Hybridization

Background §

• atomic orbitals are purely mathematical constructs
• only genuine wavefunction we know is in one electron system
• orbitals in multi-electron systems are approx
  • atomic orbitals = basis set

Hybridization §

• hybridization: useful mathematical manipulation of orbitals to describe behavior of the second period in Bonds
  • 3 types; $sp$, $s{p}^2$, $s{p}^3$
  • $\pi$ represents hybrid orbitals
  • ex1: $Be{H}_2$ has linear geo, use hybridization to understand
    • basis set: 1s, 2s, 2p
    • valence: 2s, 2p
      • $p_x,p_y,p_z$
    • mix $2s$ and $2p_z$
    • ${\pi }_1(r)=C(-2s-2p_z)$
    • ${\pi }_2(r)=C(-2s+2p_z)$
  • $B{H}_3$
    • trigonal planar geo
    • basis set: $2s,2p_x,2p_y,2p_z$
    • ${\pi }_2(r)={\left(\frac{1}{3}\right)}^{1/2}(-2s)+2(\frac{1}{6}{)}^{1/2}(2p_x)$
      • $s{p}^2$ orbital
    • ${\pi }_1(r)={\left(\frac{1}{3}\right)}^2(-2s)-{\left(\frac{1}{6}\right)}^{1/2}{p}_x+(\frac{1}{2}{)}^{1/2}2p_y$
      • need to use x and y because of angle required
    • ${\pi }_3(r)={\left(\frac{1}{3}\right)}^2(-2s)-{\left(\frac{1}{6}\right)}^{1/2}{p}_x-(\frac{1}{2}{)}^{1/2}2p_y$
  • $C{H}_4$
    • tetrahedral geo
    • basis set: $2s,2p_x,2p_y,2p_z$
      • ${\pi }_1(r)=-\frac{1}{2}(2s+2p_x+2p_y+2p_z)\to$ 109.5 degree angle
  • carbon can be described using $sp,s{p}^2,s{p}^3$ hybridization
    • $C_2{H}_4$
    • $s{p}^2$ hybridization b/c steric number of 3
    • double bond $⟹$ $\sigma ,\pi$ bond together
    • non-hybridized $p$ orbitals bond for $\pi$ bond
    • triple bond example: acetylene