- Email: [email protected]
Theoretical study on the structures and properties of the isomers of Nn(CH)8−nH8 (n = 0–7)
Journal of Molecular Structure: THEOCHEM 870 (2008) 77–82
Contents lists available at ScienceDirect
Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
Theoretical study on the structures and properties of the isomers of Nn(CH)8 nH8 (n = 0–7) Bo-Hua Xu a, Lai-Cai Li b,*, Li Sun b, AN-Min Tian c a
Department of Chemistry, Yangtze Normal University, Fuling, Chongqing 408003, PR China Department of Chemistry, Sichuan Normal University, Chengdu 610066, PR China c Department of Chemistry, Sichuan University, Chengdu 610064, PR China b
a r t i c l e
i n f o
Article history: Received 26 June 2008 Received in revised form 4 September 2008 Accepted 6 September 2008 Available online 18 September 2008 Keywords: Hydronitrogen compounds Density functional theory (DFT) Energy Heat of formation
a b s t r a c t With replacement of N atoms by CH groups in the most stable chain isomer of N8H8, 34 possible isomers of Nn(CH)8 nH8 (n = 0–7) have been designed and optimized at the B3LYP/6-311++G** level of theory. The natural bond orbital (NBO) and atoms in molecules (AIM) analysis are carried out to study the bonding nature and relative stabilities of these conformers. G3MP2 method is applied to calculate energies and heats of formation. The results indicate that the hyperconjugation effect from lone pairs of nitrogen atoms to germinal C–N bonds is the major factor which caused the change of the C–N bond length. With the more replacement of nitrogen atoms by CH groups, the heats of formation of the isomers of Nn(CH)8 nH8 (n = 0–7) decrease gradually, but the energies increase linearly. Crown copyright Ó 2008 Published by Elsevier B.V. All rights reserved.
1. Introduction Energetic materials, a substance with small volume and big heat-storing, play very important roles in aviation, ordnance industry and other high-tech fields. Los Alamos National Laboratory (LANL) of USA reported that high nitrogen content high materials (HNC-HEMs) is a kind of energetic material which have great potential, because its decomposition results in the formation of N2 and the release of a large quantity of energy [1]. In the high energy density compound, nitrogen-containing substances attract much attention of the chemists [2–6]. Since 1950s chemists have paid much attention to the theoretical and experimental researches on the NnHm clusters due to its contribution to the energetic materials although it is thermodynamically stable but kinetically unstable [7–8]. By quantum chemistry methods, one can obtain much information such as geometric configuration, energy, stability, bonding properties, spectroscopic properties, and etc. In recent years, more and more researches on NnHm are reported about its configuration parameters, vibrational frequencies, decomposition reactions and heat of formation [9–13]. We have reported the stability and tautomerism of N8H8 chain isomer [14]. Recently, a Gaussian-3 theory investigation using B3LYP geometries was carried out to examine the stability of (CH)xN8-x(0 6 x 6 8) isomers [15]. In present paper, a series of new Nn(CH)8 nH8 (n = 0–7) molecules are
* Corresponding author. E-mail addresses: [email protected], [email protected] (L.-C. Li).
obtained by successive replacement of N atoms with CH groups in a relatively stable configuration of the N8H8 chain isomers [14]. The geometric configurations, energies, discipline of the heat of formation, and density of this series of new Nn(CH)8 nH8 molecules are studied in detail by using the quantum chemical method. We also investigate the properties of the new energetic materials such as the heat of formation (HOF) and density. Our ultimate goal is to find the relationship between the nitrogen content and HOF or density and provide some new ideas for designing new energetic materials. 2. Computational details A molecular design was performed for the possible (CH)8 isomers. We replaced of the CH groups by nitrogen atoms to increase the nitrogen content as well as reduce the hydrogen content. We have obtained 34 possible structures. These isomers of Nn(CH)8 nH8 have been fully optimized at the B3LYP/6311++G** level of theory. For each species, the analyses of vibration are performed to obtain the zero point vibrational energies (ZPE) and to verify whether it is a minimum or not. Meanwhile, the electronic charge densities of critical points were calculated with AIM 2000 program package [16]. Furthermore, the orbital interaction is analyzed with the natural bond orbital (NBO) theory [17]. In addition, G3MP2 method is used to obtain more accurate energy and calculate the HOF at 298 K (DfHh(298K)). All calculations are carried out by using the Gaussian 98 program [18].
