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What are homoleptic complexes?

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Hint: Homo is used as a prefix that means “throughout same” and the word homoleptic is used in inorganic chemistry to define a class of transition metal complexes having the same type of ligands attached to the metal atom.

Complete answer:
Transition metals are metals that belong to the d-block of the periodic table and have partially filled d-orbitals. These transition metals form coordination compounds by accepting pairs of electrons in their valence shell orbitals from Lewis bases (electron-donating species). The ions or molecules which act as a Lewis base and bind to transition metals to form coordination complexes are called ligands.
The ligands attached to a central metal atom can be either all the same or different. When all same ligand atoms are attached to a metal atom in a coordination complex then such compounds are known as homoleptic complexes. The prefix homo here means all the same ligands.
When at least one or more than one ligand attached to the central metal atom is of a different type then such complex compounds are known as heteroleptic complexes. Hetero means different.
To get a better understanding of these two types of complexes, let’s look at their examples.
Example of Homoleptic complex: Tetracarbonyl nickel, \[\left[ \text{Ni}{{\left( \text{CO} \right)}_{4}} \right]\], constitutes nickel as a central atom attached to four same carbonyl groups. Thus, it is a homoleptic complex.
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Example of Heteroleptic complex: Tetraaminedichloro cobalt (III), ${{\left[ \text{Co}{{\left( \text{N}{{\text{H}}_{3}} \right)}_{\text{4}}}\text{C}{{\text{l}}_{2}} \right]}^{+}}$, constitutes cobalt as a central atom attached to four amino groups and two chlorine atoms. Thus, it is a heteroleptic complex.
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Note:
There is a term known as ‘polynuclear complexes ‘which is used to refer to coordination complexes having two metal atoms attached to ligands. However, it can also be a heteroleptic complex if at least one of the ligands attached to metal atoms is different from the other.