Octahedral molecular geometry

Octahedral molecular geometry
Examples	SF6, Mo(CO)6
Point group	Oh
Steric number	6
Coordination number	6
Bond angle(s)	90°
μ (Polarity)	0

Structure of sulfur hexafluoride, an example of a molecule with the octahedral coordination geometry.

In chemistry, octahedral molecular geometry describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa. The octahedron is one of the Platonic solids, although octahedral molecules typically have an atom in their centre and no bonds between the ligand atoms. A perfect octahedron belongs to the point group O_h. Examples of octahedral compounds are sulfur hexafluoride SF₆ and molybdenum hexacarbonyl Mo(CO)₆. The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves. For example, [Co(NH₃)₆]³⁺, which is not octahedral in the mathematical sense due to the orientation of the N-H bonds, is referred to as octahedral.^[1]

The concept of octahedral coordination geometry was developed by Alfred Werner to explain the stoichiometries and isomerism in coordination compounds. His insight allowed chemists to rationalize the number of isomers of coordination compounds. Octahedral transition-metal complexes containing amines and simple anions are often referred to Werner-type complexes.

Bioctahedral molecular geometry

The sharing of an edge of an octahedron gives a structure called bioctahedral. Many metal pentahalide and pentaalkoxide compounds exist in solution and the solid with bioctahedral structures. One example is niobium pentachloride. Metal tetrahalides often exist as polymers with edge-sharing octahedra. Zirconium tetrachloride is an example.^[2]

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  Ball-and-stick model of niobium pentachloride, a bioctahedral coordination compound.

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  Ball-and-stick model of zirconium tetrachloride, an inorganic polymer based on edge-sharing octahedra.

Isomerism in octahedral complexes

When two or more types of ligands (L^a, L^b, ...) are coordinated to an octahedral metal centre (M), the complex can exist as isomers. The naming system for these isomers depends upon the number and arrangement of different ligands.

cis and trans

For ML^a₄L^b₂, two isomers exist. These isomers of ML^a₄L^b₂ are cis, if the L^b ligands are mutually adjacent, and trans, if the L^b groups are situated 180° to each other. It was the analysis of such complexes that led Alfred Werner to the 1913 Nobel Prize–winning postulation of octahedral complexes.

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  cis-[CoCl₂(NH₃)₄]⁺
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  trans-[CoCl₂(NH₃)₄]⁺

Facial and meridional isomers

For ML^a₃L^b₃, two isomers are possible - a facial isomer (fac) in which each set of three identical ligands occupies one face of the octahedron surrounding the metal atom, so that any two of these three ligands are mutually cis, and a meridional isomer (mer) in which each set of three identical ligands occupies a plane passing through the metal atom.

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  fac-[CoCl₃(NH₃)₃]
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  mer-[CoCl₃(NH₃)₃]

Chirality

More complicated complexes, with several different kinds of ligands or with bidentate ligands can also be chiral, with pairs of isomers which are non-superimposable mirror images or enantiomers of each other.

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  Λ-[Fe(ox)₃]³⁻
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  Δ-[Fe(ox)₃]³⁻
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  Λ-cis-[CoCl₂(en)₂]⁺
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  Δ-cis-[CoCl₂(en)₂]⁺

Other

For ML^a₂L^b₂L^c₂, a total of six isomers are possible.^[3]

1. One isomer in which all three pairs of identical ligands are trans
2. Three distinct isomers in which one pair of identical ligands (L^a or L^b or L^c) is trans while the other two are cis.
3. Two enantiomeric chiral isomers in which all three pairs of identical ligands are cis.