0166-1280/$ - see front matter Crown copyright Ó 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2008.09.007
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Fig. 1. The optimized geometries of Nn(CH)8
nH8
(n = 0–7) (a) bond length (nm); (b) charge density q in the bond critical point (a.u.); (c) Laplacian (a.u.)
B.-H. Xu et al. / Journal of Molecular Structure: THEOCHEM 870 (2008) 77–82
79
Fig. 1 (continued)
3. Results and discussions 3.1. Geometries analysis The 34 isomers are classified into eight groups: isomers A (the total is three) are used CH groups to replace one nitrogen atom in the most stable chain isomer of N8H8; the isomers E (the total is nine), F (the total is five), H (the total is five), I (the total is five), J (the total is three), and K (the total is three) are obtained by using CH groups to replace 2, 3, 4, 5, 6, 7 nitrogen atoms, respectively. The isomers O (only one) are formed by using CH groups to replace all nitrogen atoms. The vibration analysis indicates that the vibrational frequencies of these isomers are all positive, which show that these isomers are the minima on the potential energy surfaces. The optimized geometries of the 34 isomers are depicted in Fig. 1. The calculated geometric parameters, charge density q in
the bond critical point and Laplacian D2q are also presented in Fig. 1. As shown in Fig. 1, the N–N, N@N, C–N, C@N, C–C, and C@C bond lengths of these isomers are in the rang of 0.1349–0.1454, 0.1232–0.1246, 0.1365–0.1493, 0.1256–0.1282, 0.1501–0.1552, and 0.1334–0.1343 nm, respectively. While the standard bond lengths of N–N, N@N, C–N, C@N, C–C, C@C are 0.1450, 0.1250, 0.1470, 0.1280, 0.1540, and 0.1330 nm, respectively. One notice that the calculated bond distance is close to the corresponding standard bond lengths. Thus, the optimized structures of the species are reasonable. Meanwhile, a trend of bond length change can be found according to the data in Fig. 1. From Fig. 1, one can see that the C7–N4 bond connect to the C7@N3 double bond in the E8 isomer. The bond length of C7–N4 bond is 0.1369 nm, which is shorter than the other single bonds. The second-order stabilization energies (E (2)) of the isomer are
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Table 1 Total energies at the B3LYP level, G3MP2 energy, relative energies at the G3MP2 level, heat of formation at the 298.15 K, and density of Nn(CH)8 Compound B2-3 A2 A3 A1 E6 E8 E2 E9 E5 E4 E1 E3 E7 F3 F4 F2 F1 F5 H4 H2 H5 H1 H3 I1 I4 I3 I5 I2 J2 J1 J3 K2 K3 K1 O1
EB3LYP (a.u.) 442.635120 426.612323 426.606453 426.603981 410.655965 410.642261 410.634294 410.62395 410.605142 410.581469 410.569712 410.56765 410.557633 394.640043 394.609766 394.606681 394.601369 394.585956 378.58749 378.575111 378.552999 378.55763 378.545733 362.530592 362.52876 362.524148 362.521751 362.515153 346.472171 346.469364 346.462681 330.409274 330.402582 330.400545 314.349653
EG3MP2 (a.u.) 439.857847 423.890577 423.886245 423.883246 407.992422 407.977078 407.969401 407.95789 407.941832 407.914209 407.907008 407.903213 407.884503 392.031664 391.99955 391.999083 391.993575 391.975679 376.033875 376.02116 375.999731 375.99708 375.99563 360.032118 360.030653 360.025898 360.023448 360.015683 344.029023 344.026583 344.002355 328.021461 328.007195 328.004303 312.00958
calculated. The value of E (2) of the lone pair electrons of N4 atom and the p antibond orbital of C7–N3 bond is 126.1 kJ/mol. Thus, a p ? p conjugation interaction exists between the lone pair electrons of N4 atom and the p antibond orbital of C7–N3 bond. The interaction result in that the bond length of the C(7)–N(4) is shorter than other C–N single bonds. Therefore, the hyperconjugation effect between the p antibond orbital of C@N double bond and the lone pair electrons of neighboring N atom lead to the shorting of the neighboring C–N single bonds. A topological analysis of charge density q and its Laplacian D2q is carried out with the AIM theory. The Laplacian value of the bond critical point measures whether the electron density is locally concentrated (D2q < 0) or depleted (D2q > 0). As shown in Fig. 1, all lapacian values of the 34 isomers are negative, which shows that the N–N, N@N, C–N, C@N, C–C, and C@C bonds of Nn(CH)8 nH8 isomers are covalent bond. The charge density q of the bond critical point is a measurement of the bond strength and it has been observed to correlate with the traditional bond order. As shown in Fig. 1, the q of N–N bond is the biggest. The q of C–C bond is less than that of the C–N bond. Therefore, the descending order of bond lengths is the C–C bond > the C–N bond > the N–N bond. The C–C bond is weaker than those of the N–N bond. In other words, the bond critical point charge density q is bigger, the bond length is shorter.
