Octahedral molecular geometry

File:Octahedral-3D-balls.png

Idealized structure of a compound with octahedral coordination geometry.

In chemistry, octahedral molecular geometry describes the shape of compounds where in six atoms or groups of atoms or ligands are 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: [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.

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.

Isomerism in octahedral complexes

Main Article: Stereochemistry

When two or more types of ligands are coordinated to an octahedral metal centre, 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 lead Alfred Werner to the 1913 Nobel Prize winning postulation of octahedral complexes.

For ML^a₂L^b₂L^c₂, cis and trans isomers are also possible. All three types of ligands L^a, L^b and L^c may be trans, or one type may be trans while the other two are cis. This latter case gives two unique isomers (for a total of three).

• 
  cis-[CoCl₂(NH₃)₄]⁺
• 
  trans-[CoCl₂(NH₃)₄]⁺
• 
  fac-[CoCl₃(NH₃)₃]
• 
  mer-[CoCl₃(NH₃)₃]

Facial and meridional isomers

For ML^a₃L^b₃, two isomers are possible - a facial isomer (fac) where the three identical ligands are mutually cis, and a meridional isomer (mer) where the three ligands are coplanar.

Chirality

More complicated complexes, with several different kinds of ligands or with bidentate ligands can also be chiral.

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

Other

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
MLa5Lb	1	0
MLa4Lb2	2	0
MLa3Lb3	2	0
MLa4LbLc	2	0
MLa3Lb2Lc	3	0
MLa2Lb2Lc2	6	1
MLa3LbLcLd	5	1
MLa2Lb2LcLd	8	2
MLa2LbLcLdLe	15	6
MLaLbLcLdLeLf	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 that 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 d-orbitals in octahedral complexes

Main article: Ligand field theory

For a "free ion", e.g. gaseous Ni²⁺ or Mo⁰, the d-orbitals are equi-energetic, that is they are "degenerate." In an octahedral complex, this degeneracy is lifted. 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 d_xz, d_xy, and d_yz orbitals, the so-called t_2g set, are not. 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 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 a anation. The reverse reaction, water replacing an anionic ligand, is called an "aquation reaction." For example, the [Co(NH₃)₅Cl]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
• Bailar twist

External Links

• Chem| Chemistry, Structures, and 3D Molecules
• Indiana University Molecular Structure Center
• Point Group Symmetry| Point Group Symmetry Interactive Examples
• Molecular Modeling
• Animated Trigonal Planar Visual

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