A Covalent Bonding Model - Embracing Molecular Orbital Theory

It's perhaps a bit confusing to assert that such a thing as coordinate covalent bonds exist, and then to introduce a theory based on purely ionic interactions. Even clawing back some of the concept by asserting mixed bonding character seems a grudging concession. So what's so wrong with a purely covalent model? One of the most obvious answers is that, by its localized atom-to-atom nature, covalent models deal poorly with both shape and interpretation of spectroscopic observations. Since the value of any model lies in its applicability in the interpretation of physical observations, not achieving this tends to limit its attractiveness. It's a bit like sun worship compared with space physics; interpretation in the former is dominated by belief, in the latter by scientific facts and models. Sun-worship is fine if you're so disposed, except changing to moon-worship then becomes a much bigger decision than simply applying scientific methodology to a different celestial body. Scientists should be sufficiently flexible that they are able to accept that a system is capable of sustaining several models, whose usefulness depends on the demands placed on them. Thus there is room for a simple covalent model - but it will have limitations.

Let's revise the simple valence bond model discussed earlier. For our main focus of current attention, the octahedral shape, there are several small molecules or molecular ions of this shape that tend to be regarded as simple covalent compound rather than coordination compounds, such as PF6, for which an adequate bonding model exists. We can draw on this as we develop a model for an octahedral metal complex, ML6. With a pure covalent model, six M-L bonds require six appropriate orbitals on the central metal atom with which a lone pair of electrons on each of six ligands can interact. The valence shell of a d-block metal can be considered to consist of the five nd orbitals, as well as the energetically similar (n+1)s and three (n+1)p orbitals - a total of nine orbitals. Since physical observations show that all six bonds in an ML system with one ligand type are identical, it is necessary to have involved not only six orbitals on the metal, but six identical orbitals. This is achieved by hybridization, using the one s, three p and two of the five d orbitals to form six equivalent d'sp3 hybrids (see Figure 1.2 for an example of this), each capable of accepting a pair of electrons - if empty. Therein lies a problem, as the d orbitals at least may contain electrons, and perhaps too many to reside out of the way in the three nonparticipating d orbitals. One can make a virtue out of a necessity by asserting that the number of d electrons limits the number and type of coordinate covalent bonds that can form, and there is certainly a relationship of sorts here, or else use the next highest set of (empty) d orbitals. But it's all rather unsatisfactory.

A somewhat more sophisticated approach to this description (though still not capable of dealing fully with spectroscopic and magnetic properties) is to look at a more 'molecular' approach, by considering six of the nine available bonding orbitals on the metal interacting or mixing with the six lone pairs on the ligands to form six bonding and six antibonding orbitals. In effect, we can visualize the bonding component in this case essentially as in the simple model discussed above. However, we are moving to a molecular orbital (MO) approach to bonding, which is a holistic approach to bonding. The key to molecular orbital theory is that it involves combinations of orbitals from components to produce a new set of orbitals of different energy from those of the separate components. However, importantly, the number of orbitals in the molecular assembly exactly matches the number in the components. In the simplest case, where we are combining one orbital from atom A and one orbital from atom X, we produce two orbitals; one is stabilized versus the parent orbitals (that is, it is of lower energy), the other destabilized (that is, it is of higher energy). The former is called the bonding orbital, the latter an antibonding orbital; these names reflect their character, as electrons inserted in the former lead to a more stable situation when A and X are linked by a bond, whereas electrons in the latter destabilize the assembly. An excess of electrons in bonding compared with antibonding orbitals leads to a stable compound AX. The model can accommodate σ and π bonding, as well as orbitals in some cases that do not participate directly in bonding (called nonbonding orbitals).

These concepts extend to joining molecular species to form a new bond, and an example for a simple coordination compound F3B-NH3 is shown in Figure 3.10, featuring only the relevant two 'frontier' orbitals of the BF3 and NH3 molecules involved in formation of the coordinate bond. It is not uncommon, not only simply for ease of visualization but also because the energy levels of frontier bonding orbitals are central to the theory, to restrict a MO diagram to solely depicting 'orbitals of interest'. In this case, the pair of electrons

Figure 3.10

A molecular orbital diagram for F3B-NH3, reporting only the orbital interaction of the lowest unoccupied molecular orbital (LUMO) on the precursor molecule BF3 and the highest occupied molecular orbital (HOMO) on the precursor molecule NH3. Only if there is useful overlap of the orbital contributions from each precursor are the new orbitals formed.

originally in the N orbital occupy what we can consider as the bonding MO, leading to a more stable situation for the B-N assembly (the electrons occupying a lower energy orbital compared with the energy of the orbital on the original N centre), and hence a stable bonding outcome. In more complicated metal complexes, it is again convenient to consider just the one relevant orbital on each donor molecule or atom (effectively the lone pair in the valence bond description) together with the valence orbitals on the central metal in building the MO diagram.

In our ML6 model, there were originally nine orbitals of similar energy on the metal considered (five d, one s and three p), yet to form bonds to six ligand orbitals only six are required. This means that three are not involved in forming bonds to the ligands, and are thus designated as nonbonding orbitals (Figure 3.11). While it is not necessarily a good idea to always seek linkages between models, these nonbonding levels effectively correspond to the 12g set of the ionic model already discussed. Overall, 15 'orbitals of interest' appear in the diagram, capable of accommodating up to 30 electrons. Like all MO models, the number of participating orbitals in the components (the metal and six ligand orbitals here) must equal the number of MOS in the assembly (ML, here). Moreover, equal numbers of bonding and antibonding orbitals, the former of lower energy and the latter of higher energy than the parent orbitals, must form.