Erel (kJ/mol) 0.00 0.00 11.37 19.24 0.00 40.28 60.44 90.66 132.82 205.34 224.25 234.21 283.34 0.00 84.31 85.54 100.00 146.98 0.00 33.38 89.64 96.60 100.41 0.00 3.84 16.33 22.76 43.15 0.00 6.40 70.01 0.00 37.45 45.04 0.00
DfHh(298.15K) (kJ/mol) 808.10 592.89 609.58 619.06 272.71 310.49 335.87 359.13 414.52 473.08 507.64 519.67 539.23 117.68 198.39 208.17 222.25 264.64 63.12 83.19 156.52 140.88 163.19 19.09 22.59 34.42 32.22 41.65 22.69 16.10 2.10 60.43 38.72 41.34 101.62
nH8
(n = 0–7)
q (g/cm3) 1.309 1.1578 1.109 1.139 1.159 0.983 1.188 1.156 1.180 0.983 1.178 0.981 0.969 0.967 0.974 1.071 1.060 1.005 1.046 0.920 1.029 1.103 1.103 0.852 1.010 0.997 1.149 0.933 0.819 0.865 0.825 0.931 0.773 0.993 0.861
gen content, their averaged total energies of as a function of nitrogen atoms numbers (N) are presented in Fig. 2. The values of averaged total energies are the average of summation of all species containing same number nitrogen atoms. As shown in Fig. 2, it can be found that the energies of Nn(CH)8 nH8 gradually increase along with the increased replacement of CH groups by nitrogen atoms. The averaged total energies decreased linearly with the increase of the number of the nitrogen atoms. The energy will decrease about 16 a.u. with addition of one nitrogen atom. Our calculation can show that the stabilities of the isomers will reduce with the increment of the number of the CH groups to replace nitrogen atoms, which is agreement with the conclusion of the ref [15]. We choose the isomers of B2-1 and B3-3 with the similar energy to isomer B2-3 in order to compare the stability of isomer with the similar energy to N8H8 replaced by CH. We use the same methods
3.2. Energies analysis In Table 1, the total energy calculated at the B3LYP/6-311++G** and G3MP2 levels and corresponding relative energies are listed. The order of relative energies at the B3LYP6-311++G** and G3MP2 levels are almost same. For the species with different nitro-
Fig. 2. The averaged total energy of Nn(CH)8 content.
nH8
(n = 0–7) as a function of N
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Fig. 3. The optimized geometries of B2-1, B3-3, A4, A5, A6 and A7.
Table 2 Energies and relative energies at the G3MP2 level, heat of formation and density of some isomers Compound B2-3 B2-1 B3-3 A2 A3 A1 A5 A4 A7 A6
EB3LYP (a.u.) 442.635120 442.636855 442.633244 426.612323 426.606453 426.603981 426.599785 426.597612 426.594785 426.592558
EG3MP2 (a.u.) 439.857847 439.854994 439.855106 423.890577 423.886245 423.883246 423.875953 423.873109 423.872858 423.871319
Erel (kJ/ mol)
DfHh(298.25K) (kJ/mol)
q (g/
0.00 7.49 7.20 0.00 11.37 19.24 38.380 45.84 46.50 50.54
808.10 807.41 733.48 592.89 609.58 619.06 627.23 625.84 639.01 643.47
1.309 1.090 1.314 1.158 1.109 1.139 1.199 1.147 1.174 1.348
cm3)
Fig. 4. Schematic map of energy relationship of A1–A7.
