zabardasti   claims the molecule is aromatic , whereas korkin   suggests the hcno monomer spontaneously trimerizes in order to reach a more stable configuration , a feature which if proved correct would indicate that aromaticity is an indication of stabilization energy . korkin   discovered that it manifests strong stabilization energy and likewise tarko   revealed it has descriptors of aromaticity and one of their targets is this same hexahydrotriazine derivative . molecular structure and electronic behavior ( charge distribution ) of cyanuric acid has also been the focus of x - ray and neutron difraction studies [ 57 ] . in this context , the important point is that the planarity of the molecule and its electronic delocalization has been achieved , both of which are important characteristics for evaluating aromaticity . theoretical calculations of these molecules have been carried out for the purpose of studying an array of topics . the marked capability of cyanuric acid for generating hydrogen bonds has been analyzed in terms of nanostructures   and intrinsic capability . furthermore analogs containing sulfur atoms instead of oxygen atoms in the carbonyl groups have also been theoretically studied and compared with cyanuric acid [ 10 , 11 ] . hydrogen bonded supramolecular clusters   of cyanuric acid and melamine in particular have been the focus of several studies because these clusters display interesting electrical   and material   behavior . besides , some adducts to a metallic complex have been prepared , showing promising characteristics in terms of their supramolecular chemistry for the development of new materials . another particularity of cyanuric acid , also derived from this characteristic of facile hydrogen bond formation is the formation of hamilton complexes [ 1618 ] . these kinds of complexes result from the interaction of a substrate containing electron donor ends with terminal hydrogen atoms , which have the capacity to easily interact with negative charge densities . this feature offers several possibilities for preparing novel compounds with applications in different fields , for example biochemistry , synthesis or in the pharmaceutical industry , as in the case of barbituric acid [ 1618 ] . the goal of the present manuscript is to evaluate from different points of view , the intrinsic electronic characteristics that we foresee helping to explain the possible aromatic character of these compounds . the evaluation was carried out by applying the homa method [ 19 , 20 ] and the ase   approximation , employing isodesmic reactions [ 2224 ] . all structures were optimized in the gas phase using the jaguar 4.0 package . a pure dft method which included becke s gradient correction   for exchange and perdew - wang s for correlation   was used for the energy evaluations . frequency calculations were carried out at the same level of theory in order to confirm that the optimized structures were at the minimum of the potential surface . these frequencies were then used to evaluate the zero - point vibrational energy , the thermal vibrational corrections to the enthalpy and the total enthalpy values , calculated at 273k . the bond lengths of the optimized structures were incorporated into the harmonic oscillator model of aromaticity ( homa ) method [ 19 , 20 ] used to study aromaticity . in almost all cases , the molecules in this study resemble the general structure depicted in fig . 1general structure of the compounds in this study general structure of the compounds in this study the calculation of the tautomer of compound ( 5 ) that corresponds to the structure shown in fig .  2 2tautomer of compound ( 5 ) tautomer of compound ( 5 ) it is a known fact that in the majority of cases , the keto form of any species manifesting keto - enolic tautomerism is more stable that its corresponding enol form . this phenomenon is due to the fact that a stronger bond exists between carbon and oxygen than the bond between carbon - carbon ( considering  bonds ) . however , the presence of non bonding electrons in heteroatoms close to carbonyl groups , in this case causes a cyclic delocalization , resulting in an aromatic system ( 4n  +  2 ) , n  =  1 . surprisingly , the calculation of both tautomers gives a total energy difference of 28.87  kj  mol , with the keto form taking the lead . this result contradicts the previous premise concerning aromatics because the enol form shows the typical delocalization of an aromatic compound , in contrast to the keto form which does not ; thus we return to the initial question the ase results come from the evaluation of the isodesmic reactions based on cyanic acid ( ncoh ) and its interaction with several simple molecules ; the set of reactions is as follows : 
