[Enthalpy]

I've made pictures of compounds known to exist, grouped as (A) unsaturated (B) saturated linear and cycles (c) saturated polycycles.

Incidentally, some would be interesting as rock... oh, you guessed  :

• Guanidine recomposes without soot, well-known
  
• Bis(dimethylamino)metane (Sigma-Aldrich, Cole-Parmer. Measured heat of formation? Longer chain?), azetidine and C₆H₈N₄ as energetic fuels
• Tetrakis(dimethylamino)ethene as pyrophoric igniter with liquid oxygen? At RT it reacts with air.
• C₆H₈N₄ as hypergol with N₂O₄?

Hexamine and C₆H₈N₄ result from formaldehyde reacting with ammonia or ethylene diamine ("Ethyleneamines" by Huntsmann p32, what amount?), something miraculous to me.
http://www.huntsman.com/performance_products/Media%20Library/a_MC348531CFA3EA9A2E040EBCD2B6B7B06/Products_MC348531D0B9FA9A2E040EBCD2B6B7B06/Amines_MC348531D0BECA9A2E040EBCD2B6B7B06/Ethyleneamines_MC348531D0CD3A9A2E040EBCD2B6B7B06/files/ethyleneamines_brochure_huntsman_ethyleneamines.pdf

As Anders already suggested, the amines are tertiary, or the carbon that carries them has multiple bonds. Apart from the suggested stability reasons, could it be that splitting into ammonia and an imine during the synthesis hinders geminal polyamines? That would be consistent with existing compounds, and would suggest to synthesize unsaturated compounds as an intermediary step.

[Enthalpy]

Urea-Formaldehyde http://en.wikipedia.org/wiki/Urea-formaldehyde
is an other example where the geminal amines bind easily enough to create a polycondensate.

[Enthalpy]

Geminal positions of tertiary amines stabilize the molecule (sketch appended). If my data is correct and unless I botched something:

• The heat of formation of 2,4-dimethylpentane is known.
• I hand-estimate the monoaza from trimethylamine and triethylamine (-27.3kJ/mol per added -CH₂-) to get -73kJ/mol for ethyldimethylamine, then add -25.4kJ/mol for each -CH₂- and -4.9 for the but-last methyl isomerization.
• The diaza comes from the Crc Handbook of Chemistry and Physics.
• The first aza adds +106kJ/mol, the second +78kJ/mol, indicating a stabilizing interaction of -28kJ/mol.

In a double-check attempt, I deduce the heat of formation of the tetramethyldiaminomethane from its heat of synthesis
http://webbook.nist.gov/cgi/cbook.cgi?ID=C51809&Mask=8#Thermo-React
H₂CO + 2NH(CH₃)₂ -> (CH₃)₂N-CH₂-N(CH₃)₂ + H2O releasing 191kJ/mol (92% yield!)
Interpreting "gas phase" as "all species gaseous", the heats of formation are
-108.6kJ -18.8kJ*2 -241.8kJ per mole
giving -95.4kJ/mol of gaseous tetramethyldiaminomethane, and by misusing at 298K the 32.3kJ/mol vaporization heat, -127.7kJ/mol of liquid tetramethyldiaminomethane. That's quite different from the previous -51kJ/mol, not very credible, and would indicate an even stronger stabilizing interaction. But probably, some reactants or products are liquid.

So while geminal tertiary amines are infrequent, interaction energy wouldn't explain that.

Welcome to double-checkers...
If you have better experimental thermo data about the cited molecules, please tell!
Or credible thermo data about adamantane and hexamethylene tetramine, or about trimethyl-triazinane for instance.

[Enthalpy]

On message #15, I suggested that geminal polyamines are uncommon because they split to an imine and ammonia. It may be already known, and is inspired by geminal alcohols that are uncommon because they split to a ketone or aldehyde and water. This explanation is consistent with the easy synthesis of geminal tertiary amines while primary ones are scarce.

It is also consistent with the stability of urea, guanidine and the like. As the sketch illustrates, if the diaminated carbon has already a double bond, the expulsion of ammonia would create cumulated double bonds, which is energetically unfavourable. A polymer would be unfavourable too as it would contain hydrazines.

I wish I had credible heats of formation for imines and geminal polyamines.

Pushing the similarity with geminal alcohols, where cyclopropanone reacts with water to make the diol because a carbon unfavourably cumulates a small ring ans a double bond, the hypothetical stability of gem-diaminocyclopopane would be a test for this explanation. As on the other sketch, just react dihalocyclopropane with excess ammonia, for instance as warm gases.

Exaggerating further, the hypothetical hexaaminocyclopropane might be interesting for rockets. With H=4×C, it would need little additional hydrogen (mix with a guanidine) to decompose without soot and produce heat, and may also burn efficiently in oxygen.

Marc Schaefer, aka Enthalpy

[Enthalpy]

More heats of formation for zero, one or two amines at the same carbon: acetone, acetamide and urea. All gaseous at +298°C at least in figures.

This time primary amines replace primary carbons, and the common carbon makes a carbonyl. The replacement releases heat here, the second one less so.

[Enthalpy]

Nist has narrowed the range of heat of formation for adamantane and hexamine
http://webbook.nist.gov/cgi/inchi?ID=C281232&Mask=2#Thermo-Condensed
http://webbook.nist.gov/cgi/inchi?ID=C100970&Mask=2#Thermo-Condensed
from that, geminal tertiary N replacing CH add +79kJ/mol each.

The effect of one single tertiary N replacing CH is +97kJ/mol with data from the CRC Hdbk of Chem & Phys.

The heat of fusion and vaporization is nearly the same for an alkane and the homologue tertiary amine, so comparing liquid and solid pairs is legitimate.

Like in Replay #17, geminal positions reduce the heat of formation of ("stabilize" if you wish) tertiary amines.

[Enthalpy]

Tris(dimethylamino)methane HC(N(CH₃)₂)₃ or CN(C)C(N(C)C)N(C)C has three (tertiary) amines on one carbon, hence is a geminal triamine
http://www.sigmaaldrich.com/catalog/product/aldrich/221058
https://en.wikipedia.org/wiki/Tris(dimethylamino)methane

Despite being saturated, it decomposes already at +150°C into an alkene and the unfavourable dimethylamine. Would someone see its heat of formation? This compound might be a decent rocket fuel - or a similar one, possibly with a methyl at the central carbon. Thanks!

Marc Schaefer, aka Enthalpy

[Enthalpy]

And the tetrakis has been known since 1966:
Preparation http://pubs.acs.org/doi/abs/10.1021/ja00964a071
Pyrolysis http://pubs.acs.org/doi/abs/10.1021/jo01286a107
plus 1000 hits at google with "Tetrakis(dimethylamino)methane", including Houben-Weyl.

It too decomposes around +150°C to dimethylamine and a tar, so it may have a good heat of formation as a rocket fuel. Dissolve some in (methylated?) tri(dimethylamino)methane to raise the flash point and depress the melting point?

Marc Schaefer, aka Enthalpy