Isolobal principle

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The isolobal principle (more formally known as the isolobal analogy) is way to predict bonding properties of organometallic compounds. In organometallic chemistry, it relates the structure of organic ligands that can bind to inorganic molecular fragments.[1] Roald Hoffmann described molecular fragments as isolobal "if the number, symmetry properties, approximate energy and shape of the frontier orbitals and the number of electrons in them are similar – not identical, but similar."[2] One can predict the bonding and reactivity of a lesser-known pieces from that of a better-known pieces if the two molecular fragments have similar frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Isolobal compounds are analogs to isoelectronic compounds that share the same number of valence electrons 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.

Figure 1: Basic example of the isolobal analogy.

For his work on the isolobal analogy, Hoffmann was awarded the Nobel Prize in Chemistry in 1981, which he shared with Kenichi Fukui.[3] In his Nobel Prize lecture, Hoffmann stressed that the isolobal analogy is a useful, yet simple, model. It does fail in certain instances.[1]

Construction of isolobal fragments[change | change source]

To be the starting point of an isolobal fragment, the molecule must meet certain criteria.[4] Molecules based around main group elements should satisfy the octet rule when all bonding and nonbonding molecular orbitals (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 makes a methyl radical. The molecule retains its molecular geometry as the frontier orbital points in the direction of the missing hydrogen atom. Further removal of a hydrogen from the methyl radical 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.

Figure 2: Construction of frontier orbitals from methane.

The isolobal fragments of octahedral complexes, such as ML6, can be created in a similar way. Transition metal complexes should initially satisfy the eighteen electron rule, have no net charge, and their ligands should be two-electron donors (Lewis bases). 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. Breaking the bond between the metal center and one ligand results in a ML5 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 MoL5 complex because Mo has obtained an additional electron making it d7. To remedy this, Mo can be exchanged for Mn, which would from a neutral d7 complex in this case. This trend can continue until only one ligand is left coordinated to the metal center, as shown in Figure 3.

Figure 3: Production of a frontier orbital in an octahedral complex. Since the process is not charge producing, the metal center must change from d6 Mo to d7 Mn to retain the neutral charge.

Relationship between tetrahedral and octahedral fragments[change | change source]

Figure 4: Isolobal fragments of tetrahedral and octahedral geometries.

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 d8 ML4 complex formed from an octahedral starting complex (Figure 4). Similar analogies can be made between either CH3 and d7–ML5 or CH and d9–ML3.

MO theory dependence[change | change source]

Any sort of saturated molecule (that does not have a C−C double bond) can be the starting point for generating isolobal fragments.[5][6] The molecules' bonding and nonbonding MOs should be filled and the antibonding MOs empty. With each consecutive generation of a 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.

Figure 5: Molecular orbital diagram depiction of frontier orbitals in methane and a basic ML6 metal complex.

As seen above, when a fragment is formed from CH4, one of the sp3 hybrid orbitals 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[change | change source]

The isolobal analogy has applications beyond simple octahedral complexes. It can be used with a variety of ligands, charged species and non-octahedral complexes.[7]

Ligands[change | change source]

Typical ligands used in the isolobal analogy are two-electron donors such as phosphines, halogens or carbonyls. However, other types of ligands can be used. If ligands donate multiple pairs of electrons, they will occupy multiple coordination sites. For example, the cyclopentadienyl anion is a six-electron donor, so it occupies three coordination sites. Polydentate ligands can also be used in the analogy, such as ethylenediamine, a bidentate ligand, or triethylenetetramine, a tetradentate ligand.

Figure 6: Example of cyclopentadiene, a multiply coordinating ligand, in the isolobal analogy.

Isoelectronic fragments[change | change source]

The isolobal analogy can also be used with isoelectronic fragments having the same coordination number. This allows charged groups to be considered. For example, Re(CO)5 is isolobal with CH3 and therefore, [Ru(CO)5]+ and [Mo(CO)5] 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, [Re(CO)5]+ is isolobal with CH3+.[8]

Non-octahedral complexes[change | change source]

Figure 7: Isolobal relationship between octahedral and square planar complexes.
d6: Mo(CO)5 d8: [PdCl3]-
d8: Os(CO)4 d10: Ni(PR3)2
Figure 8: Examples of non-basic shapes in the isolobal analogy.

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, MLn, where M has a dx electron configuration to a square planar analogous fragment, the formula MLn−2 where M has a dx+2 electron configuration should be followed.

Further examples of the isolobal analogy in various shapes and forms are shown in Figure 8.

References[change | change source]

  1. 1.0 1.1 Hoffmann, R. (1982). "Building Bridges Between Inorganic and Organic Chemistry (Nobel Lecture)". Angew. Chem. Int. Ed. 21 (10): 711–724. doi:10.1002/anie.198207113 .
  2. In reference 10 of his Nobel Prize acceptance speech, Hoffmann states that the term "isolobal" was introduced in reference 1e, "Elian, M., Chen, M. M.-L., Mingos, D. M. P. and Hoffmann, R., Inorg. Chem., 15, 1148 (1976)", but that the concept is older.
  3. "The Nobel Prize in Chemistry 1981: Kenichi Fukui, Roald Hoffmann". Retrieved December 22, 2010.
  4. Department of Chemistry. Modern Approached to Inorganic Bonding. University of Hull.
  5. Joan Ribas Gispert (2008). Coordination Chemistry. WILEY-VCH. pp. 172–176.
  6. Shriver, D.F.; Atkins, P.; Overton, T.; Rourke, J.; Weller, M.; Armstrong, F. (2006). Inorganic Chemistry. Freeman.
  7. Miessler, G. L.; Tarr, D. A. (2008). Inorganic Chemistry (3rd ed.). Pearson Education, Inc..
  8. Douglas, B.; McDaniel, D.; Alexander, J. (1994). Concepts and Models of Inorganic Chemistry (3 ed.). Wiley & Sons.