Which of these ions cannot form both high- and low-spin octahedral complexes: (a) \(\mathrm{Ti}^{3+}\) (b) \(\mathrm{Co}^{2+} ;\) (c) \(\mathrm{Fe}^{2+} ;\) (d) \(\mathrm{Cu}^{2+} ?\)

High-spin complexes occur when the electrons of a transition metal in an octahedral field occupy the higher energy orbitals to remain unpaired. This happens when the energy difference between the high and low orbitals (known as the crystal field splitting energy, \(\text{Δ} \text{_o}\)) is small.
When the crystal field splitting energy is less than the pairing energy (the energy required to pair two electrons in an orbital), electrons prefer to occupy different orbitals to stay unpaired.
Here are some key points to understand high-spin complexes:

• High-spin complexes have a larger number of unpaired electrons.
• They typically form in the presence of weak field ligands (like \( \text{Cl}^\text{-} \) or \( \text{F}^\text{-} \)).
• High-spin complexes are usually paramagnetic due to the presence of unpaired electrons.

An example of a high-spin complex is \( \text{[Mn(H2O)6]}^{2+} \), where \( \text{Mn}^\text{2+} \) in an octahedral field of water ligands has a \(3d^5\) configuration with all electrons unpaired.

Low-spin complexes occur when electrons of a transition metal in an octahedral field prefer to pair up in lower energy orbitals due to a large crystal field splitting energy, \(\text{Δ} \text{_o}\).
When the crystal field splitting energy is greater than the pairing energy, electrons tend to double up in lower energy orbitals rather than occupying higher ones.
Here are some key points to understand low-spin complexes:

• Low-spin complexes have fewer unpaired electrons.
• They typically form in the presence of strong field ligands (like \( \text{CN}^- \) or \( \text{CO} \)).
• Low-spin complexes can be either paramagnetic (if there are unpaired electrons) or diamagnetic (if all electrons are paired).

An example of a low-spin complex is \( \text{[Fe(CN)_6]}^{4-} \), where \( \text{Fe}^\text{2+} \) has a \(3d^6\) configuration with electrons pairing up in the lower energy orbitals.

Electronic configuration is the arrangement of electrons in the orbitals of an atom or ion. It determines the chemical and physical properties of the element.
For transition metals, the electronic configuration is especially important in understanding their behavior in complexes.
Some basic rules to determine electronic configurations include:

• The Aufbau principle: Electrons fill orbitals starting from the lowest energy level.
• Hund's rule: Electrons occupy degenerate orbitals singly first, and then start to pair up.
• The Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

For example, in the problem, \( \text{Ti}^{3+} \) with configuration \( [\text{Ar}] 3d^1 \) has only one electron and cannot exhibit different spin states.
On the other hand, \( \text{Co}^{2+} \) with a configuration \( [\text{Ar}] 3d^7 \) can form both high- and low-spin configurations depending on the ligand field strength.