9.3 Molecular Orbital Theory for Coordination Compounds

Molecular Orbital Theory explains bonding in coordination compounds by considering interactions between metal and ligand orbitals. It helps us understand how these interactions affect the complex's structure, stability, and properties.

This theory builds on previous bonding models, offering a more complete picture of electron distribution in coordination compounds. It's crucial for predicting and explaining their magnetic, spectroscopic, and reactivity characteristics.

Molecular Orbital Formation

Ligand and Metal Orbital Interactions

• Ligand group orbitals consist of symmetry-adapted linear combinations (SALCs) of individual ligand orbitals
• Metal d orbitals include five degenerate orbitals ($d_{xy}$, $d_{yz}$, $d_{xz}$, $d_{x^2-y^2}$, and $d_{z^2}$) in isolated metal ions
• Symmetry-adapted linear combinations form from the overlap of ligand and metal orbitals with matching symmetry
• Bonding molecular orbitals result from constructive interference between metal and ligand orbitals (lower energy than constituent orbitals)
• Antibonding molecular orbitals arise from destructive interference between metal and ligand orbitals (higher energy than constituent orbitals)
• Nonbonding molecular orbitals remain unchanged in energy and do not participate in bonding

Orbital Symmetry and Energy Levels

• Symmetry determines which orbitals can interact and form molecular orbitals
• Energy levels of molecular orbitals depend on the extent of orbital overlap and relative energies of constituent orbitals
• Stronger overlap leads to greater energy separation between bonding and antibonding orbitals
• Molecular orbital diagram illustrates the relative energies and electron occupancy of orbitals in a complex

Coordination Geometries

Common Coordination Geometries

• Octahedral complexes feature six ligands arranged around a central metal atom forming an eight-faced polyhedron
• Tetrahedral complexes have four ligands arranged at the vertices of a tetrahedron around the central metal atom
• Square planar complexes contain four ligands arranged in a square around the central metal atom (common for d8 metal ions)

Types of Bonding in Coordination Compounds

• Sigma bonding involves head-on overlap between metal and ligand orbitals along the metal-ligand axis
• Pi bonding occurs through side-on overlap of metal d orbitals with ligand p orbitals perpendicular to the metal-ligand axis
• Delta bonding arises from the overlap of metal d orbitals with ligand orbitals in a unique orientation (rare, observed in some metal-metal multiple bonds)

Factors Affecting Geometry

• Electronic configuration of the metal ion influences the preferred coordination geometry
• Ligand field stabilization energy determines the stability of different geometries
• Steric factors of ligands can impact the adopted geometry (bulky ligands may favor lower coordination numbers)

Electronic Configuration and Properties

Spectrochemical Series and Ligand Field Strength

• Spectrochemical series ranks ligands based on their ability to cause d-orbital splitting ($\Delta_o$)
• Weak-field ligands (I-, Br-, Cl-, OH-) produce small orbital splitting
• Strong-field ligands (CO, CN-, NO2-) generate large orbital splitting
• Ligand field strength affects the electronic configuration and properties of coordination compounds

Spin States in Coordination Complexes

• High-spin complexes form when the energy required to pair electrons exceeds the orbital splitting energy
• High-spin complexes typically have weak-field ligands and more unpaired electrons
• Low-spin complexes occur when the orbital splitting energy surpasses the electron pairing energy
• Low-spin complexes usually involve strong-field ligands and fewer unpaired electrons

Magnetic and Spectroscopic Properties

• Number of unpaired electrons determines the magnetic behavior of coordination compounds
• High-spin complexes exhibit stronger paramagnetism due to more unpaired electrons
• Low-spin complexes show weaker paramagnetism or diamagnetism depending on the number of unpaired electrons
• Electronic transitions between molecular orbitals give rise to characteristic absorption spectra
• Colors of coordination compounds result from d-d transitions and charge transfer bands