Hydrostatic Pressure Effects on Structural and Electronic Properties of

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Hydrostatic Pressure Effects on Structural and Electronic Properties of ETN and PETN from First Principles Calculations Igor Alexsandrovich Fedorov, Tatyana Petrovna Fedorova, and Yuriy N. Zhuravlev J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03335 • Publication Date (Web): 29 Apr 2016 Downloaded from http://pubs.acs.org on May 6, 2016

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The Journal of Physical Chemistry

Hydrostatic Pressure Effects on Structural and Electronic Properties of ETN and PETN from First Principles Calculations Igor A. Fedorov,* Tatyana P. Fedorova and Yuriy N. Zhuravlev Physics Faculty, Kemerovo State University, Krasnaya 6, 650043, Kemerovo, Russia. ABSTRACT We studied the structural and electronic properties of pentaerythritol tetranitrate (PETN) and erythritol tetranitrate (ETN) crystals within the framework of density functional theory with van der Waals interactions. The computed lattice parameters have good agreement with experimental data. Electronic and structural properties of the crystals under 0-20 GPa hydrostatic pressure were studied. The parameters of equations of state calculated from the theoretical data show good agreement with experiment within the studied pressure intervals. We have also calculated the detonation velocity and pressure.

1. INTRODUCTION Study of energetic materials has been of great interest to scientists for many decades due to their wide practical application.1-12 Computer simulation is used to study energetic materials because of the rapid decomposition processes. Pentaerythritol tetranitrate (PETN, C5H8N4O12) and erythritol tetranitrate (ETN, C5H6N4O12) are secondary high explosive materials. The main objective of this work is to study the properties of ETN crystal. Since there is little information on this crystal, the 1

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obtained properties will be compared to those of PETN. Similar approach was applied in a recent study where structural parameters of ETN crystal were determined for the first time.13 Despite the fact that PETN has been repeatedly studied, theoretically and experimentally, it still is of scientific interest. Now there are many experimental and theoretical data about energetic materials. We are going to review a small part which is of importance for our investigation. Gan et al. calculated hydrostatic compression of PETN using density-functional theory (DFT).14 The description of the study of electronic structure of crystalline PETN containing an edge dislocation using Hartree-Fock theory can be found in the works of Kuklja and Kunz.15 Landerville et al. studied energetic materials, including PETN, upon hydrostatic compression.16 Tsyshevsky et al.17,18 conducted investigation of the crystalline PETN electronic structure and optical properties using DFT calculations. Mukhanov studied electronic excitation energies in PETN crystal.19 Velizhanin et al. calculated the vibrational properties of PETN crystal.20 Volume as a function of pressure was experimentally determined by Olinger et al. (up 10 GPa)21 and Yoo et al. (up 12 GPa).22 The structure of ETN and his electronic properties under pressure have not been investigated. Since PETN and ETN are similar, it is possible to use numerable experimental data for PETN and further, using proven computational schemes, to study the pressure effect on the ETN properties, as well as determine its detonation characteristics.

The dispersion interaction is very important for the formation of molecular crystals. Since correlated motion and many-body effects is the cause of the dispersion interaction, it is not taken into consideration in the standard approximations of DFT.23 Various algorithms have recently been suggested, as a result this interaction is now possible to include into existing DFT schemes.24 Kohn and coworkers have showed the possibility of inclusion of van der Waals (vdW) energies in DFT.25 The well-known schemes are the vdW density functional (vdW-DF)26 and DFT-D.27-29 The more detailed information on different schemes may be found in the works in ref. 30–34. Sorescu and Rice studied the properties of 10 energetic molecular crystals within the framework of DFT-D.35 It is evident from the obtained results that the contribution of dispersion interactions in

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molecular crystals is essential. We used the DFT-D method to study crystalline aromatic compounds (including TATB).36-39 Lee et al. was suggested the vdW-DF2.40 At the normal conditions the PETN unit cell has the space group

4

P 4 1 21 c ,

ETN –

P 21 / c .

13

In a

recent study some fundamental physical properties (such as structure, density, hygroscopicity, detonation velocity, brisance) of ETN were investigated.41,42 The ETN molecule contains an inversion center. The unit cells are shown in Figure 1. The PETN and ETN molecule is shown in Figure 1.

