VSEPR Theory: Tetrahedral Geometry

When a central atom has four electron domains, VSEPR theory predicts a tetrahedral electron geometry with ideal bond angles of 109.5°, and the molecular shape is tetrahedral, trigonal pyramidal or bent depending on how many of the domains are lone pairs. In brief: CH₄ (no lone pairs) is tetrahedral, NH₃ (one lone pair) is trigonal pyramidal with an H–N–H angle of about 107°, and H₂O (two lone pairs) is bent with an angle of 104.5°.

The tetrahedral arrangement is the most important in chemistry: it is the basis of organic chemistry, of the structure of water and of the geometry of many ions such as ammonium, sulfate and phosphate. This article explains why four domains form a tetrahedron, how lone pairs change the shape, and compares the bond angles of methane, ammonia and water.

Why is a tetrahedron the best arrangement?

Four electron domains can be placed around a central atom in many ways. A flat square would give angles of 90°, but a tetrahedron, in which the atoms sit at four corners of a regular pyramid with a triangular base, makes all the angles 109.5°, which is the maximum possible separation. The exact value is arccos(−1/3) = 109.47°. A tetrahedron fits inside a cube, with the central atom in the middle of the cube and the four atoms at alternate corners.

What shapes can four electron domains form?

Tetrahedral: AX₄

With four bonds and no lone pair the shape is tetrahedral, with angles of 109.5°. Examples are CH₄, CCl₄, NH₄⁺, SO₄²⁻, PO₄³⁻ and ClO₄⁻.

Trigonal pyramidal: AX₃E

With three bonds and one lone pair, the atoms form a pyramid with the central atom at the top. Examples include NH₃, PCl₃, H₃O⁺ and ClO₃⁻.

Bent: AX₂E₂

With two bonds and two lone pairs the molecule is bent. Examples include H₂O, H₂S, OF₂ and SCl₂.

How do lone pairs change bond angles?

A lone pair is held by only one nucleus, so its electron cloud is broader and spreads out more than that of a bonding pair, which is stretched between two nuclei. As a result, the repulsion strength follows the order:

lone pair – lone pair > lone pair – bonding pair > bonding pair – bonding pair

Each lone pair therefore pushes the bonding pairs closer together, and the bond angle falls below 109.5° by about 2–3° for each lone pair. In ammonia, with one lone pair, the angle is 106.7°, and in water, with two lone pairs, it is 104.5°.

Bond angles in tetrahedral families

The angles in PH₃ and H₂S are close to 90°. For larger central atoms, the bonds are longer, the bonding pairs are far apart and bonds use almost pure p orbitals, so VSEPR overestimates the angles in these cases.

Worked examples

Example 1: the ammonium ion

NH₄⁺ has 5 + 4 − 1 = 8 valence electrons, which form four N–H bonds. There are no lone pairs, so the shape is tetrahedral with angles of 109.5°.

Example 2: the hydronium ion

H₃O⁺ has 6 + 3 − 1 = 8 valence electrons: three bonds and one lone pair. The notation is AX₃E and the shape is trigonal pyramidal, similar to ammonia, with an H–O–H angle of about 113° in the gas phase.

Example 3: sulfate

SO₄²⁻ has four electron domains around sulfur, and no lone pairs, so the shape is tetrahedral. Its Lewis structure can be drawn with four single bonds or with two double bonds; in both cases the geometry is the same, and all four S–O bonds are equal.

Example 4: dichloromethane

CH₂Cl₂ is tetrahedral, although it is not a perfect tetrahedron: both the Cl–C–Cl angle and the H–C–H angle are about 112°. The C–H and C–Cl bonds differ in length and polarity, which distorts the ideal angles, and the molecule is polar.

What is the link to sp³ hybridization?

In valence bond theory, the carbon atom mixes one 2s and three 2p orbitals to form four equivalent sp³ hybrid orbitals directed at the corners of a tetrahedron. The same hybridization is used for nitrogen in ammonia and oxygen in water, where some of the hybrid orbitals hold lone pairs. Four domains around an atom always correspond to sp³.

Where does the tetrahedral carbon come from?

In 1874 Jacobus van ‘t Hoff and, independently, Joseph Le Bel proposed that the four bonds of carbon point towards the corners of a tetrahedron. This idea explained why some carbon compounds exist in two mirror-image forms and founded stereochemistry. Linus Pauling’s hybridization model of 1931 gave the quantum-mechanical explanation. Van ‘t Hoff received the first Nobel Prize in Chemistry in 1901, but for his work on solutions and chemical dynamics.

Which mistakes are common?

• Drawing the tetrahedron flat: the bond angles are 109.5°, not 90°.
• Calling NH₃ tetrahedral: its electron geometry is tetrahedral, but its molecular shape is trigonal pyramidal.
• Ignoring the effect of lone pairs: angles in NH₃ and H₂O are smaller than 109.5°.
• Treating all tetrahedral molecules as nonpolar: only symmetric ones such as CH₄ and CCl₄ are nonpolar.
• Applying the angles of period-2 compounds to heavier atoms: PH₃ and H₂S have angles close to 90°.