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Topic: Molecular orbital theory of He2  (Read 14237 times)

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Offline TBeezee

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Molecular orbital theory of He2
« on: December 26, 2007, 01:31:21 PM »
My apologies for these fundamental questions...

I have recently learned that according to molecular orbital theory (MOT), anti-bonding sigma* 1s shells exist (in terms of potential energy) between bonding sigma 1s and 2s orbitals. This means in other words that the anti-bonding sigma* 1s orbitals are filled before the bonding 2s orbitals. One example I read used this model to illustrate the fact that He2 does not readily exist, explaining that placing electrons in the anti-bonding sigma* 1s orbitals negates the effect of the electrons first placed in the bonding 1s orbitals.

My first question, concerning He2, is: given that the change in energy from non-bonding atomic orbitals of He atoms to the bonding and anti-bonding 1s sigma orbital is the same, is not the net energy the same for bonding the same then compared to non-bonding? In other words, if putting electrons in the anti-bonding sigma* 1s orbitals results in as much negative effect as the positive effect of putting electrons in the bonding sigma orbitals; given that there is an equal number in both is this not the same net energy effect as not bonding at all?
I understand that this would not be ideal for bonding, but surely if that were true, shouldn't there be an equal likelihood of finding bonding and non-bonding He?

My second question is more far-out and perhaps more indicative of my essential lack-of-grasp of the concept of molecular bonding in general... : Why can't an two electrons (one from each He atom) form one bonding sigma 1s orbital, and two others (again one from each) from another bonding sigma 1s orbital? (which would be ideal if it were possible!) Is this the same illogical question as saying why can't two 1s atomic orbitals exist?

Thank you for you time. :)
« Last Edit: December 26, 2007, 03:13:56 PM by Mitch »

Offline Mitch

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Re: MOT!!!!!
« Reply #1 on: December 26, 2007, 01:34:32 PM »
The antibonding orbital is higher in energy than the bonding orbital is lower. Its a subtlety you'll learn later if you continue with Chemistry.

Your last question doesn't make any sense. Its an energetics issue, not a molecule can choose to do whatever it feels like.
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Offline TBeezee

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Re: MOT!!!!!
« Reply #2 on: December 26, 2007, 02:08:51 PM »
Thanks very much for your answer Mitch  :) That first point is subtle!! And actually, it's one that a little annoyingly my text-book hid from me, confusingly showing for the energy diagram for He2 that the change in energy up to the anti-bonding orbital was (albeit positively) the same value for the change in energy down to the bonding orbital.
Anyway, it makes sense now so thanks again.

Is there any chance you could elaborate about the second point?

Offline Rabn

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Re: MOT!!!!!
« Reply #3 on: December 26, 2007, 02:28:56 PM »
In response to your second question...it becomes a matter of what orbitals the atom has available to it. He only has the 1s orbital and so only has enough room to store 2 electrons, in order for diatomic to exist you would have to produce a 2s orbital in odred to fit four electrons.  There is a decent explanation of this here http://mysite.du.edu/~jcalvert/phys/helium.htm. One thing to keep in mind as you consider bonding between atoms is what orbitals the atom has available to it in it's ground state. Those orbitals are the only ones it has to use for promotion, to modify an atoms orbitlas you need to add energy. Energy which it doesn't have naturally.

Offline Yggdrasil

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Re: MOT!!!!!
« Reply #4 on: December 26, 2007, 02:53:09 PM »
if putting electrons in the anti-bonding sigma* 1s orbitals results in as much negative effect as the positive effect of putting electrons in the bonding sigma orbitals; given that there is an equal number in both is this not the same net energy effect as not bonding at all?
I understand that this would not be ideal for bonding, but surely if that were true, shouldn't there be an equal likelihood of finding bonding and non-bonding He?

You are correct that there is no energy penalty associated with a He2 molecule.  However, there is an entropic penalty.  Because you lose entropy by forming one He2 molecule from two He atoms, the overall change in free energy for the formation of He2 is positive and therefore it will not occur.

Offline Mitch

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Re: MOT!!!!!
« Reply #5 on: December 26, 2007, 02:53:24 PM »
To answer the 2nd part...

There is a rather famous Chemist, named Pauling, who discovered that for every electron in a molecule or an atom it will have its own very unique set of quantum numbers that describe it completely. No, electron will have the same quantum numbers as an other electron.

For the sigma bonding in He2: There is one electron in the bonding sigma bond with a quantum number that we say is spin up, and an other electron in the bonding sigma bond with a quantum number we say is spin down.

If He2 could make an other bonding sigma bond with its 1s orbitals, than those electrons would have the same quantum numbers as those already used to make the original bonding sigma bond and violate quantum mechanics.

This is all well summarized as the Pauli exclusion principle: http://en.wikipedia.org/wiki/Pauli_exclusion_principle
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Offline Mitch

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Re: MOT!!!!!
« Reply #6 on: December 26, 2007, 03:00:31 PM »
As you can see in Chemistry there are many ways to rationalize phenomena. So far we have Rabn's adherence to MO energetics, Yggdrasil's use of entropy (but H2 would be a good counter argument), and Mitch's use of a basic quantum mechanics principle.
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Offline Yggdrasil

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Re: MOT!!!!!
« Reply #7 on: December 26, 2007, 03:17:01 PM »
In the case of H2, the enthalpic gain from bond formation outweighs the entropic loss so you overall have a negative change of free energy for bond formation.  In addition, if you consider free energy, you can explain why chemical bonds cannot exist above certain temperatures.

Offline Rabn

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Re: Molecular orbital theory of He2
« Reply #8 on: December 26, 2007, 03:38:15 PM »
For He2, using the Delta G argument, it is not only the negative  delta S, but also the positive delta H,due to the energy necessary to promote the four electrons to the 2s orbital, that contributes to the lack of spontaneity...What tends to happen is that each explanation is equivalent when reduced to root issue which is that of energy, it is an interesting game that can be played with all of these equalities.

Offline FeLiXe

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Re: Molecular orbital theory of He2
« Reply #9 on: December 28, 2007, 04:46:31 AM »
by the way:
the weak bond in He2 is caused by van der waals dispersion forces. to understand those you can not look at independent MOs but you have to consider how electrons affect each other dynamically. if you go beyond MO theory and do correlated computations, you will find that electrons move away from each other, causing what is called induced  dipole moments
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Offline TBeezee

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Re: Molecular orbital theory of He2
« Reply #10 on: January 02, 2008, 04:06:16 AM »
Thanks to all for your helpful answers (thumbs up) :) I'll be chewing these things over for quite a bit I imagine, but in any case, I am most appreciative!!

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