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According to the Molecular Orbital Theory, the method to check whether a given compound is paramagnetic or diamagnetic is to draw the molecular orbitals and then to see whether we have all the electrons paired or is there some unpaired electron. However, I want to know, is there a quick way to find the magnetic nature without drawing the orbital diagrams?

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Well, for some compounds it's easy, because there are an odd number of electrons - thus there's no way to pair them all.

Otherwise, there is no quick-fire way without doing the MO diagram.

Consider $O_2$ which has an even number of electrons, but is a ground-state triplet with two unpaired electrons. The only way to know is to look at the MO diagram.

If you practice, you'll realize certain patterns and develop more of an intuition.

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    $\begingroup$ Just a small addition: If you have a completely unsymmetric molecule with an even number of electrons, it is usually a singlet. And then again, a qualitative MO scheme will not really help with compounds with a small HOMO-LUMO gap. $\endgroup$ – Martin - マーチン Sep 16 '14 at 17:38
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    $\begingroup$ To clarify the last bit from @Martin, compounds with small HOMO LUMO gap are tricky because unpaired electrons can go into the LUMO or other low-lying orbitals. $\endgroup$ – Geoff Hutchison Sep 16 '14 at 18:27

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