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I was recently told that a sigma bond between two $\mathrm{3p}$ orbitals is possible but a $\pi$ bond between the same orbitals is not possible.

Although I was not told the reason, I am speculating that a $\pi$ bond between them is not possible due to a comparatively larger size in comparison to $\mathrm{2p}$ orbital.

Is it the same reason why $\ce{S2}$ does not exist?

Can someone confirm the theory and give reason for the same ?

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    $\begingroup$ Pi bond is not impossible, just very weak. $\endgroup$ – orthocresol May 26 '17 at 12:23
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    $\begingroup$ Can you please edit your question to include a more descriptive title? $\endgroup$ – Berry Holmes May 26 '17 at 12:28
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    $\begingroup$ @Anmol there is diatonic sulfur, en.m.wikipedia.org/wiki/Disulfur. $\endgroup$ – Oscar Lanzi May 26 '17 at 13:50
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    $\begingroup$ Your statement is unclear. Total (that is, integrated all over $\mathbb R^3$) electron probability on a 3p orbital is 1, as it is for 2p or any other orbital. Probability values at particular coordinates are higher at some places and lower elsewhere. $\endgroup$ – Ivan Neretin May 26 '17 at 15:55
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    $\begingroup$ $\ce{S2}$ does exist above 1000K. $\endgroup$ – Pritt Balagopal May 26 '17 at 16:24
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The most common explanation for the poor multiple bonding in 3rd row main group compounds is poor orbital overlap due to the radial node of the 3p orbital.

Since the 2p orbitals have no radial nodes, the lobes can overlap in-phase to form a reasonably favorable bonding interaction. The radial node of 3p orbitals makes it so that when the outermost (most overlapping) parts of 3p orbitals are overlapping in-phase (stabilizing), the part that penetrates into the inner parts are by definition out of phase (destabilizing). Hence the overall interaction is much, much weaker. Bonding through 3p orbitals are much more favorable when they are more end-on than when they are side-on like in multiple bonds. Hence, $\ce{P4}$ is much more stable than $\ce{P2}$ and $\ce{S_2}$ is less stable than larger sulfur cycles.

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