Geometrical shapes of the complexes formed by the reaction of \(\mathrm{Ni}^{2+}\) with \(\mathrm{Cl}^{-}, \mathrm{CN}^{-}\) and \(\mathrm{H}_{2} \mathrm{O}\), respectively, are (A) octahedral, tetrahedral and square planar (B) tetrahedral, square planar and octahedral (C) square planar, tetrahedral and octahedral (D) octahedral, square planar and octahedral

Ligand field theory (LFT) is critical for understanding the behavior of transition metal complexes. It helps explain the electronic structures, colors, magnetism, and reactivity of these complexes. At the heart of LFT is the idea that ligands, which are molecules or ions that bind to a central metal atom or ion, can split the d-orbitals of the metal into different energy levels. The difference in energy between these levels is called the ligand field splitting energy, denoted by \(\Delta\).

LFT modifies the older, simpler crystal field theory by considering the covalent, or shared, nature of the interactions between the ligands and the metal. Strong field ligands, like \(\mathrm{CN}^{-}\), cause a greater splitting of the d-orbitals. This can result in a low-spin complex where electrons pair up in the lowest orbitals, often leading to square planar or octahedral geometries. Weak field ligands, such as \(\mathrm{Cl}^{-}\), cause less splitting and commonly result in a high-spin complex with unpaired electrons, leading to different geometries like tetrahedrals. The field strength of a ligand affects the distribution of electrons within the d-orbitals, which, in turn, determines the geometry of the complex.

The geometry of a complex ion describes the three-dimensional arrangement of the ligands around the central metal ion. Several factors influence this arrangement, including the number of ligands, their charge, the electronic configuration of the metal ion, and ligand field strength, all crucial aspects of coordination chemistry. The most common geometries observed in complex ions are octahedral, where six ligands are symmetrically arranged around the metal; tetrahedral, with four ligands; and square planar, which involves four ligands in a square arrangement.

In the context of \(\mathrm{Ni}^{2+}\) complexes, \(\mathrm{Ni}^{2+}\) with \(\mathrm{Cl}^{-}\) forms a tetrahedral complex due to the weak field strength of the chloride ligands, allowing the electrons to remain unpaired and occupy more orbitals. With \(\mathrm{CN}^{-}\), a strong field ligand, \(\mathrm{Ni}^{2+}\) forms a square planar complex, pairing the electrons and adopting a geometry that minimizes electron repulsion. Finally, with water ligands \(\mathrm{H}_{2}\mathrm{O}\), the moderately strong field strength leads \(\mathrm{Ni}^{2+}\) to form an octahedral complex, filling the d-orbitals in a way that accommodates the six ligand molecules.

Transition metal complexes consist of a central transition metal ion surrounded by molecules or ions called ligands. These complexes are of immense interest due to their varied applications in catalysis, biological systems, and materials science. One of the intriguing aspects of transition metals is their ability to exhibit different oxidation states and coordination numbers, which contributes to the versatility of the geometries and properties of their complexes.

For example, nickel (\(\mathrm{Ni}^{2+}\)) can form complexes with coordination numbers of four or six, leading to different geometrical shapes. Its electron configuration allows it to pair with ligands of different field strengths to form stable complexes like tetrahedral, square planar, or octahedral, as seen in the exercise with chloride, cyanide, and water ligands.

The choice of ligands not only determines the geometry but also the electronic distribution, overall stability, reactivity, and physical properties of these metal complexes. Therefore, understanding the interplay between the metal ion and its surrounding ligands is central to predicting and explaining the behavior of transition metal complexes.