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Many p-block elements which are the first in their respective groups show $pπ-pπ$ multiple bonding. Why doesn't carbon do so?

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    $\begingroup$ What's wrong with graphite, diamond, fullerenes, and several other carbon allotropes? $\endgroup$ – Nicolau Saker Neto May 10 '15 at 17:03
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    $\begingroup$ ...or all of organic chemistry. $\endgroup$ – ron May 10 '15 at 17:05
  • $\begingroup$ but those are allotropes of carbon. $\endgroup$ – Anoneemus May 10 '15 at 17:06
  • $\begingroup$ @shashikant So? ... They are carbons bonded to other carbons! BTW look at this : {en.wikipedia.org/wiki/Diatomic_carbon} $\endgroup$ – NeilRoy May 10 '15 at 17:11
  • $\begingroup$ @shashikant I believe you are talking about carbon-carbon π bonding. Is it? $\endgroup$ – Rajat Jain May 10 '15 at 17:16
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Okay, I believe that you mean to ask why a $C_2$ molecule does not exist? Well, it does exist. So, when we use molecular orbital theory to calculate the bond order of $C_2$, which is

$$B.O.=\frac{\mathrm{(No.~of~electrons~in~bonding~orbitals) - (No.~of~electrons~in~ antibonding~orbitals)}}{2}$$

We have 4 electrons in bonding and 0 in antibonding for $C_2$So putting in formula-$B.O.=(4-0)/2=2$As the bond order is 2, the molecule cannot exist.

But when a more rigorous approach to MOT is applied, it shows that both the bonds present in the molecule must be π bonds and no sigma bonds must be present. This according to me is not possible.

While Wikipedia also confirms that there is a speculation regarding the structure. It says -

A recent paper by S. Shaik reports that a quadruple bond exists in $C_2$

And hence though the actual molecule has been found, its chemistry is still being studied.

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    $\begingroup$ Actually, the electrons not in the bonding orbitals are in non-bonding orbitals, not anti-bonding orbitals. $\endgroup$ – LDC3 May 10 '15 at 17:27
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    $\begingroup$ $\ce{C2}$ does exist, see here $\endgroup$ – ron May 10 '15 at 17:27
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    $\begingroup$ @Rajat Jain You should edit it again, now it's self- contradictory $\endgroup$ – Mithoron May 10 '15 at 19:09
  • $\begingroup$ In support of ron's comment, we actually have already a question about it on the network: chemistry.stackexchange.com/q/594/4945 $\endgroup$ – Martin - マーチン May 22 '15 at 9:16
  • $\begingroup$ Diatomic carbon does not have a quadruple bond but a double bond. It only exists in the gas phase. $\endgroup$ – Ali Caglayan Jun 10 '15 at 14:57

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