 1\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{3ncoh } } \to { { \hbox{c}}_3}{{\hbox{n}}_3}{{\hbox{o}}_3}{{\hbox{h}}_3 } $ $ \end{document}2\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{3ncoh } } + { \hbox { c}}{{\hbox{h}}_3}{\hbox{n}}{{\hbox{h}}_2 } + { \hbox { c}}{{\hbox{h}}_3 } - { \hbox{c}}{{\hbox{h}}_3 } \to { { \hbox{c}}_6}{{\hbox{n}}_3}{{\hbox{o}}_3}{{\hbox{h}}_9 } + { \hbox { n}}{{\hbox{h}}_3 } $ $ \end{document}3\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{3ncoh } } + { } { { \hbox{h}}_2}{\hbox{c}}{{\hbox{o}}_2 } + { } { { \hbox{o}}_2 } \to { { \hbox{c}}_3}{{\hbox{n}}_3}{{\hbox{o}}_6}{{\hbox{h}}_3 } + { } { { \hbox{h}}_2}{\hbox{co } } $ $ \end{document}4\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{3ncoh } } + { \hbox { 3p}}{{\hbox{h}}_3 } + { \hbox { 2c}}{{\hbox{h}}_4 } \to { { \hbox{c}}_3}{{\hbox{n}}_3}{{\hbox{p}}_3}{{\hbox{o}}_3}{{\hbox{h}}_6 } + { \hbox { c}}{{\hbox{h}}_3 } - { \hbox{c}}{{\hbox{h}}_3 } + { 4}{{\hbox{h}}_2 } $ $ \end{document}5\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{3ncoh } } + { \hbox { 3n}}{{\hbox{h}}_3 } + { \hbox { 2c}}{{\hbox{h}}_4 } \to { { \hbox{c}}_3}{{\hbox{n}}_6}{{\hbox{o}}_3}{{\hbox{h}}_6 } + { \hbox { c}}{{\hbox{h}}_3 } - { \hbox{c}}{{\hbox{h}}_3 } + { 4}{{\hbox{h}}_2}. $ $ \end{document } the isodesmic reaction ( 1 ) yields unsubstituted cyanuric acid , the ch3- derivative is obtained by a means reaction ( 2 ) , whereas oh- , ph2 and nh2 derivatives are the result of reactions ( 3 ) , ( 4 ) , and ( 5 ) respectively . the ase values relating to these isodesmic reactions are shown in table  1 . table  1ase values from the isodesmic reactionsmoleculeasehydoh92.87  kj / molhydch3119.23  kj / molhydh135.56  kj / molhydph82.20  kj / molhydnh253.97  kj / mol ase values from the isodesmic reactions the greatest stabilization energy corresponds to unsubstituted cyanuric acid ( hydh ) ; therefore the inductive effect has little importance in this kind of molecule . first , the most aromatic species in this set is the enol form of cyanuric acid ( 5b ) , with the next strongest value corresponding to the keto form of the same derivative . likewise , this result suggests that the enol form will turn out to be the most stable isomer . however , the energy results indicate the contrary , and as outlined above the explanation for this phenomenon arises from the existence of a zwitterionic species which converts from 5 to become 5b , based on the proton mobility of both species . on the other hand , the same zwitterionic species is also described as having a canonical structure as in 5 , presented in scheme  1 benzene homa is 0.999moleculehomahydch3 ( 1)0.710hydoh ( 2)0.691hydn2 ( 3)0.6hydph2 ( 4)0.612hydh ( 5)0.7373hydrol ( 5b)0.998scheme  1contributing structures in cyanuric acid direct homa for the compounds being considered . for comparison purposes benzene homa is 0.999 contributing structures in cyanuric acid these results can be compared to those for a different molecule that has little resemblance to cyanuric acid , in order to evaluate the suitability of the homa method for the present study . 3 ) . with respect to this species , it has the same three oh substituents , but in this case it is expected to be very difficult to detect the phenomenon of tautomerism because the hydrogen atoms which leave the hydroxyl groups converting to the keto form should unite with the free carbon atoms on the ring , resulting in a severe distortion . the homa results for the enol and keto forms of this species are 0.9995 and 0.357 respectively . the difference between these two cases is larger than those in the case of cyanuric acid because this last is constituted from nitrogen atoms with dangling bonds which favor the keto - enolic equilibrium . thus our comparison is useful in this context to validate the use of the homa method . ( a ) enol form ( b ) keto form the cyanuric acid molecule presents two zones of electronic flow ; the first one is the typical delocalization zone in the ring , generated by the movement of the three electronic pairs inherent in the c  =  n bond . the second zone is that generated by the electrons associated with the three oxygen atoms in the carbonyl groups . thus , two contributions to the stabilization of the molecule exist , relating to these two sets of electrons that will be analyzed with reference to the molecular orbitals analysis . a diagram of molecular orbital ( mo ) interaction is shown in fig first , cyanuric acid seems to represent a very strange case of aromaticity because of its particular mo arrangement . several aromatic compounds manifest the set of six delocalized electrons in one single mo ( homo ) and a two - fold degenerate set ( homo-1 ) which causes the resonant interaction , generating the aromatic cloud . the cyanuric acid molecule belongs to the d3h symmetry group , therefore the sets that contain the six electrons of the resonant group belong to the e and a2  irreducible representations . however , the energy of the three orbitals is practically the same , so that we have a strange case of an accidental triple degenerated set . this set keeps the electrons that participate in the aromatic flow at the center of the molecule , indeed this set is very curious because it is not common to find that all the mo s manifest the same energy and neither is it common to find this set representing the homo-1 group . besides , although it might be expected that the homo would participate in aromaticity , at first sight this is not the case , because it seems that all  central  aromaticity is found in the homo-1 group . irreducible representation that occupies almost the same region as the homo , therefore , it seems to be a classical set of three orbitals , separated by 1.115  ev depicting an aromatic set . however the set of the homo-1 orbitals is localized at the middle of the scheme . 5 . 
