In VBT, one can understand the example of hydrogen like this - Two hydrogen atoms come closer to each other, and their orbitals overlap, stabilize, and ultimately result in a bond. This is not too difficult to understand, and can easily be visualized and seen in an intuitive manner.

MOT however, is different. Instead of the two orbitals overlapping each other to stabilize the molecule, they both mix together to form a bonding and anti bonding orbitals. Alright, the electrons from both the Hydrogen atoms go into the lowest energy orbital, which is the bonding orbital.

My main doubt however, comes from the electrons of both atoms being SHARED in a covalent bond. When two orbitals overlap in the same phase, they add up to each other (BMO). And when they overlap in opposite phase, they cancel each other (AMBO). So, two hydrogen atoms overlap in the same phase, and they make a bond and so stabilize each other and form a bonding molecular orbital. Wouldn't this mean that both the electrons are shared between the two atoms and hence both their orbitals are filled? Is this a false understanding of how bonds are formed?

Does this have to do with the mathematical equations themselves? They're as of now, too advanced for my course.

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    $\begingroup$ Once you use the AOs to form the MOs, the AOs no longer exist. It is like, if you use two oranges to make two cups of orange juice, the oranges no longer exist (if they do, please tell me the secret so that I can set up an infinite orange juice factory). So it is not particularly useful to think about "both their orbitals are filled" – both their orbitals are no longer things. Once you form MOs, it is just "the bonding MO is filled". And note that the bonding MO is lower in energy than the original AOs, so the process of forming these MOs stabilises the system, i.e. it is a bond. $\endgroup$ – orthocresol May 5 '20 at 5:59
  • $\begingroup$ And if we're taking a look at the individual atom's (in the molecule) electronic configurations, they all will have filled orbitals, right? Like bringing back the orange juice and stuffing them up into the peel of the individual oranges? $\endgroup$ – ChlodiumSoride May 5 '20 at 10:17
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    $\begingroup$ Well, no, not really; it would take four electrons to fill up both the 1s orbitals, and you only have two to play with. It's just that it's more stable for those two electrons to be in a bonding MO, rather than in their own AOs. So the orange analogy kind of ends there, unless we stretch it even further, but it becomes kind of silly. (For example: you could have two half-juicy oranges, and together you could squeeze out one full cup of juice and one empty cup of juice. But you can't stick the juice back into both oranges to make them both full. Oranges = AOs, cups = MOs, juice = electrons) $\endgroup$ – orthocresol May 5 '20 at 10:30

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