Octahedral molecular geometry - AbsoluteAstronomy.com

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, octahedral molecular geometry describes the shape of compounds where in six atoms or groups of atoms or ligand

Ligand

In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal-ligand bonding can range from...

s are symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron

Octahedron

In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

has eight faces, hence the prefix octa. The octahedron is one of the Platonic solid

Platonic solid

In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...

s, although octahedral molecules typically have an atom in their centre and no bonds between the ligand atoms. A perfect octahedron

Octahedron

In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....

belongs to the point group

Point group

In geometry, a point group is a group of geometric symmetries that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O...

O_h. Examples of octahedral compounds are sulfur hexafluoride

Sulfur hexafluoride

Sulfur hexafluoride is an inorganic, colorless, odorless, and non-flammable greenhouse gas. has an octahedral geometry, consisting of six fluorine atoms attached to a central sulfur atom. It is a hypervalent molecule. Typical for a nonpolar gas, it is poorly soluble in water but soluble in...

SF₆ and molybdenum hexacarbonyl

Molybdenum hexacarbonyl

Molybdenum hexacarbonyl is the chemical compound with the formula Mo6. This colorless solid, like its chromium and tungsten analogues, is noteworthy as a volatile, air-stable derivative of a metal in its zero oxidation state.-Structure and properties:Mo6 adopts an octahedral geometry consisting...

Mo(CO)₆. The term "octahedral" is used somewhat loosely by chemists: [Co(NH₃)₆]³⁺

Cobalt(III) hexammine chloride

Hexamminecobalt chloride is the chemical compound with the formula [Co6]Cl3. This coordination compound is considered an archetypal "Werner complex", named after the pioneer of coordination chemistry, Alfred Werner. This salt consists of [Co6]3+ trications with three Cl− anions...

, 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

Alfred Werner

Alfred Werner was a Swiss chemist who was a student at ETH Zurich and a professor at the University of Zurich. He won the Nobel Prize in Chemistry in 1913 for proposing the octahedral configuration of transition metal complexes. Werner developed the basis for modern coordination chemistry...

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

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 led Alfred Werner

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).

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

Chirality (chemistry)

A chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....

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
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

Complexity

In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

than the tetrahedron that dominates organic chemistry

Organic chemistry

Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, composition, reactions, and preparation of carbon-based compounds, hydrocarbons, and their derivatives...

. 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

Symmetry group

The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

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

Hexamethyl tungsten

Hexamethyltungsten is the chemical compound W6. Classified as an organometallic compound, hexamethyltungsten is an air-sensitive, red, crystalline solid at room temperature; however, it is extremely volatile and sublimes at −30 °C...

. 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

Bailar twist

The Bailar twist is a mechanism proposed for the racemization of octahedral complexes containing three bidentate chelate rings. Such complexes typically adopt an octahedral molecular geometry and are thus chiral. One pathway by which these compounds can racemize is via the formation of a trigonal...

." An alternative pathway for the racemization of these same complexes is the Ray-Dutt twist

Ray-Dutt twist

The Ray-Dutt twist is a mechanism proposed for the racemization of octahedral complexes containing three bidentate chelate rings. Such complexes typically adopt an octahedral molecular geometry in their ground states and are thus chiral. The pathway entails formation of an intermediate of C2v...

Splitting of d-orbitals in octahedral complexes

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

Crystal field theory

Crystal field theory is a model that describes the electronic structure of transition metal compounds, all of which can be considered coordination complexes. CFT successfully accounts for some magnetic properties, colours, hydration enthalpies, and spinel structures of transition metal complexes,...

and the more comprehensive Ligand Field Theory

Ligand field theory

Ligand field theory describes the bonding, orbital arrangement, and other characteristics of coordination complexes. It represents an application of molecular orbital theory to transition metal complexes. A transition metal ion has nine valence atomic orbitals, five d, one s, and three p orbitals...

. 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 wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

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
Coordination sphere
In coordination chemistry, the coordination sphere refers to a central atom or ion and an array of molecules or anions, the ligands, around.Molecules that are attached noncovalently to the ligands are called the second 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 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.

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