Jamie
Mar 15, 2017

Inorganic – Why do MO's = AO's

MO: Molecular Orbital

AO: Atomic Orbital

 

 

The number of MO's formed from AO's totals the number of reacting AO's

 

Example:

2 AO's form 2 MO's – 1 bonding MO & 1 antibonding MO

 

How does this happen?

 

Bonding MO's are formed by constructive interference between AO's and antibonding MO's by destructive interference between AO's.

 

To form both a bonding and antibonding MO this suggests the AO's must be simultaneously constructively and destructively interfering which doesn't make sense.

 

Have I misinterpreted this concept?

1 comment0 replies
k.taee
May 17, 2017

Hi Jamie

You can think of it in terms of the 1st law of thermodynamics - Energy cannot be created or destroyed but is instead converted to different forms. When two AOs come together, you get a lower energetic bonding molecular orbital (MO). This is due to how you two nuclei pulling on the bonding electrons, which stabilizes the electrons. However, if only one lower energy orbital was formed, then this would break the first law of thermodynamics! This is why we say there is also a higher energy anti-bonding molecular orbital ((MO)*) being formed. If stabilization energy E relative to the energy of the AOs (Assuming they are degenerate) then the stabilization energy of the (MO)* would be -E.

So the total energy is now E + (-E) = 0 which is equal to the energy of the AOs (We assumed the orbitals are degenerate and energy stabilsation is relative)

 

To answer the second part, all atoms have an infinite number of energy levels, with the ground state starting from n = 1 up to infinity (essentially to the point of ionisation). In a bonding situation, no. of MOs = AOs and the MO is lower energy as discussed before. In the (MO)*, you have the repulsion between the two atoms as the electrons will occupy outside bonding region which is always higher in energy. This is why (MO)*s have nodes between the atoms.

The interference between AOs accounts for the wave like nature of electrons, but they do not constructively and destructive interfere at the same (Only occurs between AOs then attempt bonding but are perpendicular to each other). They just explain the different relative energies of the MO and (MO)*. By considering repulsions between atoms/electrons and the different interference accounts for the wave-particle duality of electrons.

 

TL;DR - They do not interfere at the same time, rather they possible energetic states the electrons can occupy as they exist already. The AOs = MOs due to the first law of thermodynamics, where the relative stabilisation energy of the MO to the AO (E) must equal the relative destabilisation energy of the (MO)* to the AO (-E), as E + (-E) = 0 (The relative stabilsation energy of the AOs, assuming they are degenerate)

Good web sources for this:

http://www.chemguide.co.uk/analysis/uvvisible/bonding.html

https://www.quora.com/Why-do-antibonding-molecular-orbitals-have-higher-energy-than-bonding-molecular-orbitals

https://ch301.cm.utexas.edu/section2.php?target=imfs/mo/antibonding-orbitals.html

 

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