Molecular Orbitals

Quantum Picture of Chemical Bond §

As 2 $H$ atoms approach each other,

• effective potential energy curve is caused by repulsive forces between nuclei, attractive forces between nuclei and electrons, and repulsive forces between electrons
• lower energy = more stable $⟹$ understanding potential energy is key to understanding molecule
• above picture of two hydrogen atoms can also be interpreted as the merging of wave functions of electrons

• can mathematically calculate effective potential energy using

Born-Oppenheimer Approximation §

• electrons move much faster than nuclei
• assume nuclei are fixed in space when solving Schrodinger’s equation

$$2{\sigma }_u^{\ast }$$

• 2: integer that tracks relative energies for each symetry type
• $\sigma$: descirbes orientation around internuclear axis
  • $\sigma$: cylindrical symmetry
  • $\pi$: $\Psi$ has nodal plane that contains internuclear axis
• $u$: describes inversion symmetry
  • $u$: ungerade, $g$: gerade
• *: node on internuclear axis