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How many different organic structures (from the pure theoretical viewpoint) can be drawed with only 4 (exact) carbon atoms and with/without hydrogen? Polycyclic compounds and bridged compounds are also allowed. Please, name them all as well! :)

Remark: I have drawed the chemical graphs in a piece of paper (the skeletons) and I get 37 graphs (including linear with simple, double and triple bonds, and planar and nonplanar compounds), without geometric isomerism (cis/trans). Is that OK?

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    $\begingroup$ I top out at 23. I'd be curious to see your list. $\endgroup$
    – jerepierre
    Nov 13, 2014 at 18:25
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    $\begingroup$ I think pentavalent carbon is more realistic than some of those: scs.illinois.edu/denmark/presentations/2007/gm-2007-04-17.pdf $\endgroup$
    – DavePhD
    Nov 13, 2014 at 21:05
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    $\begingroup$ There is also cis/trans 2-butene in real world. In theoretical world you could draw cis/trans isomers for some cyclobutenes too $\endgroup$
    – K_P
    Nov 13, 2014 at 21:10
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    $\begingroup$ @Ron Because carbon can bond hydrogens, not just other carbons. $\endgroup$
    – DavePhD
    Nov 14, 2014 at 12:14
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    $\begingroup$ oeis.org/A134818 Here's the latest list, stereoisomers ignored. $\endgroup$
    – Dave Consiglio
    May 25, 2016 at 3:11

2 Answers 2

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Final update, all earlier edits incorporated.

Groundrules: Considering compounds with:

  • only carbon and hydrogen
  • only 4 bonds to carbon

There are 37 isomers without considering trans isomers; 49 when trans isomers are included. Also, many of these compounds seem extremely unstable and therefore unlikely to exist.

Note to self: check back in 20 years and see how many of the unlikely ones have been detected.

enter image description here

Names by row:

  • butane, isobutane
  • but-1-ene, but-2-ene, 2-methylpropene
  • buta-1,3-diene, buta-1,2-diene, buta-1,2,3-triene
  • but-1-yne, but-2-yne, but-1-ene-3-yne, buta-1,3-diyne
  • methylcyclopropane, 2-methylcyclopropene, 1-methylcyclopropene, methylenecyclopropane, methylenecyclopropene, methlycyclopropadiene
  • methylcyclopropyne, methlenecyclopropyne
  • cyclobutane, cyclobutene, cyclobuta-1,2-diene, cyclobuta-1,3-diene, cyclobutatriene, cyclobutatetraene, cyclobutyne, cyclobutenyne, cyclobutadiyne
  • bicyclobutane, bicyclobut-1(3)-ene, bicyclobut-1(2)-ene, bicyclobuta-1,3-diene, bicyclobuta-1,2-diene
  • tetrahedrane, tetrahedrene, tetrahedradiene
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    $\begingroup$ @ron You might want to include a note for posterity that some of these "compounds" are incredibly strained and likely unstable. (This was why I was including ?? marks in my answer.) $\endgroup$
    – Geoff Hutchison
    Nov 14, 2014 at 0:45
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    $\begingroup$ @GeoffHutchison There is a higher than normal barrier to rotation about the 2,3-bond in 1,3-butadiene due to a contribution from the resonance structure with a 2-3 double bond. However, the barrier is still low enough that the s-cis and s-trans forms are generally considered rotamers. $\endgroup$
    – ron
    Nov 14, 2014 at 0:58
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    $\begingroup$ Is it legitimate to refer to cyclobutatetraene and cyclobutadiyne as different compounds, or are they just different resonance structures? Both are just a ring of 4 carbon atoms and no hydrogen. $\endgroup$
    – DavePhD
    Nov 14, 2014 at 15:31
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    $\begingroup$ Cyclobutatetraene?? Are you kidding me? $\endgroup$
    – Pritt says Reinstate Monica
    Jun 2, 2017 at 10:00
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    $\begingroup$ @PrittBalagopal It fits within the stated "ground rules". $\endgroup$
    – ron
    Jun 3, 2017 at 19:59
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How many different organic structures (from the pure theoretical viewpoint) can be drawed with only 4 (exact) carbon atoms and with/without hydrogen?

We could make strict rules like each carbon has exactly 4 bonds and get a specific answer, but this is not reality. There can be lone pair electrons and unpaired electrons. The octet rule is not stictly followed.

$\ce {C_4}$ actually has been observed and is linear.

:C=C=C=C:

$\ce {C_4}$ has been the subject of numerous theoretical and experimetal papers because of its possible occurrence in nebulae. It has been debated whether a singlet linear, triplet linear or rhombic (kite shape) state is the lowest energy state. http://www.sciencedirect.com/science/article/pii/S0009261400005765

Neither the linear nor rhombic states follow the naive rules.

Linear $\ce{C_4H}$ has been observed both in the lab and outer space.

In fact according to the University of Kohn lists Molecules in Space, linear $\ce{C_4H}$ is one of only 61 molecules and molecular ions found in extragalactic space and of only 190 found in the interstellar medium or circumstellar shells as of 2016.

For $\ce{C_4H_2}$ linear butadiyne in known. Cyclobutatriene, cyclobutenyne and tetrahedrene have been ruled out theoretically as not represtenting any actual potential energy local minimum, while similar to $\ce {C_4}$, structures having lone pair or unpaired electrons and not following the octet rule (such as carbenes) have been calculated to represent actual minima. See the following references for theoretical cyclic $\ce{C_4H_2}$ structures:

http://onlinelibrary.wiley.com/doi/10.1002/jcc.540020211/pdf

http://pubs.acs.org/doi/pdf/10.1021/jo060698k

http://pubs.acs.org/doi/pdf/10.1021/jo000941u

In outer space, not only has the usual HCCCCH isomer been found but also $\ce{H2CCCC}$

See Observations of cumulene carbenes, H2CCCC and H2CCC, in TMC-1

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  • $\begingroup$ Yes, I was wondering as well how many of these structures are in fact known from the experimental side... $\endgroup$
    – riemannium
    Nov 15, 2014 at 19:34

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