The Organometallic Reader

Dedicated to the teaching and learning of modern organometallic chemistry.

Gee, I’m a Tree: Predicting the Geometry of Organometallic Complexes

with 12 comments

An important issue that we’ve glossed over until now concerns what organometallic complexes actually look like: what are their typical geometries? Can we use any of the “bookkeeping metrics” we’ve explored so far to reliably predict geometry? The answer to the latter questions is a refreshing but qualified “yes.” In this post, we’ll explore the possibilities for complex geometry and develop some general guidelines for predicting geometry. In the process we’ll enlist the aid of a powerful theoretical ally, crystal field theory (CFT). CFT provides some intuitive explanations for geometry the geometry of OM complexes. Here we go!

Because OM complexes feature a variety of coordination numbers, the possibilities for geometry are numerous. The common geometries of organic chemistry—linear, pyramidal, trigonal planar, and tetrahedral—are available to OM complexes too. Many complexes exhibit a second kind of four-coordinate geometry, square planar. Five-coordinate complexes may exhibit either square pyramidal or (my personal favorite) trigonal bipyramidal geometries. Six-coordinate complexes feature either octahedral geometry or the rare but intriguing trigonal prismatic arrangement. The figure below summarizes these possibilities (minus the two-coordinate geometries, which we won’t deal with).

Common geometries of organometallic complexes.

Common geometries of organometallic complexes.

Geometries whose names are colored blue are favored for steric reasons (that is, ligands are as far apart as possible). Geometries colored green may be favored for electronic reasons, and our next task is to understand the meaning behind the cryptic phrase “electronic reasons.” Important questions to keep in mind: what is meant by the term “electronic factors”? When are electronic factors important? And most fundamentally, how do we imagine ligands perturbing the energies of electrons on a metal center?

Let’s return to the primordial analogy of negatively charged, electron-rich ligands flying through space toward an atomic metal cation to form an organometallic complex. Let’s begin with a prescribed geometry…say, square planar. The fundamental tenet of crystal field theory is that, as the negatively charged ligands approach the metal, they will influence the energy of the metallic d orbitals with which they overlap. More specifically, filled ligand orbitals will raise the energy of orbitals with which they most directly overlap. This makes intuitive sense—like charges repel, and d orbitals (which contain negative electrons) should increase in energy when exposed to negatively charged (and/or electron-rich) filled ligand orbitals. Now, let’s imagine the ligands approaching in the xy-plane, along the positive and negative x– and y-axes, to form the square planar geometry. This approach is shown in the figure below, overlaid on images of the d orbitals. White arrows (some of which are omitted to indicate occlusion by the orbital) illustrate the “attack vectors” of the ligands.

Ligands approaching a metal center along the "attack vectors" of the square planar geometry. How can we justify the indicated orbital energy changes?

Ligands approaching a metal center along the "attack vectors" of the square planar geometry. How can we justify the indicated orbital energy changes?

The right half of the diagram shows how the distribution of d orbital energies changes as the ligands approach. Notice that the dx2y2 orbital, whose lobes directly oppose the attack vectors, becomes the highest-energy orbital! This isn’t surprising in light of the ideas of crystal field theory described above. The dxy orbital faces a similar fate, although the overlap is not quite as direct, so its increase in energy is not as severe. Even the dz2 orbital seems to exhibit some overlap via its “donut” lobe. The orbitals completely perpendicular to the xy-plane, the dxz and dyz orbitals, exhibit no overlap with the approaching filled ligand orbitals, and in fact are strongly stabilized by the approaching ligands. A similar analysis can be carried out for the other possible geometries; see this link for the results. I encourage you to try some of the others on your own! The octahedral case is particularly instructive—which two orbitals would you expect to be strongly destabilized by approaching octahedral ligands?

Crystal field theory’s perturbed d orbital sets can be used, in combination with the number of d electrons on the metal center, to predict geometry with a fair degree of accuracy. The key question we need to address is: which arrangement of d orbital energies (that is, which geometry) keeps the d electrons as stable as possible? Let’s explore an example. d8, Pd(II) complexes like (PPh3)2Pd(Ph)Br are ubiquitous in palladium-catalyzed cross-coupling reactions. Two geometries are possible here, and I’ve provided the perturbed d orbital “scaffolds” for each arrangement. Which orbital set holds the 8 d electrons in the more stable way?

Try mentally filling each orbital set with 8 electrons. Which geometry provides the most stability?

Try mentally filling each orbital set with 8 electrons. Which geometry provides the most stability?

We can see that the tetrahedral orbital set would cause significant problems for 8 electrons, as four would end up in the antibonding levels, and two would be unpaired. The square planar orbitals make the best of a bad situation and accommodate one antibonding lone pair, which is well compensated for by the six bonding electrons. Additionally, the energy of the highest occupied orbital is lower overall for the square planar complex. Thus, we should expect the Pd(II) complex to be square planar. Crystallographic studies support this prediction.

