First principle calculations of solid nitrobenzene under high pressure

Accepted Manuscript First principle calculations of solid nitrobenzene under high pressure Wen-Peng Wang, Fu-Sheng Liu, Qi-Jun Liu, Zheng-Tang Liu PII: DOI: Reference:

S2210-271X(15)00413-2 http://dx.doi.org/10.1016/j.comptc.2015.10.014 COMPTC 1961

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Computational & Theoretical Chemistry

Received Date: Revised Date: Accepted Date:

31 July 2015 10 October 2015 13 October 2015

Please cite this article as: W-P. Wang, F-S. Liu, Q-J. Liu, Z-T. Liu, First principle calculations of solid nitrobenzene under high pressure, Computational & Theoretical Chemistry (2015), doi: http://dx.doi.org/10.1016/j.comptc. 2015.10.014

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First principle calculations of solid nitrobenzene under high pressure Wen-Peng Wang a, b, Fu-Sheng Liu a, b, , Qi-Jun Liu a, b, Zheng-Tang Liu c a

School of Physical Science and Technology, Southwest Jiaotong University, Key

Laboratory of Advanced Technologies of Materials, Ministry of Education of China, Chengdu 610031, People’s Republic of China b

Sichuan Provincial Key Laboratory (for Universities) of High Pressure Science and

Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China c

State Key Laboratory of Solidification Processing, School of Materials Science and

Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China



Corresponding author at : Institute of High Temperature and High Pressure Physics, Southwest Jiaotong University, Key Laboratory of Advanced Technologies of Materials, Ministry of Education, Chengdu 610031, PR China. Tel.: +86 02887601758. E-mail address: [email protected] 1

Abstract The dispersion corrected density functional theory (DFT-D) calculations were performed to study the structural and vibrational properties of solid nitrobenzene at ambient pressure. Assignments of the calculated vibrational modes were provided. Moreover, using the norm-conserving pseudopotential plus GGA-PBE function, the unit cell parameters, geometries and vibrational frequencies of nitrobenzene were examined under hydrostatic pressure from 0 to 10 GPa. The calculated pressure dependence of lattice parameters and volume were found to be close to the experimental results, but a distinct change in the bond lengths and bond angles was found around 7 GPa. According to the phonon calculations, the pressure-induced changes of the vibrational frequencies were also observed around 7 GPa. These calculated results all suggest a possible structural transformation in the crystalline nitrobenzene.

Key words: nitrobenzene, DFT, high pressure

1. Introduction Nitrobenzene (NB) is widely known as a prototype energetic material, it has the simplest structure of aromatic nitro compounds. Over the past few decades, many teams of researchers have studied its physical and chemical properties. In particular, the molecular structure has been widely investigated by microwave [1], gas-phase electron diffraction [2], and X-ray diffraction technique [3, 4] as well as some

2

theoretical efforts [5, 6]. Moreover, extensive studies of its decomposition mechanisms and processes [7-9] have been proposed. The structural properties of energetic materials are known to be pressure dependence, thus one should expect noticeable differences between the isolated molecules and condensed phase [10-15]. The crystalline structure of NB at zero pressure has been determined by Boese [3] and Trotter [4]. As shown in Figure 1, the structure of NB crystal is a monoclinic lattice with space group P21/c, which includes four molecules per unit cell. The dimer was formed through intermolecular hydrogen bonds C-H1…O2 [3,10]. Because of the limited of empirical studies, there was no more studies examined the crystal phase under high-pressure except Kozu [16]. The first principles calculation based on density functional theory (DFT) has become one of the most powerful tools to study energetic materials, and some accurate and interesting calculated results have been obtained [17-22]. Compared with the standard DFT, the DFT-D as parameterized by Grimme [23] provides significant improvements for describing intermolecular interactions in molecular crystals [24]. To the best of our knowledge, there are no theoretical reports available on solid NB. Thus, present work may expect to conduct and further get much more valuable information on NB through the DFT calculations.

