The electrons in the d–orbitals – are they from the metal or the ligands.why?

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Metals. Those d orbitals are what form ligand bonds.

The electrons in the d-orbitals can come from both the metal and the ligands in coordination complexes. The d-orbitals of the metal ion play a significant role in coordinating with the ligands, while the ligands contribute their own electrons to form stable coordination complexes. However, it is important to note that the d-electrons of the metal ion are primarily responsible for forming the coordination bonds and determining the geometry and electronic properties of the complex.

To determine where the electrons come from, you can consider the electron configuration of the metal ion. Transition metals have partially filled d-orbitals in their neutral state, and when a ligand coordination occurs, electrons from the metal's d-orbitals can be used to form the bonding interactions. The ligands, on the other hand, can also contribute electrons to the complex through their lone pairs.

For example, let's consider an example of the complex [Fe(CN)6]4-. The iron (Fe) ion has the electron configuration [Ar]3d^6, indicating that it has six d-electrons available for bonding. The cyanide (CN-) ligand, having a lone pair of electrons, can use its lone pair to form a coordinate bond with the Fe ion. In this case, both Fe and CN- contribute electrons to the d-orbitals to form the coordination complex.

In summary, the electrons in the d-orbitals of a coordination complex can come from both the metal and the ligands, depending on their electron configurations and bonding abilities.