Advanced aspects of chemical bonding

Crystal field theory

Although complex formation is an example of the linking together of species by the formation of covalent (but highly polar) bonds, the first systematic approach to the explanation of the properties of complexes was based on a model in which the effect of the ligands was treated as an essentially ionic problem. In this crystal field theory, each ligand was represented by a negative point charge. (This point charge models the lone pair of electrons that is responsible for the bond formation.) There are then two contributions to the binding energy. One is the electrostatic attraction between the central cation and the negative point charges, which is largely responsible for the stability of the complex. There is also the differential effect of the array of the point charges on the energies of the d orbitals of the ion. Whereas in a free atom all five d orbitals have the same energy, in an octahedral crystal field they split into two groups (Figure 18), with three orbitals (labeled t_2g; the labeling is based on details of their symmetry) lower in energy than the remaining two (labeled e_g). The difference in energy between the two sets is denoted Δ and is called the crystal field splitting energy (CFSE). This energy is the parameter that is used to correlate a variety of spectroscopic, thermodynamic, and magnetic properties of complexes.

The essential feature of crystal field theory is that there is a competition between the magnitude of the CFSE and the pairing energy, which is the energy required to accommodate two electrons in one orbital. When the pairing energy is high compared with the CFSE, the lowest-energy electron configuration is achieved with as many electrons as possible in different orbitals. The arrangement of a d⁵ ion, for instance, is t_2g³e_g², with all spins parallel (as in Figure 18B). However, if the ligands give rise to a very strong crystal field, so that the CFSE is large compared with the pairing energy, then the lowest-energy electron configuration is that with as many electrons as possible in the lower (t_2g) set of orbitals. In such a case, a 3d⁵ ion would adopt the configuration t_2g⁵, with only one unpaired spin as in Figure 18A. Thus, because magnetism arises from the presence of electron spins, it can be seen that the magnetic properties of the complex can be correlated with the size of the CFSE. The same is true of spectroscopic and thermodynamic properties. In particular it is found that ligands can be arranged in order of the strength of the crystal field that they generate, and this so-called spectrochemical series can be used to rationalize and predict the properties of complexes.

Ligand field theory

Crystal field theory is an artificial parameterization of the bonding in complexes, for it models the actual bonding in terms of an array of point charges. A superior theory is a modification of crystal field theory known as ligand field theory, which is more securely based in MO theory and allows for a more appropriate degree of delocalization of electrons over the metal ion and the ligands.

In essence, in ligand field theory molecular orbitals of complexes of first-transition-series (i.e., period-4) metals are constructed from the five 3d orbitals of the central metal cation and one orbital from each of the six ligand atoms that are directly attached to the metal cation. It follows that in such an octahedral complex there are 5 + 6 = 11 molecular orbitals to accommodate the 3d electrons of an [Ar]3dⁿ species and 12 electrons from the six ligand atoms, giving 12 + n electrons in all. The 11 MOs span a range of energies. Twelve of the electrons occupy the six lowest-energy MOs, which are largely ligand-atom in character. The remaining n electrons are to be accommodated in the e_g and t_2g sets of orbitals. The energy separation between these two sets of orbitals, the ligand-field splitting energy (LFSE) is the ligand field version of the CFSE in crystal field theory, and from this point on the construction of the lowest-energy electron configuration is much the same as in crystal field theory. However, ligand field theory is less artificial, allows for electron delocalization, and is more readily extended to more complex patterns of bonding between the central metal ion and the ligands (such as the incorporation of bonds with π symmetry).

Organometallic compounds

A particular class of complexes consists of the organometallic compounds, in which there are bonds between a metal atom and a carbon atom. Among the most important of such compounds are the carbonyls, which are complexes in which one or more of the ligands is a carbon monoxide molecule, CO, either linked to one atom or bridging two. Another interesting class of organometallic compounds is composed of the metallocenes, informally called “sandwich compounds,” in which the metal atom sits between two planar hydrocarbon rings, analogous to the meat in a sandwich. Of these, ferrocene [Fe(C₅H₅)₂] was among the first to be synthesized.

The stabilities of organometallic compounds follow certain empirical rules, among which the 18-electron rule is the analogue of the octet rule of main-group compounds. According to this rule, the most stable organometallic compounds are those having 18 electrons in the valence shell, a term in this context extended to include the outermost d orbitals. Nickel tetracarbonyl, Ni(CO)₄, a poisonous gas used in the refining of nickel, has 10 electrons provided by the neutral nickel atom and two from each of the four CO ligands, giving 18 electrons in all.

The electronic structures of organometallic compounds can be expressed most effectively in MO terms, and they can be regarded as no more than a special case of ligand field theory. There are certain details that make them particularly interesting, however. To give a sense of the detail in which the structure of a metal-carbon bond may be expressed, attention will be focused here on the link between a metal atom (M) and a carbonyl group (CO): M―CO.

A CO molecule has much the same electronic structure as an N₂ molecule, because it has the same number of electrons—that is, the two species are isoelectronic. There are two important features of this structure, which differ in detail from N₂ on account of the different electronegativities of the two elements in CO. One is that the highest occupied molecular orbital, the HOMO, is largely confined to the carbon atom and can be interpreted as being a lone pair occupying an orbital with σ symmetry. This lone pair enables CO to act as a Lewis base and to link to the metal atom by forming a σ bond to it by overlap with one of the lobes of a d orbital. However, the lowest unfilled molecular orbital, the LUMO, has π symmetry and can accept electrons from an appropriate d orbital of the metal, and thus it can help the ligand to act as a Lewis acid. It is this ability of the ligand to act as both a Lewis base and a Lewis acid that is responsible for the stability of metal carbonyls.