2. Computational details DFT calculations were performed with Cambridge Sequential Total Energy Package (CASTEP) code [25, 26]. Pseudo atomic calculations were performed for

3

H1s1, C2s22p2, N2s22p3 and O2s22p4. The generalized gradient approximation (GGA) with the PBE parameterization [27] and plane-wave basis set with norm-conserving pseudopotentials [28] and energy cutoff of 830 eV was used. The empirical dispersion correction by Grimme [23] was used to take into account weak interactions. The Broyden, Fletcher, Goldfrab, and Shannon (BFGS) algorithm [29] was utilized to optimize the unit cell parameters and atomic coordinates, while constraining the space group of NB. Structural optimizations were achieved by setting the convergence criteria for maximum total energies of 5×10-6 eV/atom, maximum force of 0.01 eV/ Å，maximum stress of 0.02 GPa and maximum displacement of 5×10-4 Å. The Brillouin zone sampling was obtained using constant Monkhorst−Pack [30] grid of 4×1×1 points. As starting input for the calculations, we adopted the experimental crystal structure of solid NB [3], its cell parameters were a = 3.801 Å, b = 11.615 Å, c = 12.984 Å and V = 571.4 Å3. Following the full optimization of the lattice parameters at ambient pressure, we simulated the gradual loading of hydrostatic pressure up to 10 GPa. Crystalline vibrations were obtained by computing phonon frequencies at Gamma point using the finite displacement method [31].

3. Results and discussion 3.1 Crystal and molecular structure at ambient pressure The calculated structural parameters of solid NB compared with the experimental data [3, 4] are presented in Table 1. The results show that the optimized atomic coordinates are in good agreement with the experimental data. Also, the calculated

4

equilibrium lattice parameter c is overestimated by 0.79%; a and b are underestimated by 2.9% and 1.1% respectively. Moreover, our simulations predict that the unit cell volume is smaller than experimental results, namely the value of the V is underestimated by 4.6%. It may be a substantial thermal expansion of the crystal lattices at room temperature [21]. In contrast, the standard GGA calculations overestimate a, b, c and V by 34.3%, 1.8%, 7.8% and 44.9%, respectively; while LDA calculations underestimate by 4.6%, 3.8%, 3.9% and 11.6%, respectively, which confirmed that the DFT-D approach can correctly describe the solid NB at ambient pressure. The geometric parameters of NB molecule in the crystal at ambient pressure are listed in Table 2. The calculated bond lengths of C1-C2, C2-C3, and C3-C4 are found to be 1.396 Å, 1.389 Å and 1.396 Å respectively. Compared with the corrected experimental results, our calculated mean error is 0.16%. The bond lengths of C-N and N-O are 1.455 Å and 1.261 Å. Both the 6-31G and 6-31G* methods [5] underestimated the C-N bond compared with experimental values [3]. Moreover, the theoretical C-N-O and O-N-O bond angles are in good agreement with the experimental results. The calculated results indicated that DFT-D approach able to be used in describing the intramolecular geometry. 3.2 Vibrational properties at ambient pressure Vibrational spectroscopy is a valuable tool for probing molecular changes on the atomic or molecular level [9-11, 32]. Based on the optimized structures, we have calculated the vibrational modes of crystal NB using the finite displacement method

5

[31]. There are 56 atoms in the unit cell of solid NB. For space group P21/C, a group theoretical analysis classifies the vibrational modes into 42Au + 42Bu + 42Ag + 42Bg. They include internal and lattice vibrations, where Au and Bu are IR active, Ag and Bg are Raman active. The previous PBE-D work calculated the similar molecular crystal [33, 34], where the calculated vibrational modes were in good agreement with experiments. The computed vibrations and mode assignments of solid NB are listed in Table 3. For simplicity, we only present the internal vibrations of the Raman modes with frequency higher than 390 cm-1. Because of the lack of experimental data about solid NB, we only compare with previous liquid results [6]. The lower frequency modes, from 390 to 600 cm-1, correspond to the modes of the C-C-C out (in) of plane bending and NO2 bending. The modes of C-H out of plane bending are found around 670-970 cm-1. The vibrations between 1000 and 1300 cm-1 combine with C-H in of plane bending, C-C-C triangle bending and C-N stretching. The modes of NO2 stretching and ring stretching are located at the frequency range from 1350 to 1600 cm-1. In the high-frequency region, 3100-3150 cm-1 correspond to C-H stretch modes, which are higher than the liquid experimental results [6]. The difference is possibly associated with intermolecular interaction [35]. 3.3 High-Pressure Behavior of Solid NB. 3.3.1. The pressure effects on the lattice parameters. The pressure effects on the lattice parameters of the crystal NB are shown in Figure 2. The results are compared with previous X-ray diffraction data [16]. Overall, the trends of the calculated cell parameters with the increasing pressure are in

