Solutions to the Schrodinger equation – atomic orbitals

Ψ1s Ψ2s Ψ2px Ψ2py Ψ2pz

Hybridization – Valence Bond Approach to bonding

3 sp (Ψ2s + Ψ2px + Ψ2py + Ψ2pz)

2 sp (Ψ2s + Ψ2px + Ψ2py) + Ψ2pz

sp (Ψ2s + Ψ2px) + Ψ2py + Ψ2pz

A common situation, and the one many resonance contributing O O structures describe, occurs when three 2p orbitals combine on C C adjacent atoms. A good example is the carboxylate anion. When H O H O three adjacent 2p orbitals interact (we add the three 2p orbital wave functions ), three new molecular orbitals are produced; a low energy bonding “pi-way”, a non- O 0.5 bonding orbital and an antibonding orbital as shown below. This Resonance hybrid pattern of three molecular orbitals is generally the same C whenever three 2p orbitals interact even if there are different H O 0.5 atoms involved, for example the enolate ion or allyl cation. There Carboxylate anion are four electrons in the pi system of the carboxylate anion, (you can see this by looking at either of the contributing structures; two electrons from the pi bond and two from the third lone pair on the negatively charge O atom). Note the non-bonding orbital contains the electron density of two electrons that are paired, do NOT think of it as having one upaired electron on each O atom. I know, weird, but remember it is best to think of bonding electrons as waves, not particles. Note the electron density on only the O atoms of the non-bonding orbital explains why the negative charge is localized on the O atoms in the carboxylate anion.

H

C O O 0.5 0.5 Carboxylate anion Resonance hybrid

Antibonding orbital

Non-bonding orbital

“π-way” orbital H

H C H

H Methane

Molecular Orbital Theory approach to bonding: Just add the individual orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz

Valence Bond Theory approach to bonding: Hybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨC1s + (ΨC2s + ΨC2px + ΨC2py + ΨC2pz)

H

C H H

H H H

H C C H

H H Ethane

Molecular Orbital Theory approach to bonding: Just add the individual orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨC1s + ΨC2s + ΨC2px

+ ΨC2py + ΨC2pz + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz

Valence Bond Theory approach to bonding: Hybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨC1s + (ΨC2s + ΨC2px

+ ΨC2py + ΨC2pz) + ΨC1s + (ΨC2s + ΨC2px + ΨC2py + ΨC2pz)

H H

C C H H

H H H H C C H H Ethene (Ethylene)

Molecular Orbital Theory approach to bonding: Just add the individual orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz

+ ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz

Valence Bond Theory approach to bonding: Hybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨH1s + ΨC1s + (ΨC2s + ΨC2px + ΨC2py) + ΨC2pz

+ ΨC1s + (ΨC2s + ΨC2px + ΨC2py) + ΨC2pz

H H C C

H H HC CH Ethyne (Acetylene)

Molecular Orbital Theory approach to bonding: Just add the individual orbital wave functions:

ΨH1s + ΨH1s + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz

Valence Bond Theory approach to bonding: Hybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave functions:

ΨH1s + ΨH1s + ΨC1s + (ΨC2s + ΨC2px) + ΨC2py + ΨC2pz + ΨC1s + (ΨC2s + ΨC2px) + ΨC2py + ΨC2pz

H C C H

O O Contributing C C structures H O H O

O 0.5 Resonance C hybrid H O 0.5 Carboxylate anion

Molecular Orbital Theory approach to bonding: Just add the individual orbital wave functions:

ΨH1s + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz + ΨO1s + ΨO2s + ΨO2px + ΨO2py + ΨO2pz+ ΨO1s + ΨO2s + ΨO2px + ΨO2py + ΨO2pz

Valence Bond Theory approach to bonding: Hybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave functions: ΨH1s + ΨC1s + (ΨC2s + ΨC2px + ΨC2py) + ΨC2pz + ΨO1s + (ΨO2s + ΨO2px + ΨO2py) + ΨO2pz+ ΨO1s + (ΨO2s + ΨO2px + ΨO2py) + ΨO2pz

Sigma ( bonding - overlap π-way bonding - overlap of 3 adjacent unhybridized 2p σ) orbitals of hybridized orbitals ΨC2pz + ΨO2pz + ΨO2pz

O O Antibonding C H O

C O Non-bonding H O C H O

O Bonding C H O O O

C H C H Contributing H C H C structures Minor Major H H

O 0.8 Resonance hybrid C 0.2 H H C

Enolate anion H Molecular Orbital Theory approach to bonding: Just add the individual orbital wave functions:

ΨH1s + ΨH1s + ΨH1s + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz + ΨC1s + ΨC2s + ΨC2px + ΨC2py + ΨC2pz+ ΨO1s + ΨO2s + ΨO2px + ΨO2py + ΨO2pz

Valence Bond Theory approach to bonding: Hybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave functions: ΨH1s + ΨH1s + ΨH1s + ΨC1s + (ΨC2s + ΨC2px + ΨC2py) + ΨC2pz + ΨC1s + (ΨC2s + ΨC2px + ΨC2py) + ΨC2pz+ ΨO1s + (ΨO2s + ΨO2px + ΨO2py) + Ψ O2pz π-way bonding - overlap of 3 adjacent unhybridized 2p Sigma (σ) bonding - overlap orbitals of hybridized orbitals ΨC2pz + ΨC2pz + ΨO2pz O

H C Antibonding O H C

H O C H C H H C Non-bonding H C

H

H O

C H Bonding H C

H