Figure 1. The Ray-Dutt transition state for Ga(acac)3 Λ/Δ interconversion.
Figure 2. the Bailar transition state for Ga(acac)3 Λ/Δ interconversion.
The ring of a metal(acac) [acac= 2,4-pentandionate] complex (also known as a metallacycle) can be represented with the following valence bond structure. In this representation, one O...M bond is dative, the other covalent (although of course the two bonds are identical because two such valence structures are equally probable). There are two features of this structure which determine its properties.
One way therefore of answering the question of whether ligand exchange in a metal(acac) complex will occur by non-dissociative ligand permutation, or by heterolytic-dissociation of M...O bonds is to ask whether the metallacycle is aromatic or not at the appropriate transition state. This concept of transition state aromaticity is a useful one which has been developed in organic chemistry to answer questions such as whether pericyclic reactions (which are thought to occur through conjugated cyclic transition states) will occur.2 We can apply this theory here to analysing the fluxional behaviour of two metal complexes, Co(acac)3 and Ga(acac)3.
As explained in detail elsewhere2 we need a quantitative measure of cyclic aromaticity. Whilst over the years there have been many such measures, the most useful one in the present context is a magnetic index known as NICS. Developed by Schleyer3, it measures a property of the electronic ring current at the centre of the ring. This can either be diatropic, which is associated with ring aromaticity, paratropic, which is associated with ring anti-aromaticity, or neither (unsurprisingly associated with non-aromaticity). The NICS index has its own problems, and in particular, it does not formally separate any magnetic ring currents induced within the σ framework (including so called local effects caused by metal atoms), from those induced by the π electrons. The aromaticity we are considering here is purely a π-electron phenomenon. A first order approximation to separating the σ/π effects is to measure the NICS value not at the actual ring centroid (where the σ effects may be strong) but vertically displaced above this centroid (where only the σ effects decrease rapidly, allowing the π effects to become dominant). Here we select a displacement 2Å above the centroid, called NICS(2), which achieves a reasonable measure of σ/π separation for such complexes. In general, negative values of NICS(2) indicate aromaticity, positive anti-aromaticity, and zero values non-aromaticity. Thus the NICS(2) value for C6h symmetric benzene itself (the archetypal aromatic molecule) is approx. -6 ppm (it depends slightly on the method and basis set used) and for C4h symmetric cyclobutadiene (the archetypal anti-aromatic system) is +85.0 ppm.
We are now ready to analyze some M(acac)3 systems to see whether the fluxional ligand behaviour can be linked with ring aromaticity.
A related species (with a slightly different form of the ligand) has been elegantly shown using NMR techniques to permute ligands by non-dissociative behaviour occurring via two concurrent dynamic processes proceeding through two different transition states.4 The C2v (the Ray-Dutt) geometry is shown to be one true transition state for interconverting Λ/Δ forms. Only one negative force constant is calculated for this system (corresponding to 85i cm-1) and the eigenvectors of this force constant show the correct form for ligand exchange (See Figure 1). At this geometry, the three ligand rings form two groups comprising two and one unique ring. The NICS(2) value for these are respectively 0.2 and 0.05 ppm. All the rings in the Ray-Dutt ligand exchange transition state for Ga(acac)3 are therefore firmly in the non-aromatic class. Transition state aromaticity must play no role in either inducing or suppressing any dissociative ligand behaviour. The D3 symmetric ground state for this complex also shows non-aromaticity (NICS(2) -0.5 ppm), indicating there to be no change on passing from the ground state to the transition state.
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Figure 1. The Ray-Dutt transition state for Ga(acac)3 Λ/Δ interconversion. |
Figure 2. the Bailar transition state for Ga(acac)3 Λ/Δ interconversion. |
The D3h (Bailar) geometry is likewise a true transition state for non-dissociative ligand exchange (with a negative force constant corresponding to 99i cm-1, Figure 2) Here, all three rings are equivalent, and the NICS(2) value is exactly 0.0 ppm. Again, this transition state is non-aromatic.
 Figure 3. The first imaginary vibrational mode for Co(acac)3 showing dissociative behaviour for one ligand. |
 Figure 4. The second imaginary vibrational mode for Co(acac)3 showing Ray-Dutt Λ/Δ interconversion. |
The C2v (the Ray-Dutt) geometry for this metal shows quite different behaviour from its Ga analogue. Two negative force constants are calculated. The more negative of these (corresponding to 981i cm-1) shows the unique ring to be distorting in a manner which corresponds to heterolytic cleavage of that ring; the other two rings show no such dissociation in this mode (Figure 3). The second mode (corresponding to 816i cm-1) is the true Ray-Dutt mode seen for the Ga analogue (Figure 4).
The dissociating ring shows a NICS(2) value of +213 ppm. A strongly positive NICS value is taken to indicate a paratropic ring current, arising from an anti-aromatic ring. The two non-dissociating rings reveal NICS(2) values of -46 ppm. This corresponds to a diatropic ring current, and is associated with strongly aromatic rings. We emphasize again that aromatic rings tend to resist disruption (in this case equated with no dissociation), but the corollary is that anti-aromatic rings, as seen here for one ring, tend to strongly seek disruption. Here this is achieved by Co...O heterolytic dissociation in the anti-aromatic ring only, desymmetrising the overall system. It is also worth noting that the ground state chelate, with D3 symmetry, for which all three rings are equivalent, has a NICS(2) value of -1.2 ppm, in essence non-aromatic. The process of twisting the rings with respect to each other, from D3 to C2v symmetry, converts three non-aromatic rings into two that are aromatic and one which is anti-aromatic. This is in marked contract to the Ga(acac)3 complex, where no change in ring aromaticity occurs when the transition state is achieved.
 Figure 5. The first imaginary vibrational mode for Co(acac)3 showing no dissociation or Λ/Δ interconversion, but instead symmetry reduction to C3h. |
The D3h (Bailar) geometry has different characteristics. Although it only has one negative calculated force constant (corresponding to 39i cm-1), this corresponds to neither dissociative ligand behaviour, nor to the Bailar mode of ligand exchange. Instead it indicates the geometry deforms to a lower (C3h) symmetry (Figure 5). The NICS(2) value at any one (equivalent) ring for the D3h geometry is -48ppm, indicating all three rings are strongly aromatic. This aromaticity presumably acts to inhibit ligand dissociation in any of the rings.
These results show that the six membered ring formed between the five atoms of the acac ligand and one metal atom can be classified as either antiaromatic, non-aromatic or aromatic on the basis of the magnetic properties of the ring π electrons. Mnemonics for predicting such aromaticity in a single ring containing such π electrons are very well known, originating from the work of Huckel, and subsequently formulated as the 4n+2 rule.1 However, the theoretical aspects of three such rings joined by a common metal atom (siamese rings) and contributing not one pπ but one or more dπ atomic orbitals to the topology are rather less well understood.5. In particular the relationship between the interaction of the central metal dπ-orbitals and the three individual ligand pπ sets, and how this impacts upon the individual aromaticity (or not) of any of the rings is an interesting problem, deferred for further discussion elsewhere.