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On the choice of optimal protocol for calculation of 13C and 15N NMR isotropic chemical shifts in nitramine systems
Journal of Molecular Structure: THEOCHEM 940 (2010) 124–128
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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
On the choice of optimal protocol for calculation of isotropic chemical shifts in nitramine systems
13
C and
15
N NMR
Ricardo Infante-Castillo a, Samuel P. Hernández-Rivera b,* a b
Department of Physics–Chemistry, University of Puerto Rico-Arecibo, P.O. Box 4010, Arecibo PR 00613-4010, Puerto Rico Department of Chemistry, University of Puerto Rico-Mayagüez, Call Box 9000, Mayagüez PR 00681-9000, Puerto Rico
a r t i c l e
i n f o
Article history: Received 12 August 2009 Received in revised form 21 October 2009 Accepted 21 October 2009 Available online 25 October 2009 Keywords: CSGT GIAO 13 C and 15N NMR Nitramines
a b s t r a c t Calculated nuclear magnetic resonance (NMR) chemical shifts (13C and 15N) are reported for the RDX conformers and additional nine cyclic and acyclic nitramines. In order to establish a convenient and consistent protocol to be employed for confirming the experimental 13C and 15N NMR spectra of nitramine compounds, different combinations of models and basis sets were considered. The most reliable results were obtained at B3LYP/6-311+G(2d,p) level and CSGT model and can be used to calculate 13C and 15N NMR chemical shifts with a very high accuracy for nitramine compounds. These results show that the agreement between theoretical and experimental 15N NMR chemical shieldings of nitramines could be used for the evaluation of the intrinsic relationship between structure and explosive properties. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It is well known that nuclear magnetic resonance (NMR) is one of the most powerful and extensively used experimental methods to probe the electronic and molecular structures of a wide range of compounds. A significant part of the NMR spectral information is the chemical shifts which are used in structural assignments. Liquid solution NMR is one of the techniques that have been used to study energetic materials. Relationships between liquid-state isotropic chemical shifts and explosive characteristics have been investigated by Zeman and co-workers [1–3]. On the basis of 15N NMR spectroscopy data, Zeman suggested that the centers of initiation reactivity (hot spots) in molecules of nitramines depend on the electron density and steric effects on its aza-atoms [2]. The chemical shifts of these atoms should correlate with characteristics of individual energetic materials. In this sense, the measured NMR spectra in combination with calculations of NMR chemical shifts have proven to be useful tools in interpreting experimental data [4–6]. Several computational methods have been developed for the calculation of nuclear magnetic shielding tensors. It is generally accepted that accurate prediction of these properties within the finite basis approximation requires gauge-invariant procedures [7] and a correction for electron correlation. Density functional theory (DFT) has emerged in the past decade as an approximate but computationally inexpensive method of treating electron correlation. This often gives performance comparable to a second order * Corresponding author. Tel.: +1 787 832 4040x3450; fax: +1 787 265 5404. E-mail address: [email protected] (S.P. Hernández-Rivera). 0166-1280/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.10.026
Møller–Plesset theory (MP2) and has already yielded promising results for the calculation of NMR shieldings [8]. The root mean square (RMS) error achieved at the B3LYP/6-311+G(2d,p) level for 13 C chemical shifts was 4.2 ppm [9]. The present work is focused on predicting NMR shielding tensors at the DFT/B3LYP level of theory with two different models: gauge-including atomic orbital (GIAO) [10] and continuous sets of gauge transformations (CSGT) [11], and two different basis sets, 6-311+G(2d,p) and cc-pvtz [12]. The solvent effect on the theoretical NMR parameters was included using the Integral Equation Formulation (IEF) for the Polarizable Continuum Model (PCM) [13]. The consistency and efficiency of the considered combinations of models and basis sets considered on NMR calculations were thoroughly checked by the analysis of statistical parameters involving computed and experimental 13C NMR/15N NMR chemical shift values. The tested nitramines were four acyclic compounds: (1) 1-nitro-1-azaethane (MNA); (2) N,N-dimethylnitramine (DMNA); (3) 1,1-dinitro-1-aza-ethane (MDN); (4) N,N-diethylnitroamine (DENA) and six cyclic compounds: (5) 1,3-dinitro-1,3-diazacyclobutane (TETRAGEN); (6) 1,1,3-trinitroazetidine (TNAZ); (7) 1,3-dinitro-1,3-diazacyclopentane (CPX); (8) N-nitropiperidine (NP); (9) 1,4-dinitro-1,4-diazacyclo-hexane (DNDC) and (10) hexahydro1,3,5-trinitro-s-triazine (RDX) (see Fig. 1 for the chemical structures). Molecules of nitromethane and tetramethylsilane (TMS) were also included as reference compounds. In addition, we also report the 15N chemical shift tensors of a- and b-RDX and discussed the theoretical model necessary to accurately calculate these values according to the molecular structure. The a-form is the stable polymorph at room temperature with Cs symmetry.
R. Infante-Castillo, S.P. Hernández-Rivera / Journal of Molecular Structure: THEOCHEM 940 (2010) 124–128
CH 3
N
NO 2 H
N CH 3
(1)
N CH 3
CH 3
(2) N
CH 3 CH 2
NO 2
NO 2
(3) NO 2
NO 2
NO 2
N
N
CH 2 CH 3
NO 2
NO 2
N
(4) O 2N
(5)
O 2N
(6)
N
N
NO 2 O 2N
N
N N
O 2N
NO2
(8)
(7)
NO 2
125
optimizations at a relatively low computational expenditures. The calculations of NMR shielding tensors were done at the B3LYP level of theory using GIAO and CSGT models, and using as input the structure optimized at the B3LYP/6-311+G(d,p) level. Two basis sets were applied to perform these calculations. One of them is the standard Pople style basis set 6-311+G(2d,p) which is a triple split valence with one additional diffuse sp-function and two d-functions on heavy atoms and one p-function on hydrogen atoms. The other basis set which was tested was the correlation consistent polarized Valence Triple Zeta (cc-pVTZ) which gave good results in describing the effect of a strong electron-withdrawing group (NO2) in the NMR shielding tensors [17]. The chemical shifts were calculated against the selected shielding of appropriate nuclei in the reference molecule and calculated for the same solvent, basis set and computational method: di = rrefri.