The number of possible isomers can reach 30 for an octahedral complex with six different ligands (in contrast, only two stereoisomers are possible for a tetrahedral complex with four different ligands). The following table lists all possible combinations for monodentate ligands:

Formula	Number of isomers	Number of enantiomeric pairs
ML6	1	0
ML^a5L^b	1	0
ML^a4L^b2	2	0
ML^a4L^bL^c	2	0
ML^a3L^b3	2	0
ML^a3L^b2L^c	3	0
ML^a3L^bL^cL^d	5	1
ML^a2L^b2L^c2	6	1
ML^a2L^b2L^cL^d	8	2
ML^a2L^bL^cL^dL^e	15	6
ML^aL^bL^cL^dL^eL^f	30	15

Thus, all 15 diastereomers of ML^aL^bL^cL^dL^eL^f are chiral, whereas for ML^a₂L^bL^cL^dL^e, six diastereomers are chiral and three are not: the ones where L^a are trans. One can see that octahedral coordination allows much greater complexity than the tetrahedron that dominates organic chemistry. The tetrahedron ML^aL^bL^cL^d exists as a single enatiomeric pair. To generate two diastereomers in an organic compound, at least two carbon centers are required.

Trigonal prismatic geometry

For compounds with the formula MX₆, the chief alternative to octahedral geometry is a trigonal prismatic geometry, which has symmetry D_3h. In this geometry, the six ligands are also equivalent. There are also distorted trigonal prisms, with C_3v symmetry; a prominent example is W(CH₃)₆. The interconversion of Δ- and Λ-complexes, which is usually slow, is proposed to proceed via a trigonal prismatic intermediate, a process called the "Bailar twist." An alternative pathway for the racemization of these same complexes is the Ray–Dutt twist.

Splitting of the energy of the d-orbitals in octahedral complexes

For a "free ion", e.g. gaseous Ni²⁺ or Mo⁰, the energy of the d-orbitals are equi-energetic, that is they are "degenerate." In an octahedral complex, this degeneracy is lifted. The energy of the d_z² and d_x²−y², the so-called e_g set, which are aimed directly at the ligands are destabilized. On the other hand, the energy of the d_xz, d_xy, and d_yz orbitals, the so-called t_2g set, are stabilized. The labels t_2g and e_g refer to irreducible representations, which describe the symmetry properties of these orbitals. The energy gap separating these two sets is the basis of Crystal Field Theory and the more comprehensive Ligand Field Theory. The loss of degeneracy upon the formation of an octahedral complex from a free ion is called crystal field splitting or ligand field splitting. The energy gap is labeled Δ_o, which varies according to the number and nature of the ligands. If the symmetry of the complex is lower than octahedral, the e_g and t_2g levels can split further. For example, the t_2g and e_g sets split further in trans-ML^a₄L^b₂.

Ligand strength has the following order for these electron donors:

weak: iodine < bromine < fluorine < acetate < oxalate < water < pyridine < cyanide :strong

So called "weak field ligands" give rise to small Δ_o and absorb light at longer wavelengths.

Reactions

Given that a virtually uncountable variety of octahedral complexes exist, it is not surprising that a wide variety of reactions have been described. These reactions can be classified as follows:

• Ligand substitution reactions (via a variety of mechanisms)
• Ligand addition reactions, including among many, protonation
• Redox reactions (where electrons are gained or lost)
• Rearrangements where the relative stereochemistry of the ligand change within the coordination sphere.

Many reactions of octahedral transition metal complexes occur in water. When an anionic ligand replaces a coordinated water molecule the reaction is called an anation. The reverse reaction, water replacing an anionic ligand, is called aquation. For example, the [CoCl(NH₃)₅]²⁺ slowly aquates to give [Co(NH₃)₅(H₂O)]³⁺ in water, especially in the presence of acid or base. Addition of concentrated HCl converts the aquo complex back to the chloride, via an anation process.

See also

• Octahedral clusters
• AXE method
• Molecular geometry

References

1. von Zelewsky, A. "Stereochemistry of Coordination Compounds" John Wiley: Chichester, 1995. ISBN 047195599X.
2. Wells, A.F. (1984) Structural Inorganic Chemistry, Oxford: Clarendon Press. ISBN 0-19-855370-6.
3. Miessler G.L. and Tarr D.A. Inorganic Chemistry (2nd ed. Prentice-Hall 1999) p.290

External links

• Chem| Chemistry, Structures, and 3D Molecules
• Indiana University Molecular Structure Center
• Point Group Symmetry Examples