Clever chemists pleaase help!! :)

Got a question on polarization and bond stability and energy

What is the actual relationship between how polarized a bond is and how high the energy of its LUMO is and why?

It seems to me that for bonds that are highly polarized, e.g. carbonyl bond C=O, the anti-bonding pi * orbital is of lower energy than say a bond that is slightly less polarized e.g. the C-X alkyl halide anti-bonding sigma * orbital.

And the C-X anti-bonding sigma * orbital seems to be of lower energy than the C-H bond's sigma * orbital, as C-X is more polarized than C-H as a bond.

Anyone know the rationale behind this? Why should a bond being more electronegative result in greater stability and lower energy?

I'm studying about the HOMO-LUMO interactions in nucleophilic substitution by the way

Thanks X

The relative energy of the Antibonding orbital to the atomic orbitals depends upon the energy difference and the extent of orbital overlap. If the energy difference and the overlap is poor, then bonding will be weak.

The antibonding orbital will be only slightly higher in energy than the higher energy Atomic orbital, whereas the bonding orbital will be only slightly lower than the lower energy atomic orbital.

In contrast, for similar energy orbitals, with good overlap, the bonding is much stronger so the bonding to antibonding gap is much larger than the energy difference between the two atomic orbitals. This does not mean the energy gap is greater (bonding-antibonding) is greater for the strongly bonded - similar energy regime.

To be honest, in your example about C=O vs C-X the difference is due to it being a pi* vs sigma*
The sigma* is higher in energy for all these simple cases (sometimes this order is reversed, but rarely), so for that reason only the C-x * is higher in energy.

Sorry I didn't really understand that sentence - could you explain again please? ^




So we're saying that because sigma bonds have greater overlap between atomic orbitals than pi bonds do, the energy gap between bonding and anti bonding will be greater than the energy gap between bonding and anti bonding orbitals for the pi and for that reason the C-x * is greater than the C=O * ?

And thank you, your repsonse was very much appreciated - but I still feel there is much I don't understand on this topic. Take Clayden's explanation as to why elimination rather than substitution occurs:

We can rationalize selectivity for elimination versus substitution or attack of H versus attack on C in terms of hard and soft electrophiles. In an SN2 substitution, the carbon centre is a soft electrophile - it is essentially uncharged and with leaving groups such as halide the C-X sigma * is a relatively low energy LUMO.

Substitution is therefore favoured by nucleophiles whose HOMOs are best able to intereact with this LUMO - in other words soft nucleophiles. ( Now I don't understand this because I thought that soft nucleophiles had high energy HOMOs)

In contrast, the C-H sigma * is higher in energy because the atoms are less electronegative. This coupled with hydrogen's small size makes the C-H bond a hard electrophilic site and a a result nucleophiles favour elimination.

The bits in bold are the bits I really don't understand. Any pearls of wisdom?

Thanks.

Yeah, typo.... take out the 2nd is greater. Should make sense then...

Afraid I am now getting a bit confused with all this contradictory info .... I assume you are 1st year? I'm 3rd year and as such am trying to bring together far more topics. i.e. the MO theory I've been trying to explain. I can rationalise the difference in reactivity from a different angle.... The C-H bond is fairly symmetrical in terms for charge distribution and also coefficients of the MO's.... i.e. the antibonding orbital is fairly equally spread across the bond. In C-X the antibonding orbital is largely localised on the carbon, making it more reactive towards nucleophiles as effective overlap is easier to achieve.

Have you covered Hard-Soft in inorganic yet? It is mostly used in that context, rather than in Organic. Try reading up in your inorganic textbook rather than clayden... (what inorganic textbook do you have btw?)

Ok I'll have a read of my inorganic and then come back to you later on all this - and I have Shriver and Atkins' Inorganic.

Yeah first year and I don't recall it from inorganic but I will do the reading you suggested and see if it sheds any light.

Also yeah sorry to be an idiot but I still don't get that sentence you wrote lol - I thought that you said that being strongly bonded did mean that there would be a greater energy gap between bonding and anti-bonding. Could you clarify?

Thanks a lot.

P.S. Could you recommend any good reads on molecular orbital theory?

Yes, stronger bonds have a greater bonding - antibonding gap.

Look up HSAB theory...

Atkins will have some MO in it.... what edition do you have? I could reference the page if we have the same copy.

The relative energy of the Antibonding orbital to the atomic orbitals depends upon the energy difference and the extent of orbital overlap. If the energy difference and the overlap is poor, then bonding will be weak. The antibonding orbital will be only slightly higher in energy than the higher energy Atomic orbital, whereas the bonding orbital will be only slightly lower than the lower energy atomic orbital.
In contrast, for similar energy orbitals, with good overlap, the bonding is much stronger so the bonding to antibonding gap is much larger than the energy difference between the two atomic orbitals. This does not mean the energy gap is greater (bonding-antibonding) is greater for the strongly bonded - similar energy regime.

To be honest, in your example about C=O vs C-X the difference is due to it being a pi* vs sigma*
The sigma* is higher in energy for all these simple cases (sometimes this order is reversed, but rarely), so for that reason only the C-x * is higher in energy.

The difficulty here is that it is much easier to rationalise energy gaps rather than absolute energies.... I am working largely from transition metal descriptive chem which talks a lot about energy gaps between the HOMO and LUMO.

Yes, the key point here which you've said but I'd like to reinforce, is that the energy of a molecular orbital depends mainly on the atomic orbitals it is made of, not how strongly bonding / anti-bonding it is.

For C-X bonds the relevant X oribtials are the 3s (3p?) orbitals which will be much higher in energy than the O 2p orbitals, creating higher energy bonding and antibonding orbitals.

I'm not convinced it's a particularly useful explanation. Clayden of course knows his stuff, but I get the feeling here that this is a bit of a wishy washy explanation for convenience. The energy calculations behind molecular orbitals are quantum mechanical and difficult,(impossible to do exactly for all but the simplest systems) and I would be surprised as a concept as simple as electronegativity could be used to make accurate predictions about lumo energies!

Yeah, typo.... take out the 2nd is greater. Should make sense then...

Afraid I am now getting a bit confused with all this contradictory info .... I assume you are 1st year? I'm 3rd year and as such am trying to bring together far more topics. i.e. the MO theory I've been trying to explain. I can rationalise the difference in reactivity from a different angle.... The C-H bond is fairly symmetrical in terms for charge distribution and also coefficients of the MO's.... i.e. the antibonding orbital is fairly equally spread across the bond. In C-X the antibonding orbital is largely localised on the carbon, making it more reactive towards nucleophiles as effective overlap is easier to achieve.

Have you covered Hard-Soft in inorganic yet? It is mostly used in that context, rather than in Organic. Try reading up in your inorganic textbook rather than clayden... (what inorganic textbook do you have btw?)

You know what, another point, I've realised all this information is contradictory.

I don't for a second doubt your MO theory is correct, but you say the C-X bond is less symmetrical with more anti bonding charge density on the carbon, making it the more reactive bond relative to the relatively symmetrical C-H *. Now the textbook says the opposite- that the C-H * is higher in energy than the lower energy C-X *.

There must be more factors at play. Annoying. I'm just going to take the textbooks' explanation at face-value and hope some useful informaiton about MO theory surfaces at some point to explain all this.

Cheers

It isn't antibonding charge..... It is the coefficient of the carbon orbital involved in the antibonding orbital. It is larger for the carbon in a c-x bond than the C-H bond