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I am trying to understand mechanisms through HOMO/LUMO and am struggling to understand 3 points from a lecture slide I found on the internet:

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Focusing on sigma*(C-F), sigma*(C-O) and sigma*(C-C), I don't know why the energy of sigma* decreases across a period.
Here's my understanding:

the lower the difference between the 2 atomic orbitals, the more stabilized the bonding MO and the higher the energy the antibonding MO is.

With this, I thought sigma(C-C) has a much better stabilization than sigma(C-F), since F has orbitals with much lower energy than C, so the energy difference is much higher when forming the sigma bond.

This is why I think:

the bonding MO energy is like (from lowest to highest): C-C < C-N < C-O < C-F, meaning the sigma(C-F) is the most nucleophilic.

the antibonding MO energy is like (from lowest to highest): C-F < C-O < C-N < C-C, meaning the sigma(C-C) is the most electrophilic.

But this is completely the reverse of what is observed.

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I understand that through pi conjugation (differential extents of e- delocalization by combinations of phases of p orbitals), many more orbitals are formed so HOMO energy is raised and LUMO energy is lowered. But for EWG (withdrawing) and EDG (donating), all I can tell is resonance (EWG: e- delocalization of pi electrons in alkene; EDG: increased e- density of pi electrons in alkene), but I can't relate this to HOMO/LUMO energy.

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I have no idea why protonation lowers BOTH bonding and antibonding orbitals? What I mean is how sigma (O-H) formed (as in carbonyl) lowers the pi(C-O) AND pi*(C-O). My wild guess is: I am adding a proton to O --> increasing its Zeff--> further shifting the e- density to O --> lowering all sigma, sigma*, pi, pi*. (to me it should be of the same explanation as in why sigma*(C-F) is lower than that of sigma*(C-O))

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The energy of molecular orbitals is strongly correlated to the length of the bonds and the electronegativity of the atoms involved.


  • The energy of bonding molecular orbitals decreases as bond length decreases, that means going down a group the bonding orbital to carbon ($\ce{C-X}$) gets higher in energy (more nucleophilic) because of the increase in atomic radius that makes the bond longer. (this is why $\ce{C-H}$ bond is so stable (low in energy), it's a short bond between the $\ce{C}$ orbitals and the small $\ce{1s}$ orbital of $\ce{H}$ that results in a short (=strong) bond)

  • The energy of antibonding molecular orbitals decreases as bond length increases (weaker bond), because longer bond are easier to break. That translates directly into the lowering of antibonding orbitals (easier for nucleophiles to donate into).

Energy Diagram C-Halogen bond MOs


  • The energy of all molecular orbitals decrease as the electronegativity of the atoms involved increases because electrons near electronegative atoms are lower in energy (greater positive charge stabilizes the negatively charged electrons more).

Energy Diagram C-period 2 element bond MOs

  • This also applies to non-bonding orbitals of atoms (this is why $\ce{F-}$ is more stable than $\ce{HO-}$ for example or why carbanions ($\ce{H3C-}$) are extremely unstable compared to the other period 2 elements or why $\ce{N}$ lone pairs are usually more nucleophilic than $\ce{O}$).

Energy Diagram of non-bonding MOs


  • Conjugation increases the energy of the HOMO, while also decreasing the energy of the LUMO. This is because, as you likely know, the double bonds aren't fully localized in conjugated polyenes so the single bonds have some double bond character and the double bonds have more single bond character (longer bond = higher HOMO, lower LUMO) than normal double bonds.

Energy Diagram of polyenes MOs


  • If you replace one carbon atom in a polyene with a more electronegative atom, you get as a result the lowering of all molecular orbitals, so the HOMO is lower (less nucleophilic double bond), but more importantly the LUMO is lower (more electrophilic double bond). This is why epoxidation of $\alpha,\beta$ unsaturated carbonyl compounds is possible with $\ce{H2O2 + NaOH}$ (the nucleophilic $\ce{HOO-}$ adds to the LUMO in a 1,4 fashion, followed by breaking of the weak $\ce{O-O}$ bond by the attack of the enolate). This also applies to conjugated nitriles, nitro compounds and other electron withdrawing groups.

Energy Diagram of butadiene compared to acrolein


  • Lastly, as you figured out, protonation of a carbonyl compounds lowers all molecular orbitals because the positive charge that accumulated on oxygen has a stabilizing effect on the negatively charged electrons involved.

TL;DR

  • Longer bonds are more nucleophilic (bonding orbitals higher in energy);
  • Longer bonds are easier to break (antibonding orbitals lower in energy);
  • Electronegativity correlates with lower orbital energies (greater positive charge from the nucleus, greater stabilization of negatively charged electrons);
  • Conjugation raises HOMO;
  • Conjugation lowers LUMO.

if I made any spelling mistakes or other mistakes please point them out

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