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We know that metals can form complexes with different coordination numbers, but I was told that certain metals have a greater probability to have a certain coordination number.

But I was not able to find any such list that correlates a metal with its most favorable coordination number.

As an example, I guess $\ce{Fe^3+}$ forms complexes with coordination number 6, but can I actually predict the coordination number in a reaction or not?

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Summary of molecular orbital theory for coordination compounds-Ligand Field Theory

Molecular Orbital Diagram can explain what you are looking for. First, you choose the geometries you expected to have with corresponding metal cation and ligands. You need to do this since different complex structures will have different more and less energetic d-orbitals.

Second, do MO diagrams for all geometries, and compare the energies, or more properly, stabilities of compounds. Looking at antibonding interactions with ligands you can even predict which bonds of the ligands are becoming more vulnerable to attack.

Additionally, there are such lists in inorganic chemistry textbooks in general. Ferric ion; for instance, can make stable 7-ligand-complex. However, ligands are also very crucial on this aspect and there is ongoing research, like this one:

8 coordinate ferric ion

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