(9) 4. Results
NO 2 N N
N
O 2N
NO 2
(10) Fig. 1. Representation of chemical structures of studied compounds.
On the other hand, the b-polymorph has a molecular symmetry of C3v. The structural sensitivity of 15N chemical shifts provides an opportunity to use 15N solid-state NMR spectroscopy in conjunction with theoretical calculations to study the conformational differences present in the RDX polymorphs. Based on the present study, we suggest that, among the methods and basis sets considered, the best prediction of the 13C and 15N values was obtained at the CSGT model using the 6-311+G(2d,p) basis set. 2. Experimental All NMR measurements were performed using a Bruker 500 MHz spectrometer system and a Varian 300 MHz spectrometer. Samples were examined in DMSO-d6 solutions and compared with previous acetone-d6 solution results [14]. The solvent signal, calibrated against Me4Si, was used as a reference for proton and carbon-13 spectra. The 15N chemical shifts were referenced to the signal of an external standard: CH3NO2. 13C (99%) enriched RDX was obtained from Cambridge Isotope Laboratories, Inc. (Andover, MA) as 1 mg/mL acetonitrile solution and 15N (99%) enriched RDX was obtained from Dr. Ronald Spanggord, Stanford Research Institute, Menlo Park, CA., as solid material. Solid-state Cross-Polarization/Magic Angle Spinning (CP/MAS) 15N NMR spectra were obtained from Dr. Kevin Thorn, U.S. Geological Survey. These were recorded on a Chemagnetics CMX-200 spectrometer at a nitrogen resonant frequency of 20.27 MHz. Acquisition parameters included a 2.0 ms contact time, pulse delay of 0.5 s and spinning rate of 5 kHz. The 13C and 15N NMR chemical shifts for some nitramines were obtained from literature [14,15]. The 15N NMR chemical shifts for substances not yet synthesized have been predicted and reported [1]. 3. Computations The GAUSSIAN 03 [16] software package was used for all theoretical calculations. All the molecular geometries were optimized at the B3LYP/6–311+(d,p) level, which can give good geometry
Table 1 shows the calculated NMR chemical shifts in solution and their comparison with the experimental data for 10 nitramines. The DFT B3LYP hybrid functional with 6-311G(d,p) basis sets was used to generate the optimized structure of the studied compounds. 13C and 15N chemical shielding calculations were converted into the predicted chemical shifts using tetramethylsilane and nitromethane values, calculated at the same level of the theory. NMR experiments were measured in acetone and dimethylsulfoxide solutions. The predicted chemical shift values using DFT method of calculations are in agreement with the corresponding NMR experimental values. The theoretical calculations of 15N and 13C NMR chemical shifts for acyclic nitramines and cyclic nitramines (Table 1) were performed with GIAO and CSGT models, through the B3LYP level of theory applying two different basis sets. Based on the 13C and 15N chemical shifts, data presented in Table 1 and the fits (Fig. 2), one can deduce that the DFT approach, combined with an appropriate model and basis set represents a good compromise between accuracy and computational time, yielding carbon and nitrogen chemical shifts in agreement with experimental values. Results of linear regression fits between experimental and calculated chemical shifts (13C) performed for the ten nitramines tested are summarized in Table 2. The regression coefficients (R2) between calculated and experimental chemical shifts ranged from a high of 0.991 for 13C in the CSGT/cc-pVTZ model to a low 0.979 in the GIAO/cc-pVTZ model. Also, the 15N amine chemical shifts in acyclic nitramines show a robust correlation coefficient of 0.997 ± 0.001 using the CSGT model in both basis sets (6-311+G(2d,p) and cc-pVTZ). Most of the experimental chemical shifts were smaller than the calculated values. The largest deviations from experimental values were observed in the 15N (amine) calculated chemical shifts. Fig. 3 shows the effects of the basis sets in the GIAO and CSGT calculations when the geometry optimizations of the structures utilized as inputs in the GIAO and CSGT calculations were performed at DFT theory. The solid-state CP/ MAS 15N NMR spectrum of RDX is shown in Fig. 4. 5. Discussion The CSGT/6-311+G(2d,p) model was the most efficient in predicting the 13C chemical shifts of the compounds taken in consideration, displaying both the lowest mean absolute error (MAE) parameters and the highest linear correlation coefficients (R2). This is illustrated in Fig. 3 and is supported by the results presented in Tables 2 and 3. The presence of anomalous trends in reproducing the experimental chemical shifts determined by each combination of models of NMR parameters calculations and basis sets used can be outlined by inspecting Table 3 and by looking the trends shown
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Table 1 13 C and
15
N experimental and theoretical chemical shifts for nitramines using different models and basis set.