The above analysis hinged on an understanding of how approaching ligands influence d orbital energies, and there are a couple of other considerations we need to address to fully flesh out these ideas. First of all, the nature of the ligands influences how extreme the energy perturbations are. More electron-donating ligands, generally, cause more significant energy perturbations. The spectrochemical series can be used to predict the extent of splitting caused by approaching ligands. We’ll leave it at that, but it’s worth keeping in mind that “electronic factors” are more important for some ligands than others. Secondly, the metal’s size influences the relative importance of steric and electronic factors. For d8 nickel(II) complexes, steric factors can be quite important and tetrahedral geometry is often observed. However, tack strongly electron-donating ligands like CH3 on to the nickel(II) center, and all of a sudden, square planar geometry is favored because electronic factors dominate. In cases like this, it can be difficult to predict which factor, sterics or electronics, will dictate geometry.

We’re nearly ready to dive in to a survey of the most common ligands in organometallic chemistry. Before getting there, however, I’m planning on developing a couple of posts related to the molecular orbital theory of transition-metal complexes (including the powerful isolobal analogy). Stay tuned!

Written by Michael Evans

January 10, 2012 at 12:54 pm

12 Responses

Subscribe to comments with RSS.

  1. The images of the d orbitals used in this post were pulled from Mark Winter’s Orbitron website.

    One last useful principle: in general, d10 and d0 complexes exhibit sterically favored geometries, because electronic factors become irrelevant in these cases.

    mevans86

    January 10, 2012 at 12:56 pm

  2. […] repulsion, while the dπ orbitals essentially remain non-bonding. What LFT adds to these CFT ideas is a description of the fate of the remaining unfilled metal valence orbitals and the filled ligand […]

  3. […] let’s consider any electronic factors that may influence the preferred geometry. We’ve already seen that electronic factors can overcome steric considerations when it comes to complex geometry! To […]

  4. […] complexes typically have square pyramidal or distorted TBP geometries. This is just the geometry prediction process in action! TBP geometry is electronically disfavored for d6 metals. Distorted TBP and SP […]

  5. I know this is a bit late, but I am trying to find out what the arrangement of orbitals would look like in an LFT diagram for the two-coordinate geometry. I cannot seem to find it online, do you know what they would look like?

    AMF

    June 29, 2012 at 7:40 pm

  6. ^ I forgot to specify: the d-orbital arrangement

    AMF

    June 29, 2012 at 7:40 pm

  7. “We can see that the tetrahedral orbital set would cause significant problems for 8 electrons, as four would end up in the antibonding levels, and two would be unpaired. The square planar orbitals make the best of a bad situation and accommodate one antibonding lone pair, which is well compensated for by the six bonding electrons. Additionally, the energy of the highest occupied orbital is lower overall for the square planar complex. Thus, we should expect the Pd(II) complex to be square planar. Crystallographic studies support this prediction.”

    I feel uneasy about your explanation of the orbitals that increase in energy here being antibonding orbitals. Can you elaborate?

    Jeff Therrien

    July 4, 2012 at 5:58 pm

    • Jeff—take a look at the “Try mentally filling…” figure. The dotted line indicates the energy of an isolated d orbital (the “nonbonding” energy). Levels above that energy are antibonding, and below that energy are bonding. Within the square planar orbital set, the dz2 orbital is bonding, while the dxy and dx2-y2 orbitals are antibonding.

      If you fill 8 electrons in each of the orbital sets in that figure, you’ll see that the electrons are on the whole more stable in the square planar set, since (a) the HOMO is lower in energy and (b) there are no unpaired electrons present.

      Thanks for reading!

      mevans

      July 4, 2012 at 9:55 pm

  8. Any ideas on how to use CFT to reason for the other splitting pattern for the square planar geometry (i.e. in increasing energy, z^2 < xz, yz < xy < x^2-y^2)? I have been pondering this, but from what I have worked out so far is that it seems that this is one of those things that has us turn to LFT to answer this question. It would seem as though CFT makes the assumption that these "point charges" approaching behave as pi-acids. I feel like CFT is saying "hey, consider ligand effects, but also just think of them as straight up charges" which sounds contradictory. I think of a point charge as something with a fixed size and strength of charge, and that fixed size/charge has been universally applied to all of the geometries to show the splitting patterns. These are just some preliminary thoughts, I am going to check out more of the literature….

    ps. it's fun seeing my comments from over a year ago and noticing how much more I have learned since then

    AMF

    July 19, 2013 at 1:43 am

    • It hit me today: I’ve been confusing the energetics of orbital overlap vs. electrostatic repulsion.

      Figured out the question, but still glad to hear thoughts!

      MAF

      July 19, 2013 at 10:07 pm


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: