C–N bond dissociation energies: An assessment of contemporary DFT methodologies

Journal of Molecular Structure: THEOCHEM 961 (2010) 97–100

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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem

C–N bond dissociation energies: An assessment of contemporary DFT methodologies Cai Qi a, Qiu-Han Lin a, Ya-Yu Li a, Si-Ping Pang a,⇑, Ru-Bo Zhang b,⇑⇑ a b

School of Material, Beijing Institute of Technology, Beijing 100081, China School of Science, Beijing Institute of Technology, Beijing 100081, China

a r t i c l e

i n f o

Article history: Received 3 March 2010 Received in revised form 3 September 2010 Accepted 3 September 2010 Available online 16 September 2010 Keywords: DFT evaluation CBS-QB3 C–CN bond Bond dissociation energies (BDE)

a b s t r a c t The assessment of the C–N bond dissociation energies is performed by using the various density functionals at 6-31+g(d,p) level. CBS-QB3 method was used to provide the theoretical benchmark values. The present results show that the three hybrid meta GGA functionals, BB1K, MPWB1K and M06 reproduce the experimental values well. M06-2X could normally overestimate the homolytic C–N bond dissociation energies. For the hybrid functionals, B3P86 and PBE1PBE can also behave almost as well as the above meta GGA functionals. Thus, they should be recommended as the most reliable method to estimate the energetic C–N bond dissociation energies. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction C–N bond plays an essential role in the modern high energy density materials (HEDMs). Such materials are characterized by high positive heat of formation, which is partially attributed to a large number of energetic C–N bonds included in the HEDMS, which contain N3, NH2 and NO2 groups [1]. In addition, the strength of the C– N bond is often used to indicate the stability and sensitivity of the HEDMs in some surroundings to some degree [2]. Therefore, an accurate estimation of the energetic C–N bond dissociation energy (BDE) will not only be useful to understand the decomposition mechanism and process of the energetic materials but also contribute to design and synthesize the new high-performance HEDMs. Nowadays, there are several experimental methods used to determine BDE values, such as the study of radical kinetics, the photoionization mass spectrometry method, and the acidity/electron affinity cycle method [3], most of which are focused on R–H bond. It is well known that many nitrogen radicals are highly reactive and unstable [4,5], so that the BDEs of the HEDMs are not facile to be obtained by the direct experimental techniques. Thanks to the rapid development of computer technology and theoretical chemistry, it becomes possible to estimate accurate BDEs based on the theoretical methods [6]. CBS series [7], Gn series [8–10], QCISD(T) [11], CCSD(T) [12] approaches are often used as ⇑ Corresponding author. Tel.: +86 1062767759. ⇑⇑ Corresponding author. E-mail addresses: [email protected] (S.-P. Pang), [email protected] (R.-B. Zhang). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.09.005

the benchmarking methods to calculate the BDE values unavailable experimentally. Unfortunately, their applications are greatly limited to the rather small systems. Density functional theories (DFT) have attracted much attention during the past ten years [13,14] because of its well cost-to-performance ratio and broad applicability. Among the DFT methods, the B3LYP had been popularly used. However, it has been pointed out that B3LYP has unsatisfactory performance issues, such as poor performances for transition metals, systematically underestimation of reaction barrier heights, and the inaccurate estimation of the weak interactions dominated by medium range correlation energy [13]. It is also worthy to be mentioned that a new family of hybrid meta functionals, which are involved with M06, M06-2X developed by Truhlar and Zhao et al., has been proved their validity in main group thermochemistry, thermochemical kinetics, noncovalent interactions and excited states [15]. In the present paper, the accurate assessment of the homolytic BDE of the C–N bond in the R–X (X = N3, NH2, NO2) molecules could be carried out in terms of the recently developed DFT methods so as to provide a solid basis for the rapid and accurate estimation of the HEDMs’ properties in the future. 2. Methodology The bond dissociation energy (BDE) is commonly known as the reaction enthalpy of the bond homolytic reaction (1).