and groups to perform geometric optimization, a series of new molecules A4, A5, A6 and A7 are obtained by replacing one nitrogen atom in N8H8 with a CH group in the configuration of B2-1 and B3-3 isomers; compare the result with that of using B2-3 to replace the same and discuss the corresponding stability. The optimized geometries of the B2-1, B3-3, A4, A5, A6 and A7 isomers, The calculated geometric parameters, charge density q in the bond critical point and Laplacian D2q all present in Fig. 3. In Table 2, we list the total energy (au) and relative energy Erel (kJ/mol) of B2-1, B3-3, B2-3, A1, A2, A3, A4, A5, A6 and A7 isomers. Energy results comparison of A1, A2, A3, A4, A5, A6 and A7 isomer on G3MP2 level are listed in Fig. 4. Our research results show that the energies of A1, A2 and A3 are lower than that of A4, A5, A6 and A7; Perhaps the stability of B2-3 is higher than that of B2-1 and B33, the stabilities of A1, A2 and A3 are higher than that of A4, A5, A6 and A7.; but A4, A5, A6 and A7 isomers we got by replacing B2-1 and B3-3 with CH-group are also stable. We also found that the formation heats of compounds which are replaced by CH groups have decreased to some degree. 3.3. Heats of formation (HOF) It is well-known that the HOF is an important property of energetic materials. An explosive with high performance show have high HOF. The experimental data of HOFs for many stable com-
Fig. 5. Heats of formation of Nn(CH)8
nH8
(n = 0–7) as a function of N content.
pounds have been obtained. However, it is impractical or dangerous for metastable compound, the energetic materials, to measure their HOFs experimentally. In these cases, the theoretical computation are carried out to predict their HOFs. In present paper, G3MP2 method is applied to calculate the HOF at 298 K of the Nn(CH)8 nH8 isomer molecule. The calculated values are present in Table 1. The results show that the isomers with high nitrogen
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content have high positive HOFs. The HOFs of studied molecules as a function of N content are presented in Fig. 5. As shown in Fig. 5, it is found that the heats of formation of the Nn(CH)8 nH8 molecules decrease along with the replacement of nitrogen atoms by CH groups. The HOFs become larger with the increment of N, which is agreement with the conclusion of the ref [15]. When the CH groups replaced the five nitrogen atoms of B2-3 frame, the HOFs become negative value. Our calculations show that the HOF of the C–N compound has good linear relationship with its nitrogen content. The molecules with high nitrogen content have high positive HOF.
bond and the lone pair electrons of neighboring N atom lead to the shorting of the neighboring C–N single bonds. The bigger the bond critical point charge density q is, the shorter the bond length becomes. The results show that the isomers with high nitrogen content have high positive HOFs. The heats of formation of the Nn(CH)8 nH8 molecules decrease along with the replacement of nitrogen atoms by CH groups. The HOF of the C–N compound has good linear relationship with its nitrogen content. The molecules with high nitrogen content have high positive HOF. The density of skeleton B2-3 is 1.309 g/cm3, which is the biggest one in the series of Nn(CH)8 nH8 compounds. Our calculations also show that the higher the nitrogen contains, the greater the density is.
3.4. Density The density of the compounds is also an important factor to affect explosives detonation. In order to obtain the density of Nn(CH)8 nH8, we used of Monte-Carlo method with B3LYP optimized structure to estimate the molar volume of molecule (based on the volume space which surrounded by 0.001/bohr3 equal density surface). Their densities are obtained by density formula: q = MT/Vmol (MT: the mole mass). From Table 1, we can see that the densities of the Nn(CH)8 nH8 (n = 0–7) molecule have no obvious change along with the replacement of nitrogen atoms by CH groups. But in general, the density of skeleton B2-3 is 1.309 g/ cm3, the biggest one in the series of Nn (CH) 8-nH8 compounds. It can also be found that the higher the nitrogen contains, the greater the density is. 4. Conclusions Quantum chemical methods are applied to study the 34 Nn(CH)8 nH8 (n = 0 7) isomers. The results show that the hyperconjugation effect between the p antibond orbital of C@N double
References [1] L.E. Fried, M.R. Manaa, P.F. Pagoria, R.L. Simpson, Annu. Rev. Mater. Res. 31 (2001) 291. [2] V. Hang, M.A. Hiskey, D. Chavez, J. Am. Chem. Soc. 127 (2005) 12537. [3] K. Muralidharan, B.A. Omotowa, B. Twamleym, Chem. Comm. (2005) 5193. [4] D.L. Strout, J. Phys. Chem. 110 (2006) 4089. [5] R. Sivabalan, M.B. Talawar, N. Senthilkumar, J. Therm. Anal. Cal. 78 (2004) 781. [6] T.M. Klapotke, B. Krumm, J. Galvez-ruiz, J. Inorg. Chem. 44 (2005) 9625. [7] P.A. Giguere, I.D. Liu, J. Chem. Phys. 20 (1952) 136. [8] U. Schurath, R.N. Schindler, J. Phys. Chem. 74 (1970) 188. [9] M. Zhao, B.M. Gimarc, J. Phys. Chem. 98 (1994) 7497. [10] M. Glukhovtsev, R.D. Bach, S. Laiter, Int. J. Quant. Chem. 62 (1997) 373. [11] D.W. Ball, J. Mol. Struct. (Theochem.) 619 (2002) 37. [12] W.B. David, J. Phys. Chem. A 105 (2001) 465. [13] S. Mao, X.M. Pu, L.C. Li, Y.J. Shu, A.M. Tian, Acta Chim. Sinica 64 (2006) 1429. [14] X.T. Su, L.C. Li, X. Wang, A.M. Tian, Acta Chim. Sinica 65 (2007) 1975. [15] G. Zhou, X.M. Pu, N.B. Wong, A.M. Tian, H.W. Zhou, J. Phys. Chem. A 110 (2006) 4107–4144. [16] K.F. Biegler, J. Schonbohm, R. Derdan, D. Bayles, R.F.W. Bader, AIM 2000. Version 2000. [17] A.E. Reed, F. Weinhold, L.A. Curtiss, D.J. Pochatko, J. Chem. Phys. 84 (1986) 5687. [18] M.J. Frisch, G.W. Trucks, H.B.A. Schlegel, et al., Gaussian 98, Revision A.7, Gaussian. Inc., Pittsburgh, PA, 1998.
