Trigonal Bipyramidal and Octahedral Geometries

When a central atom has five electron domains, VSEPR theory predicts a trigonal bipyramidal geometry, and with six domains an octahedral geometry; lone pairs then give shapes such as seesaw, T-shaped, square pyramidal and square planar. In brief: PCl5 is trigonal bipyramidal with angles of 90° and 120°, SF6 is octahedral with all angles 90°, and XeF4 with two lone pairs is square planar.

These geometries occur in molecules in which the central atom has more than four electron domains, mostly with elements from the third period and below. They are less common than the shapes with two, three and four domains, but they are important in inorganic chemistry, in the chemistry of the noble gases and in transition-metal complexes. This article lists the shapes, explains where the lone pairs go and gives worked examples.

What is trigonal bipyramidal geometry?

The five domains are arranged as two axial positions at the top and bottom, at 180° from each other, and three equatorial positions in a plane at 120° angles. The angle between an axial and an equatorial position is 90°. The two kinds of position are not equivalent, so the bond lengths differ. In PCl5 the axial P–Cl bonds are 219 pm long and the equatorial bonds are 204 pm. In the molecule PF5 the lengths are 158 pm and 153 pm.

Equatorial positions have only two neighbors at 90°, while axial positions have three. For this reason, the axial bonds are more crowded and a bit longer. The central atom is considered to be sp3d hybridized in the simplest model, though modern calculations show that d orbitals play only a small role.

Perspective sketches of a trigonal bipyramidal and an octahedral molecule P Cl Cl Cl Cl Cl S F F F F F F PCl5 trigonal bipyramidal angles 90°, 120°, 180° SF6 octahedral angles 90° and 180°
Perspective sketches of PCl5 (five domains) and SF6 (six domains). In the trigonal bipyramid the two axial bonds are at 180° to each other and at 90° to the three equatorial bonds, which are 120° apart. In the octahedron every bond is at 90° to its four neighbors.

Where do lone pairs go with five domains?

Lone pairs take more space, so they occupy equatorial positions, where they have fewer 90° contacts with other pairs. This gives three shapes:

What is octahedral geometry?

With six domains, the best arrangement places them at the corners of an octahedron, with all angles 90° between neighbors and 180° across the center. All six positions are equivalent. SF6 is the best-known example: all S–F bonds are 156 pm long, and the molecule is very stable, nonpolar and chemically inert. Other examples are PF6−, SiF62− and the hexaaquairon(III) ion [Fe(H2O)6]3+.

What shapes occur with six domains?

Because all positions are equivalent, the first lone pair can go anywhere. The second goes opposite the first, to minimize repulsion.

Summary of five- and six-domain shapes

Molecular shapes for five and six electron domains
Domains Notation Molecular shape Example Polar?
5AX5Trigonal bipyramidalPCl5No
5AX4ESeesawSF4Yes
5AX3E2T-shapedClF3Yes
5AX2E3LinearXeF2No
6AX6OctahedralSF6No
6AX5ESquare pyramidalBrF5Yes
6AX4E2Square planarXeF4No

Worked examples

Example 1: sulfur tetrafluoride, SF4

  1. Valence electrons: 6 + 4 × 7 = 34.
  2. Four S–F bonds use 8 electrons. Each fluorine gets three lone pairs (24 electrons), and the remaining 2 electrons form one lone pair on sulfur.
  3. Sulfur has five domains (four bonds and one lone pair): AX4E.
  4. The electron geometry is trigonal bipyramidal, with the lone pair in an equatorial position, so the shape is seesaw.

Example 2: xenon tetrafluoride, XeF4

  1. Valence electrons: 8 + 4 × 7 = 36.
  2. Four Xe–F bonds use 8 electrons, the fluorines take 24 and the remaining 4 electrons form two lone pairs on xenon.
  3. Xenon has six domains: AX4E2.
  4. The lone pairs lie on opposite sides, so the shape is square planar, and the molecule is nonpolar since the bond dipoles cancel.

Example 3: the triiodide ion, I3−

Valence electrons: 3 × 7 + 1 = 22. The central iodine forms two bonds and holds three lone pairs, so it has five domains: AX2E3. The shape is linear. This ion forms when iodine dissolves in an iodide solution, and it is responsible for the blue-black color of the starch–iodine test.

How were these shapes discovered?

The octahedral shape of the six-coordinate complexes was proposed by Alfred Werner in 1893, and brought him the Nobel Prize in Chemistry in 1913. The existence of noble gas compounds was a great surprise: Neil Bartlett prepared the first one, an xenon compound with platinum hexafluoride, in 1962, and XeF4 was reported by Howard Claassen, Henry Selig and John Malm the same year. Its square planar shape was confirmed by neutron diffraction in 1963, and was an early success of VSEPR.

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