Chemistry 251A – Problem Set 2 Key

2+ 1. The averaged M–O bond lengths (in Angstroms) in the series of [M(OH2)6] complexes are shown in the Table below:

Metal Distance V 2.127(5) Cr 2.17(2) Mn 2.177(17) Fe 2.128(18) Co 2.11(3) Ni 2.056(11) Cu 2.09(1) Zn 2.10(2)

a. Develop a molecular orbital model that accounts for the trends in the distances.

Because the energy difference between the σ-donor orbitals on the ligands and the d orbitals on the metal decreases as Zeff increases, σ bond strength should increase (and ligand field splitting should increase) moving from left to right across the periodic table. Furthermore, the increase in Zeff moving across the periodic table should lead to a contraction in atomic radius, leading to shorter bonds.

However, deviations from these trends are caused by the weak-field nature of water as a ligand (water is a primarily a σ-donor, but is not a very good one). These complexes are all high spin (at least in cases where there is ambiguity – d4-7). Thus, * 4 5 9 10 the added electron is placed in an antiobonding eg orbital for d , d , d , and d electron configurations, leading to an increase in bond length. This matches the increases seen in the Cr, Mn, Cu, and Zn complexes, respectively.

b. The average deviation from the mean is large for Cr and Cu. The individual symmetry related distances for these complexes are: Cr: 2.327(1), 2.122(1), and 2.052(1) and Cu: 2.222(1), 2.074(1), and 1.964(1). Develop a bond model that accounts for the large differences in the M–O distances.

This can be explained by a Jahn-Teller distortion. Both Cr2+ and Cu2+ octahedral complexes have unevenly populated degenerate orbitals. More rigorously, both 5 2 Cr(II) and Cu(II) have ground states that are degenerate: Eg and Eg, respectively. A first order Jahn-Teller distortion is possible via an Eg normal mode, resulting in D4h symmetry, and so two sets of symmetry inequivalent bond lengths.

Further deviation from this geometry is likely due to a pseudo second-order or seond-order Jahn-Teller distortion wherein a normal mode enables mixing between orbitals that would normally be symmetry forbidden. If you check the crystal structures of these compounds, you will find that they maintain inversion symmetry, and can be considered D2h molecules.

3− 2. The average M–C bond distances (in Angstroms) in the series of [M(CN)6] complexes are shown in the table below.

Metal Distance Ti 2.202(8) V 2.068(1) Mn 1.998(1) Fe 1.934(1) Co 1.89(1)

a. Develop a molecular orbital bond model that accounts for the trends in the distances.

Cyanide is a strong field ligand and all of these complexes are low spin. In hexacyanide complexes, the t2g orbitals are bonding, further population of this orbital will lead to a higher bond order. Going from Ti3+ (d1) to Co3+ (d6), the bond order increases and the M–C bond distance decreases accordingly. It should be noted that this effect is also influenced by improved energy overlap between the d- orbitals and the ligand σ orbitals. Together, these effects more than compensate for the reduced energy alignment between metal and ligand π orbitals.

b. Compare and contrast the absolute differences in the bond distance between the M– O distances in the previous problem and the M–C distances in this problem. What do these bond distances tell you about the nature of the M–L bound in these different sets of complexes?

There are numerous comparisons to be made with these two series: 1. The hexaaquo complexes are high spin while the hexacyanide complexes are low spin. 2. Population of the t2g orbital in the hexacyanide complexes significantly decreases the bond length due to π-backbonding, meanwhile adding electrons to the t2g orbital in the hexaaquo complexes only slightly decreases the bond length, which can be attributed to the change in Zeff. 3. Comparing isoelectronic species, the M–L bond distances are drastically shorter in the hexacyano complexes due a combined effect of greater Zeff and a higher metal ligand bond order.

3. The Fe–C and C–N distances (in Angstroms) in the two isostructural and isomorphous complexes, that is they crystallize in the same space group, are as shown in the table below.

Complex Fe–C C–N Cs2Mg[Fe(CN)6] 1.900(7) 1.138(10)

Cs2Li[Fe(CN)6] 1.926(3) 1.148(5)

Do these bond distances and the infrared stretching frequencies in Problem Set 1 support the postulate that a cyanide ligand is a π-acceptor ligand? Justify your answer.

The Fe–C bond distances indicate that the cyanide ligands are π-acceptors. The Fe3+ complex has a longer bond distance despite having a smaller ionic radius and better energetic matching between the d electrons and the σ-donor orbitals on the ligands. This indicates that the cyanide ligands must be participating in some degree of π- 3+ backbonding as the Fe complex would have less electrons in the t2g orbital, leading to a reduced bond order.

The C–N bond distances are crystallographically indistinguishable, and should not be used as evidence for or against π-backbonding. Because the C-N bond length is influenced by σ-donation, the improved energy overlap of Fe3+ could lead to a lower C-N bond order, regardless of π-effects. If we wanted to read into this a lot, then we could say that it’s strange that the CN vibrations change substantially even as the bond distances remain pretty similar. Outer-sphere effects in these complexes may play some role in these bond distances (we would need to see what sort of interactions occur between Cs/Li/Mg and the nitrogen ligands). This may play a role in the bond distances.

Metallocene Question

(i) The molecular orbital picture for ferrocene is established in Cotton’s book, so I will not go through the nitty gritty of modeling and generating the metal and ligand orbitals. If you have questions about doing this, I would be happy to discuss this in office hours.

This site provides an alternate picture of the MOs of ferrocene: http://www.chemie.unibas.ch/~pc2/2013/ferrocene_MO.pdf

Note that the HOMO is different between the model proposed in Cotton and the model in the provided link. The a1g’ orbital is an orbital of ambiguous character (from a qualitative sense). It contains character from the s and d metal orbitals, as well as the ligand orbitals. Some models have it as weakly bonding, others weakly antibonding. It is probably best represented as a weakly bonding orbital, though the extent of stabilization shown in Cotton’s book likely overestimates its bonding character.

Thus, removing electrons from this weakly bonding orbital could be expected to lead to the observed lengthening of the Fe-C bonds. However, the fact that the frontier MOs of these complexes contain significant metal and ligand character does slightly complicate this assignment of the oxidation state.

The authors of this paper propose an alternate approach in which oxidation of the metal leads to more substantial lowering of the s-orbitals than the d-orbitals,

helping to stabilize the a1g orbital which they assign as antibonding in neutral ferrocene. Thus, as the compound oxidizes, this orbital becomes less anti-bonding (in turn, some ligand-centered orbitals become more bonding). This model also seems to work. I personally find it less satisfying as it requires the assumption that oxidation is almost entirely metal-based when it likely has substantial ligand character also (i.e. the stabilization of s/d orbitals is small).

As I’ve mentioned in office hours, neither answer would be “correct” on the test. As long as your answer addresses some of the challenges and discusses relevant orbitals, then your answer will be accepted.

(ii) The Mn and Cr analogues should be isoelectronic with the iron monocation and dication respectively. Assuming no change in the order of the molecular orbitals, the explanation used in part I translates well to Mn and Cr, with the increase in bond length explained by removal of electrons from weakly bonding orbitals.