# Octahedral molecular geometry

Octahedral molecular geometry is the arrangement of six atoms or ligands around a central atom at the corners of an octahedron, with all adjacent bond angles at 90° and opposite bonds at 180°. In VSEPR notation it is the AX<sub>6</sub> case: six bonding regions and no lone pairs on the central atom, as in sulfur hexafluoride, SF<sub>6</sub><sup>[1](https://chemguide.co.uk/atoms/bonding/shapes.html)</sup>. The same arrangement also dominates six-coordinate transition-metal complexes.<sup>[2](https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_%28Moore_et_al.%29/22%3A_Metals/22.09%3A_Geometry_of_Complexes)</sup>

| Key fact | Detail |
|---|---|
| VSEPR class | AX<sub>6</sub>: six bonding pairs, zero lone pairs; electron-group and molecular geometry coincide<sup>[1](https://chemguide.co.uk/atoms/bonding/shapes.html)</sup> |
| Bond angles | 90° between adjacent bonds, 180° between opposite (trans) bonds<sup>[3](https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_002A/UCD_Chem_2A/ucd_chem_2a__general_chemistry_i/07%3A_Homework/7.50%3A_Exercise_Solutions/7.50.09%3A_Solution_Set_9)</sup> |
| Hybridization model | Six equivalent sp<sup>3</sup>d<sup>2</sup> hybrid orbitals directed to the corners of an octahedron<sup>[4](https://openstax.org/books/chemistry-atoms-first-2e/pages/5-2-hybrid-atomic-orbitals?modal=MH)</sup> |
| Reference molecule | SF<sub>6</sub>: experimental S–F length 1.561 Å, F–S–F angles 90.0° and 180.0°; nonpolar<sup>[5](https://cccbdb.nist.gov/listgeomexpx.asp?casno=2551624&charge=0)</sup><sup> • </sup><sup>[3](https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_002A/UCD_Chem_2A/ucd_chem_2a__general_chemistry_i/07%3A_Homework/7.50%3A_Exercise_Solutions/7.50.09%3A_Solution_Set_9)</sup> |
| Derived shapes | One lone pair gives square pyramidal (BrF<sub>5</sub>, F–Br–F 84.8°); two lone pairs give square planar (XeF<sub>4</sub>)<sup>[6](https://chem.libretexts.org/Courses/UW-Whitewater/Chem_260%3A_Inorganic_Chemistry_%28Girard%29/02%3A_Molecular_Orbital_Theory/2.02%3A_The_Shapes_of_Molecules_%28VSEPR_Theory%29_and_Orbital_Hybridization)</sup> |
| Coordination chemistry | Six-coordinate complexes are almost always octahedral, e.g. [Co(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup><sup> • </sup><sup>[2](https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_%28Moore_et_al.%29/22%3A_Metals/22.09%3A_Geometry_of_Complexes)</sup> |
| Crystal field | The ligand field splits the five d orbitals into e<sub>g</sub> (raised by 0.6Δ<sub>o</sub> each) and t<sub>2g</sub> (lowered by 0.4Δ<sub>o</sub> each) sets<sup>[7](https://chem.libretexts.org/Courses/Kutztown_University_of_Pennsylvania/CHM_320%3A_Advanced_Inorganic_Chemistry_textbook/07%3A_Ligand_Field_Theory_%28LFT%29_and_Crystal_Field_Theory_%28CFT%29_of_Octahedral_Complexes/7.01%3A_Introduction_to_Crystal_Field_Theory_%28Octahdral_complexes%29)</sup> |

## Geometry and the octahedron

An octahedron is a solid with twelve equal edges, eight equilateral triangular faces, and six identical corners. The name comes from the eight faces, but chemists use the six corners: an octahedral arrangement involves six atoms, not eight.<sup>[8](https://chem.libretexts.org/Courses/Duke_University/CHEM_210D%3A_Modern_Applications_of_Chemistry/3%3A_Textbook-_Modern_Applications_of_Chemistry/01%3A_Primer/1.03%3A_Further_Aspects_of_Covalent_Bonding/1.3.03%3A_The_Shapes_of_Molecules)</sup> Four atoms form a square in a plane around the central atom, and the other two sit above and below that plane on a line through the center.<sup>[9](https://chem.libretexts.org/Bookshelves/General_Chemistry/Concept_Development_Studies_in_Chemistry_%28Hutchinson%29/7%3A_Molecular_Geometry_and_Electron_Domain_Theory/Section_3%3A_Observation_1%3A_Geometries_of_molecules)</sup>