Contents lists available at ScienceDirect
Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
Theoretical study on the structures and properties of the isomers of Nn(CH)8 nH8 (n = 0–7) Bo-Hua Xu a, Lai-Cai Li b,*, Li Sun b, AN-Min Tian c a
Department of Chemistry, Yangtze Normal University, Fuling, Chongqing 408003, PR China Department of Chemistry, Sichuan Normal University, Chengdu 610066, PR China c Department of Chemistry, Sichuan University, Chengdu 610064, PR China b
a r t i c l e
i n f o
Article history: Received 26 June 2008 Received in revised form 4 September 2008 Accepted 6 September 2008 Available online 18 September 2008 Keywords: Hydronitrogen compounds Density functional theory (DFT) Energy Heat of formation
a b s t r a c t With replacement of N atoms by CH groups in the most stable chain isomer of N8H8, 34 possible isomers of Nn(CH)8 nH8 (n = 0–7) have been designed and optimized at the B3LYP/6-311++G** level of theory. The natural bond orbital (NBO) and atoms in molecules (AIM) analysis are carried out to study the bonding nature and relative stabilities of these conformers. G3MP2 method is applied to calculate energies and heats of formation. The results indicate that the hyperconjugation effect from lone pairs of nitrogen atoms to germinal C–N bonds is the major factor which caused the change of the C–N bond length. With the more replacement of nitrogen atoms by CH groups, the heats of formation of the isomers of Nn(CH)8 nH8 (n = 0–7) decrease gradually, but the energies increase linearly. Crown copyright Ó 2008 Published by Elsevier B.V. All rights reserved.
1. Introduction Energetic materials, a substance with small volume and big heat-storing, play very important roles in aviation, ordnance industry and other high-tech fields. Los Alamos National Laboratory (LANL) of USA reported that high nitrogen content high materials (HNC-HEMs) is a kind of energetic material which have great potential, because its decomposition results in the formation of N2 and the release of a large quantity of energy [1]. In the high energy density compound, nitrogen-containing substances attract much attention of the chemists [2–6]. Since 1950s chemists have paid much attention to the theoretical and experimental researches on the NnHm clusters due to its contribution to the energetic materials although it is thermodynamically stable but kinetically unstable [7–8]. By quantum chemistry methods, one can obtain much information such as geometric configuration, energy, stability, bonding properties, spectroscopic properties, and etc. In recent years, more and more researches on NnHm are reported about its configuration parameters, vibrational frequencies, decomposition reactions and heat of formation [9–13]. We have reported the stability and tautomerism of N8H8 chain isomer [14]. Recently, a Gaussian-3 theory investigation using B3LYP geometries was carried out to examine the stability of (CH)xN8-x(0 6 x 6 8) isomers [15]. In present paper, a series of new Nn(CH)8 nH8 (n = 0–7) molecules are
* Corresponding author. E-mail addresses: [email protected], [email protected] (L.-C. Li).