AAB ! A  ðgÞ þ B  ðgÞ

ð1Þ

For many organics, the reaction enthalpy of reaction (1) is almost numerically equivalent to the reaction energy. Thus, the bond

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C. Qi et al. / Journal of Molecular Structure: THEOCHEM 961 (2010) 97–100

dissociation energy and bond dissociation enthalpy often appear interchangeably in the literature [3]. The R–X molecules are selected herein since the hemolytic BDEs of their C–N bonds could be available experimentally. R can be represented by the various groups and read in the following section. Geometries were optimized using B3LYP functional [16–18], combined with the standard 6-31+g(d,p) basis set. Frequency calculations were performed at the same level of theory, to confirm the correct nature of the stationary points and to extract the zero-point vibrational energies (ZPE). Afterwards, a series of single point calculations were performed using the four hybrid meta GGA functionals (BB1K [19], MPWB1K [20], M06 [15], M06-2X [15]) and the nine hybrid GGA functionals (B3LYP, B3P86 [16,18,21], B3PW91 [16,18,22], B97-1 [23], BH&HLYP [16,17], O3LYP [17,24,25], PBE1PBE [26], X3LYP [27], MPW1K [28]), combined with 6-31+G(d,p) basis set. The CBS-QB3 calculations were implemented to provide the benchmark values of the BDE. All the calculations were carried out using Gaussian 03 [29] and GAMESS-US [30] programs. 3. Results and discussion The 13 DFT functionals were used to calculate the C–N BDE of the nine molecules. In addition, a high-level ab initio CBS-QB3 method was performed to give an extensive comparison to the available experimental values. All the BDE values, together with the available experimental values, were shown in Table 1. Meanwhile, the RMSE of DFT methods with the CBS-QB3 results as the

reference data was also given. As shown in Table 1, the results of CBS-QB3 could normally reproduce the experimental values quite well and have the absolute error within 2.0 kcal/mol. Some exceptions could be found for C(NO2)3N3, C6H5NO2 and C6H5NH2 systems with the absolute error of 4  7 kcal/mol. Note that for the C–N bond dissociation, the BDE values from CBS-QB3 method always exhibit large error when the C is unsaturated [31]. Additionally, G3 calculation was carried out for C(NO2)3N3 and C6H5NO2. There is little difference between the BDE result of C6H5NO2 for G3 and CBS-QB3, whereas the evaluation of the BDE value of C(NO2)3N3 is beyond our current computational facility. Thus one could discretely compare experimental BDE values to those of the highquality ab initio CBS-QB3. 3.1. Homolytic dissociation of C–N bonds in R–N3 First, the three R–N3 molecules (R = methyl, phenyl, trinitromethyl) are selected in this section. The total performances of the thirteen functionals could be analyzed through mean unsigned errors (MUEs) and mean signed error (MSEs), which are displayed in Figs. 1 and 2, respectively. Seen from Fig. 1, the performance of the four hybrid meta GGA functionals is normally superior to that of the hybrid GGA functionals. The MUEs of BB1K, MPWB1K and M06 are ca. 2.5 kcal/ mol, while it is 4.1 kcal/mol for M06-2X. For the hybrid GGA functionals, B3P86 shows the MUE value less than 3.0 kcal/mol, while BH&HLYP shows the greatest MUE of 10.2 kcal/mol. The MUEs of

Table 1 Bond dissociation energies of the C–N bonds in the selected molecules (kcal/mol).

Methyl azide Phenyl azide Trinitromethyl azide Methylamine Benzenamine Benzylamine Nitromethane Nitrobenzene Nitromethyl benzene Max deviation Min deviation RMSE RMSEb a b

