Molecular orbital theory explains how atoms combine to form molecules, providing insights into chemical bonding and reactivity. It describes how atomic orbitals merge to create molecular orbitals, where electrons reside in molecules instead of individual atoms.

This theory is crucial for understanding biomolecular structures and interactions. It helps explain protein folding, DNA base pairing, and enzyme function. In bioengineering, it's used to design drugs, engineer enzymes, and develop new biomaterials.

Fundamentals of Molecular Orbital Theory

Principles of molecular orbital theory

• Molecular Orbital (MO) Theory describes electronic structure of molecules combines atomic orbitals to form molecular orbitals where electrons reside instead of atomic orbitals
• Linear Combination of Atomic Orbitals (LCAO) mathematically combines atomic wave functions to create molecular orbitals
• Bonding and antibonding orbitals form when atomic orbitals interact constructively or destructively
• Energy level diagrams visually represent molecular orbital energies and electron occupancies
• Sigma ($\sigma$) orbitals result from head-on overlap of atomic orbitals (single bonds)
• Pi ($\pi$) orbitals form from side-by-side overlap of p orbitals (double and triple bonds)

Construction of molecular orbital diagrams

• Construct MO diagrams:

1. Identify valence electrons and atomic orbitals of constituent atoms
2. Determine molecular symmetry to predict orbital interactions
3. Combine atomic orbitals to form molecular orbitals based on symmetry and energy
4. Fill molecular orbitals with electrons following Aufbau principle and Hund's rule

• Interpret MO diagrams:
  • Calculate bond order using formula $(bonding - antibonding) / 2$ to predict stability
  • Determine magnetic properties based on unpaired electrons (paramagnetic or diamagnetic)
• Examples:
  • Homonuclear diatomics (H₂, O₂, N₂) show symmetrical orbital combinations
  • Heteronuclear diatomics (CO, NO) display asymmetric orbital mixing
  • Triatomic molecules (H₂O, CO₂) involve multiple atomic orbital interactions

Molecular orbitals in biomolecular structure

• Electronic structure of biomolecules shapes protein secondary structures (α-helices, β-sheets) and DNA base pairing
• MO theory explains biomolecular interactions through hydrogen bonding, van der Waals forces, and π-π stacking in nucleic acids
• Spectroscopic techniques utilize MO theory principles:
  • UV-Vis spectroscopy probes electronic transitions between molecular orbitals
  • Fluorescence spectroscopy examines excited state relaxation processes
  • Circular dichroism analyzes chiral molecular structures

Applications in bioengineering molecules

• Frontier Molecular Orbital Theory focuses on HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) to predict reactivity
• Predict molecular reactivity by identifying nucleophilic and electrophilic sites and analyzing redox properties
• Assess stability through resonance structures and concepts of aromaticity and antiaromaticity
• Apply MO theory in rational drug design optimizing drug-target interactions
• Enzyme engineering utilizes MO principles to modify catalytic activity and substrate specificity
• Biomaterials development leverages MO theory to design materials with specific electronic properties