obtained by successive replacement of N atoms with CH groups in a relatively stable configuration of the N8H8 chain isomers [14]. The geometric configurations, energies, discipline of the heat of formation, and density of this series of new Nn(CH)8 nH8 molecules are studied in detail by using the quantum chemical method. We also investigate the properties of the new energetic materials such as the heat of formation (HOF) and density. Our ultimate goal is to find the relationship between the nitrogen content and HOF or density and provide some new ideas for designing new energetic materials. 2. Computational details A molecular design was performed for the possible (CH)8 isomers. We replaced of the CH groups by nitrogen atoms to increase the nitrogen content as well as reduce the hydrogen content. We have obtained 34 possible structures. These isomers of Nn(CH)8 nH8 have been fully optimized at the B3LYP/6311++G** level of theory. For each species, the analyses of vibration are performed to obtain the zero point vibrational energies (ZPE) and to verify whether it is a minimum or not. Meanwhile, the electronic charge densities of critical points were calculated with AIM 2000 program package [16]. Furthermore, the orbital interaction is analyzed with the natural bond orbital (NBO) theory [17]. In addition, G3MP2 method is used to obtain more accurate energy and calculate the HOF at 298 K (DfHh(298K)). All calculations are carried out by using the Gaussian 98 program [18].
0166-1280/$ - see front matter Crown copyright Ó 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2008.09.007
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Fig. 1. The optimized geometries of Nn(CH)8
nH8
(n = 0–7) (a) bond length (nm); (b) charge density q in the bond critical point (a.u.); (c) Laplacian (a.u.)
B.-H. Xu et al. / Journal of Molecular Structure: THEOCHEM 870 (2008) 77–82
79
Fig. 1 (continued)
3. Results and discussions 3.1. Geometries analysis The 34 isomers are classified into eight groups: isomers A (the total is three) are used CH groups to replace one nitrogen atom in the most stable chain isomer of N8H8; the isomers E (the total is nine), F (the total is five), H (the total is five), I (the total is five), J (the total is three), and K (the total is three) are obtained by using CH groups to replace 2, 3, 4, 5, 6, 7 nitrogen atoms, respectively. The isomers O (only one) are formed by using CH groups to replace all nitrogen atoms. The vibration analysis indicates that the vibrational frequencies of these isomers are all positive, which show that these isomers are the minima on the potential energy surfaces. The optimized geometries of the 34 isomers are depicted in Fig. 1. The calculated geometric parameters, charge density q in
the bond critical point and Laplacian D2q are also presented in Fig. 1. As shown in Fig. 1, the N–N, N@N, C–N, C@N, C–C, and C@C bond lengths of these isomers are in the rang of 0.1349–0.1454, 0.1232–0.1246, 0.1365–0.1493, 0.1256–0.1282, 0.1501–0.1552, and 0.1334–0.1343 nm, respectively. While the standard bond lengths of N–N, N@N, C–N, C@N, C–C, C@C are 0.1450, 0.1250, 0.1470, 0.1280, 0.1540, and 0.1330 nm, respectively. One notice that the calculated bond distance is close to the corresponding standard bond lengths. Thus, the optimized structures of the species are reasonable. Meanwhile, a trend of bond length change can be found according to the data in Fig. 1. From Fig. 1, one can see that the C7–N4 bond connect to the C7@N3 double bond in the E8 isomer. The bond length of C7–N4 bond is 0.1369 nm, which is shorter than the other single bonds. The second-order stabilization energies (E (2)) of the isomer are
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Table 1 Total energies at the B3LYP level, G3MP2 energy, relative energies at the G3MP2 level, heat of formation at the 298.15 K, and density of Nn(CH)8 Compound B2-3 A2 A3 A1 E6 E8 E2 E9 E5 E4 E1 E3 E7 F3 F4 F2 F1 F5 H4 H2 H5 H1 H3 I1 I4 I3 I5 I2 J2 J1 J3 K2 K3 K1 O1
EB3LYP (a.u.) 442.635120 426.612323 426.606453 426.603981 410.655965 410.642261 410.634294 410.62395 410.605142 410.581469 410.569712 410.56765 410.557633 394.640043 394.609766 394.606681 394.601369 394.585956 378.58749 378.575111 378.552999 378.55763 378.545733 362.530592 362.52876 362.524148 362.521751 362.515153 346.472171 346.469364 346.462681 330.409274 330.402582 330.400545 314.349653
