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In the present study, a theoretical study of 1,1diaminohexaazidocyclotetraphophazene (DAHA) and its isomers has been performed, using quantum computational density functional theory (B3LYP and B3PW91 methods) with 631G* and 631G** basis sets implemented in Gaussian 03 program suite. Molecular structure and bonding, vibrational frequencies, Milliken population analysis, and natural bond orbit (NBO) have been studied. The heats of formation from atomization energies have also been calculated based on the optimized geometry. The obtained heats of formation data are compared with their homologous cyclophosphazene in order to demonstrate the accuracy of the methods, which indicate that the studied compounds might be potentially used as high energetic materials. In addition, the relative stability of five isomers have been deduced based on the total energy and the gap of frontier orbital energies.
Research involving the search for and synthesis of new high energy (HE) compounds is an ongoing quest. There are many molecules that fall into this category, and analysis of their characteristics yields information about trends in structure and chemistry. These trends include strained ring structures, molecules that are unstable with respect to their combustion products, and the inclusion of various phosphazene ring containing functional groups, such as azido, nitro and amino groups. Based on these traits, a phosphazene ring containing amino and azido groups would be a kind of possible highenergy compound.
Compounds that contain azido groups are most often highly energetic and some tend to be unstable. However, over the last years, relatively stable azido substituted carbonnitrogen heterocycles with densities >1.7 g·cm^{−3} and with very high heats of formation have been reported [
Cyclophosphazene derivatives have attracted much interest and have been reviewed over the years [
In previous publications, we have ever reported the preparation, structural characterization, and theoretical studies of 1,1spiro(ethylenediamino)3,3,5,5tetrachlorocyclotriphosphazene and its nitration product [
All of the structures were fully optimized without any symmetry limitation using the B3LYP [
For there is no obvious deviation in optimized parameters for the five isomers,
We can see from the
As examples
Analysis of the calculated vibrational frequencies shows that the frequencies of the five compounds show no large deviations. We find that the molecules have a sharp peak between 3,500 cm^{−1}−3,700 cm^{−1} correspond to the stretching vibration of the NH bond. The modes rang from 22,00 cm^{−1}−2,350 cm^{−1} and 1,300 cm^{−1}−1,360 cm^{−1} have been identified as the stretching vibrations of the −N_{3} group, while the peaks at 1,266 cm^{−1} (1,689 cm^{−1}) and 1,371 cm^{−1} (748 cm^{−1}) are attributed to the inplane stretching of PNP bonds, which are in agreement with the PNP stretch seen in (NPF_{2})_{4} [
From the data, we can conclude that the position of the amino group has an effect on the stabilization energy. By analysing the data, we find the strongest interaction mainly occurs on the lone pair of N_{α} and the π antibond orbit of N_{β}N_{γ}. There are weak mutual interactions among the PN bonds in the phosphazene ring, which indicate that the PN bonds have a tendency to offer electrons to each other and there are weak conjugated interactions in the ring. Between the σ orbit of PN_{α} bonds and the lone pair of N atom in the ring there also exist weak interactions; we consider there is conjugated interaction. In the 1,5diaminohexaazidocyclotetraphosphazene molecule it can be found that there are stronger interactions existing between the PN in the eightmember ring and the PN_{α} bond, the two PN_{α} bonds linked on the same phosphorus atom also have strong mutual interaction and the maximal interaction between σ*_{PNα} and π*_{PNα}. It indicates that there exists a strong repulsion between two azido groups. In addition, the interaction between the PN_{α} bond and the N_{β}N_{γ} bond is also strong, but the interaction between PN (amino) and PN_{α} is weaker than that between two PN_{α} bonds, it also indicate that amino group and azido group linked on the same phosphorus atom is more stable than that two azido groups link on one phosphorus, so we can infer that the PN_{α} bond is unstable and easy to separate from the ring. In the 1,3diaminohexaazidocyclotetraphosphazene molecule, the interaction mainly occur between σ*_{PN} and σ*_{PN} in the ring, the n_{Nα} → π*_{NβNγ} interaction between the lone pair of the N_{α} and π*_{NβNγ} antibond is also stronger than other interactions. There exist a N≡N at the end of the azido groups. The interactions between the σ_{PNα} bond and the σ*_{PNα} antibond, σ_{PN} (amino) bond and σ*_{PNα} antibond are all about 3.20 kcal·mol^{−1}, weaker than that in 1,5diaminohexaazidocyclotetraphosphazene. It also indicates the two azido groups are more stable than in 1,5diaminohexaazidocyclotetraphosphazene. There is weak interaction between the PN_{α} bond and the separated PN (ring) bonds, which show there is conjugated interaction in the phosphazene ring and the whole structure is stable. From the stabilization energies between these bonds, we can conclude that the interaction in the 1,1diaminohexaazidocyclotetraphosphazene molecule is stronger and there exists a strong repulsion between two azido groups linked on the same phosphorus atom and the molecule is unstable.