The 12 electrons from the six ligands lone pairs are used to occupy the six bonding molecular σ-orbitals created (defined by their symmetry labels as aig (singlet) fiu (triplet) and eg (doublet)), which lie lower but fairly close in energy to the initial ligand orbital energy levels, with the metal d electrons then inserted in the next highest energy levels (12g, eg*) of the molecular assembly. This means that insertion of d electrons commences in the model at the nonbonding orbitals derived from the original d-orbital set. This set of three nonbonding levels along with the six bonding orbitals provide an upper limit of 18 electrons before antibonding orbitals must be employed, which would then lead to an inherently reduced stability for the system. Moreover, there are some benefits for some types of complexes in having this nonbonding set filled fully with filling leading to some favourable

Figure 3.11

Molecular orbital diagram for an octahedral ML, complex.

lowering of their energy. This gives rise to the so-called '18-electron rule', met particularly in organometallic chemistry, and discussed earlier in Section 3.3. The model is rather unsophisticated in assuming that sixfold and threefold degeneracy, for the participating ligand and nonbonding d orbitals levels respectively, actually exists, and a higher order treatment is necessary to accommodate this deficiency and allow interpretation of properties. The molecular orbital theory, as a holistic model, is based on the recognition that it is not essential to limit bonding to linkages between only two atoms at a time. Rather, it allows a MO to spread out over any number of atoms in a molecule, from two to even all atoms. This is a complex and mathematically intensive theory, which is not explored here in depth. It applies mathematical group theory to determine the allowed combinations of metal orbitals and ligand orbitals (or orbital overlap) that lead to bonding situations. One example of a combination involving many centres is the overlap of the metal s orbital with all six of the lone pair orbitals from the six ligands at once. This seven-centre combination produces both a bonding molecular orbital (designated as ag in group theory) and a complementary antibonding orbital (designated as ag*); a representation of the bonding orbital is shown in Figure 3.12.

The three p orbitals differ only in spatial orientation, and it is hardly surprising to find their interactions with donor orbitals are energetically equivalent, leading to a set of three degenerate levels (designated as tu in Figure 3.11). The five d orbitals interact as two sets due to their spatial arrangement into two groups - those lying along axes and those between axes, as was the case in CFT. The outcome for the d2.2 and d orbitals interacting with ligand orbitals is the formation of a degenerate set of two bonding levels (designated as e) and of two degenerate antibonding levels (eg). A key to the formation of allowed bonding interactions in terms of a pictorial concept is orbital orientation - the lobes of the orbitals need to point along a line joining the atomic centres. This is readily achieved with a d_x2-y2 orbital for example, but simply cannot occur with an orbital like dry due to its spatial

Figure 3.12

Model, for octahedral symmetry, of the components of the ag bonding molecular orbital formed from overlap of the metal s orbital (centre. of symmetry a1g) with the six ag ligand group orbital (LGO) lobes formed considering all six-ligand lone-pair orbitals. A set of three degenerate t1u LGOS match to the degenerate set of three p orbitals, and a set of two eg LGOS match to the two degenerate eg d orbitals. Overall, six LGOS combine with six of the nine available s, p, d metal orbitals, forming six bonding and six antibonding molecular orbitals. The metal's set of three 12 orbitals are nonbonding.

orientation relative to the lone pair orbitals (Figure 3.13). Thus, in this model, the three remaining d orbitals with lobes oriented between the axes become nonbonding orbitals, as a degenerate set (designated as 12g). The overall bonding model is shown in Figure 3.11. This is somewhat similar to that evolved from the valence bond approach in Figure 3.5, but the six bonding and antibonding levels do not form a degenerate set here. Further, note that the f2g and eg* levels correspond to the f2g and eg levels of the crystal field model splitting diagram, although arising through quite different concepts. It may be a bit confusing, but may also be comforting to find that there is some common ground between the models. This certainly supports the mixing in of ionic and covalent concepts in 'hybrids' such as LFT. What has been done above for the octahedral geometry can likewise be applied to other shapes, but it is not the intent to labour the point by pursuing these here. What we have established is another viable model for dealing with metal complexes, albeit based on simple σ-bonding concepts; we will return to look beyond this level later.

Figure 3.13 Orbital orientation as a contributor to effective molecular orbital formation: effective d_x2-y2-orbital interaction versus ineffective dxy-orbital interaction. The circles represent ligand orbitals located equidistant from the metal centre in each case.

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مواضيع ذات صلة

An Ionic Bonding Model - Introducing Crystal Field Theory

Holding On - The Nature of Bonding in Metal Complexes

Complex Shape - Not Just Any Which Way

The Foundation of Coordination Chemistry

Photo-Oxidative Degradations of Polymers

Oxidation of Step-Growth Polymers

Hydrolytic Degradation of Polymers at Elevated Temperatures

The Termination Reaction

صناعة حمض الكبريتيك

تركيب حامض الكبريتوز

كلوريد الثيونيل Thionyl Chloride

حامض الكبريتوز: Sulphureous Acid