1 VB Theory vs MO Theory

Atomic means single atom, Molecule means multiple combined atoms

• MO Theory
  • Atomic Orbitals combine to form Molecular Orbitals
  • Electrons can occupy the molecular orbitals classified
    {Antibonding, Bonding}
• VB Theory
  • Molecular Orbitals do not exist
  • Molecules consist of Atomic Orbitals and the INTERSECTION of Atomic orbitals classified
    {Sigma-bond, Pi-Bond}

2 MO Theory

Atomic orbitals combine to form Molecular Orbitals .
Linear combination of atomic orbitals(LCAO) is used to calculate MO.

• INPUT:
  • \(\psi_A :: AtomicOrbital\)
  • \(\psi_B :: AtomicOrbital\)
    
• OUTPUT:
  • \(\psi_A + \psi_B=\psi_{bonding} :: MolecularOrbital\)
    
  • \(\psi_A - \psi_B=\psi_{antibonding} :: MolecularOrbital\)

Conservation of Orbitals: If we input n number of Atomic Orbitals we will output n number of Molecular Orbitals.

\[\Psi = \text{e} ^{ \text{i}(kx- \omega t)}~~~(= \cos(kx- \omega t)+ \text{i} \sin(kx- \omega t)~)\]
\[\dfrac{ \text{d} \Psi }{ \text{d} x}= \text{i}k \, \text{e} ^{ \text{i}(kx- \omega t)}= \text{i}k \Psi\] \[\dfrac{ \text{d}^2 \Psi}{ \text{d}x^2}= \text{i}k \, \text{i}k \Psi= -k^2 \Psi\] \[k= \dfrac{p}{ \hbar}~~~~~ \left ( [k]=~ \frac{kg \cdot \frac{m}{s}}{J \cdot s}= \frac{kg \cdot m}{Nm \cdot s^2}= \frac{kg }{kg \cdot \frac{m}{s^2} \cdot s^2}= \frac{1}{m}~ \right )\] \[\dfrac{ \text{d}^2 \Psi}{ \text{d}x^2}= -\dfrac{p^2}{ \hbar^2} \Psi\] \[- \hbar^2 \, \dfrac{ \text{d}^2 \Psi}{ \text{d}x^2}= p^2 \, \Psi\] \[E= E_k+E_p= \frac{p^2}{2m}+E_p \] \[E \Psi= \frac{p^2}{2m} \Psi+E_p \Psi=\frac{p^2 \Psi}{2m}+E_p \Psi=\dfrac{- \hbar^2}{2m} \, \dfrac{ \text{d}^2 \Psi}{ \text{d}x^2}+E_p \Psi \\\]

Orbital geometry AKA electron domain geometry. Hybridization is based on # of electron domains surrounding an atom.
An sp3 hybridized atom mixes s and p subshells ( 1 s and 3 p orbitals) to form 4 equivalent orbitals. These orbitals point at the vertices of a tetrahedron.

3 Categorical chemistry?

• Objects are chemicals wrt protons
  • Isotopes are functors wrt neutrons
  • Ions are functors wrt electrons