pairs — six electron domains, octahedral electron-domain geometry. The two lone pairs occupy opposite (axial) positions to keep them as far apart as possible, leaving the four fluorine atoms arranged in a single plane around xenon: a square planar molecular geometry, with F–Xe–F bond angles of exactly $90^\circ$.

7. The Relative Strength of Repulsion: Lone Pair vs Bonding Pair

A lone pair is held by only one nucleus, so its electron density spreads out more than a bonding pair's, which is pulled between two nuclei and held more tightly in a narrower region. This makes a lone pair's repulsive effect stronger than a bonding pair's, giving the well-established ordering:

This ordering explains every bond-angle compression seen above: each time a bonding pair is replaced by a lone pair within the same electron-domain count (e.g. $\text{CH}_4 \to \text{NH}_3 \to \text{H}_2\text{O}$, all based on four electron domains), the remaining bonding pairs are pushed closer together by the lone pair's stronger repulsion, so the measured bond angle decreases: $109.5^\circ \to 107^\circ \to 104.5^\circ$.

Worked reasoning. Why does $\text{H}_2\text{O}$'s bond angle ($104.5^\circ$) compress further than $\text{NH}_3$'s ($107^\circ$), even though both are based on the same tetrahedral electron-domain geometry? Water has two lone pairs, generating one lone pair–lone pair interaction (the strongest kind) in addition to four lone pair–bonding pair interactions; ammonia has only one lone pair, generating three lone pair–bonding pair interactions and no lone pair–lone pair interaction at all. The additional, strongest-category repulsion in water compresses its bond angle further.

8. Common Exam Pitfalls

• Confusing electron-domain geometry with molecular geometry. The electron-domain geometry (which includes lone pairs) is tetrahedral for both $\text{CH}_4$ and $\text{NH}_3$; the molecular geometry — the one almost always asked for — differs: tetrahedral for $\text{CH}_4$, trigonal pyramidal for $\text{NH}_3$.
• Counting a double or triple bond as more than one electron domain. A C=O double bond is one electron domain, pointing in one direction, exactly like a single bond — never count it as two or three separate domains.
• Forgetting that lone pairs occupy specific positions in a trigonal bipyramidal arrangement. Equatorial and axial positions are not equivalent; lone pairs always go equatorial first, to minimize their number of $90^\circ$ neighbours.
• Quoting exactly $109.5^\circ$, $120^\circ$ or similar ideal angles for a molecule with lone pairs present. Only the zero-lone-pair cases ($\text{AX}_2$, $\text{AX}_3$, $\text{AX}_4$, etc.) have the exact ideal angle; any lone pair compresses the true bond angle below it.
• Treating an incomplete-octet or expanded-octet central atom as a special VSEPR case. VSEPR applies identically regardless of octet exceptions — it simply counts whatever electron domains the (correct) Lewis structure actually shows, however many that happens to be.
• Mixing up which lone-pair count gives see-saw versus T-shaped versus linear within the trigonal bipyramidal family. Track the exact count (one, two, or three lone pairs) carefully, since all three share the same five-electron-domain starting point.

Summary

• VSEPR theory predicts molecular shape from a completed Lewis structure: electron domains (bonding pairs, counting a multiple bond once, plus lone pairs) repel each other into the arrangement of maximum separation.
• Electron-domain geometry describes the full arrangement including lone pairs; molecular geometry describes only the arrangement of atoms, and the two differ whenever lone pairs are present.
• Two domains: linear ($180^\circ$). Three domains: trigonal planar ($120^\circ$, zero lone pairs) or bent ($\approx 119^\circ$, one lone pair).
• Four domains: tetrahedral ($109.5^\circ$, zero lone pairs), trigonal pyramidal ($\approx 107^\circ$, one lone pair), or bent ($\approx 104.5^\circ$, two lone pairs).
• Five domains (expanded octet): trigonal bipyramidal (zero lone pairs), see-saw (one), T-shaped (two), or linear (three) — with lone pairs always occupying equatorial positions first.
• Six domains (expanded octet): octahedral (zero lone pairs), square pyramidal (one), or square planar (two, lone pairs opposite each other).
• Repulsion strength follows lone pair–lone pair $>$ lone pair–bonding pair $>$ bonding pair–bonding pair, explaining every bond-angle compression below the ideal, lone-pair-free value.
• The next chapter builds directly on these shapes to determine whether individual bond dipoles cancel or combine into an overall molecular dipole moment.