Theoretical study of cyameluric acid and related compounds

DFT calculations (B3LYP/6-31G*) have been carried out on the seventeen tautomers of cyameluric acid. The C 3h trioxo tautomer 258 is the most stable. Some energies and absolute NMR shieldings (GIAO) were calculated for 258 and other tri-s -triazines, including cyamelurine and Pauling mystery molecule


Introduction
It is known that the last molecule represented on Pauling's chalkboard (1994, preserved to this day by his friends) was the azide derivative 1 1,2 of tri-s-triazine 2 (1,3,4,6,7,9,9bheptaazaphenalene or cyamelurine): Compound 2 was fully characterized by Leonard and coworkers in the eighties 3 and more recently the X-ray structure of the trichloro derivative 3 was reported by Kroke et al. 4 .The interest of Pauling for compound 1 (called "the mystery molecule" 1 ), is related to some polymeric unidentified old compounds known as melon, melem, dimelemon and dates from very early in his career.For instance, in The Nature of the Chemical Bond (Second edition, 1945) 5  These molecules appeared in a publication by Pauling in 1937 6 .Therefore, it seems that he had been interested in these "resonant" structures for nearly sixty years!
Not considering the orientation of the OH group, cyameluric acid (4) can exist in seventeen tautomeric forms: one mono-hydroxy, three di-hydroxy, four tri-oxo and nine mono-hydroxy (Scheme 1).

Scheme 1
All the possible tautomers (not considering the OH orientation) of the cyameluric acid have been calculated at the B3LYP/6-31G* level (see Computational details).The total and relative energies are gathered in Table 1.These results indicate that the most stable tautomer corresponds to the tri-oxo a (258).The tri-hydroxy tautomer 147 is 20 kcal/mol above the global minima in the gas phase.The difference between 147 and 147b lies in the orientation of the OH groups: in 147 all point in the same direction (C 3h ) while in 147b (0.34 kcal mol -1 less stable) one of them points in an opposite direction (C s ).The structural information on the parent compound 2 can be summarized as follows.Leonard et al. reported its 1 H, 13 C and 15 N NMR chemical shifts 3b, 13 .Semiempirical calculations of the Dewar and Pariser-Parr-Pople type were carried out 14 and resonance energies calculated 15 .
Besides energy and density were estimated by Politzer et al. 16 as well as aromaticity by Cyranski and Krygowski 17 and heteroaromaticity by Bird 18 .The σ absolute shieldings calculated for compound 2 by means of the GIAO method (Table 2) can be transformed into δ values by means of equations previously reported 19

Computational Details
All the calculations have been carried out with the Gaussian-98 package 22 using the 6-31G* basis 23 set at the B3LYP computational level 24,25 .The geometry of all the molecules has been optimized maintaining an almost C s symmetry in all the cases.For some selected cases, the minimum nature of the structure has been confirmed by frequency calculations.The absolute isotropic chemical shieldings have been calculated for some of the most representative structures with the GIAO method 26 at the same computational level mentioned before.

Table 1 .
Total and relative energy of the different tautomers of the cyameluric acid

Table 2 .
20,21hieldings of compounds 2 and 258 According to the calculations reported for 4, it is expected that Pauling compound 1 should not exist as a dihydroxy tautomer but in the dioxo form.Calculations at the same level affords -927.77591 and -927.79299hartreesrespectively, that is, the dioxo tautomer should be 10.72 kcal mol -1 more stable than the dihydroxy one.It has been reported that Pauling's error to represent uracil in the hydroxy form prevented him to reach the structure of the double helix before Watson and Crick20,21.