**Why six pairs choose this shape.** VSEPR (valence shell electron pair repulsion) theory places electron pairs around a central atom as far apart as possible. Placing six points on a sphere at maximum mutual distance gives the octahedron, and this prediction matches the observed geometry of SF6, in which all bond lengths are identical and the bond angles are 90° and 180°. [9](https://chem.libretexts.org/Bookshelves/General_Chemistry/Concept_Development_Studies_in_Chemistry_%28Hutchinson%29/7%3A_Molecular_Geometry_and_Electron_Domain_Theory/Section_3%3A_Observation_1%3A_Geometries_of_molecules).<sup>[9](https://chem.libretexts.org/Bookshelves/General_Chemistry/Concept_Development_Studies_in_Chemistry_%28Hutchinson%29/7%3A_Molecular_Geometry_and_Electron_Domain_Theory/Section_3%3A_Observation_1%3A_Geometries_of_molecules)</sup><sup> • </sup><sup>[17](https://cccbdb.nist.gov/listangleexp3x.asp?bi=11&descript=aFSF&mi=1)</sup> In the valence bond picture, the 3s, three 3p, and two 3d orbitals of sulfur combine into six equivalent sp<sup>3</sup>d<sup>2</sup> hybrid orbitals, each pointing to a different corner of an octahedron.<sup>[4](https://openstax.org/books/chemistry-atoms-first-2e/pages/5-2-hybrid-atomic-orbitals?modal=MH)</sup>

**The reference example.** [Sulfur hexafluoride](https://www.edgepedia.org/sulfur-hexafluoride) has six bonding pairs and no lone pairs, so its molecular geometry is identical to its electron-group geometry. Experiment gives an S–F bond length of 1.561 Å and F–S–F angles of exactly 90.0° and 180.0° by symmetry.<sup>[5](https://cccbdb.nist.gov/listgeomexpx.asp?casno=2551624&charge=0)</sup> Because the six identical S–F bond dipoles cancel, the molecule is nonpolar.<sup>[3](https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_002A/UCD_Chem_2A/ucd_chem_2a__general_chemistry_i/07%3A_Homework/7.50%3A_Exercise_Solutions/7.50.09%3A_Solution_Set_9)</sup> Other sp<sup>3</sup>d<sup>2</sup> species include PCl<sub>6</sub><sup>−</sup>, IF<sub>6</sub><sup>+</sup>, and the xenon atom in XeF<sub>4</sub>.<sup>[4](https://openstax.org/books/chemistry-atoms-first-2e/pages/5-2-hybrid-atomic-orbitals?modal=MH)</sup>

## Derived shapes with lone pairs

When one or two of the six electron pairs are lone pairs, the electron-group geometry remains octahedral but the molecular geometry changes, because molecular geometry counts only the positions of atoms.<sup>[6](https://chem.libretexts.org/Courses/UW-Whitewater/Chem_260%3A_Inorganic_Chemistry_%28Girard%29/02%3A_Molecular_Orbital_Theory/2.02%3A_The_Shapes_of_Molecules_%28VSEPR_Theory%29_and_Orbital_Hybridization)</sup> Lone pairs repel more strongly than bonding pairs (the ordering is bonding pair–bonding pair < lone pair–bonding pair < lone pair–lone pair), so they take the positions that minimize these repulsions.<sup>[10](https://chem.libretexts.org/Courses/Western_Oregon_University/Chemistry_for_Health_Professions/05%3A_Molecular_Structure_Polarity_and_Intermolecular_Forces/5.02%3A_Molecular_Geometry_-_Using_VSEPR_Theory_to_Predict_Molecular_Shape)</sup>

