## Posts Tagged ‘**number of d electrons**’

## Dissociative Ligand Substitution

Associative substitution is unlikely for saturated, 18-electron complexes—coordination of another ligand would produce a 20-electron intermediate. For 18-electron complexes, dissociative substitution mechanisms involving 16-electron intermediates are more likely. In a slow step with positive entropy of activation, the departing ligand leaves, generating a coordinatively unsaturated intermediate. The incoming ligand then enters the coordination sphere of the metal to generate the product. For the remainder of this post, we’ll focus on the kinetics of the reaction and the nature of the unsaturated intermediate (which influences the stereochemistry of the reaction). The reverse of the first step, re-coordination of the departing ligand (rate constant *k*_{–1}), is often competitive with dissociation.

### Reaction Kinetics

Let’s begin with the general situation in which *k*_{1} and *k*_{–1} are similar in magnitude. Since *k*_{1} is rate limiting, *k*_{2} is assumed to be much larger than *k*_{1} and *k*_{–1}. Most importantly, we need to assume that variation in the concentration of the unsaturated intermediate is essentially zero. This is called the **steady state approximation**, and it allows us to set up an equation that relates reaction rate to observable concentrations Hold onto that for a second; first, we can use step 2 to establish a preliminary rate expression.

(1) rate = *k*_{2}[L_{n}M–◊][L^{i}]

## Ligand Field Theory & Frontier Molecular Orbital Theory

In this post, we’ll begin to explore the molecular orbital theory of organometallic complexes. Some background in molecular orbital theory will be beneficial; an understanding of organic frontier molecular orbital theory is particularly helpful. Check out Fukui’s Nobel Prize lecture for an introduction to FMO theory. The theories described here try to address how the approach of ligands to a transition metal center modifies the electronics of the metal and ligands. The last post on geometry touched on these ideas a little, but we’ll dig a little deeper here. Notably, we need to address the often forgotten *influence of the metal on the ligands—*how might a metal modify the reactivity of organic ligands?

### Ligand Field Theory

The **ligand field theory (LFT)** fleshes out the ideas of crystal field theory with molecular orbital theory concepts. It provides a method for understanding M–L bonding and antibonding orbitals; however, it has been strongly disputed by computational studies in favor of valence bond models that incorporate hypervalency. Still, LFT provides a more complete picture of complex bonding than crystal field theory, so we’ll discuss it here. Furthermore, the portions of LFT under dispute have nothing to do with CFT, so “no harm no foul.” Let’s take a look at the molecular orbitals of a hypothetical octahedral ML_{n} complex to begin hashing out LFT.

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

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).

## Simplifying the Organometallic Complex (Part 3)

So far, we’ve seen how deconstruction can reveal useful “bookkeeping” properties of organometallic complexes: number of electrons donated by ligands, coordination number, oxidation state, and *d* electron count (to name a few). Now, let’s bring everything together and discuss **total electron count**, the sum of non-bonding and bonding electrons associated with the metal center. Like oxidation state, total electron count can reveal the likely reactivity of OM complexes—in fact, it is often more powerful than oxidation state for making predictions. We’ll see that there is a definite norm for total electron count, and when a complex deviates from that norm, reactions are likely to happen.

Let’s begin with yet another new complex. This molecule features the common and important cyclopentadienyl and carbon monoxide ligands, along with an **X**-type ethyl ligand.

The **Cp** or **cyclopentadienyl** ligand is a polydentate, six-electron **L**_{2}**X** ligand. The two pi bonds of the free anion are dative, **L**-type ligands, which we’ll see again in a future post on ligands bound through pi bonds. Think of the electrons of the pi bond as the source of a dative bond to the metal. Since both electrons come from the ligand, the pi bonds are **L**-type binders. The anionic carbon in Cp is a fairly standard, anionic **X**-type binder. The **carbon monoxide** ligands are interesting examples of two-electron **L**-type ligands—notice that the free ligands are neutral, so these are considered **L**-type! Carbon monoxide is an intriguing ligand that can teach us a great deal about metal-ligand bonding in OM complexes…but more on that later. Read the rest of this entry »