Compound
Experimental
GIAO
CSGT
6–311+(2d,p)
cc-PVTZ
6–311+(2d,p)
cc-PVTZ
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
1
32.40
220.2 22.2
35.61
220.42 29.53
35.30
222.09 28.40
35.34
222.94 29.44
35.35
222.97 30.17
2
40.00
215.6 23.6
40.91
227.70 35.41
45.51
207.34 18.24
41.70
213.40 28.8
41.71
215.3 30.34
3
41.50
89.7 38.8
43.1
74.2 42.35
45.6
94.31 57.54
42.2
81.3 42.1
43.91
104 66.94
4
46.40 11.80
192.6 27.6
49.60 12.10
196.00 40.01
49.80 12.60
198.00 38.00
50.00 12.20
197.46 39.54
50.05 12.62
201 39.58
5
/
203.62 27.83
86.64
226.35 27.84
86.48
226.88 26.42
86.08
226.40 26.90
85.95
229.21 29.24
6
65.0 105.0
212
70.73 116.76
231.90 16.94 28.07
70.55 116.46
232.67 14.52 26.43
70.11 114.46
232.41 16.42 27.57
70.24 114.93
234.16 15.26 28.33
209.01 31.21
70.86 51.82
196.09 35.98
70.95 51.94
197.02 34.54
70.20 51.21
197.52 35.58
71.11 5205
200.11 36.54
196.0 22.0
47.31 25.24 21.91
220.35 40.29
48.59 24.97 21.84
205.53 33.97
48.46 24.67 21.75
203.37 35.62
48.03 26.53 23.56
221.33 40.02
205.49 26.26
50.69
200.37 32.50
50.81
202.24 31.77
50.3
201.82 32.15
51.14
203.71 33.13
AAA 59.96
AAA 195.17 44.51 EEE 207.75 47.61 AAE
AAA 60.16
AAA 195.27 42.52 EEE 209.33 45.27 AAE
AAA 59.51
AAA 196.71 43.67 EEE 209.7 47.25 AAE
AAA 60.37
AAA 198.37 44.42 EEE 211.55 47.3 AAE
7 8
49.3 25.2 23.8
9 10 b-RDX
60.80
199.10 34.7
EEE 64.49 AAE
a-RDX
61.5
61.80
187.5/175.4
202.1/193.0 38.2/35.8
EEE 65.02 AAE 63.48
206.7/195.1 40.1/41.0
AAE 61.6
206.4/196.3 41.4/40.9
EEE 65.14 AAE 62.63
207.6/196.4 42.0/41.3
Table 2 Slope (a), intercept (b) and linear correlation coefficient (R2) found for the different combinations of models and basis sets for 13C and 15N NMR calculations.
70
60
Calculated chemical shift (ppm)
EEE 64.10
Straight-line
a
b
R2
13
1.01 ± 0.04 1.02 ± 0.05 1.01 ± 0.04 0.99 ± 0.03 1.16 ± 0.06 0.95 ± 0.06 1.07 ± 0.04 0.90 ± 0.03
0.21 ± 1.70 0.64 ± 2.22 0.14 ± 1.67 1.51 ± 1.43 30.12 ± 11.31 9.96 ± 11.89 14.38 ± 7.88 23.49 ± 5.81
0.987 0.979 0.988 0.991 0.995 0.992 0.997 0.998
C-GIAO/6-311+G(2D,P) C-GIAO/CC-PVTZ C-CSGT/6-311+G(2D,P) 13 C-CSGT/CC-PVTZ 15 N-GIAO/6-311+G(2D,P)a 15 N-GIAO/CC-PVTZa 15 N-CSGT/6-311+G(2D,P)a 15 N-CSGT/CC-PVTZa 13
50
13
40
30 a
Acyclic nitramines.
20
10
0 10
20
30
40
50
60
70
Experimental chemical shift (ppm) Fig. 2. Linear relationships and regressions between experimental and theoretical DFT predicted 13C NMR chemical shifts for cyclic and acyclic nitramines using different models and basis set; (s) GIAO/6-311+G(2d,p), (d) GIAO/cc-pVTZ, (N) CSGT/6-311+G(2d,p), (4) CSGT/ cc-pVTZ.
in Fig. 3. For the GIAO and CSGT calculations, it is interesting to note that a general overestimation of 15N-(amine/nitro) chemical shifts occurs using the 6-311+G (2d,p) and cc-pVTZ basis sets,
respectively. The corresponding MAE values are 11.52/8.25 and 9.80/8.46. In contrast, best results were obtained using the 6-311+G(2d,p) basis set together with the CSGT model. The R2 values reported suggest that the improvement of the 13C NMR results involved the CSGT model and cc-pVTZ basis set (see Table 2). However, the use of 6-311+G(2d,p) basis set in the 13C CSGT calculations provided better results according to the lowest MAE values. The results from Tables 2 and 3 show slight discrepancies for the GIAO model between theoretical and experimental data. This behavior could be attributed to some limitation of the GIAO model in describing the effect of the strong electron-withdrawing group (NO2) in the NMR shielding tensor. To evaluate this hypothesis, the GIAO model was replaced by CSGT to predict the NMR shielding tensors for nitramines 1–10, using the 6-311+G(2d,p) and cc-pVTZ basis sets. The CSGT model at the B3LYP/6-311+G(2d,p) level led to the best agreement between theoretical and experi-
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12 11 10
Mean absolute error (MAE)
9 8 7 6 5 4 3 2 1 0 GIAO/6-311+G(2d,p)
GIAO/CC-PVTZ
CSGT/6-311+G(2d,p)
CSGT/CC-PVTZ
Model / basis set Fig. 3. Mean absolute error for the 13C (d), 15N -Nitro (s) and 15N-amine (N) NMR calculations at different models using different basis set. The geometry optimizations of the structures utilized as inputs were performed at B3LYP/6-311+G(2d,p) theory level.
