Octahedral and Square-Pyramidal Shapes

Introduction

Six electron domains in a basic VSEPR model occupy an octahedral arrangement. When all six are bonds, as in SF₆, the molecular shape is octahedral. When one is a lone pair, as in BrF₅, the remaining five bonded atoms form a square pyramid.

Core explanation

An octahedral arrangement places domain directions along +x, -x, +y, -y, +z and -z around the central atom. Four lie in a square plane and two lie above and below it. Adjacent ideal positions are 90° apart; opposite positions are 180° apart. Despite the name, the molecule has six vertices around the centre, while an octahedron as a geometric solid has eight triangular faces.

SF₆ is the standard AX₆ example in a conventional Lewis/VSEPR treatment. Six S–F bonding domains and no central lone pairs give octahedral electron and molecular geometry. The six equivalent F positions in the ideal structure yield cancellation of equal S–F bond-dipole vectors, so the whole molecule is nonpolar in this symmetry model even though individual S–F bonds are polar.

BrF₅ has five Br–F bonding domains and one central lone pair, AX₅E, in the elementary Lewis count. Six total domains retain an octahedral electron scaffold. Put the lone pair at one vertex; the opposite position becomes the apex F, while four F atoms form a square base. The atom-only shape is square pyramidal. Its bond angles are near, but not necessarily exactly, the 90° ideal because the lone pair distorts the arrangement.

The six-domain scaffold also leads to square planar AX₄E₂ if two lone pairs occupy opposite positions, discussed next. Their opposition reduces lone-pair proximity and leaves four bonded atoms in a plane. Thus counting central lone pairs distinguishes octahedral, square pyramidal and square planar atom shapes even though all share the same electron geometry.

Hypervalent Lewis drawings of SF₆ and BrF₅ are useful for shape bookkeeping but should not be interpreted as proof of six independent conventional two-electron bonds formed through large d-orbital promotion. Detailed bonding is more delocalised. VSEPR's geometry prediction and a sophisticated orbital explanation operate at different levels.

Step-by-step reasoning

1. Count six central electron domains from a Lewis model. 2. Draw four positions in a square plane and two opposite vertical positions. 3. For AX₆, name both electron and molecular geometry octahedral. 4. For AX₅E, replace one vertex with a lone pair and name square pyramidal. 5. Treat 90° and 180° as ideal angle references.

Visual explanation

Draw six arrows from a central atom along three perpendicular axes. Label SF₆ with F at all tips. Then shade the bottom tip as a lone pair and draw BrF₅ with four F at base corners and one F at the top apex.

Real-world analogy

Six directions resemble the faces of a cube around a central point: left, right, front, back, up and down. Replacing one occupied direction with an invisible lone pair leaves five visible atoms in a square-pyramid silhouette.

Real-world example

Sulfur hexafluoride's high symmetry is useful for testing the difference between polar bonds and a polar molecule: the S–F bonds are polar, but their six equal vectors cancel in an ideal octahedron.

Why?

Why is BrF₅ not called octahedral molecular shape? The sixth domain is a lone pair rather than an atom. Electron-domain geometry includes it, but molecular shape names only the positions of Br and F nuclei.

Common misconception

“Octahedral means eight bonded atoms.” The geometric solid has eight faces but six vertices. An octahedral AX₆ molecule has six surrounding bonded atoms in the simple model.

Worked example

Determine BrF₅'s domains. Br has seven valence electrons; five Br–F single bonds use five of its electrons in bond-sharing bookkeeping, leaving one lone pair at Br in the conventional structure. Five bonded neighbours plus one lone pair make six domains. Electron arrangement is octahedral. The four basal F and one axial F make square-pyramidal molecular shape; the lone pair occupies the opposite axial direction.

Quick check

1. How many domains surround sulfur in the basic SF₆ VSEPR drawing? Answer: Six bonding domains and no central lone pairs.

Exam focus

Draw the six vertex directions and distinguish octahedral electron geometry from square-pyramidal atom shape. Do not confuse the octahedron's eight faces with its six vertices. Qualify exact angle claims in lone-pair cases.

Advanced insight

An AX₅E molecule can distort away from a perfect square pyramid depending on ligand identity and electronic effects. VSEPR gives a useful family shape, while diffraction or spectroscopy is needed for precise bond lengths and angles.

Summary

Six domains define an octahedral electron scaffold. SF₆ with six bonds is octahedral as a molecule; BrF₅ with five bonds and one lone pair is square pyramidal. The ideal scaffold has 90° adjacent and 180° opposite directions.

Practice questions

1. What is SF₆'s molecular shape? Answer: Octahedral. 2. What is BrF₅'s electron geometry and molecular shape? Answer: Octahedral electron geometry and square-pyramidal molecular shape. 3. What are ideal adjacent angles in an octahedral arrangement? Answer: 90°. 4. Why do S–F bond dipoles cancel in ideal SF₆? Answer: Equal bond vectors point in opposite pairs along the three axes.