We normally talk about transition metal chemistry as being the chemistry of partially filled diorbitals. Diorbitals have two nodal planes and they're very much directional in three-dimensional space and this directionality that diorbitals has has all sorts of consequences for chemistry. So the deorbitals fall into two main classes. They fall into the class of orbital that lies between the axis. So here we have dyz, dxy and dxz. Those orbitals are lying between our set of atomic coordinate axes that we've defined. We have two other orbitals that the z squared orbital and the dx squared minus y squared orbital where those orbitals point directly along the set of axes that we've defined. Now why does that matter? Well it matters because if we're considering an octahedral coordination and normally in transition metal chemistry we will be considering an octahedral coordination of ligands. And then an octahedral coordination of ligands essentially what you've got is a ligand sitting at the top and the bottom at the left and the right of each of these axes. So in the case of these three orbitals the orbitals are pointing between the ligands and in the case of these two orbitals the orbitals are pointing right at the ligands. Right now why is it that transition metals are so conducive, so useful, so frequently found as catalysts? Well one point is their ability to adopt variable oxidation states. The other point that goes hand in hand with this is the ability to form different geometries using those de-orbitals. Those de-orbitals sometimes in combination with other atomic orbitals but frequently the de-orbitals can be arranged in various fashions to get various geometries. So the ones that you've probably encountered will be tetrahedral. So you will have come across examples of tetrahedral transition metal complexes. Most the vast majority actually of transition metal complexes are actually certainly an aqueous solution octahedral. So the by far the most important geometry of transition metal complexes is octahedral and we see a lot of transition metal chemistry driven by a desire if you like to get six ligands in the coordination sphere. So most classical coordination chemistry is octahedral chemistry. Tetrahedral is important under special circumstances and they're quite a few of these special circumstances but certain classes of compound tend to adopt square planar geometries. So the three most important classes of geometry that you find in transition metal in order a guess of importance would be octahedral followed closely by a tie between tetrahedral and square planar. But you have great much greater flexibility in transition metal chemistry. You can, given the right ligand sets, the right metal find all sorts of other geometries. Well how do I predict the geometry of a transition metal compound? In transition metal chemistry you don't have to worry about lone pairs. All that you have to do is arrange the ligands in space around your transition metal to minimize it. Generally in transition metal chemistry just count the ligands and arrange them in space as far apart as possible. So using the kind of skills that you learnt in VSEPR but without a preoccupation for lone pairs. As soon as you start getting beyond six ligands to six ligands, seven ligands, eight ligands, nine ligands, then what you need to, what you would have to have is a large transition metal ion and a small ligand. If you've got large ligands you are not or even medium-sized ligands, you are not going to exceed a coordination number of six. So these are rather exotic species. And there are examples of coordination number eight and coordination number nine but only with very small ligands. The only example of a metal compound I know with a coordination number of nine is Renium. Renium being a larger transition metal ion with nine hydride ligands around it. So the smallest ligand that we can imagine and one of the largest transition metal ions in order to get to these numbers.