 fig .  4interaction mo diagram showing both sets of electronic interaction for compound 5fig . ( b ) classic aromaticity set formed by homo and homo-2 interaction mo diagram showing both sets of electronic interaction for compound 5 ( a ) accidental triple degenerated set corresponding to homo-1 . ( b ) classic aromaticity set formed by homo and homo-2 the conclusion to all this is that we have two aromatic sets ( double aromaticity [ 33 , 34 ] ) ; homo-1 represents one set , and homo , homo-2 the other one , and there is interaction between them . these two sets do not occupy the same space , although there is some overlap . this means that there must be competition between them and that they should thus shield each other . in other words , thus , the molecule should have a very weak aromatic character concurring with the result obtained when aromaticity indexes are used . applying this framework we can reveal the inductive effect due to the different substituents , but a drastic change is not expected because the strong interaction of molecular orbitals causes the molecule to imitate the same electronic behavior . in scheme  1 the scheme is relatively simple in the case where the substituents are hydrogen atoms ; however it can become very complicated in cases where compounds of this kind contain other types of substituents . firstly ; other substituents may not have the same mobility as hydrogen , therefore , it is to be expected that they will remain in their position on the nitrogen atom , secondly ; it is a known fact that certain substituents have inductive effects , strongly affecting the electronic behavior of the aromatic ring . the zwitterionic form continues to be aromatic and display interesting electronic properties . in order to evaluate the aromaticity of this family , the homa method is once again applied , however in this case we are using the theory designed by krygowski   in order to develop an equation with specific characteristics , permitting a comparison to be made between the different aromaticity values for these substances . the keto form of the cyanuric acid ( molecule 5 in the last table ) has the most geometrically regular structure of any of the molecules in this study , therefore , we consider this species to represent the ideal model and establish that this is the most aromatic example out of the entire family . thus the parameters of this molecule are applied to the krygowski scheme , in the following way . krygowski s general equation is presented as : 
 6\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{homa } } = { 1 } --{\hbox{a}}/{\hbox{n}}{({{\hbox{r}}_{\rm{opt } } } - { { \hbox{r}}_{\rm{ij}}})^2 } , $ $ \end{document}where  corresponds to an empirical constant that helps take into account the length and angles of a particular ring and is evaluated in terms of 
 7\documentclass[12pt]{minimal } 
				 \usepackage{amsmath } 
				 \usepackage{wasysym } 
				 \usepackage{amsfonts } 
				 \usepackage{amssymb } 
				 \usepackage{amsbsy } 
				 \usepackage{mathrsfs } 
				 \usepackage{upgreek } 
				 \setlength{\oddsidemargin}{-69pt } 
				 \begin{document}$$ { \hbox{a } } = { 2}{\left ( { { { \left [ { { \hbox{r}}\left ( { \hbox{s } } \right ) { } --{{\hbox{r}}_{\rm{opt } } } } \right]}^2 } + { } { { \left [ { { \hbox{r}}\left ( { \hbox{d } } \right ) - { { \hbox{r}}_{\rm{opt } } } } \right]}^2 } } \right)^ { - { 1}}}. $ $ \end{document } by taking ( 6 ) and ( 7 ) , an equation was developed for the purpose of evaluating the changes in cyanuric acid and its derivatives . considering the calculated measurements of cyanuric acid itself as a pattern for evaluating  , substituting r(s )  =  1.465 ( the length of a single bond n - c as is described in the same work by krygowski ) , r(d )  =  1.269 ( the length of a double bond between n and c as described by krygowski ) and ropt  =  1.387 in eq . 7 yields a value of 99.96 for . all these parameters were included in eq . 6 and the relative homa aromaticity ( named  internal  homa ) for all species are presented in table  3 . homa for the compounds included in this study the order is the same as that in table  2 , but this time the molecules with substituents , which extract electronic charge from the ring ( -cooh , -cn and no2 ) have also been included . it should be noted that in the case of hydno2 , the value of aromaticity is increased , almost to the level of the reference molecule ( hydh ) . this phenomenon is due to the presence of high electronic density in the substituent , which strongly reinforces the electronic flow on the periphery of the ring , in strong contrast to classic aromatic molecules . cyanuric acid and several derivatives were calculated in order to study their possible aromatic character . all species are aromatic in the enol form , but the keto form is more stable than the enol one . therefore the aromaticity of all species in keto form was analyzed using ase and homa methods . the explanation is thus found in the frontier molecular orbitals analysis , where it is possible to identify two aromatic systems for cyanuric acid in keto form but it seems these systems are opposed , thus tending to decrease the overall aromatic character . as a result