3.1.3.5 - Shapes of Molecules and Ions

Counting electron pairs and understanding repulsion

To predict a shape, start with the central atom and count the pairs of electrons in its outer shell. Each bonding pair and each lone pair acts as a region of negative charge, often described as a charge cloud, and these charge clouds repel one another.

A useful sequence is:

1. identify the central atom
2. count the outer-shell electron pairs around that atom
3. decide how those pairs arrange themselves in space
4. name the shape from the positions of the atoms, not from the lone pairs

For molecules with H or halogen atoms joined by single bonds, add the central atom's outer electrons to one electron from each attached atom. Add one for each negative charge or subtract one for each positive charge, then divide by two. Subtract the number of bonds to find the number of lone pairs. For $\ce{NH4+}$, $(5+4-1)/2=4$ pairs, all bonding.

A double or triple bond contains more than one shared pair but counts as one region of electron density when predicting shape. Thus $\ce{CO2}$ has two bonding regions around carbon and is linear, not tetrahedral. The simple electron-count shortcut above is for single bonds to monovalent atoms; use the displayed bonding for other cases.

The bond angle is the angle between two covalent bonds around the central atom. If there are only bonding pairs, the bond angle is the ideal angle for that arrangement. If lone pairs are present, the angle is usually reduced.

The strength of repulsion is not the same for every pair. A lone pair is held by one nucleus only, so its charge cloud is slightly closer to the central atom and more spread out. A bonding pair is shared between two nuclei, so it is pulled into a narrower region of space. That is why the repulsion order is:

lone pair-lone pair > lone pair-bond pair > bond pair-bond pair

The diagram below shows why lone pairs squeeze bonding pairs more strongly than bonding pairs squeeze one another.

[DIAGRAM: asset_name: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 1; asset_slug: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 1; recommended_method: retained_png; description: Electron-pair repulsion increases from bonding-pair/bonding-pair to lone-pair/bonding-pair to lone-pair/lone-pair.]

This ranking is the reason lone pairs squeeze bonding pairs closer together and reduce bond angles.

The base arrangements for two to six electron pairs

If a central atom has only bonding pairs, the molecular shape matches the electron-pair arrangement directly.

• 2 electron pairs: linear, $180 {}^\circ$, as in $\ce{BeCl2(g)}$
• 3 electron pairs: trigonal planar, $120 {}^\circ$, as in $\ce{BF3}$
• 4 electron pairs: tetrahedral, $109.5 {}^\circ$, as in $\ce{CH4}$ or $\ce{NH4^+}$
• 5 electron pairs: trigonal bipyramidal, with bond angles of $120 {}^\circ$, $90 {}^\circ$ and $180 {}^\circ$, as in $\ce{PCl5}$
• 6 electron pairs: octahedral, $90 {}^\circ$ between neighbouring bonds and $180 {}^\circ$ between opposite bonds, as in $\ce{SF6}$

These five geometries are the starting point for any harder example with lone pairs.

The diagram below summarises these five base arrangements in one place.

[DIAGRAM: asset_name: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 2; asset_slug: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 2; recommended_method: retained_png; description: Linear, trigonal planar, tetrahedral, trigonal bipyramidal and octahedral arrangements with their characteristic bond angles.]

The geometry matters. A trigonal bipyramid is not a flat five-point shape. It has three equatorial bonds $120 {}^\circ$ apart in one plane, and two axial bonds that are each $90 {}^\circ$ to the equatorial bonds. An octahedron has six positions, not eight: four in a plane, one above, and one below.

For ions, the same approach still works. The overall charge changes the total electron count, but once you have counted the electron pairs around the central atom, the repulsion rules are exactly the same.

How lone pairs change both shape and bond angle

Lone pairs are the reason many real molecules do not keep the ideal bond angle of the base arrangement.

The most important family to compare is the set with four electron pairs around the central atom.

In methane, $\ce{CH4}$, there are four bonding pairs and no lone pairs. The shape is tetrahedral and the bond angle is $109.5 {}^\circ$.

