Draw orbital-energy splitting diagrams and use the spectrochemical series to show the orbital occupancy for each of the following (assuming that \(\mathrm{H}_{2} \mathrm{O}\) is a weak-field ligand): (a) \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (b) \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}\) (c) \(\left[\mathrm{FeF}_{6}\right]^{3-}\)

The spectrochemical series is a ranking of ligands based on the field strength that influences the splitting of the metal's d-orbitals. High-field ligands cause a large splitting, while low-field ligands cause a smaller splitting. For the given exercise, \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{F}^{-}\) are considered weak-field ligands, leading to smaller energy differences between the \(t_{2g}\) and \(e_g\) orbitals. The position of a ligand in the spectrochemical series helps predict whether a complex will exhibit a high-spin or low-spin configuration. Weak-field ligands result in a high-spin state, where electrons occupy higher energy levels to minimize electron pairing.

High-spin configurations are usually observed when weak-field ligands are present, as these ligands do not cause much splitting of the d-orbitals. In a high-spin complex, electrons fill the higher energy orbitals (e.g., \(e_g\)) before pairing up in the lower energy ones (e.g., \(t_{2g}\)).
This typically follows Hund's rule, which states that electrons will occupy separate orbitals with parallel spins as much as possible. In the provided exercise, all complexes with \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{F}^{-}\) ligands are expected to exhibit high-spin configurations. For example:

• For \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\), the 3+ charge on Cr implies a d\textsuperscript{3} configuration, so electrons will occupy three separate \(t_{2g}\) orbitals.
• For \(\left[\mathrm{FeF}_{6}\right]^{3-}\), the 3- charge on Fe implies a d\textsuperscript{5} configuration, resulting in five electrons in all five d-orbitals in a high-spin manner.

Ligand field theory (LFT) explains the effects of ligand bonding on the energies of metal d-orbitals. In an octahedral field, metal d-orbitals split into two sets: \(t_{2g}\) (lower energy) and \(e_g}\) (higher energy). The type of ligand and its position in the spectrochemical series dictate the extent of the splitting. In weak-field ligands, such as \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{F}^{-}\), the splitting is small, leading to high-spin configurations. In tetrahedral fields, the situation somewhat reverses and the d-orbitals split differently, commonly into \(e\) and \(t_{2}\) sets. Applying LFT helps in constructing the orbital-energy splitting diagrams, vital for understanding the electronic properties of complexes.

Determining the electronic configuration involves identifying the central metal ion, its oxidation state, and then writing out its d-electron count. For instance:

• For \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\), Cr is in oxidation state +3, leading to an electron configuration of \(\left[\mathrm{Ar}\right]3d^{3}\).
• For \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+} \), Cu is in oxidation state +2, with an electron configuration of \(\left[\mathrm{Ar}\right]3d^9\).
• For \(\left[\mathrm{FeF}_{6}\right]^{3-}\), Fe has an oxidation state of +3, leading to an electron configuration of \(\left[\mathrm{Ar}\right]3d^5\).

Using these configurations, and considering the weak-field nature of the ligands, we can deduce the high-spin arrangements, where overall minimized pairing energy is preferred over minimizing electronic repulsion within partially filled orbitals.