B3LYP

B3P86

64.1 81.2 62.7

68.9 86.4 68.1

B3PW91 B97-1 66.1 83.3 64.9

68.4 85.0 67.0

BH&HLYP 59.6 77.7 63.4

MPW1K 03LYP 64.1 82.3 67.4

65.0 80.9 59.7

PBE1PBE 67.8 85.5 68.7

X3LYP 64.7 82.0 64.0

BB1K 68.4 85.7 71.4

MPWB1 M06 69.3 86.8 73.1

68.5 84.9 71.4

M06-2X 72.1 90.0 81.6

71.2 91.6 77.2

86.3 98.8 64.2 54.1 67.2 40.7

91.1 103.9 69.8 58.1 71.5 44.9

88.2 100.8 66.9 55.1 68.1 42.1

91.4 103.5 69.3 58.0 70.5 44.3

82.8 95.2 61.7 55.1 69.1 42.3

87.0 99.5 66.5 57.2 70.9 44.7

87.3 98.8 64.6 51.6 62.8 37.6

90.0 102.9 69.3 57.4 70.8 44.8

86.9 99.5 65.0 55.0 68.3 41.7

91.5 103.0 70.7 59.0 72.1 46.1

92.4 104.1 71.8 60.3 73.7 47.5

91.4 103.2 70.3 59.7 72.6 47.5

93.3 105.9 75.2 62.0 75.4 52.1

84.7 106.7 73.5 60.9 77.2 50.3

8.3 0.3 2.7 9.2

5.1 0.8 1.3 5.2

7.2 1.8 1.9 7.6

5.4 0.9 1.6 5.9

12.1 1.6 3.3 10.3

7.6 0.2 2.3 6.8

11.4 1.3 3.2 10.8

4.9 0.1 1.6 5.4

7.3 0.9 2.4 8.3

5.5 0.4 1.5 4.6

6.4 0.2 1.6 3.8

5.4 0.6 1.5 4.5

11.0 0.3 3.3 3.5

6.6 0.5 2.2

The result of G3 calculation is 76.0 kcal/mol. CBS-QB3 results as the reference data.

Fig. 1. Mean unsigned errors (MUEs) of the 13 DFT functionals for the homolytic dissociation of C–N bonds.

CBS-QB3

Ref. 71.7 [33] 89.0 [33] 70.6 [33]

a

86.0 102.6 72.0 62.3 70.7 49.0

[34] [34] [35] [36] [35] [35]

C. Qi et al. / Journal of Molecular Structure: THEOCHEM 961 (2010) 97–100

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Fig. 2. Mean signed errors (MSEs) of the 13 DFT functional for the hemolytic dissociation of C–N bonds.

other hybrid GGA functionals such as B3LYP, O3LYP, and X3LYP are more than 7.0 kcal/mol. The performance of M06-2X should be addressed. Using this functional, Zhao and Truhlar calculated the BDEs of C–H, C–C, C–O and C–F bonds. Their conclusions showed that M06 and M06-2X could provide the best accuracy, compared to other functionals [32]. Herein, when R is methyl and phenyl groups, the resulting deviations of M06-2X are generally within 1.0 kcal/mol, as seen in Table 1 and Fig. 3. However, for trinitromethyl azide, M06-2X functional could overestimate the BDE value with a deviation of 11.0 kcal/mol. BB1K and M06 give the smallest deviation values of less than 1.0 kcal/mol for trinitromethyl azide, which are better than the cases for methyl azide and phenyl azide. It is also found from Table 1 and Fig. 2 that most of the functional underestimate the BDE values and give negative MSE values. It is absolutely true for B3LYP, BH&HLYP and O3LYP functionals. M062X is the only functional that has the positive MSE value. It needs to be emphasized that there are nearly no systematic deviations for MPWB1K, since the MSE of the method is approximate to zero.

All the meta GGA functionals outperform the hybrid GGA ones, except for M06-2X, as shown in Fig. 1. Each of BB1K, MPWB1K and M06 has an average MUE close to 2.6 kcal/mol. The MUE of M062X is 4.6 kcal/mol. For the hybrid GGA functionals, only B3P86 and PBE1PBE have the MUEs less than 3.0 kcal/mol and the maximum MUE is 7.0 kcal/mol found from BH&HLYP. All of the four meta GGA functionals overestimate the BDE value of methylamine largely, with the deviation values greater than 5.0 kcal/mol, as shown in Table 1 and Fig. 3. The maximum deviation value is 7.3 kcal/mol given by M06-2X. In contrast, several hybrid GGA functionals, namely B3LYP, MPW1K, X3LYP, become the best-performers for methylamine, with the deviation values less than 1.0 kcal/mol. However, their deviations are always large for the other two R–NH2 molecules. It could be concluded that the best-performing functionals for the BDE prediction of R–NH2 molecules are BB1K, MPWB1K, M06 and B3P86, PBE1PBE.