In ammonia, $\ce{NH3}$, there are still four electron pairs in total, but one of them is a lone pair. The electron pairs are arranged tetrahedrally, yet the shape of the molecule is called trigonal pyramidal because only the atoms are used to name the shape. The lone pair repels the bonding pairs more strongly than a bonding pair would, so the $\ce{H-N-H}$ angle is reduced to about $107 {}^\circ$.

In water, $\ce{H2O}$, there are again four electron pairs, but now two are lone pairs. The electron-pair arrangement is still tetrahedral. However, with only two bonded atoms visible, the molecular shape is non-linear (or V-shaped). Because there are two lone pairs, the bonding pairs are squeezed even closer together, so the $\ce{H-O-H}$ angle is reduced further to $104.5 {}^\circ$.

The diagram below compares these three four-pair examples and shows how extra lone pairs steadily reduce the bond angle.

[DIAGRAM: asset_name: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 3; asset_slug: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 3; recommended_method: retained_png; description: Methane, ammonia and water show four, three and two bonds, with increasing lone-pair repulsion reducing bond angles.]

The logic is simple: the total number of electron pairs tells you the underlying arrangement, but the number of bonded atoms tells you the named molecular shape. This is why $\ce{NH3}$ is not called tetrahedral even though its electron pairs are tetrahedrally arranged.

Do not treat lone pairs as causing one fixed drop in angle in every case. The key idea is stronger repulsion and greater squeezing, with the exact angle depending on the arrangement.

Applying the method to ions and six-pair geometries

The same reasoning works for ions as well as molecules. For example, the ammonium ion, $\ce{NH4^+}$, has four bonding pairs and no lone pairs around nitrogen, so it is tetrahedral with bond angles of $109.5 {}^\circ$. The positive charge does not create a new shape rule; it just changes the electron count you start from.

For higher pair numbers, careful geometry matters. If there are five electron pairs, begin from a trigonal bipyramidal arrangement. The equatorial positions are $120 {}^\circ$ apart from each other and $90 {}^\circ$ from the axial positions, so a lone pair prefers an equatorial position because that gives fewer close $90^\circ$ interactions. If there are six electron pairs, begin from an octahedral arrangement and place lone pairs as far apart as possible.

It helps to model the counting explicitly for an ion. In the chlorine tetrafluoride ion, $\ce{ClF4^-}$, chlorine contributes 7 outer-shell electrons, the $-1$ charge adds 1, and the four fluorines each contribute 1 electron to a bond. The total around chlorine is therefore 12 electrons, or six pairs. Four are bonding pairs, leaving two lone pairs on the central atom. That makes six electron pairs in total.

Six pairs give an octahedral electron-pair arrangement, but the two lone pairs repel most strongly, so they occupy opposite positions. That leaves the four fluorine atoms in one plane around the chlorine atom.

The shape is therefore square planar. Adjacent $\ce{F-Cl-F}$ bond angles are $90 {}^\circ$, while fluorine atoms across the square are $180 {}^\circ$ apart. The diagram below shows how that square planar shape comes from an octahedral electron-pair arrangement once the two lone pairs occupy opposite positions.

[DIAGRAM: asset_name: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 4; asset_slug: 1.3.5 - Shapes of Simple Molecules and Ions - Diagram 4; recommended_method: deterministic_code; description: ClF4− has four fluorines in a square plane and two opposed lone pairs on the perpendicular axis; its electron-pair arrangement is octahedral.]

The same pattern gives you the other higher-pair shapes as well:

No separate rule is needed for each named ion or molecule. The logic is always the same: count the pairs, choose the base arrangement, place the lone pairs to minimise repulsion, then name the shape from the atoms only.

The same reasoning can be summarised as:

• count all electron pairs around the central atom
• choose the base electron-pair arrangement
• place lone pairs where repulsion is smallest overall
• name the final shape from the positions of the atoms only

Taken together, these ideas let shapes and bond angles across simple molecules and ions be predicted from electron-pair repulsion rather than memorised one by one.