- **AX<sub>5</sub>E, square pyramidal.** BrF<sub>5</sub> has five bonds and one lone pair; the ideal 90° angle is compressed to 84.8° by the lone pair's repulsion.<sup>[6](https://chem.libretexts.org/Courses/UW-Whitewater/Chem_260%3A_Inorganic_Chemistry_%28Girard%29/02%3A_Molecular_Orbital_Theory/2.02%3A_The_Shapes_of_Molecules_%28VSEPR_Theory%29_and_Orbital_Hybridization)</sup>
- **AX<sub>4</sub>E<sub>2</sub>, square planar.** XeF<sub>4</sub> has four bonds and two lone pairs. Placing the lone pairs 90° apart would put them at right angles; instead they go opposite each other, 180° apart, minimizing lone pair–lone pair repulsion and leaving the four fluorines in a square plane.<sup>[1](https://chemguide.co.uk/atoms/bonding/shapes.html)</sup><sup> • </sup><sup>[11](https://openstax.org/books/chemistry-atoms-first-2e/pages/4-6-molecular-structure-and-polarity)</sup> The ion ClF<sub>4</sub><sup>−</sup> has the same electron count and the same shape.<sup>[1](https://chemguide.co.uk/atoms/bonding/shapes.html)</sup>

## Octahedral coordination complexes

In coordination chemistry, a coordination number of six almost always means an octahedral complex, as in SF<sub>6</sub> itself or [Cr(H<sub>2</sub>O)<sub>6</sub>]<sup>3+</sup>. All six ligands are equidistant from the central metal, and ligand–metal–ligand angles are 90° between adjacent ligands and 180° between opposite ligands; the structure can be viewed as a square planar arrangement with one ligand added above and one below the plane.<sup>[2](https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_%28Moore_et_al.%29/22%3A_Metals/22.09%3A_Geometry_of_Complexes)</sup><sup> • </sup><sup>[18](https://chem.libretexts.org/Courses/Centre_College/CHE_332%3A_Inorganic_Chemistry/05%3A_Coordination_Chemistry-_Structure_and_Isomers/5.05%3A_Isomerism)</sup> Unlike main-group VSEPR cases, the metal's nonbonding d electrons do not change the ligand arrangement.<sup>[12](https://openstax.org/books/chemistry-atoms-first/pages/19-2-coordination-chemistry-of-transition-metals)</sup> The trigonal prism is the main alternative six-coordinate shape, but it is rare: a search of the 2016 [Cambridge Structural Database](https://www.edgepedia.org/cambridge-structural-database) found that of about 113,000 structures with a transition metal bonded to six main-group elements, only about 200 (approximately 2%) have a regular trigonal prismatic geometry.<sup>[13](https://www.sciencedirect.com/science/article/pii/S0010854517301923)</sup>

**Isomerism.** Because the six octahedral positions are equivalent, an MA<sub>5</sub>B complex has only one geometric form, but complexes with two kinds of ligands show stereoisomerism.<sup>[14](https://chem.libretexts.org/Courses/Northern_Michigan_University/CH_215%3A_Chemistry_of_the_Elements_Fall_2023/06%3A_Transition_Metals_and_Coordination_Chemistry/6.04%3A_Isomers/6.4.01%3A_Geometric_Isomerism)</sup> In an MA<sub>4</sub>B<sub>2</sub> complex such as [Co(NH<sub>3</sub>)<sub>4</sub>Cl<sub>2</sub>]<sup>+</sup>, the two B ligands can be adjacent (cis, 90° apart) or opposite (trans, 180° apart); the cis form of [Co(NH<sub>3</sub>)<sub>4</sub>Cl<sub>2</sub>]Cl is violet and the trans form green, and the isomers differ in dipole moment, solubility, and reactivity.<sup>[2](https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_%28Moore_et_al.%29/22%3A_Metals/22.09%3A_Geometry_of_Complexes)</sup><sup> • </sup><sup>[15](https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_-_Atoms_First_2e_%28OpenStax%29/19%3A_Transition_Metals_and_Coordination_Chemistry/19.03%3A_Coordination_Chemistry_of_Transition_Metals)</sup> With three of each ligand, as in Co(NH<sub>3</sub>)<sub>3</sub>Cl<sub>3</sub>, the three identical ligands can occupy one triangular face of the octahedron (facial, fac) or lie in a plane through the metal forming a T shape (meridional, mer).<sup>[16](https://chem.libretexts.org/Ancillary_Materials/Worksheets/Worksheets%3A_Inorganic_Chemistry/Structure_and_Reactivity_in_Organic_Biological_and_Inorganic_Chemistry/05%3A_Stereochemistry/5.17%3A_Stereochemistry_in_Octahedra%3A_Cis_vs_Trans__and_Fac_vs._Mer)</sup>

