Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz

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1 Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz

2 ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py) + Ψ 2 pz sp (Ψ 2 s + Ψ 2 px) + Ψ 2 py + Ψ 2 pz

orbitals combine on adjacent atoms. A good example is the carboxylate anion.

energy bonding pi- way, a non- bonding orbital and an antibonding orbital as shown below.

involved, for example the enolate ion or allyl cation.

structures; two electrons from the pi bond and two from the third lone pair on the negatively charge atom).

3 arboxylate anion Resonance hybrid A common situation, and the one many resonance contributing structures describe, occurs when three 2p orbitals combine on adjacent atoms. A good example is the carboxylate anion. When 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- bonding orbital and an antibonding orbital as shown below. This pattern of three molecular orbitals is generally the same whenever three 2p orbitals interact even if there are different atoms involved, for example the enolate ion or allyl cation. There 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 atom). Note the non- bonding orbital contains the electron density of two electrons that are paired, do NT think of it as having one upaired electron on each 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 atoms of the non- bonding orbital explains why the negative charge is localized on the atoms in the carboxylate anion arboxylate anion Resonance hybrid Antibonding orbital Non- bonding orbital π- way orbital

4 Methane Molecular rbital Theory approach to bonding: Just add the individual orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz Valence Bond Theory approach to bonding: ybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz )

5 Ethane Molecular rbital Theory approach to bonding: Just add the individual orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz Valence Bond Theory approach to bonding: ybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz ) + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz )

6 Ethene (Ethylene) Molecular rbital Theory approach to bonding: Just add the individual orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz Valence Bond Theory approach to bonding: ybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz

7 Ethyne (Acetylene) Molecular rbital Theory approach to bonding: Just add the individual orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz Valence Bond Theory approach to bonding: ybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave Ψ 1s + Ψ 1s + Ψ 1s + (Ψ 2s + Ψ 2px ) + Ψ 2py + Ψ 2pz + Ψ 1s + (Ψ 2s + Ψ 2px ) + Ψ 2py + Ψ 2pz

8 ontributing structures arboxylate anion Resonance hybrid Molecular rbital Theory approach to bonding: Just add the individual orbital wave Ψ 1s + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz Valence Bond Theory approach to bonding: ybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave Ψ 1s + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz Sigma (σ) bonding - overlap of hybridized orbitals π-way bonding - overlap of 3 adjacent unhybridized 2p orbitals Ψ 2pz + Ψ 2pz + Ψ 2pz Antibonding Non-bonding Bonding

9 Minor Major ontributing structures 0.8 Enolate anion Molecular rbital Theory approach to bonding: Just add the individual orbital wave Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz + Ψ 1s + Ψ 2s + Ψ 2px + Ψ 2py + Ψ 2pz Valence Bond Theory approach to bonding: ybridize the atomic orbitals on atoms first, then look for overlap with remaining orbital wave Sigma (σ) bonding - overlap of hybridized orbitals 0.2 π-way bonding - overlap of 3 adjacent unhybridized 2p orbitals Resonance hybrid Ψ 1s + Ψ 1s + Ψ 1s + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz + Ψ 1s + (Ψ 2s + Ψ 2px + Ψ 2py ) + Ψ 2pz Ψ 2pz + Ψ 2pz + Ψ 2pz Antibonding Non-bonding Bonding

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