3.2. Homolytic dissociation of C–N bonds in R–NH2

In this section, the BDE of the C–N bonds are calculated using the following R–NO2 molecules, namely R = methyl, phenyl, benzyl. Since each of the four meta GGA functionals can give an average MUE of 2.0–4.0 kcal/mol, the performance of them should be better than that obtained from the hybrid GGA ones, as seen in Fig. 1. The

In this section, the homolytic BDEs of the C–N bonds in the amino-containing molecules, R–NH2 (R = methyl, phenyl, benzyl), are discussed.

3.3. Homolytic Dissociation of C–N bonds in R–NO2

Fig. 3. Deviations of the 13 DFT functional for the homolytic dissociation of C–N bonds.

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most accurate functional is M06, with a MUE of 2.0 kcal/mol. Besides the meta GGA functionals, some hybrid GGA ones, such as B3P86, B97-1, MPW1K, PBE1PBE also perform well, with the calculated MUEs of ca. 3.0 kcal/mol. Amongst the hybrid GGA functionals, O3LYP behaves worst and its MUE is close to 10.0 kcal/mol. It should be noted that the performance of most of the functionals is excellent for the calculated BDE of the C–N bond of nitrobenzene, as seen in Table 1 and Fig. 3. For example, PBE1PBE and B97-1 have the deviation values of 0.1 and 0.2 kcal/mol, respectively, much lower than they do in the other two R–NO2 molecules. M06-2X shows its better performance in the case of nitromethane. Its deviation value is 0.3 kcal/mol, while they are 4.7 and 3.1 kcal/ mol for nitrobenzene and nitromethyl benzene, respectively. The totally outlined performance of the 13 DFT functionals on the calculated BDE of the C–N bonds in the R–X molecules (X = N3, NH2, NO2) are also presented in Figs. 1 and 2. Based on our results, the performance of the four meta GGA functionals is more stable than that of the hybrid GGA functionals. MPWB1K, M06 and BB1K perform best amongst the selected functionals and their MUEs are 2.4, 2.4 and 2.5 kcal/mol, respectively. The second-best are B3P86 and PBE1PBE and their MUEs are close to 2.8 kcal/mol. Compared to the above functionals, B97-1 and M06-2X were less accurate, but still outperform the other remaining ones. The most popular functional, B3LYP, has a large MUE of 6.1 kcal/mol, as shown in Fig. 1. Meanwhile, the calculated BDEs with B3LYP are always lower by 6.0–8.0 kcal/mol than the corresponding experimental data, while M06-2X functional normally seems to more or less overestimate the C–N bond strength. The maximum deviation of M06-2X is 11.0 kcal/mol for trinitromethyl azide. Thus, the three meta GGA functionals – MPWB1K, M06, BB1K and the two hybrid GGA functionals – B3P86 and PBE1PBE are the reliable methods used for the estimation of the homolytic BDEs of the C–N bonds in R–X (X = N3, NH2, NO2).

4. Conclusions The 13 DFT functionals, including the nine hybrid GGA functionals and the four hybrid meta GGA functionals have been applied in the estimation of the BDE values of some energetic C–N bonds. Based on the present computational results, some conclusions could be drawn as follows: (1) Upon the calculation of the homolytic BDE of the C–N bond, the performance of the meta GGA functionals is normally more stable than that of the hybrid GGA functionals. (2) Based on the calculated MUE and MSE values, MPWB1K, BB1K, M06 and B3P86, PBE1PBE should be recommended to calculate the homolytic BDE of the C–N bond.

(3) M06-2X could normally overestimate the homolytic C–N bond dissociation energies, while B3LYP significantly underestimates the BDE values by 6–8 kcal/mol. Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant Nos. 20772011, 20703004.

