Question

Draw the crystal-field energy-level diagrams and show the placement of electrons for the following complexes: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-},\) (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) | (a high-spin complex) \((\mathbf{c})\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{3+}\) (a low-spin complex), \((\mathbf{d})\left[\mathrm{NiCl}_{4}\right]^{2-}\) (tetrahedral), ( e) \(\left[\mathrm{PtBr}_{6}\right]^{2-},(\mathbf{f})\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\).

Short answer

For the given complex ions, their geometries, d-electron configuration, and crystal-field energy-level diagrams are as follows: (a) \(\left[\mathrm{VCl}_{6}\right]^{3-}\): Octahedral, d² \[ \uparrow\downarrow \quad _{ (t_{2g)} }\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\quad\uparrow\quad_{e_g} \] (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\): Octahedral, high-spin d⁵ \[ \uparrow\downarrow \quad _{ (t_{2g)} }\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\quad\uparrow\quad\uparrow\quad_{e_g} \] (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{3+}\): Octahedral, low-spin d⁶ \[ \uparrow\downarrow \quad _{ (t_{2g)} }\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\downarrow\quad_{e_g} \] (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\): Tetrahedral, d⁸ \[ \uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\quad_{t_{2}} \] (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-}\): Square planar, dsp² \[ \uparrow\downarrow\quad\uparrow\downarrow\quad_{d_{x^2 - y^2}}\quad \uparrow\downarrow\quad_{d_{z^2}} \] (f) \(\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\): Octahedral, d¹ \[ \uparrow\downarrow\quad\uparrow\quad_{(t_{2g)}} \]

Step-by-step solution

For each complex, find the geometry and d-electron configuration by looking at the central atom and the ligands. The geometry would depend on the number of ligands and their strength. For this exercise, consider the effective atomic number rule, where the ligands are classified as follows: - Non-polarizable, weak field ligands, such as Cl⁻ and F⁻, favor high-spin and tetrahedral geometry. - Polarizable, strong field ligands, such as Br⁻ and (en)bidentate chelating ligand, favor low-spin and octahedral/square planar geometries. Complex (a) \(\left[\mathrm{VCl}_{6}\right]^{3-}\): Geometry: Octahedral d-electron configuration: d². Complex (b) \(\left[\mathrm{FeF}_{6}\right]^{3-}\): Geometry: Octahedral d-electron configuration: High-spin d⁵. Complex (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{3+}\): Geometry: Octahedral d-electron configuration: Low-spin d⁶. Complex (d) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\): Geometry: Tetrahedral d-electron configuration: d⁸. Complex (e) \(\left[\mathrm{PtBr}_{6}\right]^{2-}\): Geometry: Square Planar d-electron configuration: dsp². Complex (f) \(\left[\mathrm{Ti}(\mathrm{en})_{3}\right]^{2+}\): Geometry: Octahedral d-electron configuration: d¹. #Step 2: Draw Crystal-Field Energy-Level Diagrams#

For each complex, draw the appropriate crystal-field energy-level diagram based on the geometry and d-electron count identified in Step 1. Place the electrons in the orbitals according to the energy levels and the electron configuration determined. Complex (a): Octahedral, d² \[ \uparrow\downarrow \quad _{ (t_{2g)} }\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\quad\uparrow\quad_{e_g} \] Complex (b): Octahedral, high-spin d⁵ \[ \uparrow\downarrow \quad _{ (t_{2g)} }\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\quad\uparrow\quad\uparrow\quad_{e_g} \] Complex (c): Octahedral, low-spin d⁶ \[ \uparrow\downarrow \quad _{ (t_{2g)} }\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\downarrow\quad_{e_g} \] Complex (d): Tetrahedral, d⁸ \[ \uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\downarrow\quad\uparrow\quad_{t_{2}} \] Complex (e): Square planar, dsp² \[ \uparrow\downarrow\quad\uparrow\downarrow\quad_{d_{x^2 - y^2}}\quad \uparrow\downarrow\quad_{d_{z^2}} \] Complex (f): Octahedral, d¹ \[ \uparrow\downarrow\quad\uparrow\quad_{(t_{2g)}} \]

Key concepts

d-Electron Configuration

Understanding the d-electron configuration is crucial in the study of transition metal complexes. Transition metals, the elements in the d-block of the periodic table, can have between one to ten electrons in their d subshells. These configurations are fundamental in predicting the chemical and physical properties of coordination complexes.

The number of d-electrons is determined by the oxidation state of the metal and its position in the periodic table. In coordination chemistry, we often ascribe an effective atomic number to the central metal ion, considering not just its own electrons but also those provided by its ligands. The total electron count includes the central metal's d-electrons plus the number of electrons donated by the ligands.

For instance, in a complex where iron has a +3 charge as in \(\left[\mathrm{FeF}_{6}\right]^{3-}\), the d-electron configuration would be high-spin d⁵. The terms 'high-spin' and 'low-spin' refer to the energy gap between different sets of d-orbitals and whether the electrons will pair up in lower energy orbitals or occupy higher energy orbitals singly. Understanding the correct d-electron configuration of a complex enables one to predict magnetic properties, color, and reactivity.

Coordination Complexes

The coordination complexes consist of a central metal atom or ion which is surrounded by molecules or ions known as ligands. The ligands are donors of electron pairs, and their arrangement around the central metal atom is defined by the coordination geometry—common geometries include octahedral, tetrahedral, and square planar.

In the given exercise, the different geometries of the complexes have a profound impact on the d-electron configuration. The type of ligands (whether they are strong field or weak field) and their arrangement can greatly influence whether a complex is high-spin or low-spin. For example, halides like Cl⁻ tend to be weak field and thus favor high-spin complexes, as in \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) with a tetrahedral arrangement. On the other hand, chelating ligands like (en) are strong field and favor low-spin complexes, impacting the overall properties of the complexes such as magnetic behavior and spectroscopic signatures. Coordination complexes are fundamental in many biological systems and industrial processes, making their study essential in both biochemistry and applied chemistry.

Crystal Field Theory

The crystal field theory is a model that describes how the energy levels of d-orbitals are affected by the presence of ligands around the central metal ion in a complex. It explains the electron distribution within the d-orbitals and helps in predicting the magnetic and spectral properties of coordination complexes.

In crystal field theory, the d-orbitals split into different energy levels depending on the geometry of the complex. For an octahedral complex such as \(\left[\mathrm{VCl}_{6}\right]^{3-}\), the d-orbitals split into two sets: the lower energy t_2g and the higher energy e_g. In contrast, for a tetrahedral complex, the energy split is reversed with e_g being lower in energy.

The crystal-field energy-level diagrams are visual tools used to depict this orbital splitting and electron placement, providing insight into the complex's potential reactivity and color. Diagrams like those in the given exercise show at a glance whether a complex will be high-spin or low-spin and the consequent magnetic properties. Moreover, crystal field theory assists in understanding the impact of ligand field strength, which affects whether electrons will pair up in lower energy orbitals or occupy all orbitals singly before pairing.