Table 3 Mean absolute error (MAE) for the different combinations of models and basis sets used for 13C and 15N NMR calculations. Model/basis set
Mean absolute error (MAE) 13
GIAO/6-311+G(2d,p) GIAO/CC-PVTZ CSGT/6-311+G(2d,p) CSGT/CC-PVTZ
Fig. 4. Solid-state CP/MAS
15
N NMR spectrum of a-RDX.
mental data for the 10 studied nitramines. An important point that should be mentioned is that while the cc-pVTZ basis set gives 534 basis functions for RDX, the 6-311+G(2d,p) produces 441 basis functions which lead to shorter computational time with the same accuracy level for the 13C and 15N NMR chemical shifts. For all methods, the full qualitative agreement between the calculated and experimental values of the chemical shifts was achieved. The order of the values of the chemical shifts is comparable with the experimentally determined values.
C NMR
1.57 2.22 1.52 1.57
15
15
11.52 8.00 7.33 9.80
8.25 7.86 6.83 8.46
N (Amine)
N (Nitro)
In the case of RDX, the solid-state CP/MAS 15N NMR spectrum of solid RDX (Fig. 4) was compared to the solution spectrum. The solid-phase 15N NMR spectrum of the RDX provided additional resolution over the liquid solution spectrum. The two resonances observed in the 15N NMR CP/MAS spectrum (Fig. 4) from 170 to 190 of RDX suggest a non-equivalent magnetic environment. The relative sizes of the peaks are related, in part, to the number of each type of nitrogen atom present in the molecule. It is noteworthy that in Fig. 4 the peak at 187.5 ppm is much larger than the 175.4 ppm peak. This peak (187.5 ppm) is generated by the two nitrogen atoms with the NO2 groups in axial positions. The 15N NMR spectrum of the solid RDX is significantly different from that in a solution. For the 15N NMR spectrum in a solution only one amine signal was found. The difference arises because in solution, the molecular symmetry of RDX is C3V, whereas, in the solid-state, the molecules occupy sites of Cs symmetry and the amine–nitrogen atoms are different. The increase in symmetry from Cs to C3V is consistent with the decrease in the resonance signals in the solution spectrum of RDX. Two possible structures with C3V symmetry are possible in solution: all nitro groups occupying axial positions (AAA conformer) and all nitro groups occupying pseudo-equatorial positions (EEE conformer). Theoretical predictions of chemical shifts indicate that the molecular geometry of RDX, in solution, is consistent with
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R. Infante-Castillo, S.P. Hernández-Rivera / Journal of Molecular Structure: THEOCHEM 940 (2010) 124–128
the AAA conformer. On the other hand, the solid-state CP/MAS 13C NMR spectrum of RDX exhibited a single peak at 61.5 ppm, close to the liquid state chemical shift of 60.8 ppm in deuterated dimethylsulfoxide. The 13C NMR chemical shift is less susceptible to the chemical environment for the polymorphs of RDX. One of the most valuable properties of the chemical shieldings is their sensitivity to the molecular geometry and environment. The experiments provided only the values of chemical shifts, which were later assigned into the molecular framework by comparison with the calculated values. The high accuracy achievable by modern chemical shielding calculations allows its use in revising questionable assignments.
6. Conclusions In order to suggest a convenient and consistent protocol to be employed to confirm the experimental 13C and 15N spectra of nitramine compounds, different combinations of models and basis sets were considered. The CSGT was considered to be a better model than the GIAO to evaluate the gauge origin of the vector potential describing the external magnetic field for the compounds studied here. The most reliable results were obtained at B3LYP/6311+G(2d,p) level and CSGT model and can be used to calculate 13 C and 15N NMR chemical shifts with very high accuracy for nitramine compounds. The theoretical results of chemical shielding obtained in this study for RDX compared with experimental results indicate 15N-amine NMR chemical shift sensitivity to the molecular geometry. These results show that the agreement between theoretical and experimental 15N-amine NMR chemical shieldings of nitramines could be used to evaluate the intrinsic relationship between structure and explosive properties. Acknowledgments This work was supported by the U.S. Department of Defense, University Research Initiative Multidisciplinary–University Research Initiative (URI)-MURI Program, under Grant No. DAAD1902-1-0257. The authors also acknowledge contributions from Aaron LaPointe of Night Vision and Electronic Sensors Directorate, Department of Defense. The project was also supported by the U.S. Department of Homeland Security under Award No. 2008-ST-061-ED0001. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security.