## Crystal field splitting

In an octahedral complex, the six ligands' negative charge interacts differently with the five d orbitals. The d<sub>x²−y²</sub> and d<sub>z²</sub> orbitals point directly at the ligands and rise in energy as the e<sub>g</sub> set, each by 0.6Δ<sub>o</sub>, while the d<sub>xy</sub>, d<sub>xz</sub>, and d<sub>yz</sub> orbitals point between the ligands and fall as the t<sub>2g</sub> set, each by 0.4Δ<sub>o</sub>. The splitting energy Δ<sub>o</sub> (the subscript o stands for octahedral) depends on the metal ion's charge, its position in the periodic table, and the ligands. The splitting conserves total d-orbital energy: 2 × 0.6Δ<sub>o</sub> + 3 × (−0.4Δ<sub>o</sub>) = 0.<sup>[7](https://chem.libretexts.org/Courses/Kutztown_University_of_Pennsylvania/CHM_320%3A_Advanced_Inorganic_Chemistry_textbook/07%3A_Ligand_Field_Theory_%28LFT%29_and_Crystal_Field_Theory_%28CFT%29_of_Octahedral_Complexes/7.01%3A_Introduction_to_Crystal_Field_Theory_%28Octahdral_complexes%29)</sup> For d<sup>4</sup>–d<sup>7</sup> configurations, two electron arrangements are possible, and the one with more unpaired electrons is called high-spin.<sup>[7](https://chem.libretexts.org/Courses/Kutztown_University_of_Pennsylvania/CHM_320%3A_Advanced_Inorganic_Chemistry_textbook/07%3A_Ligand_Field_Theory_%28LFT%29_and_Crystal_Field_Theory_%28CFT%29_of_Octahedral_Complexes/7.01%3A_Introduction_to_Crystal_Field_Theory_%28Octahdral_complexes%29)</sup>

## Related six- and seven-coordinate geometries

The octahedron sits in a family of electron-group geometries: five electron domains give the trigonal bipyramid (as in PCl<sub>5</sub>) and seven give the pentagonal bipyramid (as in IF<sub>7</sub>, with 90°, 72°, and 180° angles).<sup>[6](https://chem.libretexts.org/Courses/UW-Whitewater/Chem_260%3A_Inorganic_Chemistry_%28Girard%29/02%3A_Molecular_Orbital_Theory/2.02%3A_The_Shapes_of_Molecules_%28VSEPR_Theory%29_and_Orbital_Hybridization)</sup> Octahedral arrangements also appear in ionic solids: in crystals of LiH and NaCl, six anions surround each cation and six cations surround each anion octahedrally.<sup>[8](https://chem.libretexts.org/Courses/Duke_University/CHEM_210D%3A_Modern_Applications_of_Chemistry/3%3A_Textbook-_Modern_Applications_of_Chemistry/01%3A_Primer/1.03%3A_Further_Aspects_of_Covalent_Bonding/1.3.03%3A_The_Shapes_of_Molecules)</sup>