From the data, we can conclude that the position of the amino group has an effect on the stabilization energy. By analysing the data, we can find the strongest interaction mainly occur on the lone pair of N_{α} and the π antibond orbit of N_{β}N_{γ}. There are weak mutual interactions among the PN bonds in the phosphazene ring, which indicate that the PN bonds have the tendency to offer electrons to each other and there is weak conjugated interactions in the ring. Between the σ orbit of PN_{α} bonds and the lone pair of N atom in the ring there also exist weak interactions, so we consider there is a conjugated interaction. In the 1,5diaminohexaazidocyclotetraphosphazene molecule, it can be found there are stronger interactions existing between the PN in the eightmember ring and the PN_{α} bond, the two PN_{α} bonds linked on the same phosphorus atom also have a strong mutual interaction and the maximal interaction is between σ*_{PNα} and π*_{PNα}. It indicates that there exists a strong repulsion between the two azido groups. In addition, the interaction between the PN_{α} bond and the N_{β}N_{γ} bond is also strong, but the interaction between PN (amino) and PN_{α} is weaker than that between the two PN_{α} bonds; this also indicates that amino group and azido group linked on the same phosphorus atom are more stable than that two azido groups linked on one phosphorus, so we can infer that the PN_{α} bond is unstable and easy to break from the ring. In the 1,3diaminohexaazidocyclotetraphosphazene molecule the interaction mainly occurs between σ*_{PN} and σ*_{PN} in the ring and the n_{Nα}→π*_{NβNγ} interaction between the lone pair of the N_{α} and π*_{NβNγ} antibond is also stronger than other interactions. There exists an N≡N at the end of the azido groups. The interactions between σ_{PNα} bond and σ*_{PNα} antibond, σ_{PN} (amino) bond and σ*_{PNα} antibond are all about 3.20 kcal·mol^{−1}, weaker than that in 1,5diaminohexaazidocyclotetraphosphazene. It also indicates the two azido groups are more stable than that in 1,5diaminohexaazidocyclotetraphosphazene. There is a weak interaction between the PN_{α} bond and the separated PN (ring) bonds, which shows there is a conjugated interaction in the phosphazene ring and the whole structure is stable. From the stabilization energies between these bonds, we can conclude that the interaction in the 1,1diaminohexaazidocyclotetraphosphazene molecule is stronger and there exists strong repulsion between two azido groups linked on the same phosphorus atom and the molecule is unstable.
Bond overlap populations can reflect the electron accumulations in the bonding region, and they can provide us detailed information about the chemical bonding. As a whole, the larger the population is, the greater the bond overlaps. Though the Mulliken population analysis suffers from some shortcomings, however, for the purpose of comparing trends in the electron distribution for homologous compounds at the same calculation condition, results derived from Mulliken population analysis are still meaningful.
Inspecting the overlap populations in
The ranges and the average charge of the same kind of atoms for the five isomers of diaminohexaazidocyclotetraphophazene based on B3LYP/631G** are summarized in
The calculation of theoretical heats of formation (HOFs) is essential for many of the applications of quantum chemistry, in particular for aiding in the interpretation of experimental results and for the prediction of reaction kinetics. Several theoretical procedures such as group additive method; molecular mechanics and semiempirical MO methods have been used to estimate heats of formation. In this study, DFT methods and basis sets are selected to calculate the heats of formation through the selected atomization energies. Experimental heats of formation of element P, N, H and standard temperature corrections can be found in the literature [
The HOFs of the five isomers in the gas phase at 298.15K are predicted using B3LYP and B3PW91 methods with 631G**. The results are presented in
Because of the different positions of the amino groups, there exist five isomers of diaminohexaazidocyclotetraphosphazene. To estimate the relative stability of compounds
Density functional theory B3LYP and B3PW91 calculations have been carried out on the five isomers of diaminohexaazidocyclotetraphosphazene. The structural investigation results show that the title molecules do not have planar structures. There are no alternating single and double bonds in the phosphazene ring and the PN bond lengths are not identical, which indicate the molecules have no aromaticity. The different positions of the amine group have no large effect on the optimized parameters. The Mulliken population analysis indicates that the PN_{α} bonds are the weakest and could be ruptured initially by stimuli, the relative stability of the bonds in the molecules is: PN_{α} < N_{α}N_{β} < PNH_{2} < PN(ring) < N_{β}N_{γ}. Besides, different substituents affect the stability of the PN bonds in the ring. For thermochemical analysis on the optimized structures, it can be predicted that they all have high heats of formation and unstable in the gas phase, so they might be potential energetic materials. In addition, we concluded the relative stability of five isomers according to their total energy and the gap of frontier orbital energies.
This work is supported by the National Natural Science Foundation of China.
The structure and the atom serial number of five isomers for diaminohexaazidocyclo tetraphosphazene (the yellow, pink and blue balls denote phosphorus nitrogen, and hydrogen atoms, respectively). (a) 1,1Diamino3,3,5,5,7,7hexaazidocyclotetraphosphazene (
The selected bond lengths (Ǻ), bond angles (°) and dihedral angle (°) of 1,1diamino3,3,5,5,7,7hexaazidocyclotetraphosphazene (
Bond lengths  
N4P23  1.599  1.599  1.596  1.596 
N3P27  1.621  1.621  1.619  1.619 
N3P22  1.580  1.579  1.577  1.578 
N6P27  1.609  1.610  1.606  1.605 
N5P22  1.583  1.583  1.580  1.581 
P21N4  1.592  1.592  1.589  1.589 
P21N_{α}  1.709  1.723  1.716  1.716 
N_{α}N_{β}  1.240  1.240  1.235  1.235 
P27NH_{2}  1.667  1.666  1.663  1.661 
N_{β}N_{γ}  1.135  1.135  1.133  1.133 
N19H1  1.015  1.013  1.014  1.012 
Bond angles  
P21N4P23  135.9  135.9  135.4  135.4 
N4P21N5  120.7  120.6  120.5  120.5 
N_{α}P21N_{α}  101.4  101.4  101.5  101.5 
P21N_{α}N_{β}  118.3  118.3  118.3  118.3 
N_{α}N_{β}N_{γ}  174.2  173.7  174.2  174.2 
H1N19H2  113.2  113.6  113.4  113.9 
N3P22N5P21  68.9  68.8  68.5  68.4 
P22N5P21N4  −70.1  −70.0  −70.3  −70.3 
N5P21N4P23  26.1  26.1  26.3  26.4 
P21N4P23N6  20.8  20.7  20.3  20.5 
N4P23N6P27  −87.1  −87.2  −88.0  −87.9 
P23N6P27N3  75.9  75.7  75.3  75.7 
In the table, N_{α} is the nitrogen atom in the azido group which is connected directly with the P atom, and the N_{β} is the middle nitrogen atom in the azido group, the top nitrogen atom is N_{γ}.
Some main vibrational harmonic frequencies in cm^{−1} and their IR intensities in km mol^{−1} (given in parentheses), calculated for the optimized structures of the isomers of diaminohexaazidocyclotetraphosphazene using the B3LYP/631G** level of theory.
1  390.2 (96)  406.4 (57)  478.4(129)  PN ring inplane twist  
2  540.9 (184)