EG3MP2 (a.u.) 439.857847 423.890577 423.886245 423.883246 407.992422 407.977078 407.969401 407.95789 407.941832 407.914209 407.907008 407.903213 407.884503 392.031664 391.99955 391.999083 391.993575 391.975679 376.033875 376.02116 375.999731 375.99708 375.99563 360.032118 360.030653 360.025898 360.023448 360.015683 344.029023 344.026583 344.002355 328.021461 328.007195 328.004303 312.00958
calculated. The value of E (2) of the lone pair electrons of N4 atom and the p antibond orbital of C7–N3 bond is 126.1 kJ/mol. Thus, a p ? p conjugation interaction exists between the lone pair electrons of N4 atom and the p antibond orbital of C7–N3 bond. The interaction result in that the bond length of the C(7)–N(4) is shorter than other C–N single bonds. Therefore, the hyperconjugation effect between the p antibond orbital of C@N double bond and the lone pair electrons of neighboring N atom lead to the shorting of the neighboring C–N single bonds. A topological analysis of charge density q and its Laplacian D2q is carried out with the AIM theory. The Laplacian value of the bond critical point measures whether the electron density is locally concentrated (D2q < 0) or depleted (D2q > 0). As shown in Fig. 1, all lapacian values of the 34 isomers are negative, which shows that the N–N, N@N, C–N, C@N, C–C, and C@C bonds of Nn(CH)8 nH8 isomers are covalent bond. The charge density q of the bond critical point is a measurement of the bond strength and it has been observed to correlate with the traditional bond order. As shown in Fig. 1, the q of N–N bond is the biggest. The q of C–C bond is less than that of the C–N bond. Therefore, the descending order of bond lengths is the C–C bond > the C–N bond > the N–N bond. The C–C bond is weaker than those of the N–N bond. In other words, the bond critical point charge density q is bigger, the bond length is shorter.
Erel (kJ/mol) 0.00 0.00 11.37 19.24 0.00 40.28 60.44 90.66 132.82 205.34 224.25 234.21 283.34 0.00 84.31 85.54 100.00 146.98 0.00 33.38 89.64 96.60 100.41 0.00 3.84 16.33 22.76 43.15 0.00 6.40 70.01 0.00 37.45 45.04 0.00
DfHh(298.15K) (kJ/mol) 808.10 592.89 609.58 619.06 272.71 310.49 335.87 359.13 414.52 473.08 507.64 519.67 539.23 117.68 198.39 208.17 222.25 264.64 63.12 83.19 156.52 140.88 163.19 19.09 22.59 34.42 32.22 41.65 22.69 16.10 2.10 60.43 38.72 41.34 101.62
nH8
(n = 0–7)
q (g/cm3) 1.309 1.1578 1.109 1.139 1.159 0.983 1.188 1.156 1.180 0.983 1.178 0.981 0.969 0.967 0.974 1.071 1.060 1.005 1.046 0.920 1.029 1.103 1.103 0.852 1.010 0.997 1.149 0.933 0.819 0.865 0.825 0.931 0.773 0.993 0.861
gen content, their averaged total energies of as a function of nitrogen atoms numbers (N) are presented in Fig. 2. The values of averaged total energies are the average of summation of all species containing same number nitrogen atoms. As shown in Fig. 2, it can be found that the energies of Nn(CH)8 nH8 gradually increase along with the increased replacement of CH groups by nitrogen atoms. The averaged total energies decreased linearly with the increase of the number of the nitrogen atoms. The energy will decrease about 16 a.u. with addition of one nitrogen atom. Our calculation can show that the stabilities of the isomers will reduce with the increment of the number of the CH groups to replace nitrogen atoms, which is agreement with the conclusion of the ref [15]. We choose the isomers of B2-1 and B3-3 with the similar energy to isomer B2-3 in order to compare the stability of isomer with the similar energy to N8H8 replaced by CH. We use the same methods
3.2. Energies analysis In Table 1, the total energy calculated at the B3LYP/6-311++G** and G3MP2 levels and corresponding relative energies are listed. The order of relative energies at the B3LYP6-311++G** and G3MP2 levels are almost same. For the species with different nitro-
Fig. 2. The averaged total energy of Nn(CH)8 content.
nH8
(n = 0–7) as a function of N
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Fig. 3. The optimized geometries of B2-1, B3-3, A4, A5, A6 and A7.