6

accordance with experiment. However, it is seen that a change of the lattice parameters occurs around 7 GPa. The compressibility along a-axis orientation is higher than that along the b and c orientations due to the vdW interactions between the layers. After comparing calculated results with experiments, we can conclude that the norm-conserving pseudopotentials method provide reasonable results. In Figure 3, we plot the unit cell volume as a function of pressure, together with previous experiments. It was shown that the volume decreases monotonically with pressure. The difference between theoretical and experimental volumes decreases from 4.6% at 0 GPa to 2.3% at 5 GPa. This result implies that the PBE-D simulation performed under high-pressure might be more reliable due to the enhanced intermolecular interaction [19]. According to the unit cell volume as a function of pressure for the NB, we fitted the bulk modulus B0 and its first pressure derivative B´ using the Murnaghan equation of state [36]. The fitted values of B0 and B´are found to be 10.4 GPa and 7.1, and the experimental [16] B0 and B´are found to be 9.2 GPa and 6.2. We also calculated the bulk modulus by the Voigt-Reuss-Hill approximations [37], the calculated value of B0 is 10.1 GPa. From these results, it indicates that the calculated bulk modulus is reasonable. 3.3.2. Vibrational properties under high-pressure To gain insight on the high-pressure behavior of solid NB, the phonon calculations were employed in this work. Here, the vibrational modes were implemented by the finite displacements approach [31]. Figure 4 shows the pressure-induced frequency shifts of selected internal modes as follows: a) C-H

7

bending (800~1000 cm-1), b) C-C-C triangle bending plus C-H bending(1000-1200 cm-1), c) NO2 stretching and its combination with ring stretching modes (~1400- 1600 cm-1) and d) C-H stretching modes (~3100-3150 cm-1). It is seen that the value of the blue shifted C-H stretching is about 60 cm-1 when the pressure goes up to 6 GPa, whereas in dynamic compressed experiments [38] the maximum value is about 45 cm-1. It is noticed that the temperature of the dynamic experiments is higher than that of static compression, leading to the difference under the same pressure conditions. Similarly to the previous experiments [39], the NO2 stretching showed smaller blue shifts than C-H stretching modes due to intermolecular interactions between the NB molecules. As seen in Figure 4d, the C-H vibrational modes display a red shift due to the strengthening of C-H…O hydrogen bonds [40-42]. Especially, the Raman shift trends with pressure of the C-H stretching, C-H bending, NO2 stretching and its combination with ring stretching modes have a distinct change around 7 GPa. 3.3.3 Pressure effects on the calculated geometries. A more detailed analysis of the effects of pressure on the geometries of NB highlighted some interesting pressure-induced structural changes. Figure 5 shows the effects of pressure on the calculated C-N, N-O, C-H bond lengths and O-N-C bond angles. Like previous studies of molecular crystals such as NM [19], TATB [40] and FOX-7 [41], the C-N bonds in NB crystal were more compressible to pressure, where the length decreased smoothly by 2.5% up to 10 GPa. Also, the N-O bond lengths decreased 0.17%. It is possible to know that the NO2 stretching showing smaller blue shift which corresponds to the slightly varied bond length. Although the C-H bond

8

lengths decreases with the pressure in Figure 5a, an obvious break appears at 7 GPa in the pressure dependence of C2-H1, C5-H4 and C6-H5 bonds. Moreover, there are also evident changes noted at 7 GPa in the pressure-induced variation of bond angles O-N-C. The significant changes in the lattice parameters, vibrational frequencies and geometries of the crystal NB provided evidence for a possible pressure-induced structural transformation. We expected that, with rising pressure, the hydrogen bonding and van der Waals interactions were enhanced [42]. And then, the structure could not afford the increased intermolecular interactions with further compression [43], which resulted in the nitro groups start to become distorted to keep a balance. Consequently, above 7 GPa, the reconstruction of the C-H…O hydrogen bonds may have contributed to the structural transformation [44].