The authors also thank the Chemical Imaging Center of the Department of Chemistry of University of Puerto Rico-Mayagüez for the support of this project. References [1] S. Zeman, Analysis and predictions of the Arrhenius parameters of low temperature thermolysis of nitramines by means of the 15N NMR spectroscopy, Thermochim. Acta 333 (1999) 121–129. [2] S. Zeman, New aspects of initiation reactivities of energetic materials demonstrated on nitramines, J. Hard Mater. 132 (2006) 155–164. [3] D. Klasovity´, S. Zeman, A. Ru˚zˇicˇka, M. Jungová, M. Rohácˇ, Cis-1,3,4,6Tetranitrooctahydroimidazo-[4,5-d]-imidazole (BCHMX), its properties and initiation reactivity, J. Hard Mater. 164 (2009) 954–961. [4] R. Infante-Castillo, S.P. Hernández-Rivera, L.A. Rivera, Vibrational and NMR studies of benzimidazole and alkyl derivatives, J. Mol. Struct. 877 (2008) 10– 19. [5] R. Infante-Castillo, S.P. Hernández-Rivera, Theoretical DFT, vibrational and structural characterization of 1-propenyl-2-methylbenzimidazole and its isomers, J. Mol. Struct. 892 (2008) 477–484. [6] R. Infante-Castillo, S.P. Hernández-Rivera, DFT studies of the structure and vibrational and NMR spectra of 1-(2-methylpropenyl)-2-methylbenzimidazole, J. Mol. Struct. 917 (2009) 158–163. [7] J. Facceli, Calculations of chemical shieldings: theory and applications, Concept Magn. Reson. A 20 (2004) 42–69. [8] G. Rauhut, S. Puyear, K. Wolinski, P. Pulay, Comparison of NMR shieldings calculated from Hartree–Fock and density functional wave functions using Gauge-including atomic orbitals, J. Phys. Chem. 100 (1996) 6310–6316. [9] J.R. Cheeseman, G.W. Trucks, T.A. Keith, J.M. Frisch, A comparison of models for nuclear magnetic resonance shielding tensors, J. Chem. Phys. 104 (1996) 5497– 5508. [10] R. Ditchfield, Self consistent perturbation theory of diamagnetism. A gaugeinvariant LCAO method for NMR chemical shifts, Mol. Phys. 27 (1974) 789– 794. [11] T. Keith, R. Bader, Calculation of magnetic response properties using a continuous set of gauge transformations, Chem. Phys. Lett. 179 (1993) 479– 482. [12] T. Dunning, D. Woon, Gaussian basis sets for use in correlated molecular calculations, J. Chem. Phys. 90 (1995) 1007–1017. [13] B. Mennucci, J. Tomasi, Continuum solvation models. A new approach to the problem of solute’s distribution and cavity boundaries, J. Chem. Phys. 106 (1997) 5151–5156. [14] S. Bulusu, T. Axenrod, J.R. Autera, Application of 13C and 15N NMR spectroscopy to structural studies on nitramines, Org. Magn. Reson. 16 (1981) 52–56. [15] R. Infante-Castillo, S.P. Hernández-Rivera, Theoretical and experimental vibrational and NMR studies of RDX, Proc. SPIE 6201 (2006) 62012F (1–8). [16] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, J.L. Andres, M. Head-Gordon, E.S. Replogle, J.A. Pople, GAUSSIAN 03 (Revision A.9), Gaussian, Inc., Pittsburgh, 2003. [17] C. Tormena, G. da Silva, Chemical shifts calculations on aromatic systems: a comparison of model and basis sets, Chem. Phys. Lett. 398 (2004) 466–470.
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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
On the choice of optimal protocol for calculation of isotropic chemical shifts in nitramine systems
13
C and
15
N NMR
Ricardo Infante-Castillo a, Samuel P. Hernández-Rivera b,* a b
Department of Physics–Chemistry, University of Puerto Rico-Arecibo, P.O. Box 4010, Arecibo PR 00613-4010, Puerto Rico Department of Chemistry, University of Puerto Rico-Mayagüez, Call Box 9000, Mayagüez PR 00681-9000, Puerto Rico
a r t i c l e
i n f o
Article history: Received 12 August 2009 Received in revised form 21 October 2009 Accepted 21 October 2009 Available online 25 October 2009 Keywords: CSGT GIAO 13 C and 15N NMR Nitramines
a b s t r a c t Calculated nuclear magnetic resonance (NMR) chemical shifts (13C and 15N) are reported for the RDX conformers and additional nine cyclic and acyclic nitramines. In order to establish a convenient and consistent protocol to be employed for confirming the experimental 13C and 15N NMR spectra of nitramine compounds, different combinations of models and basis sets were considered. The most reliable results were obtained at B3LYP/6-311+G(2d,p) level and CSGT model and can be used to calculate 13C and 15N NMR chemical shifts with a very high accuracy for nitramine compounds. These results show that the agreement between theoretical and experimental 15N NMR chemical shieldings of nitramines could be used for the evaluation of the intrinsic relationship between structure and explosive properties. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It is well known that nuclear magnetic resonance (NMR) is one of the most powerful and extensively used experimental methods to probe the electronic and molecular structures of a wide range of compounds. A significant part of the NMR spectral information is the chemical shifts which are used in structural assignments. Liquid solution NMR is one of the techniques that have been used to study energetic materials. Relationships between liquid-state isotropic chemical shifts and explosive characteristics have been investigated by Zeman and co-workers [1–3]. On the basis of 15N NMR spectroscopy data, Zeman suggested that the centers of initiation reactivity (hot spots) in molecules of nitramines depend on the electron density and steric effects on its aza-atoms [2]. The chemical shifts of these atoms should correlate with characteristics of individual energetic materials. In this sense, the measured NMR spectra in combination with calculations of NMR chemical shifts have proven to be useful tools in interpreting experimental data [4–6]. Several computational methods have been developed for the calculation of nuclear magnetic shielding tensors. It is generally accepted that accurate prediction of these properties within the finite basis approximation requires gauge-invariant procedures [7] and a correction for electron correlation. Density functional theory (DFT) has emerged in the past decade as an approximate but computationally inexpensive method of treating electron correlation. This often gives performance comparable to a second order * Corresponding author. Tel.: +1 787 832 4040x3450; fax: +1 787 265 5404. E-mail address: [email protected] (S.P. Hernández-Rivera). 0166-1280/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.10.026
Møller–Plesset theory (MP2) and has already yielded promising results for the calculation of NMR shieldings [8]. The root mean square (RMS) error achieved at the B3LYP/6-311+G(2d,p) level for 13 C chemical shifts was 4.2 ppm [9]. The present work is focused on predicting NMR shielding tensors at the DFT/B3LYP level of theory with two different models: gauge-including atomic orbital (GIAO) [10] and continuous sets of gauge transformations (CSGT) [11], and two different basis sets, 6-311+G(2d,p) and cc-pvtz [12]. The solvent effect on the theoretical NMR parameters was included using the Integral Equation Formulation (IEF) for the Polarizable Continuum Model (PCM) [13]. The consistency and efficiency of the considered combinations of models and basis sets considered on NMR calculations were thoroughly checked by the analysis of statistical parameters involving computed and experimental 13C NMR/15N NMR chemical shift values. The tested nitramines were four acyclic compounds: (1) 1-nitro-1-azaethane (MNA); (2) N,N-dimethylnitramine (DMNA); (3) 1,1-dinitro-1-aza-ethane (MDN); (4) N,N-diethylnitroamine (DENA) and six cyclic compounds: (5) 1,3-dinitro-1,3-diazacyclobutane (TETRAGEN); (6) 1,1,3-trinitroazetidine (TNAZ); (7) 1,3-dinitro-1,3-diazacyclopentane (CPX); (8) N-nitropiperidine (NP); (9) 1,4-dinitro-1,4-diazacyclo-hexane (DNDC) and (10) hexahydro1,3,5-trinitro-s-triazine (RDX) (see Fig. 1 for the chemical structures). Molecules of nitromethane and tetramethylsilane (TMS) were also included as reference compounds. In addition, we also report the 15N chemical shift tensors of a- and b-RDX and discussed the theoretical model necessary to accurately calculate these values according to the molecular structure. The a-form is the stable polymorph at room temperature with Cs symmetry.
