\(\left[\mathrm{CuCl}_{4}\right]^{2-}\) is green. \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) is blue. Which absorbs higher-energy photons? Which is predicted to have a larger crystal field splitting?

Coordination compounds, also known as complex ions or coordination complexes, are molecules that consist of a central metal atom or ion (usually a transition metal) bonded to one or more ligands. These ligands can be anions, neutral molecules, or cations which donate electron pairs to the metal, forming coordinate covalent bonds.

The structure and properties of coordination compounds are key areas of study in inorganic chemistry because of their relevance in various biological processes, industrial catalysis, and dye manufacturing.

Structure and Nomenclature

In a coordination compound, the number of ligand attachments, known as coordination number, varies typically from two to nine, depending on the size and electronic configuration of the metal center as well as the type of ligands attached. The spatial arrangement of these ligands around the central atom is known as the geometric or coordination geometry.

When naming coordination compounds, the ligands are named first, in alphabetical order, followed by the metal atom/ion. If the complex is an anion, the metal's name ends with the suffix '-ate'.

The d-orbitals in the electron configuration of transition metals can exhibit different energy levels when under the influence of a crystal field, provided by the surrounding ligands in a coordination compound.

These energy differences arise because in a complex, not all d-orbitals are oriented in the same manner with respect to the ligands. Some orbitals face directly towards the ligands, while others are oriented between them. This creates an environment where the d-orbitals experience different degrees of repulsion from the negatively charged electrons in the ligands, leading to a crystal field splitting.

Crystal Field Splitting

Depending on the geometry of the coordination compound, the d-orbitals can split into two groups of differing energy—higher and lower. For example, in an octahedral field, the d-orbitals split into two sets: the higher energy e_g and the lower energy t_2g.

The difference in energy between these two sets is known as the crystal field splitting energy, denoted by Δ. The magnitude of this splitting is influenced by factors such as the nature of the ligands, the charge on the metal ion, and the geometry of the complex.

The concept of color in coordination compounds is fundamentally tied to d-orbital electron transitions. When light hits a coordination compound, photons can be absorbed if their energy matches the energy gap (Δ) caused by the crystal field splitting.

Understanding Color Perception

The color that our eyes perceive is the result of subtractive color mixing. In essence, the compound absorbs certain wavelengths of light from the visible spectrum and reflects or transmits the others. The absorbed light typically corresponds to the energy required for an electron to transition from a lower to a higher d-orbital. The remaining light forms the complementary color, which is actually observed by our eyes.

For instance, if a complex absorbs light primarily in the red region, it will appear green, which is the complementary color of red. This process is also responsible for the colorful nature of many compounds containing transition metals.

Regarding the original exercise, the \(\mathrm{CuCl}_{4}\)^{2-} complex absorbs higher-energy photons (in the blue region, hence having a larger crystal field splitting), which makes it appear green to the eye. On the other hand, the \(\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\)^{2+} complex absorbs photons in the red part of the spectrum, corresponding to a smaller crystal field splitting, and hence it appears blue.