CHEM 4A - Lecture 19: Properties of Coordination Compounds

Crystal Field Theory (CFT)

• Objective: Explains spectral and magnetic properties of transition metal complexes.
• Focus: Nonbonding electrons in the central metal atom/ion.
• Key Idea: Ligands' electrons repel metal's electrons, increasing the energy of affected d orbitals.

Crystal Field Splitting

• Definition: The energy difference between non-degenerate d-orbitals. Denoted as $\Delta<em>{oct}$ for octahedral and $\Delta</em>{tet}$ for tetrahedral complexes.
• Factors Influencing Magnitude:
  • Type of ligand.
  • Number of ligands.
  • Period of the metal.
  • Oxidation state of the metal.
• Weak Field Ligands: Cause small splittings (e.g., halogens, O, or S as lone pair donors).
• Strong Field Ligands: Cause large splittings (e.g., C, N, or P bonding to the metal).
• Ligand Number: More ligands result in greater splitting.
• Metal Period: Higher period leads to increased splitting.
• Metal Oxidation State: Higher oxidation states cause more splitting.

Energy Diagrams and Spin State

• Electron Filling Rule: Electrons individually occupy each orbital before pairing due to repulsion.
• Pairing Energy: Energy required to place two electrons in the same orbital.
• Large Crystal Field Splitting Impact: Electrons pair up rather than being excited to higher energy d-orbitals.
• Low-Spin Complexes: Electrons are paired because of a large crystal field splitting.
• High-Spin Complexes: Feature more unpaired electrons.

d-electron configurations & # of unpaired e- (octahedral complex)

• d1: 1 unpaired electron, Example: Ti3+
• d2: 2 unpaired electrons, Example: V3+
• d3: 3 unpaired electrons, Example: Cr3+
• d4: 4 (high spin), 2 (low spin) unpaired electrons, Example: Mn3+
• d5: 5 (high spin), 1 (low spin) unpaired electrons, Example: Fe3+
• d6: 4 (high spin), 0 (low spin) unpaired electrons, Example: Co3+
• d7: 3 (high spin), 1 (low spin) unpaired electrons, Example: Co2+
• d8: 2 unpaired electrons, Example: Ni2+
• d9: 1 unpaired electron, Example: Cu2+

Examples of Determining Crystal Field Splitting

• Example a): Comparing $[Fe(OH<em>2)</em>6]^{2+}$ and $[Fe(OH<em>2)</em>6]^{3+}$, the latter will have a larger $\Delta_{oct}$ due to the higher oxidation state of iron.
• Example b): Comparing $[Cr(OH<em>2)</em>6]^{3+}$ and $[Cr(NH<em>3)</em>6]^{3+}$, the latter will have a larger $\Delta<em>{oct}$ because $NH</em>3$ is a stronger field ligand than $H_2O$.

Predicting Unpaired Electrons

• $K<em>3[CrI</em>6]$: Chromium (Cr) has a +3 charge. Iodine (I) is a weak field ligand so it will result in high spin. Therefore, There are 3 unpaired electrons.
• $[Cu(en)<em>2(H</em>2O)<em>2]Cl</em>2$: Copper (Cu) has a +2 charge and has 1 unpaired electron.
• $Na<em>3[Co(NO</em>2)<em>6]$: Cobalt (Co) has +3 charge. $NO</em>2$ is a strong field ligand, so the complex is low spin. Therefore, there are 0 unpaired electrons.

Magnetic Moments of Transition Metal (TM) Complexes

• Paramagnetic: Species with unpaired electrons. They are attracted to magnetic fields.
• Diamagnetic: Species with no unpaired electrons. They do not interact with magnetic fields.
• Magnetic Moment (μ) Formula: $\mu = \sqrt{n(n + 2)}$, where n = # of unpaired electrons.
• Complexes & Magnetism: Complexes with same metal ion can be diamagnetic or paramagnetic based on geometry and spin state.

Colors of Transition Metal Complexes

• Color Origin: Crystal field splitting allows absorption of visible light photons if there's a vacancy in higher-energy orbitals.
• Color Determination: The magnitude of crystal field splitting dictates the complex's observed color.

Example problem (Colors of Transition Metal Complexes)

• The octahedral complex $[Ti(H<em>2O)</em>6]^{3+}$ has a single d electron. To excite this electron from the ground state t2g orbital to the eg orbital, this complex absorbs light in the visible region. The maximum absorbance corresponds to $\Delta<em>{oct}$ and occurs at 499 nm. Calculate the value of $\Delta</em>{oct}$ in Joules and predict what color the solution will appear.