R. Infante-Castillo, S.P. Hernández-Rivera / Journal of Molecular Structure: THEOCHEM 940 (2010) 124–128
CH 3
N
NO 2 H
N CH 3
(1)
N CH 3
CH 3
(2) N
CH 3 CH 2
NO 2
NO 2
(3) NO 2
NO 2
NO 2
N
N
CH 2 CH 3
NO 2
NO 2
N
(4) O 2N
(5)
O 2N
(6)
N
N
NO 2 O 2N
N
N N
O 2N
NO2
(8)
(7)
NO 2
125
optimizations at a relatively low computational expenditures. The calculations of NMR shielding tensors were done at the B3LYP level of theory using GIAO and CSGT models, and using as input the structure optimized at the B3LYP/6-311+G(d,p) level. Two basis sets were applied to perform these calculations. One of them is the standard Pople style basis set 6-311+G(2d,p) which is a triple split valence with one additional diffuse sp-function and two d-functions on heavy atoms and one p-function on hydrogen atoms. The other basis set which was tested was the correlation consistent polarized Valence Triple Zeta (cc-pVTZ) which gave good results in describing the effect of a strong electron-withdrawing group (NO2) in the NMR shielding tensors [17]. The chemical shifts were calculated against the selected shielding of appropriate nuclei in the reference molecule and calculated for the same solvent, basis set and computational method: di = rrefri.
(9) 4. Results
NO 2 N N
N
O 2N
NO 2
(10) Fig. 1. Representation of chemical structures of studied compounds.
On the other hand, the b-polymorph has a molecular symmetry of C3v. The structural sensitivity of 15N chemical shifts provides an opportunity to use 15N solid-state NMR spectroscopy in conjunction with theoretical calculations to study the conformational differences present in the RDX polymorphs. Based on the present study, we suggest that, among the methods and basis sets considered, the best prediction of the 13C and 15N values was obtained at the CSGT model using the 6-311+G(2d,p) basis set. 2. Experimental All NMR measurements were performed using a Bruker 500 MHz spectrometer system and a Varian 300 MHz spectrometer. Samples were examined in DMSO-d6 solutions and compared with previous acetone-d6 solution results [14]. The solvent signal, calibrated against Me4Si, was used as a reference for proton and carbon-13 spectra. The 15N chemical shifts were referenced to the signal of an external standard: CH3NO2. 13C (99%) enriched RDX was obtained from Cambridge Isotope Laboratories, Inc. (Andover, MA) as 1 mg/mL acetonitrile solution and 15N (99%) enriched RDX was obtained from Dr. Ronald Spanggord, Stanford Research Institute, Menlo Park, CA., as solid material. Solid-state Cross-Polarization/Magic Angle Spinning (CP/MAS) 15N NMR spectra were obtained from Dr. Kevin Thorn, U.S. Geological Survey. These were recorded on a Chemagnetics CMX-200 spectrometer at a nitrogen resonant frequency of 20.27 MHz. Acquisition parameters included a 2.0 ms contact time, pulse delay of 0.5 s and spinning rate of 5 kHz. The 13C and 15N NMR chemical shifts for some nitramines were obtained from literature [14,15]. The 15N NMR chemical shifts for substances not yet synthesized have been predicted and reported [1]. 3. Computations The GAUSSIAN 03 [16] software package was used for all theoretical calculations. All the molecular geometries were optimized at the B3LYP/6–311+(d,p) level, which can give good geometry
Table 1 shows the calculated NMR chemical shifts in solution and their comparison with the experimental data for 10 nitramines. The DFT B3LYP hybrid functional with 6-311G(d,p) basis sets was used to generate the optimized structure of the studied compounds. 13C and 15N chemical shielding calculations were converted into the predicted chemical shifts using tetramethylsilane and nitromethane values, calculated at the same level of the theory. NMR experiments were measured in acetone and dimethylsulfoxide solutions. The predicted chemical shift values using DFT method of calculations are in agreement with the corresponding NMR experimental values. The theoretical calculations of 15N and 13C NMR chemical shifts for acyclic nitramines and cyclic nitramines (Table 1) were performed with GIAO and CSGT models, through the B3LYP level of theory applying two different basis sets. Based on the 13C and 15N chemical shifts, data presented in Table 1 and the fits (Fig. 2), one can deduce that the DFT approach, combined with an appropriate model and basis set represents a good compromise between accuracy and computational time, yielding carbon and nitrogen chemical shifts in agreement with experimental values. Results of linear regression fits between experimental and calculated chemical shifts (13C) performed for the ten nitramines tested are summarized in Table 2. The regression coefficients (R2) between calculated and experimental chemical shifts ranged from a high of 0.991 for 13C in the CSGT/cc-pVTZ model to a low 0.979 in the GIAO/cc-pVTZ model. Also, the 15N amine chemical shifts in acyclic nitramines show a robust correlation coefficient of 0.997 ± 0.001 using the CSGT model in both basis sets (6-311+G(2d,p) and cc-pVTZ). Most of the experimental chemical shifts were smaller than the calculated values. The largest deviations from experimental values were observed in the 15N (amine) calculated chemical shifts. Fig. 3 shows the effects of the basis sets in the GIAO and CSGT calculations when the geometry optimizations of the structures utilized as inputs in the GIAO and CSGT calculations were performed at DFT theory. The solid-state CP/ MAS 15N NMR spectrum of RDX is shown in Fig. 4. 5. Discussion The CSGT/6-311+G(2d,p) model was the most efficient in predicting the 13C chemical shifts of the compounds taken in consideration, displaying both the lowest mean absolute error (MAE) parameters and the highest linear correlation coefficients (R2). This is illustrated in Fig. 3 and is supported by the results presented in Tables 2 and 3. The presence of anomalous trends in reproducing the experimental chemical shifts determined by each combination of models of NMR parameters calculations and basis sets used can be outlined by inspecting Table 3 and by looking the trends shown
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Table 1 13 C and
15
N experimental and theoretical chemical shifts for nitramines using different models and basis set.
