In
organometallic chemistry
Organometallic chemistry is the study of organometallic compounds, chemical compounds containing at least one chemical bond between a carbon atom of an organic molecule and a metal, including alkali, alkaline earth, and transition metals, and so ...
, the isolobal principle (more formally known as the isolobal analogy) is a strategy used to relate the structure of
organic and
inorganic
In chemistry, an inorganic compound is typically a chemical compound that lacks carbon–hydrogen bonds, that is, a compound that is not an organic compound. The study of inorganic compounds is a subfield of chemistry known as '' inorganic chemist ...
molecular fragments in order to predict
bond
Bond or bonds may refer to:
Common meanings
* Bond (finance), a type of debt security
* Bail bond, a commercial third-party guarantor of surety bonds in the United States
* Chemical bond, the attraction of atoms, ions or molecules to form chemica ...
ing properties of organometallic compounds.
Roald Hoffmann
Roald Hoffmann (born Roald Safran; July 18, 1937) is a Polish Americans, Polish-American theoretical chemistry, theoretical chemist who won the 1981 Nobel Prize in Chemistry. He has also published plays and poetry. He is the Frank H. T. Rhodes P ...
described molecular fragments as isolobal "if the number,
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
properties, approximate energy and shape of the
frontier orbital
A frontier is the political and geographical area near or beyond a boundary. A frontier can also be referred to as a "front". The term came from French in the 15th century, with the meaning "borderland"—the region of a country that fronts o ...
s and the number of
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s in them are similar – not identical, but similar." One can predict the bonding and
reactivity of a lesser-known species from that of a better-known species if the two molecular fragments have similar frontier orbitals, the
highest occupied molecular orbital
In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for ''highest occupied molecular orbital'' and ''lowest unoccupied molecular orbital'', respectively. HOMO and LUMO are sometimes collectively called the ''frontie ...
(HOMO) and the
lowest unoccupied molecular orbital
In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for ''highest occupied molecular orbital'' and ''lowest unoccupied molecular orbital'', respectively. HOMO and LUMO are sometimes collectively called the ''frontie ...
(LUMO). Isolobal compounds are analogues to
isoelectronic
Isoelectronicity is a phenomenon observed when two or more molecules have the same structure (positions and connectivities among atoms) and the same electronic configurations, but differ by what specific elements are at certain locations in the ...
compounds that share the same number of
valence electron
In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair forms ...
s and structure. A graphic representation of isolobal structures, with the isolobal pairs connected through a double-headed arrow with half an orbital below, is found in Figure 1.
For his work on the isolobal analogy, Hoffmann was awarded the
Nobel Prize in Chemistry
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then "M ...
in 1981, which he shared with
Kenichi Fukui
was a Japanese chemist, known as the first Asian person to be awarded the Nobel Prize in Chemistry.
Fukui was co-recipient of the 1981 Nobel Prize in Chemistry with Roald Hoffmann, for their independent investigations into the mechanisms of che ...
.
In his Nobel Prize lecture, Hoffmann stressed that the isolobal analogy is a useful, yet simple, model and thus is bound to fail in certain instances.
[
]
Construction of isolobal fragments
To begin to generate an isolobal fragment, the molecule needs to follow certain criteria. Molecules based around main group elements should satisfy the octet rule
The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule i ...
when all bonding and nonbonding molecular orbitals
In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of findin ...
(MOs) are filled and all antibonding MOs are empty. For example, methane is a simple molecule from which to form a main group fragment. The removal of a hydrogen atom from methane generates a methyl radical. The molecule retains its molecular geometry
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determ ...
as the frontier orbital points in the direction of the missing hydrogen atom. Further removal of hydrogen results in the formation of a second frontier orbital. This process can be repeated until only one bond remains to the molecule's central atom. Figure 2 demonstrates this example of step-by-step generation of isolobal fragments.
The isolobal fragments of octahedral complexes, such as type ML6, can be created in a similar fashion. Transition metal complex
A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many m ...
es should initially satisfy the eighteen electron rule, have no net charge, and their ligands
In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electro ...
should be two electron donors (Lewis base
A Lewis acid (named for the American physical chemist Gilbert N. Lewis) is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any sp ...
s). Consequently, the metal center for the ML6 starting point must be d6. Removal of a ligand is analogous to the removal of hydrogen of methane in the previous example resulting in a frontier orbital, which points toward the removed ligand. Cleaving the bond between the metal center and one ligand results in a radical complex. In order to satisfy the zero-charge criteria the metal center must be changed. For example, a MoL6 complex is d6 and neutral. However, removing a ligand to form the first frontier orbital would result in a complex because Mo has obtained an additional electron making it d7. To remedy this, Mo can be exchanged for Mn, which would form a neutral d7 complex in this case, as shown in Figure 3. This trend can continue until only one ligand is left coordinated to the metal center.
Relationship between tetrahedral and octahedral fragments
Isolobal fragments of tetrahedral and octahedral molecules can be related. Structures with the same number of frontier orbitals are isolobal to one another. For example, the methane with two hydrogen atoms removed, CH2 is isolobal to a d7 ML4 complex formed from an octahedral starting complex (Figure 4).
MO theory dependence
Any sort of saturated molecule can be the starting point for generating isolobal fragments. The molecule's bonding and nonbonding molecular orbitals (MOs) should be filled and the antibonding MOs empty. With each consecutive generation of an isolobal fragment, electrons are removed from the bonding orbitals and a frontier orbital is created. The frontier orbitals are at a higher energy level than the bonding and nonbonding MOs. Each frontier orbital contains one electron. For example, consider Figure 5, which shows the production of frontier orbitals in tetrahedral and octahedral molecules.
As seen above, when a fragment is formed from CH4, one of the sp3 hybrid orbitals
In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new ''hybrid orbitals'' (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to f ...
involved in bonding becomes a nonbonding singly occupied frontier orbital. The frontier orbital’s increased energy level is also shown in the figure. Similarly when starting with a metal complex such as d6-ML6, the d2sp3 hybrid orbitals are affected. Furthermore, the t2g nonbonding metal orbitals are unaltered.
Extensions of the analogy
The isolobal analogy has applications beyond simple octahedral complexes. It can be used with a variety of ligands, charged species and non-octahedral complexes.
Isoelectronic fragments
The isolobal analogy can also be used with isoelectronic fragments having the same coordination number, which allows charged species to be considered. For example, Re(CO)5 is isolobal with CH3 and therefore, 5">u(CO)5sup>+ and 5">o(CO)5sup>− are also isolobal with CH3. Any 17-electron metal complex would be isolobal in this example.
In a similar sense, the addition or removal of electrons from two isolobal fragments results in two new isolobal fragments. Since Re(CO)5 is isolobal with CH3, 5">e(CO)5sup>+ is isolobal with .
Non-octahedral complexes
The analogy applies to other shapes besides tetrahedral and octahedral geometries. The derivations used in octahedral geometry are valid for most other geometries. The exception is square-planar because square-planar complexes typically abide by the 16-electron rule. Assuming ligands act as two-electron donors the metal center in square-planar molecules is d8. To relate an octahedral fragment, ML''n'', where M has a d''x'' electron configuration to a square planar analogous fragment, the formula ML''n''−2 where M has a d''x''+2 electron configuration should be followed.
Further examples of the isolobal analogy in various shapes and forms are shown in figure 8.
References
{{Organometallics
Organometallic chemistry