542.2 (215)

PN ring twist
 
3  563.6 (294)  576.1 (106)  563.1(214)  556.5(188)  −N_{3} torsion, NH bending  
4  578.8 (22)

590.9 (238)

610.8(418)  −N_{3} twist, torsion  
5  689.6 (266)  754.4 (210)  709.4(275)  758.7(397)  N_{α}N_{β} in plane twist  
6  802.2 (176)  821.1 (196)  NH unsymmetrical twist  
7  939.6 (126)  923.4 (217)  920.3(149)  913.7(170)  915.9(129)  PNH_{2} inplane stretching 
8  1,034.3 (68)

1,020.1 (25)

941.7(148)  NH inplane unsymmetrical wag  
9  1,266.3 (1689)  1,281.8 (1775)  1,270.4(1847)  1,293.2(1980)  1,296.6(2017)  PNP inplane stretching 
10  1,313.8 (298)

1,314.8 (134)

1,338.3(318)  1,315.5(1282)

1,319.0(380)  N_{α}N_{γ} symmetrical stretching 
11  1,330.3 (1155)  1,307.8 (1553)  1,311.0(1096)  1,326.7(389)  1,299.3(2080)  PNP inplane stretching 
12  1,371.5 (748)  1,364.5 (586)  1,367.2(632)  1,380.8(915)  PNP symmetrical stretching  
13  1,592.4 (100)  1,587.5 (95)  −NH_{2} inplane bending  
14  2,277.9 (533)

2,295.1 (213)

2,292.2(359)

2,286.9(781)

2,286.7(730)

N_{β}N_{γ} unsymmetrical stretching 
15  3,542.0 (52)