Compound
Experimental
GIAO
CSGT
6–311+(2d,p)
cc-PVTZ
6–311+(2d,p)
cc-PVTZ
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
d13C
d15N (amine) d15N (nitro)
1
32.40
220.2 22.2
35.61
220.42 29.53
35.30
222.09 28.40
35.34
222.94 29.44
35.35
222.97 30.17
2
40.00
215.6 23.6
40.91
227.70 35.41
45.51
207.34 18.24
41.70
213.40 28.8
41.71
215.3 30.34
3
41.50
89.7 38.8
43.1
74.2 42.35
45.6
94.31 57.54
42.2
81.3 42.1
43.91
104 66.94
4
46.40 11.80
192.6 27.6
49.60 12.10
196.00 40.01
49.80 12.60
198.00 38.00
50.00 12.20
197.46 39.54
50.05 12.62
201 39.58
5
/
203.62 27.83
86.64
226.35 27.84
86.48
226.88 26.42
86.08
226.40 26.90
85.95
229.21 29.24
6
65.0 105.0
212
70.73 116.76
231.90 16.94 28.07
70.55 116.46
232.67 14.52 26.43
70.11 114.46
232.41 16.42 27.57
70.24 114.93
234.16 15.26 28.33
209.01 31.21
70.86 51.82
196.09 35.98
70.95 51.94
197.02 34.54
70.20 51.21
197.52 35.58
71.11 5205
200.11 36.54
196.0 22.0
47.31 25.24 21.91
220.35 40.29
48.59 24.97 21.84
205.53 33.97
48.46 24.67 21.75
203.37 35.62
48.03 26.53 23.56
221.33 40.02
205.49 26.26
50.69
200.37 32.50
50.81
202.24 31.77
50.3
201.82 32.15
51.14
203.71 33.13
AAA 59.96
AAA 195.17 44.51 EEE 207.75 47.61 AAE
AAA 60.16
AAA 195.27 42.52 EEE 209.33 45.27 AAE
AAA 59.51
AAA 196.71 43.67 EEE 209.7 47.25 AAE
AAA 60.37
AAA 198.37 44.42 EEE 211.55 47.3 AAE
7 8
49.3 25.2 23.8
9 10 b-RDX
60.80
199.10 34.7
EEE 64.49 AAE
a-RDX
61.5
61.80
187.5/175.4
202.1/193.0 38.2/35.8
EEE 65.02 AAE 63.48
206.7/195.1 40.1/41.0
AAE 61.6
206.4/196.3 41.4/40.9
EEE 65.14 AAE 62.63
207.6/196.4 42.0/41.3
Table 2 Slope (a), intercept (b) and linear correlation coefficient (R2) found for the different combinations of models and basis sets for 13C and 15N NMR calculations.
70
60
Calculated chemical shift (ppm)
EEE 64.10
Straight-line
a
b
R2
13
1.01 ± 0.04 1.02 ± 0.05 1.01 ± 0.04 0.99 ± 0.03 1.16 ± 0.06 0.95 ± 0.06 1.07 ± 0.04 0.90 ± 0.03
0.21 ± 1.70 0.64 ± 2.22 0.14 ± 1.67 1.51 ± 1.43 30.12 ± 11.31 9.96 ± 11.89 14.38 ± 7.88 23.49 ± 5.81
0.987 0.979 0.988 0.991 0.995 0.992 0.997 0.998
C-GIAO/6-311+G(2D,P) C-GIAO/CC-PVTZ C-CSGT/6-311+G(2D,P) 13 C-CSGT/CC-PVTZ 15 N-GIAO/6-311+G(2D,P)a 15 N-GIAO/CC-PVTZa 15 N-CSGT/6-311+G(2D,P)a 15 N-CSGT/CC-PVTZa 13
50
13
40
30 a
Acyclic nitramines.
