In a molecular orbital diagram that shows the bonding of two electrons (like a diatomic molecule), there are sigma and pi bonds, and the sigma and pi antibonds. Here is an example: http://www.westga.edu/~chem/courses/chem410/410_09/sld024.htm I don't understand how to determine where to put the pi and sigma orbitals on the diagram. The order of the different molecular orbitals (the bonding pi and sigma orbitals) are different for different atoms and elements. Is there any way to know the their order other than memorizing them without making sense of them? Thanks in advance.
The simple answer is "No - there is no easy way to make sense of the positions. Any theoretical determination of their values is very complex". But that's not the complete answer. First of all notice that there's an ambiguity almost only when it comes to the relative positions of [itex]1\pi[/itex] and [itex]3\sigma[/itex] (with molecules involving s- and/or p-block elements). The other MOs have pretty well-defined positions that mostly do not change qualitatively relative to each other. So the question filters down to (if I haven't misunderstood you): how do I know if [itex]1\pi[/itex] should lie above or below [itex]3\sigma[/itex]? To this end I suggest a simple rule of thumb that will work in the majority of cases. [tex]E_{1\pi} > E_{3\sigma}[/itex] is [itex]2\pi ^* [/itex] is unoccupied or singly occupied; else (if doubly or more occupied) it is the other way round. Let me also add that in most cases (though not at a grad level spectroscopy course), the instructor will not terribly care about the relative positions of these particular MOs, unless they've specifically lectured about it in class.