Table 2 Energies and relative energies at the G3MP2 level, heat of formation and density of some isomers Compound B2-3 B2-1 B3-3 A2 A3 A1 A5 A4 A7 A6
EB3LYP (a.u.) 442.635120 442.636855 442.633244 426.612323 426.606453 426.603981 426.599785 426.597612 426.594785 426.592558
EG3MP2 (a.u.) 439.857847 439.854994 439.855106 423.890577 423.886245 423.883246 423.875953 423.873109 423.872858 423.871319
Erel (kJ/ mol)
DfHh(298.25K) (kJ/mol)
q (g/
0.00 7.49 7.20 0.00 11.37 19.24 38.380 45.84 46.50 50.54
808.10 807.41 733.48 592.89 609.58 619.06 627.23 625.84 639.01 643.47
1.309 1.090 1.314 1.158 1.109 1.139 1.199 1.147 1.174 1.348
cm3)
Fig. 4. Schematic map of energy relationship of A1–A7.
and groups to perform geometric optimization, a series of new molecules A4, A5, A6 and A7 are obtained by replacing one nitrogen atom in N8H8 with a CH group in the configuration of B2-1 and B3-3 isomers; compare the result with that of using B2-3 to replace the same and discuss the corresponding stability. The optimized geometries of the B2-1, B3-3, A4, A5, A6 and A7 isomers, The calculated geometric parameters, charge density q in the bond critical point and Laplacian D2q all present in Fig. 3. In Table 2, we list the total energy (au) and relative energy Erel (kJ/mol) of B2-1, B3-3, B2-3, A1, A2, A3, A4, A5, A6 and A7 isomers. Energy results comparison of A1, A2, A3, A4, A5, A6 and A7 isomer on G3MP2 level are listed in Fig. 4. Our research results show that the energies of A1, A2 and A3 are lower than that of A4, A5, A6 and A7; Perhaps the stability of B2-3 is higher than that of B2-1 and B33, the stabilities of A1, A2 and A3 are higher than that of A4, A5, A6 and A7.; but A4, A5, A6 and A7 isomers we got by replacing B2-1 and B3-3 with CH-group are also stable. We also found that the formation heats of compounds which are replaced by CH groups have decreased to some degree. 3.3. Heats of formation (HOF) It is well-known that the HOF is an important property of energetic materials. An explosive with high performance show have high HOF. The experimental data of HOFs for many stable com-
Fig. 5. Heats of formation of Nn(CH)8
nH8
(n = 0–7) as a function of N content.
pounds have been obtained. However, it is impractical or dangerous for metastable compound, the energetic materials, to measure their HOFs experimentally. In these cases, the theoretical computation are carried out to predict their HOFs. In present paper, G3MP2 method is applied to calculate the HOF at 298 K of the Nn(CH)8 nH8 isomer molecule. The calculated values are present in Table 1. The results show that the isomers with high nitrogen
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content have high positive HOFs. The HOFs of studied molecules as a function of N content are presented in Fig. 5. As shown in Fig. 5, it is found that the heats of formation of the Nn(CH)8 nH8 molecules decrease along with the replacement of nitrogen atoms by CH groups. The HOFs become larger with the increment of N, which is agreement with the conclusion of the ref [15]. When the CH groups replaced the five nitrogen atoms of B2-3 frame, the HOFs become negative value. Our calculations show that the HOF of the C–N compound has good linear relationship with its nitrogen content. The molecules with high nitrogen content have high positive HOF.
bond and the lone pair electrons of neighboring N atom lead to the shorting of the neighboring C–N single bonds. The bigger the bond critical point charge density q is, the shorter the bond length becomes. The results show that the isomers with high nitrogen content have high positive HOFs. The heats of formation of the Nn(CH)8 nH8 molecules decrease along with the replacement of nitrogen atoms by CH groups. The HOF of the C–N compound has good linear relationship with its nitrogen content. The molecules with high nitrogen content have high positive HOF. The density of skeleton B2-3 is 1.309 g/cm3, which is the biggest one in the series of Nn(CH)8 nH8 compounds. Our calculations also show that the higher the nitrogen contains, the greater the density is.
3.4. Density The density of the compounds is also an important factor to affect explosives detonation. In order to obtain the density of Nn(CH)8 nH8, we used of Monte-Carlo method with B3LYP optimized structure to estimate the molar volume of molecule (based on the volume space which surrounded by 0.001/bohr3 equal density surface). Their densities are obtained by density formula: q = MT/Vmol (MT: the mole mass). From Table 1, we can see that the densities of the Nn(CH)8 nH8 (n = 0–7) molecule have no obvious change along with the replacement of nitrogen atoms by CH groups. But in general, the density of skeleton B2-3 is 1.309 g/ cm3, the biggest one in the series of Nn (CH) 8-nH8 compounds. It can also be found that the higher the nitrogen contains, the greater the density is. 4. Conclusions Quantum chemical methods are applied to study the 34 Nn(CH)8 nH8 (n = 0 7) isomers. The results show that the hyperconjugation effect between the p antibond orbital of C@N double
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