Figure 1. The unit cell of PETN (a) and ETN (c,d).The PETN (b) and ETN (e) molecule in the crystal. 2. COMPUTIONAL DETAILS A plane-wave pseudopotential approach within DFT was used to calculate total energy. The PWscf program,43 which is incorporated into Quantum ESPRESSO (QE)44 suite of electronic structure programs with the functional of Perdew, Burke, and Ernzerhof (PBE),45 was used to carry out the computations. The ultrasoft pseudopotentials of the Rabe-Rape-Kaxiras-Joannopoulos type were used for calculations.44,46 The crystal structures were optimized with the Broyden-FletcherGoldfarb-Shanno (BFGS) method.47 Monkhorst–Pack scheme48 was used for the Brillouin zone sampling. The kinetic energy cutoff and the k-points ensured the convergence of total energies. The energy cutoff equals 65 Ry. The k-point grid is 2x2x3. 3



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Geometry relaxation was completed when all components of all forces are smaller than 0.1 mRy (a.u.)-1. As the starting point structural data4,13 were used. Besides, the computations were carried out with the CRYSTAL14,49 using the PBE0 hybrid functional.50 All calculations were performed by using standard 6-31G* basis set.51 Structural data, computed by QE, were used as the entry data. Other options for the computations were not changed. We employed the full non-local exchange–correlation rev-vdW-DF2 functional in our study.26, 40, 52-54

Also, we used a DFT-D. In this scheme the empirical potential was added to the exchange–

correlation potential and the total energy is given by EDFT - D = EKS- DFT + Edisp

(1)

where EKS-DFT is the Kohn–Sham energy and Edisp is a dispersion correction.29 The QE and CRYSTAL14 include the DFT-D2 scheme.56 We performed computations within the DFT-D3(BJ).36,57-59 The dispersion energy is Edisp = −

1 C6AB C8AB s6 6 + s8 8 ∑ 0 6 0 2 A ≠ B RAB + [ f ( RAB )] RAB + [ f ( RAB )]8

, (2)

with 0 0 f ( RAB ) = a1RAB + a2 ,

0 RAB =

C8AB C6AB

(3)

. (4)

Here, the sum is over all atom pairs in the crystal. The C6 and C8 are isotropic dispersion coefficients for atom pair AB, and RAB – internuclear distance. The s6 and s8 are global (functional dependent) scaling factors. Detailed information and values of all parameters can be found in the original works.29,57,60 The lattice energy is given by Elat = Emol −

1 Ebulk n

(5)

where Emol and Ebulk are the molecule and bulk crystal total energies, respectively, and n is the number of molecules per unit cell. Thus, the lattice energy is positive for any stable crystal. 3. RESULTS AND DISCUSSION 4


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A. Geometry Optimization and Lattice Energy. Our PETN and ETN optimized lattice parameters are given in Table 1 and 2. Tables S1 and S2 present fractional coordinates (see Supporting Information section). Experimental values are also listed. The computed lattice parameters reasonably agree with the experimental ones. As the experimental lattice parameters were obtained at the room temperature, they should have bigger values than the theoretical ones computed at zero temperature. The use of rev-vdW-DF2 result in good agreement with experimental data. Table 1. The PETN computed and experimental lattice parameters at zero pressure. a (Å)

c (Å)

V (Å3)

rev-vdW-DF2

9.267

6.5813

565.152

DFT-D3(BJ)

9.431

6.7156

597.332

DFT-D235

9.4007

6.5539

579.19

ReaxFF1

9.542

7.229

658.199

ReaxFF-lg1

9.098

6.864

568.168

Exp4

9.2759

6.6127

568.972

Table 2. The ETN computed and experimental lattice parameters at zero pressure. a (Å)

b (Å)

c (Å)

β (°)

V (Å3)

rev-vdW-DF2

16.004

5.183

14.779

115.936

1102.530

DFT-D3(BJ)

16.180

5.361

14.968

115.429

1172.618

Exp13 (T=140K)

15.893

5.1595

14.731

116.161

1084.2

Exp13

16.132

5.314

14.789

116.78

1132

Exp41

15.9681

5.1940

14.7609

116.238

1098.10

Our calculated lattice energies for the PETN are given in Table 3. Experimental enthalpy of sublimation is also listed. The rev-vdW-DF2 lattice energy (T=0K) is slightly bigger than 5