4. Conclusion Density functional theory including the dispersion correction has been employed to investigate the structural properties of solid NB at ambient pressure. The Raman vibrations of NB were reproduced by the finite displacement method and the assignments of vibrational modes about internal molecular were provided. Also, the hydrostatic pressure effects on the vibrational frequencies, lattice parameters and geometries were discussed. The present calculations suggest a possible structural transformation around 7 GPa. This work demonstrates that the DFT-D calculated results are good complement to the experiments, thus helping to understand the

9

behavior of energetic molecular crystal NB under high pressure.

Acknowledgments We thank Dr. Ismail A. M. Harran for the linguistic assistance on this manuscript. This work was supported by the National Natural Science Foundation of China (Grant No. 11574254), the National Basic Research Program of China (Grant No. 2011CB808201), the Fundamental Research Fund for the Central Universities, China (Grant Nos. 2682014ZT30 and 2682014ZT31), and the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201511).

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[32] S.S. Stoyanov, D.Y. Ysncheva, B.A. Stamboliyska, DFT study on IR spectral and structural changes caused by the conversion of substituted benzophenones into ketyl radicals, Comput. Theor. Chem. 1046 (2014) 57-63. [33] S. Huter, T. Sutinen, S.F. Parker, C.A. Morrison, D.M. Williamson, S. Thompson, P.J. Gould, C.R. Pulham, Experimental and DFT-D studies of molecular organic energetic material RDX, J. Phys. Chem. C. 117 (2013) 8062-8071. [34] B.B. Averkiev, Z.A. Dreger, S. Chaudhuri, Density functional theory calculations of

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of TATB crystal by density functional theory, Phys. Lett. A. 367 (2007) 383-388. [41] J.J. Zhao, H. Liu, High-pressure behavior of crystalline FOX-7 by density functional theory calculations, Comp. Mat. Sci. 42 (2008) 698-703. [42] T.T. Yan, K. Wang, X. Tan, J. Liu, B.B. Liu, B. Zou, Exploration of hydrogen-bonded energetic material carbohydrazide at high pressures, J. Phys. Chem. C. 118 (2014) 22960-22967. [43] B.B. Sharma, C. Murli, S.M. Sharma, Hydrogen bonds and polymerization in acrylamide under pressure, J. Ram. Spec. 44 (2013) 785-790. [44] T.T. Yan, K. Wang, X. Tan, K. Yang, B.B. Liu, B. Zou, Pressure-induced phase transition in N-H…O hydrogen-bonded molecular crystal biurea: Combined Raman scattering and X-ray diffraction study, J. Phys. Chem. C. 118 (2014) 15162-15168.

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Figure 1. (a) Molecule with labeled atoms to assist with the bonding designation. (b) Crystal structure of NB; dot lines show hydrogen bonds.

16

Figure 2. Pressure dependence of lattice parameters for NB. Square denote theoretical results, circle denote experimental results from ref 16.

17

Figure 3. Unit cell volume of NB as function of hydrostatic pressure, fitted with the Murnaghan equation of state. Square denote this work, circle denote experimental data from ref 16.

18

Figure 4. Pressure induced Raman shift of selected modes: (a) C-H bending modes, (b) C-C-C triangle bending plus C-H bending modes, (c) NO2 stretching and its combination with ring stretching modes, and (d) C-H stretching modes under pressure.

19

Figure 5. Pressure-induced changes in: (a) C-H bond lengths, (b) N-O bond lengths, (c) C-N bond lengths and (d) O-N-C bond angles of NB.

