Chapter XI ML₄ and Electron Counting

In this Chapter the MOs for D_4h and T_d ML₄ will be constructed. It will be shown that different electron counts will prefer different geometries. This will lead then to a detailed discussion of electron counting in transition metal complexes.

A. D_4h ML₄

The MOs of this system are easily constructed:

There are again five MOs in the important valence region. One is strongly M-L antibonding and four are nonbonding. The z² MO is the middle member of a three orbital interaction.

Now filling the M-L bonding and nonbonding MOs leads to an electron count of (4x2)+8 = 16 electrons. For ML₆ there were 18 electrons - (6x2)+6 = 18. There is, however a very, very strong relationship between the octahedron important valence orbitals and those in the square planar system. The argument is constructed as follows:

There is actually a series of molecules, where S is the solvent of crystallization which show different Ni-S distances.

This causes different colors and a change in spin states -

The molecule on the left side is called a tetragonally distorted octahedron. In fact there are two ways that this distortion can occur and this is very common when there are 8 electrons in this valence region:

B. The D_4h to T_d transformation

The other very common geometry for an ML₄ molecule is the tetrahedron.

In the d region - the important valence region of 5 MOs there are now two MOs at low energy of e symmetry and three above of t₂ symmetry. The t₂ set is somewhat M-L antibonding, however, not strongly so. This is readily apparent from the two contour plots below for one component of e and t₂ in Ni(CO)₄.

In both MOs CO p* mixes in extensively.

A tetrahedral geometry will be preferred for molecules with the following electron counts:

dⁿ #e's example

d⁰ 8 TiCl₄

d⁴ 12 Cr(NO)₂(NO)₂

d¹⁰ 18 Ni(CO)₄

A square planar geometry is stable for a d⁸, 16 electron complex. At the tetrahedral geometry this electron count leads to a ground state triplet. In fact there are complexes like this as well as singlet square planar geometries. There are very large differences in the M-L bond lengths since the four d MOs in the square plane are nonbonding whereas at the terahedron t₂ is M-L antibonding:

Here are some average M-L bond lengths for d⁸ Ni complexes:

square planar tetrahedral

Ni-N 1.68Å 1.96Å

Ni-P 2.14 2.28

Ni-S 2.15 2.28

Ni-Br 2.30 2.36

There is an increasing need to present a conventional method for counting electrons in these transition metal complexes. We will handle this in the easiest and most informative way, but perhaps one that is treated differently in other places.

C. Electron Counting

There are two separate issues in counting electron for these molecules:

1. Assigning oxidation states - totally artificial

2. Determining the number of electrons brought by the ligands.

The convention that we will use is to treat all ligands as Lewis bases. Then typical ligands that donate two electrons are:

We are only counting the number of s electrons that are donated to the metal. Any p interactions are added on later but are not used for electron counting (this is just the way that the MOs for ML_n complexes are built up). So the electron counting first assigns an oxidation state at the metal:

and then the electron count is simply:

The virtue in using this method is that the d electron count is precisely how many electron are present in what we have labelled the important valence region. The number of d electrons for a neutral metal atom is simply:

Let's work some examples:

1.

2.

3.

4.

5.

For polyene p systems connected to the metal (this is still s-bonding between the metal and the polyene!) The number of electrons donated from the polyene is determined by taking all bonding and nonbonding polyene p MOs and using them as s donors:

For example-

One needs to be a little careful here. The number of electrons given above are correct only if all of the p AOs in the polyene are coordinated to the metal (the metal-carbon distances are <~ 2.3Å). In nearly all organometallic complexes the count does not exceed 18 electrons. Therefore, if the polyene with all carbon atoms connected to the metal would give an electron count greater than this, then the polyene instead distorts, bends away from the metal to a lower coordination number. So it is important to specify how many carbons are in fact coordinated to the metal. This is called the hapto number. It is abbreviated by h^x where x = the number of carbon atoms connected (bonded) to the metal. Here are some examples of molecules that really exist:

The last little bit of electron counting formality is how to handle metal-metal bonds. Basically this is the same as handling carbon-carbon bonds, i.e.

Here are some transition metal examples:

1.

2.

3.

Notice that it does not matter how the CO is treated:

4.

A d³ complex can only make metal-metal triple bond!

We found that complexes (organometallic, low spin ones) are stable with 18 or 16 electrons. How can one tell and why is there a difference? Let us use a generalized interaction diagram like we have done a couple of times before for the AH_n molecules:

So filling all bonding and nonbonding MOs will put 2[n+(9-n)] = 18 electrons. But this scheme is correct only if the ligands are put around the transition metal in a spherical way. In a trigonal ML₃ or square-planar ML₄ complex all of the ligands are in a plane so there is an empty p AO orthogonal to this plane which cannot mix with any of the L s-donor orbitals.

The p AO is left nonbonding but it is at a very high energy for normal transition metals and, therefore, it is not energetically favorable to fill it. Consequently trigonal ML₃ or square-planar ML₄ complexs have two less (16 elctrons) since this AO is not filled. Linear ML₂ molecules wqill have two p AOs as shown above so they are stable at 14 electrons.