How to determine coordination number in transition metal complexes?

In undergraduate courses, it ends to be either octahedral, tetrahedral, or square planar geometries, which can only have coordination numbers of #6#, #4#, or #4# respectively...

In general we classify the transition metal complexes by the number of #bbd# electrons that enter the crystal field orbitals.

Since they have significant metal character, we just approximate them as metal #d# orbitals in the splitting diagram, and say we have a "#bb(d^n)# complex".

COORDINATION NUMBER 4: TETRAHEDRAL

This is common with #d^8# complexes that contain small central atoms like #"Ni"^(2+)# (or sometimes #d^10# complexes, like with #"Cu"^+#).

Also, boron can form tetrahedral fluorides, and manganese also form tetrahedral oxides. The above examples are tetrafluoroborate, permanganate, nickel tetracarbonyl, and tetrakis(pyridine)copper(I), respectively.

COORDINATION NUMBER 4: SQUARE PLANAR

This is common with #d^8# complexes that contain large central metal atoms like #"Pd"# and #"Pt"#.

The above examples are cis-diamminedichloroplatinum(II) and tetrachloroplatinate(II), respectively.

COORDINATION NUMBER 5: TRIGONAL BIPYRAMIDAL/SQUARE PYRAMIDAL

This is not very common to see, but trigonal bipyramidal and distorted square pyramidal structures can form with #"Cu"^(2+)# (#d^10#) and #"Ni"^(2+)# (#d^8#). Again, these are rare.

The above examples are pentachlorocuprate(II) and pentacyanonickelate(II), respectively.

COORDINATION NUMBER 6: OCTAHEDRAL

This is the most common geometry, and occurs typically with #d^6# complexes (like #"Co"^(3+)#-based and #"Cr"^0#-based complexes).

Often, these complexes have #18# electrons in the ligand field (2 from each of 6 ligands, and 6 from the metal).

The above examples are tris(ethylenediamine)cobalt(III) and hexanitritocobaltate(III), respectively (the nitro groups are bonded via the nitrogen, not an oxygen).