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I am learning molecular orbital in general chemistry. I have come across this question that asks me to show that the Lewis structure of $\ce{O2}$ is actually an excited state when viewed in terms of the molecular orbital energy.(Zumdahl 9th edition, chapter 9, Excercise number 50) The solution book tells me that the Lewis structure of $\ce{O2}$ is an excited state because the two electrons in the $\pi ^*2p$ does not follow Hund's rule(the two electrons there exist in the same $\pi ^*2p$ orbital while leaving the other $\pi ^*2p$ orbital empty.) And it further states that the reason why the two electrons in $\ce{O2}$ Lewis structure are paired is because the Lewis structure of $\ce{O2}$ shows every electron to be paired. But my question here is, why does being paired in the Lewis structure equate to being paired in MO? I mean, when MO is formed, aren't all orbitals reconfigured, and therefore all electrons are also reconfigured?

While I was thinking about this, another question popped out of my mind. Why are the name of MOs like $\sigma$ and $\pi$? Doesn't $\sigma$ and $\pi$ get used when talking about $\sigma$ and $\pi$ bonds? Are $\sigma$ orbitals and $\sigma$ bonds correlated in anyway?

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    $\begingroup$ First things first, learn the difference between an apostrophe " ' ", and a backtick " ` ". The apostrophe is found above the question mark on the keyboard, while the backtick is found to the left of the "1" key. $\endgroup$ – Pritt says Reinstate Monica May 31 '17 at 11:29
  • $\begingroup$ Unfortunately you didn't keep it mind. You typed "I`ll keep that..." Backtick again. You shouldve type "I'll keep that...". $\endgroup$ – Pritt says Reinstate Monica Jun 1 '17 at 6:30
  • $\begingroup$ The reason why I tell you not to use backticks is because it's used to enclose syntaxes that you don't want to be rendered. $\endgroup$ – Pritt says Reinstate Monica Jun 1 '17 at 6:31
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Oxygen can exist in two states, the singlet and triplet state. The triplet state is the ground state whereas the singlet state is the higher energy state. In the triplet state the highest energy electrons are unpaired whereas in the singlet state the highest energy electrons are paired.

Now, take a look at the MO diagrams of both states in Wikipedia. You'll be able to tell that the singlet state does not obey Hund's first rule.

Now lets look at the Lewis diagram for a oxygen molecule:

enter image description here

As you can see, all of the electrons in this diagram are paired. The oxygen represented in the diagram above is an oxygen that has two bonds and two lone pairs. The only MO state that has lone pairs is the singlet state.

Now on to "why does being paired in the Lewis structure equate to being paired in MO?" The reason is that paired electrons in Lewis diagrams represent paired electrons. The concept of paired electrons does not depend whether you are using MO theory or Lewis diagrams. Paired electrons are electrons that are in the same orbital.

Now, the next question. "Why are the name of MOs like σ and π? Doesn't σ and π get used when talking about σ and π bonds? Are σ orbitals and σ bonds correlated in anyway?" Sigma bonds and sigma orbitals refer to the same thing. Molecular orbitals are a way to represent the bonds formed by two atoms.

Sidenote: Mulliken first proposed the sigma, pi, delta notation according to this journal article..

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