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When two atomic orbitals make one molecular orbital there must be an antibonding orbital also. Why should they make also an antibonding molecular orbital, such as the $2\mathrm b_2$ orbital in the scheme below?

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Why should they make also an antibonding molecular orbital?

Orbital symmetry must be conserved. Thus, when you mix orbitals, the number of orbitals must also be conserved. As a consequence, when two orbitals are operated on to produce new orbitals, two new orbitals must be created.

Think about it conceptually this way: When two orbitals that have the same symmetry and appropriately matched energy come together, a bonding orbital is formed. This bonding orbital contains all of the "good orbital stuff" from that pair of orbitals. But, because there were two orbitals originally, there has to be "orbital stuff" left over. This leftover "orbital stuff" forms the antibonding orbital.

Now, the screwy part is that orbitals are not real. They are mathematical constructs to describe the wave-like probabilistic properties of electrons. If there are no electrons in the orbital, then the orbital is not really "there". So, while an antibonding orbital is formed, it is not real unless it has electrons in it. In the case of water above, the antibonding orbitals are not populated, so they don't exist.

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  • $\begingroup$ Good answer, except I'd remove your last paragraph entirely. It's not necessary for the OP's understanding, as it really is a philosophical question. What do you think? $\endgroup$ – CHM Nov 21 '12 at 4:58
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    $\begingroup$ @CHM: I think it's better to leave it there -- the fact that orbitals aren't "floating balloons waiting to be filled" can get rid of quite a few misconceptions. It's fine if an answer deviates a bit :) $\endgroup$ – ManishEarth Nov 21 '12 at 6:25
  • $\begingroup$ What I mean is that the "reality" of orbitals has nothing to do with the depiction most high schoolers have of them. To me, they're just as "real" as anything else. I also happen not to agree that they spontaneously come into existence when the atom needs them. It's fine to point out that they're a solution to a mathematical equation, but I wouldn't go beyond that as the matter is a point of debate. $\endgroup$ – CHM Nov 21 '12 at 17:30
  • $\begingroup$ If antibonding orbitals do not exist, what do electrons get excited into when the molecule absorbs uv light? $\endgroup$ – Oscar Lanzi Sep 22 '17 at 13:05
  • $\begingroup$ @OscarLanzi a higher lying, multi electron excited state. At the end of the day, we know from Quantum mechanics that a multielectron state is not going to be describable exactly by a product, or linear combination of products, of one electron states unless you have an infinite number of them. But in that case, the choice of orbitals is basically arbitrary, so we can't say that one set of orbitals is more real than another. $\endgroup$ – Tyberius May 7 '18 at 13:59

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