ISOLOBAL ANALOGY (principle and application)

The isolobal analogy is a concept used in organometallic chemistry to relate the structure of organic and inorganic molecular fragments and to predict bonding properties of organometallic compounds.

Molecular fragments are considered as isolobal "if

                   i.      the number,

                   ii.      symmetry properties,

                    iii.      approximate energy

                          iv.      shape of the frontier orbitals and

                           v.      the number of electrons

in them are similar

Isolobal compounds are somewhat similar to isoelectronic compounds as they posses 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.

Construction of isolobal fragments

To begin to generate an isolobal fragment, the molecule needs to follow certain criteria.

1. Molecules should satisfy the octet rule and
2. 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 generates 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 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.

Figure 2: Construction of frontier orbitals from methane.

The isolobal fragments of octahedral complexes, such as ML₆, can be created in a similar way:

1. Transition metal complexes should initially satisfy the eighteen electron rule,
2. have no net charge, and
3. their ligands should be two electron donors (Lewis bases). 

Consequently, the metal center for the ML₆ starting point must be d⁶ (6 valence electrons+ 2x6 electrons from all two electron donor ligands = 18 e^-). 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 ML^-₅ 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 MoL^-₅ 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, as shown in Figure 3. This trend can continue until only one ligand is left coordinated to the metal center.

'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

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).

MO theory dependence

Any sort of saturated molecule can be the starting point for generating isolobal fragments.

STEP i.            The molecules' bonding and nonbonding MOs should be filled and the antibonding MOs empty.

STEP ii.            With each consecutive generation of an isolobal fragment, electrons are removed from the bonding orbitals and a frontier orbital is created.

STEP iii.            The frontier orbitals are at a higher energy level than the bonding and nonbonding MOs.

STEP iv.            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 t_2g nonbonding metal orbitals are unaltered.

Ligands

Typical ligands used in the isolobal analogy are two-electron donors such as phosphines, halogens or carbonyls. However, other types of ligands can be employed.

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.

HOW TO SOLVE QUESTIONS ON ISOLOBAL ANALOGY

Ques: Among the Following the correct statements is:

1. CH is isolobal to Co(CO)₃
2. CH₂ is isolobal to Ni(CO)₂
3. CH is isolobal to Fe(CO)₄
4. CH₂ is isolobal to Mn(CO)₄

_Ans:

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