3,539.0 (47)

3,562.9(66)  3,530.4(61)  3,574.3(56)  NH symmetrical stretching 
16  3,660.2 (66)

3,651.2 (57)

3,681.1(35)  3,683.9(38)  3,694.5(40)  NH unsymmetrical stretching 
Part of calculated results of 1,1diamino3,3,5,5,7,7hexaazidocyclotetraphosphazene (
LP(2)N7  BD*(2)N10N11  113.83 
LP(2)N7  BD*(1)N5P22  2.30 
LP(2)N7  BD*(1)N3P22  0.87 
LP(1)N7  BD*(3)N10N11  5.77 
LP(2)N8  BD*(2)N9N12  106.13 
LP(2)N8  BD*(1)N4P23  5.65 
LP(2)N8  BD*(1)N6P23  2.50 
LP(2)N13  BD*(2)N16N17  106.72 
LP(2)N14  BD*(2)N15N18  107.55 
LP(2)N20  BD*(2)N29N30  107.18 
LP(2)N31  BD*(2)N28N32  104.22 
BD(1)N20P21  BD*(1)N5P22  2.63 
BD(1)N20P21  BD*(1)N4P23  1.77 
BD(1)N19P27  BD*(1)N6P23  1.76 
BD(1)N19P27  BD*(1)N3P22  1.49 
BD(1)N3P22  BD*(1)N5P21  0.88 
BD(1)N4P21  BD*(1)N5P21  1.01 
BD(1)N7P22  BD*(3)N10N11  17.97 
BD(1)N8P23  BD*(3)N9N12  16.35 
LP(2)N3  BD*(1)N7P22  23.17 
LP(2)N3  BD*(1)N24P27  12.98 
LP(2)N4  BD*(1)N8P23  19.13 
LP(2)N4  BD*(1)P21N31  15.62 
LP(1)N19  BD*(1)N6P27  12.95 
LP(1)N24  BD*(1)N3P27  12.40 
BD*(1)N4P23  BD*(1)N6P23  24.07 
BD*(1)N6P27  BD*(1)N6P23  53.73 
BD*(1)N3P27  BD*(1)N3P22  46.89 
NBO analysis results of 1,5diamino1,3,3,5,7,7hexaazidocyclotetraphosphazene (
BD(1)N1P19  BD*(2)N5P19  47.76  
BD(1)N1P19  BD*(1)N12P19  30.31  
BD(1)N3P19  BD*(2)N12P19  82.96  
BD(1)N3P19  BD*(1)N5P19  20.46  
BD(1)N2P20  BD*(2)N6N20  50.05  
BD(1)N2P20  BD*(1)N11P20  32.63  
BD(1)N2P18  BD*(1)N17P18  2.08  
BD(1)N1P22  BD*(1)N21P22  4.97  
BD(1)N4P22  BD*(1)N21P22  1.44  
BD(1)N4P22  BD*(2)N21P22  94.77  
BD*(1)N5P19  BD*(2)N12P19  109.85  
BD*(1)N25P22  BD*(2)N21P22  34.99  
LP(2)N17  BD*(2)N23N24  111.66  
BD(1)N2P20  BD*(2)N6N20  49.58  
BD(1)N2P20  BD*(1)N11P20  32.61  
BD(1)N4P20  BD*(2)N11P20  80.24  
BD(1)N3P19  BD*(2)N12P19  84.57  
BD(1)N1P19  BD*(2)N5P19  50.43  
BD(1)P18N3  BD*(2)N17P18  11.84  
BD(1)P18N3  BD*(1)N30P18  11.37  
BD(1)N1P24  BD*(1)N21P24  3.80  
BD(1)N4P24  BD*(2)N27P24  55.88  
BD(2)N5P19  BD*(2)N8N9  95.82  
BD*(2)N17P18  BD*(1)N30P18  72.58  
BD*(2)P24N27  BD*(1)N21P24  116.83 
NBO analysis results of 1,3diamino1,3,5,5,7,7hexaazidocyclotetraphosphazene (
LP(2)N5  BD*(2)N8N9  110.94  
LP(2)N18  BD*(2)N31N32  108.18  
LP(2)N6  BD*(2)N7N10  105.75  
BD*(1)N1P16  BD*(1)N1P19  102.54  
BD*(1)N2P15  BD*(1)N2P17  97.4  
BD*(1)N5P16  BD*(1)P16N28  2.28  
BD*(1)N14P15  BD*(1)P15N25  3.95  
BD*(1)P16N28  BD*(1)N3P15  3.28  
BD*(1)N18P19  BD*(1)P19N22  4.11  
BD*(1)P19N22  BD*(1)N1P16  2.08  
BD*(1)P19N22  BD*(1)N4P17  3.27  
BD*(3)N23N24  BD*(1)N23N24  9.52  
BD*(3)N23N24  BD*(1)P19N22  6.03  
BD(1)N17P18  BD*(1)N19P18  3.20  
BD(1)P14N27  BD*(1)N30P14  3.21  
BD(1)N5P15  BD*(1)N22P15  3.22  
BD(1)N5P15  BD*(1)N5P19  20.46  
BD(1)N5P15  BD*(3)N8N9  16.04  
LP(2)N19  BD*(2)N20N21  105.23  
LP(1)N22  BD*(1)N5P15  12.77  
LP(2)N27  BD*(2)N28N29  112.74  
LP(2)N27  BD*(1)N30P14  10.01  
LP(1)N30  BD*(1)N27P14  14.36  
BD*(1)N1P15  BD*(1)N1P18  99.55  
BD*(1)N2P14  BD*(1)N2P16  90.33  
BD*(3)N25N26  BD*(1)N17P18  7.12  
BD*(3)N28N29  BD*(1)N28N29  10.3 
Ranges of the Bond Overlap Population for five isomers of diaminohexaazidocyclotetraphosphazene at the B3LYP/631G** level of theory.
0.383 ~ 0.510  0.201 ~ 0.275  0.265 ~ 0.301  0.586 ~ 0.601  0.350 ~ 0.353  0.341 ~ 0.345  
0.442 ~ 0.501  0.210 ~ 0.271  0.264 ~ 0.294  0.597 ~ 0.601  0.306 ~ 0.352  0.341 ~ 0.344  
0.445 ~ 0.498  0.219 ~ 0.276  0.266 ~ 0.303  0.595 ~ 0.597  0.310 ~ 0.353  0.341 ~ 0.347  
0.454 ~ 0.495  0.217 ~ 0.273  0.272 ~ 0.313  0.594 ~ 0.600  0.295 ~ 0.343  0.338 ~ 0.344  
0.438 ~ 0.493  0.207 ~ 0.268  0.264 ~ 0.327  0.596 ~ 0.599  0.320 ~ 0.342  0.343 ~ 0.346 
The atomic charges from the Mulliken population analysis for five isomers of diaminohexaazidocyclotetraphosphazene at the B3LYP/631G** level of theory
1.070 ~ 1.089

