Does CN4 with the following structure exist?

Question

I am a mathematician, not a chemist, so my questions are rather combinatorial. I am intrigued by the possibility of the following binary compound:

$$\ce{\overset{-}{N}=\overset{+}{N}=C=\overset{+}{N}=\overset{-}{N}}$$

which ought to be isoelectronic with carbon suboxide, and thus possibly stable. Does this compound exist, even in interstellar space?

Answer 1

This compound CN$_4$ is a subject of theoretical study, with a theoretically stable structure. Literature on the compound is scant, but this has been considered before and calculated with post Hartree-Fock ab initio molecular calculations.

Stable is a relative term, and I use it here to just mean "has an energy minimum." I have calculated the geometry and charge balance at the CCSD/aug-cc-pVTZ level of theory for this molecule as a proof of concept. In terms of viability in interstellar space, this calculation should represent that closely. It is possible that the transition-state is low enough in energy that even low-temperature vibrations of the molecule could disassociate it quickly. Regardless, to the mathematician this can reasonably be considered stable.

The N=N bond length I calculated was 1.135Å, and the C=N bond length was 1.231Å in my calculations. The partial charges are depicted here:

Answer 2

Although $\ce{CN4}$, called bis(diazo)methane, has not been experimentally observed, it has been investigated theoretically and found to be vibrationally stable.

Structure	Energy	Source	Remarks
	$\pu{499.79 kJ mol^{-1}}$	MolCalc	Non-linear geometry doesn't seem to work
	$\approx -\pu{672 kJ mol^{-1}}$	Reference 1	Bond orders may be incorrect
	$\pu{647.29 kJ mol^{-1}}$	MolCalc	-

Protonated bis(diazo)methane $\ce{HCN4+}$

As investigated by Papakondylis A. and Mavridis A. (2005), the protonated form is also stable.

Structure	Energy	Source	Remarks
	$\approx\pu{-675 kJ mol^{-1}}$	Reference 2	Also isoelectronic to bis(diazo)methane

Isoelectronic Structures

$\ce{CN4}$ belongs to a family of isoelectronic compounds with 34 electrons which have been called pseudohalide ions.$^\text{1}$. I don't fully understand why these were called pseudohalide ions; because halide ions have a complete shell (10, 18, 36, etc.). A few others to mention are:

Name	Compound	Remarks
Carbon Suboxide	$\ce{O=C=C=C=O}$	Known, stable, linear
Dicynamide	$\ce{[N=C=N=C=N]-}$	Known, stable, bent
Pentazenium	$\ce{[N#N-N=N=N]+}$	Known, stable, bent
-	$\ce{[NNBNN]-}$	Unknown, stable (predicted), bent
-	$\ce{[NNONN]+}$	Unknown, stable (predicted), bent
-	$\ce{[NNONN]+}$	Unknown, stable (predicted), bent
-	$\ce{[N#C-N=N=N]}$	Unknown, stable (predicted), bent
Boron trioxide	$\ce{O=B-O-B=O}$	Known, stable, bent

Thus, $\ce{CN4}$ isoelectronic analogs maybe linear, bent, or zig-zag (when the ends are also bent). MolCalc (MP2) shows a linear geometry with a formation energy of $\pu{499.79 kJ mol^{-1}}$.

Further Reading

Perhaps the most extensive study of these structures was carried out by Pyykkö, P and Runeberg, N. (1991)$^\text{1}$ who carried out HF and MP2 calculations with a 6-31G* basis set and found the stable geometries, energies, and vibrational levels of such compounds.

References

1. Pyykkö, P and Runeberg, N. (1991). Ab initio studies of bonding trends: Part 9. The dicyanamide-carbon suboxide-dicyanoether-cyanogen azide isoelectronic series A=B=C=D=E. Journal of Molecular Structure: THEOCHEM, 234, 279-290. 10.1016/0166-1280(91)89018-V.
2. Papakondylis A. and Mavridis A. (2005). J. Phys. Chem. A, 109(29), 6549-6554. 10.1021/jp0580975.
3. Dissertation by Susanne Klein. Quantenchemische Untersuchungen an zweiwertigen E(0)-Verbindungen der 14. Gruppe und deren Analoga der Gruppe 15. Available as PDF.