I read that an electron in a molecular anti-bonding orbital is at a higher energy compared to the atomic orbital than an electron in a bonding orbital however it does not explain why an electron in an anti-bonding orbital is at a higher energy. See attached image.

 

Without going into advanced chemical principles could someone explain why this is the case?

 

Thanks.

If two orbitals interact weakly (so this is an approximation, because bonds are rather strong interactions) their combination, or molecular orbital, can be a sum or a difference of the atomic orbitals.

 

The sum has a bigger volume, the difference a smaller one. The bigger volume means less kinetic energy, which makes the orbital bonding. The smaller volume makes the anti-bonding orbital.

 

In addition (or even the main reason), the uniform phase over both atomic orbitals means also a longer wavelength (as the phase spreads over two atoms) and a smaller kinetic energy, while the opposite phase means a smaller wavelength.