1.062 ~ 1.072

1.061 ~ 1.071

1.057 ~ 1.068

1.062 ~ 1.070
 
−0.683 ~ −0.602

−0.639 ~ −0.630

−0.649 ~ −0.622

−0.683 ~ −0.619

−0.645 ~ −0.621
 
−0.537 ~ −0.472

−0.530 ~ −0.449

−0.475 ~ −0.471

−0.472 ~ −0.470

−0.472 ~ −0.469
 
0.458 ~ 0.480

0.437 ~ 0.460

0.438 ~ 0.452

0.435 ~ 0.453

0.437 ~ 0.453
 
−0.257 ~ −0.216

−0.233 ~ −0.211

−0.234 ~ −0.214

−0.251 ~ −0.213

−0.238 ~ −0.212
 
−0.861 ~ −0.818

−0.829 ~ −0.813

−0.821 ~ −0.821

−0.823 ~ −0.823

−0.823 ~ −0.820
 
0.348 ~ 0.379

0.355 ~ 0.375

0.359 ~ 0.362

0.359 ~ 0.360

0.355 ~ 0.361

In the table, the first line number is the charge range of the same kind of atoms and the second line number is their average value in every cell.
Calculated HOFs for five isomers of diaminohexaazidocyclotetraphosphazene (kcal•mol^{−1}) from atomization energy at 298.15 K.
424.03  434.93    
423.12  433.92    
422.97  433.85    
422.86  433.65    
421.74  432.47    
Hexaazidocyclotriphosphazene  444.43  451.71  455.16 
Calculated relative total energies and the frontier orbital energies for five isomers of diaminohexaazidocyclotetraphosphazene (kcal·mol^{−1}) at the B3LYP/631G** level of theory
2.12  −1.56  −6.01  4.46  
0.00  −1.46  −6.18  4.72  
1.01  −1.50  −6.19  4.69  
1.15  −1.47  −6.06  4.59  
1.29  −1.54  −6.12  4.58 
In the table, E_{total} means total energy. E_{LUMO} and E_{HOMO} is the energy of the HOMO and LUMO, respectively. ΔE_{LH} means the gap of E_{LUMO} and E_{HOMO}.