## References

1. [Shapes of molecules and ions containing single bonds, Chemguide](https://chemguide.co.uk/atoms/bonding/shapes.html)
2. [Geometry of Complexes, Chemistry LibreTexts (ChemPRIME)](https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_%28Moore_et_al.%29/22%3A_Metals/22.09%3A_Geometry_of_Complexes)
3. [Solution Set 9, UCD Chem 2A, Chemistry LibreTexts](https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_002A/UCD_Chem_2A/ucd_chem_2a__general_chemistry_i/07%3A_Homework/7.50%3A_Exercise_Solutions/7.50.09%3A_Solution_Set_9)
4. [5.2 Hybrid Atomic Orbitals, Chemistry: Atoms First 2e, OpenStax](https://openstax.org/books/chemistry-atoms-first-2e/pages/5-2-hybrid-atomic-orbitals?modal=MH)
5. [CCCBDB experimental geometry data for SF6, NIST](https://cccbdb.nist.gov/listgeomexpx.asp?casno=2551624&charge=0)
6. [2.2 The Shapes of Molecules (VSEPR Theory) and Orbital Hybridization, Chemistry LibreTexts](https://chem.libretexts.org/Courses/UW-Whitewater/Chem_260%3A_Inorganic_Chemistry_%28Girard%29/02%3A_Molecular_Orbital_Theory/2.02%3A_The_Shapes_of_Molecules_%28VSEPR_Theory%29_and_Orbital_Hybridization)
7. [7.1 Introduction to Crystal Field Theory (Octahedral complexes), Chemistry LibreTexts](https://chem.libretexts.org/Courses/Kutztown_University_of_Pennsylvania/CHM_320%3A_Advanced_Inorganic_Chemistry_textbook/07%3A_Ligand_Field_Theory_%28LFT%29_and_Crystal_Field_Theory_%28CFT%29_of_Octahedral_Complexes/7.01%3A_Introduction_to_Crystal_Field_Theory_%28Octahdral_complexes%29)
8. [1.3.3 The Shapes of Molecules, Chemistry LibreTexts](https://chem.libretexts.org/Courses/Duke_University/CHEM_210D%3A_Modern_Applications_of_Chemistry/3%3A_Textbook-_Modern_Applications_of_Chemistry/01%3A_Primer/1.03%3A_Further_Aspects_of_Covalent_Bonding/1.3.03%3A_The_Shapes_of_Molecules)
9. [Observation 1: Geometries of molecules, Chemistry LibreTexts (Hutchinson)](https://chem.libretexts.org/Bookshelves/General_Chemistry/Concept_Development_Studies_in_Chemistry_%28Hutchinson%29/7%3A_Molecular_Geometry_and_Electron_Domain_Theory/Section_3%3A_Observation_1%3A_Geometries_of_molecules)
10. [5.2 Molecular Geometry: Using VSEPR Theory to Predict Molecular Shape, Chemistry LibreTexts](https://chem.libretexts.org/Courses/Western_Oregon_University/Chemistry_for_Health_Professions/05%3A_Molecular_Structure_Polarity_and_Intermolecular_Forces/5.02%3A_Molecular_Geometry_-_Using_VSEPR_Theory_to_Predict_Molecular_Shape)
11. [4.6 Molecular Structure and Polarity, Chemistry: Atoms First 2e, OpenStax](https://openstax.org/books/chemistry-atoms-first-2e/pages/4-6-molecular-structure-and-polarity)
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13. [Six coordinate capped trigonal bipyramidal complexes, ScienceDirect](https://www.sciencedirect.com/science/article/pii/S0010854517301923)
14. [6.4.1 Geometric Isomerism, Chemistry LibreTexts](https://chem.libretexts.org/Courses/Northern_Michigan_University/CH_215%3A_Chemistry_of_the_Elements_Fall_2023/06%3A_Transition_Metals_and_Coordination_Chemistry/6.04%3A_Isomers/6.4.01%3A_Geometric_Isomerism)
15. [19.3 Coordination Chemistry of Transition Metals, Chemistry LibreTexts (Atoms First 2e)](https://chem.libretexts.org/Bookshelves/General_Chemistry/Chemistry_-_Atoms_First_2e_%28OpenStax%29/19%3A_Transition_Metals_and_Coordination_Chemistry/19.03%3A_Coordination_Chemistry_of_Transition_Metals)
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17. [CCCBDB Compare bond angles](https://cccbdb.nist.gov/listangleexp3x.asp?bi=11&descript=aFSF&mi=1)
18. [Section 5.5: Isomerism](https://chem.libretexts.org/Courses/Centre_College/CHE_332%3A_Inorganic_Chemistry/05%3A_Coordination_Chemistry-_Structure_and_Isomers/5.05%3A_Isomerism)

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