Which of the following complexes are diamagnetic? (1) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4}\) (2) \(\left[\mathrm{Cr}(\mathrm{CN})_{6}\right]^{3-}\) (3) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}\) (4) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\) (a) \(1,2,3\) (b) \(2,3,4\) (c) \(1,2,4\) (d) \(1,3,4\)

Electron configuration is critical for understanding the magnetic properties of coordination complexes. The electron configuration of an atom describes the distribution of electrons among its various orbitals, including the d orbitals which are of particular interest in transition metals. Transition metal ions can lose different numbers of electrons and form various charged species when they become part of coordination complexes.

For example, in a complex like \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}\), the iron ion is in the +2 oxidation state (since cyanide is a -1 ligand and there are six of them). To determine the electron configuration of iron in this state, consider the atomic number of iron (26) which normally would have 26 electrons, but as Fe²⁺, it would have 24 electrons. The configuration of these electrons will determine the magnetic properties of the complex.

Understanding the initial electronic configuration of the metal ion before ligand interaction, and then re-configuring it after forming a complex, is pivotal for the subsequent prediction of magnetic properties using crystal field theory.

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electronic orbitals in transition metal complexes due to the presence of ligands. CFT explains how the energy levels of the d orbitals split into two distinct levels, with certain orbitals becoming higher in energy relative to others.

The Splitting of D Orbitals

As a simple model, in an octahedral complex, CFT predicts the splitting of the five degenerate d orbitals into two groups: three lower-energy t2g orbitals and two higher-energy e_g orbitals. This split is called the crystal field splitting, and the energy difference between the t2g and e_g orbitals is known as the crystal field splitting energy. Ligands like CN^- are considered strong field ligands and cause a large splitting.

Electrons will fill the t2g orbitals first according to Hund's Rule, to minimize repulsion, before populating the e_g orbitals. A large splitting energy can lead to pairing of electrons in the lower t2g orbitals before they occupy the higher e_g orbitals, which is key to determining if a complex is diamagnetic or not.

D orbitals play a central role in the electronic structures of transition metal complexes. Transition metals have five d orbitals denoted as d_xy, d_xz, d_yz, d_x²-y², and d_z². In complexes, these orbitals can be filled with up to ten electrons total.

In a scenario where the ligand field causes a substantial splitting of the energy levels of these orbitals, we might see all electrons are paired in the lower energy orbitals. That's a key indicator that a complex is likely diamagnetic, as in the case where there are no unpaired electrons.

When solving problems involving the prediction of magnetic behavior, it is important to sketch the d orbital diagrams showing electron placement and pairing. This visual representation can assist in understanding whether electrons are unpaired, which would result in paramagnetic behavior, or paired, which would lead to diamagnetic behavior. The step-by-step solution process elaborates on this by indicating that the electron configurations must be carefully determined to see if all electrons are paired, hence resulting in a diamagnetic complex.