20
10
0 10
20
30
40
50
60
70
Experimental chemical shift (ppm) Fig. 2. Linear relationships and regressions between experimental and theoretical DFT predicted 13C NMR chemical shifts for cyclic and acyclic nitramines using different models and basis set; (s) GIAO/6-311+G(2d,p), (d) GIAO/cc-pVTZ, (N) CSGT/6-311+G(2d,p), (4) CSGT/ cc-pVTZ.
in Fig. 3. For the GIAO and CSGT calculations, it is interesting to note that a general overestimation of 15N-(amine/nitro) chemical shifts occurs using the 6-311+G (2d,p) and cc-pVTZ basis sets,
respectively. The corresponding MAE values are 11.52/8.25 and 9.80/8.46. In contrast, best results were obtained using the 6-311+G(2d,p) basis set together with the CSGT model. The R2 values reported suggest that the improvement of the 13C NMR results involved the CSGT model and cc-pVTZ basis set (see Table 2). However, the use of 6-311+G(2d,p) basis set in the 13C CSGT calculations provided better results according to the lowest MAE values. The results from Tables 2 and 3 show slight discrepancies for the GIAO model between theoretical and experimental data. This behavior could be attributed to some limitation of the GIAO model in describing the effect of the strong electron-withdrawing group (NO2) in the NMR shielding tensor. To evaluate this hypothesis, the GIAO model was replaced by CSGT to predict the NMR shielding tensors for nitramines 1–10, using the 6-311+G(2d,p) and cc-pVTZ basis sets. The CSGT model at the B3LYP/6-311+G(2d,p) level led to the best agreement between theoretical and experi-
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12 11 10
Mean absolute error (MAE)
9 8 7 6 5 4 3 2 1 0 GIAO/6-311+G(2d,p)
GIAO/CC-PVTZ
CSGT/6-311+G(2d,p)
CSGT/CC-PVTZ
Model / basis set Fig. 3. Mean absolute error for the 13C (d), 15N -Nitro (s) and 15N-amine (N) NMR calculations at different models using different basis set. The geometry optimizations of the structures utilized as inputs were performed at B3LYP/6-311+G(2d,p) theory level.
Table 3 Mean absolute error (MAE) for the different combinations of models and basis sets used for 13C and 15N NMR calculations. Model/basis set
Mean absolute error (MAE) 13
GIAO/6-311+G(2d,p) GIAO/CC-PVTZ CSGT/6-311+G(2d,p) CSGT/CC-PVTZ
Fig. 4. Solid-state CP/MAS
15
N NMR spectrum of a-RDX.
mental data for the 10 studied nitramines. An important point that should be mentioned is that while the cc-pVTZ basis set gives 534 basis functions for RDX, the 6-311+G(2d,p) produces 441 basis functions which lead to shorter computational time with the same accuracy level for the 13C and 15N NMR chemical shifts. For all methods, the full qualitative agreement between the calculated and experimental values of the chemical shifts was achieved. The order of the values of the chemical shifts is comparable with the experimentally determined values.
C NMR
1.57 2.22 1.52 1.57
15
15
11.52 8.00 7.33 9.80
8.25 7.86 6.83 8.46
N (Amine)
N (Nitro)
In the case of RDX, the solid-state CP/MAS 15N NMR spectrum of solid RDX (Fig. 4) was compared to the solution spectrum. The solid-phase 15N NMR spectrum of the RDX provided additional resolution over the liquid solution spectrum. The two resonances observed in the 15N NMR CP/MAS spectrum (Fig. 4) from 170 to 190 of RDX suggest a non-equivalent magnetic environment. The relative sizes of the peaks are related, in part, to the number of each type of nitrogen atom present in the molecule. It is noteworthy that in Fig. 4 the peak at 187.5 ppm is much larger than the 175.4 ppm peak. This peak (187.5 ppm) is generated by the two nitrogen atoms with the NO2 groups in axial positions. The 15N NMR spectrum of the solid RDX is significantly different from that in a solution. For the 15N NMR spectrum in a solution only one amine signal was found. The difference arises because in solution, the molecular symmetry of RDX is C3V, whereas, in the solid-state, the molecules occupy sites of Cs symmetry and the amine–nitrogen atoms are different. The increase in symmetry from Cs to C3V is consistent with the decrease in the resonance signals in the solution spectrum of RDX. Two possible structures with C3V symmetry are possible in solution: all nitro groups occupying axial positions (AAA conformer) and all nitro groups occupying pseudo-equatorial positions (EEE conformer). Theoretical predictions of chemical shifts indicate that the molecular geometry of RDX, in solution, is consistent with
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the AAA conformer. On the other hand, the solid-state CP/MAS 13C NMR spectrum of RDX exhibited a single peak at 61.5 ppm, close to the liquid state chemical shift of 60.8 ppm in deuterated dimethylsulfoxide. The 13C NMR chemical shift is less susceptible to the chemical environment for the polymorphs of RDX. One of the most valuable properties of the chemical shieldings is their sensitivity to the molecular geometry and environment. The experiments provided only the values of chemical shifts, which were later assigned into the molecular framework by comparison with the calculated values. The high accuracy achievable by modern chemical shielding calculations allows its use in revising questionable assignments.
6. Conclusions In order to suggest a convenient and consistent protocol to be employed to confirm the experimental 13C and 15N spectra of nitramine compounds, different combinations of models and basis sets were considered. The CSGT was considered to be a better model than the GIAO to evaluate the gauge origin of the vector potential describing the external magnetic field for the compounds studied here. The most reliable results were obtained at B3LYP/6311+G(2d,p) level and CSGT model and can be used to calculate 13 C and 15N NMR chemical shifts with very high accuracy for nitramine compounds. The theoretical results of chemical shielding obtained in this study for RDX compared with experimental results indicate 15N-amine NMR chemical shift sensitivity to the molecular geometry. These results show that the agreement between theoretical and experimental 15N-amine NMR chemical shieldings of nitramines could be used to evaluate the intrinsic relationship between structure and explosive properties. Acknowledgments This work was supported by the U.S. Department of Defense, University Research Initiative Multidisciplinary–University Research Initiative (URI)-MURI Program, under Grant No. DAAD1902-1-0257. The authors also acknowledge contributions from Aaron LaPointe of Night Vision and Electronic Sensors Directorate, Department of Defense. The project was also supported by the U.S. Department of Homeland Security under Award No. 2008-ST-061-ED0001. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security.
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