Reference [1] M.H.V. Huynh, M.A. Hiskey, E.L. Hartline, D.P. Montoya, R. Gilardi, Angew. Chem.-Int. Edit. 43 (2004) 4924. [2] X.S. Song, X.L. Cheng, X.D. Yang, B. He, Propellants Explos. Pyrotech. 31 (2006) 306. [3] S.J. Blanksby, G.B. Ellison, Acc. Chem. Res. 36 (2003) 255. [4] C. Larson, Y. Ji, P.C. Samartzis, A. Quinto-Hernandez, J.J.M. Lin, T.T. Ching, C. Chaudhuri, S.H. Lee, A.M. Wodtke, J. Phys. Chem. A 112 (2008) 1105. [5] R.F. Klima, A.V. Jadhav, P.N.D. Singh, M.X. Chang, C. Vanos, J. Sankaranarayanan, M. Vu, N. Ibrahim, E. Ross, S. McCloskey, R.S. Murthy, J.A. Krause, B.S. Ault, A.D. Gudmundsdottir, J. Org. Chem. 72 (2007) 6372. [6] D.J. Grant, M.H. Matus, J.R. Switzer, D.A. Dixon, J.S. Francisco, K.O. Christe, J. Phys. Chem. A 112 (2008) 3145. [7] C.J. Hayes, C.M. Hadad, J. Phys. Chem. A 113 (2009) 12370. [8] H. Fukaya, T. Ono, T. Abe, J. Phys. Chem. A 105 (2001) 7401. [9] J.R.B. Gomes, J. Phys. Chem. A 113 (2009) 1628. [10] M.J. Li, L. Liu, Y. Fu, Q.X. Guo, J. Phys. Chem. B 109 (2005) 13818. [11] C. Baciu, J.W. Gauld, J. Phys. Chem. A 107 (2003) 9946. [12] P.C. do Couto, B.J.C. Cabral, J.A.M. Simoes, Chem. Phys. Lett. 421 (2006) 504. [13] Y. Zhao, D.G. Truhlar, Acc. Chem. Res. 41 (2008) 157. [14] S.F. Sousa, P.A. Fernandes, M.J. Ramos, J. Phys. Chem. A 111 (2007) 10439. [15] Y. Zhao, D.G. Truhlar, Theor. Chem. Acc. 120 (2008) 215. [16] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [17] C.T. Lee, W.T. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [18] A.D. Becke, J. Chem. Phys. 104 (1996) 1040. [19] Y. Zhao, B.J. Lynch, D.G. Truhlar, J. Phys. Chem. A 108 (2004) 2715. [20] Y. Zhao, D.G. Truhlar, J. Phys. Chem. A 108 (2004) 6908. [21] J.P. Perdew, Phys. Rev. B 33 (1986) 8822. [22] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [23] F.A. Hamprecht, A.J. Cohen, D.J. Tozer, N.C. Handy, J. Chem. Phys. 109 (1998) 6264. [24] N.E. Schultz, Y. Zhao, D.G. Truhlar, J. Phys. Chem. A 109 (2005) 11127. [25] A.J. Cohen, N.C. Handy, Mol. Phys. 99 (2001) 607. [26] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 78 (1997) 1396. [27] X. Xu, W.A. Goddard, PNAS 101 (2004) 2673. [28] B.J. Lynch, P.L. Fast, M. Harris, D.G. Truhlar, J. Phys. Chem. A 104 (2000) 4811. [29] M.J. Frisch, G.W. Trucks, H.B. Schlegel, GAUSSIAN 03, Revision B.01, Gaussian, Inc., Pittsburgh, 2003. [30] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14 (1993) 1347. [31] H. Chen, X. Cheng, Z. Ma, X. Su, J. Mol. Struct.: THEOCHEM 807 (2007) 43. [32] Y. Zhao, D.G. Truhlar, J. Phys. Chem. A 112 (2008) 1095. [33] V.I. Pepkin, Y.N. Matyushin, G.K. Khisamutdinov, V.I. Slovetskii, A.A. Fainzilberg, Khim. Fiz. 12 (1993) 1399. [34] L.M. Kostikova, E.A. Miroshnichenko, J.O. Inozemtcev, Y.N. Matyushin, Efficient energies of interaction of functional groups and energies of dissociation bonds in alkylnitrates, Inter Ann Conf of ICT, 32nd, 2001, p. 1. [35] J.B. Pedley, R.D. Naylor, S.P. Kirby, Thermochemical Data of Organic Compounds, second ed., Chapman and Hall, New York, 1986. [36] E.C.M. Chen, E.S. Chen, Int. J. Ion Mobility. Spectrom. 5 (2002) 11.