20

Table 1. Calculated and experimental unit cell parameters and atomic coordinates of solid NB at ambient pressure Experimenta Experimentb

LDA

GGA

GGA

CA-PZ

PBE

PBE-D

a(Å)

3.628

5.106

3.687

3.801

3.86

b(Å)

11.172

11.822

11.486

11.615

11.65

c(Å)

12.478

14.002

12.881

12.984

13.24

V(Å3)

505.125

828.097

544.92

571.4

592.9

β(deg)

93.05

101.59

92.68

94.98

95.58

Fractional coordinates of atoms (x, y, z) Experimenta

Theory O1 O2 N C1 C2 C3 C4 C5 C6 H1 H2 H3 H4 H5 a

(0.4795, (0.5574, (0.5922, (0.7768, (0.8873, (1.0643, (1.1264, (1.0096, (0.8318, (0.8303, (1.1557, (1.2665, (1.0557, (0.7346,

0.8896, 1.0093, 0.9121, 0.8191, 0.8414, 0.7534, 0.6454, 0.6244, 0.7113, 0.9251, 0.7689, 0.5775, 0.5399, 0.6959,

0.2184) 0.3503) 0.3089) 0.3697) 0.4731) 0.5300) 0.4838) 0.3806) 0.3224) 0.5081) 0.6104) 0.5291) 0.3452) 0.2426)

(0.4818, (0.5464, (0.5887, (0.7768, (0.8862, (1.0645, (1.1285, (1.0125, (0.8340, (0.8380, (1.1594, (1.2555, (1.0469, (0.7533,

0.8896, 1.0033, 0.9101, 0.8188, 0.8401, 0.7537, 0.6489, 0.6292, 0.7145, 0.9085, 0.7679, 0.5907, 0.5579, 0.7001,

0.2205) 0.3521) 0.3102) 0.3702) 0.4730) 0.5291) 0.4828) 0.3801) 0.3224) 0.5019) 0.6048) 0.5224) 0.3473) 0.2539)

ref 3 (results obtained at 103K). bref 4 (results obtained at 243K).

21

Table 2 Geometric parameters of NB molecule in the crystal at ambient pressurea Experiment[3]

Corrected

6-31G[5]

6-31G*[5]

values

a

This work

C1-C2

1.389

1.393

1.388

1.386

1.396

C2-C3

1.386

1.389

1.384

1.383

1.389

C3-C4

1.387

1.392

1.385

1.383

1.396

C-N

1.467

1.477

1.448

1.458

1.455

N-O

1.227

1.229

1.226

1.193

1.261

C-N-O

118.4

-

118.2

117.6

118.6

O-N-O

123.2

-

123.4

124.6

122.7

Bonds length in Å and angles in degrees.

22

Table 3. Calculated vibrational modes compared with results from previous experiment. Ag

Bg

Experiment[6]

Assignment

393

390

392

Ring in of plane bend+CN stretch

407

416

C-C-C out of plane bend

431

438

C-C-C out of plane bend

513

511

529

NO2 bend +C-H in of plane bend

607

604

671

672

679

676

611

C-C-C in of plane bend C-H out of plane bend

681

C-H out of plane bend+ NO2 wag

702

706

703

C-H out of plane bend +NO2 wag

792

797

793

C-H out of plane bend +NO2 wag

830

826

C-H out of plane bend

841

829

C-H out of plane bend +NO2 stretch

947

947

C-H out of plane bend

970

976

C-H out of plane bend

988

991

Ring breath

1005

1001

1003

C-C-C triangle bend

1009

1012

1021

C-H out of plane bend

1069

1073

1074

C-H in of plane bend

1075

1080

C-C-C triangle bend +C-N

23

stretch 1152

1150

C-H in of plane bend

1156

1162

1255

1271

NO2 stretch+ C-H bend

1292

1289

C-H in of plane bend

1352

1354

Ring stretch

1418

1420

NO2 Stretch +C-H in of

1162

C-H in of plane bend

plane bend 1453

1455

Ring stretch

1456

1467

NO2 stretch+ Ring stretch

1571

1570

Ring stretch

1585

1584

1588

Ring stretch

3113

3113

3049

C-H stretch

3127

3127

3130

3130

3143

3144

C-H stretch

3148

3148

C-H stretch

C-H stretch 3082

C-H stretch

24

Graphical abstract

25

Highlights * The structural properties of NB were investigated using the DFT calculations. * Assignments of the vibrational modes were provided. * Pressure effects on the geometries and unit cell parameters were examined. * The calculated Raman spectra indicated a structural transformation around 7 GPa.

26