oxidative addition
Imagine a metal complex picking up a molecule the way two hands grab the two ends of a snapped twig. The metal inserts itself into a bond, splitting one molecule into two pieces and keeping both, bonded to itself. In doing so the metal goes up in the world: it gains two new bonds, its oxidation state rises by two, and its electron count climbs by two. This step is called oxidative addition, and it is one of the fundamental moves from which catalytic cycles are built.
Concretely, take a molecule X-Y, which could be hydrogen H-H, a carbon-halogen bond like an aryl bromide, or a silicon-hydrogen bond. A metal complex with a spare coordination site and electrons to give breaks the X-Y bond and binds both X and Y as new ligands. Bookkeeping the change: the metal's coordination number rises by two, its formal oxidation state increases by two (because each new fragment is counted as taking a pair, formally oxidizing the metal), and its valence electron count rises by two. This is why low-valent, coordinatively unsaturated metals are the ones that do it — a 16-electron square-planar d8 complex such as a rhodium(I) or iridium(I) species has both the empty site and the electrons to be promoted to an 18-electron octahedral metal(III). The classic textbook case is Vaska's complex adding hydrogen.
Oxidative addition matters because it is how a catalyst grabs hold of its starting material. In cross-coupling, a palladium(0) complex oxidatively adds into a carbon-halogen bond, capturing the organic fragment so it can be stitched to a partner. In hydrogenation, the metal oxidatively adds hydrogen so it has hydrides to deliver to an alkene. The reverse step, reductive elimination, releases the product and returns the metal to its low oxidation state, closing the loop. The honest caveats are that oxidative addition requires the metal to have both a vacant site and accessible higher oxidation state, and that not every X-Y bond adds the same way — some add cleanly in one concerted step, others go through ionic or radical pathways.
Vaska's complex, IrCl(CO)(PPh3)2, is a 16-electron iridium(I) species. It reversibly adds H2 across the metal to give a six-coordinate iridium(III) dihydride, the oxidation state rising from +1 to +3 and the electron count from 16 to 18.
A metal splits an X-Y bond and binds both pieces, rising by two in oxidation state and electron count.
Oxidative addition needs both an empty coordination site and an accessible higher oxidation state; a metal already at 18 electrons or at its top oxidation state cannot do it without first losing a ligand.