[Meter]

I'm taking organic chemistry right now, and we have just been introduced to the concept of anti-bonding orbitals. I get that the point of the anti-bonding orbital is to conserve orbitals during bonding, but since orbital theory is just a mathematical concept which maps  the probability of where an electron has the highest chance of existing, the orbitals themselves carry no physical meaning. Why must the model account for conservation of orbitals when it seems equally convenient to just leave them out?

Please explain like I have taken some calc II and linear algebra.

[Babcock_Hall]

I have very little knowledge in this area, but I will try to explain why I think that anti-bonding orbitals are useful, which may or may not be what you are asking.  Consider the series from N₂ to O₂ to F₂.  How does MO theory explain the decrease in bond order?  The other area in which I find anti-bonding orbitals useful is in UV/VIS spectrophotometry.  The absorption of a photon promotes an electron into an anti-bonding orbital.

[Meter]

I have very little knowledge in this area, but I will try to explain why I think that anti-bonding orbitals are useful, which may or may not be what you are asking.  Consider the series from N₂ to O₂ to F₂.  How does MO theory explain the decrease in bond order?  The other area in which I find anti-bonding orbitals useful is in UV/VIS spectrophotometry.  The absorption of a photon promotes an electron into an anti-bonding orbital.

Thanks. That seems like adequate justification.

[Corribus]

I'm not sure I understand the question. If you define a molecule orbital as a linear combination of atomic orbital, then that's how you define it, and the subtractive combination is 50% of the linear combination - it's required by symmetry. In any case there is plenty of experimental evidence that is consistent with the concept of antibonding orbitals, so why would you ignore such an integral part of a theory if it's consistent with observation?

[Enthalpy]

[...] since orbital theory is just a mathematical concept which maps the probability of where an electron has the highest chance of existing [...]

Awawawawawatch!

The electron is a wave. It interacts simultaneously from all the positions covered by the wavefunction.