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experimental value of the heat of sublimation (T=298.15K). The computed lattice energy also different from the enthalpy of sublimation by the value of zero point energy and energy associated with the change in the number of degrees of the molecule freedom during crystalline-to-gaseous phase transition. Thus, lattice parameters and energy computed within rev-vdw-DF2 exhibit good agreement with experimental data. The lattice energy for the ETN calculated within DFT-D3(BJ) and rev-vdw-DF2 equal 1.27 and 1.61 eV, respectively. Table 3. Calculated lattice energies and experimental enthalpy of sublimation (eV) for PETN. Method

Energy (eV)

rev-vdw-DF2

1.83

DFT-D3(BJ)

1.34

∆Hsub

1.56± 0.0161

B. Band structures. Figures 2 and 3 present the computed band structures for PETN and ETN. The top of the valence band is the reference point. The high-symmetry points in units of reciprocal lattice vectors are X = (0, 0.5, 0), M = (0.5, 0.5, 0), Z = (0, 0, 0.5), R = (0, 0.5, 0.5), A=(0.5, 0.5, 0.5), Γ = (0, 0, 0), Y = (0.5,0,0), N = (0.5, 0, 0.5) and Z = (0, 0, 0.5). The PETN experimental optical band gap is 6.42 eV at ambient pressure.62 The calculated band gap (Egap) of 6.66 eV comparable to 6.04 (HSE06) and 7.07 eV (PBE0).27 The calculated band gap of ETN is 6.54 eV. The electronic bands of PETN and ETN have weak dispersion. The both crystals have indirect band gap.

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Figure 2. The band structure of PETN within PBE0 approximation at 0, 10 and 20 GPa. The dashed line denotes the top of the valence band (Fermi level). Figures 2 and 3 shows the band structures under hydrostatic pressure of 10 and 20 GPa. The PETN and ETN volume decreases by 30 and 33% at 20 GPa respectively. The pressure causes to band gap decrease and band dispersion increase. The calculated band gap at 10 and 20 GPa are listed in Table 4. Within the range of 0-20 GPa the PETN and ETN band gaps are very close.

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Figure 3. The band structure of ETN within PBE0 approximation at 0, 10 and 20 GPa. The dashed line denotes the top of the valence band (Fermi level). Table 4. The band gaps (eV) of ETN and PETN. Pressure (GPa)

0

10

20

PETN

6.66

6.08

5.70

ETN

6.54

5.97

5.66

The calculated density of states (DOS) at a pressure 0, 10 and 20 GPa are demonstrated in Figure 4. The PDOS shows that the oxygen electrons are the main contributors to the formation of the top valence bands. As for nitrogen, it introduced more electrons to the bottom of the conduction band.

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Figure 4. Total and projected DOS for PETN and ETN at ambient, 10 and 20 GPa hydrostatic pressure. The top of the valence band indicated by the Fermi level (dashed line). C. Equation of State. In case of explosives the change in volume of the crystal caused by external pressure is of great interest. Figure 5 and 6 shows the P(V) dependencies obtained for both crystals. There are no experimental data on the P(V) dependency for ETN. As the PETN crystal is well studied, comparative investigation between the theoretical and experimental data has been performed.21 Figure 7 shows dependence of volume compression V/V0 of PETN and ETN. Figure 5 and 6 demonstrated the variation of the unit cell parameters and volume for PETN and ETN with pressure as predicted using rev-vdW-DF2. The pressure within 3 GPa causes fast change of the lattice parameters. The computed and experimental data21 for PETN agree well.

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Figure 5. Dependence of the volume and unit cell parameters on the pressure for the PETN from theory and experiment.21

Figure 6. Dependence of the volume and unit cell parameters on the pressure for the ETN from theory. 10


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Figure 7. Dependence of volume compression V/V0 of PETN and ETN. To write pressure dependence on volume, different variants of isothermal equation of state (EOS) for solids are used. We used Vinet63 and 3rd order Birch-Murnaghan EOS.64 The Vinet EOS is given by: 2

P (V ) = 3B0 (

1

1

V −3 V V 3 ) (1 − ( ) 3 ) exp[ ( B0′ − 1)(1 − ( ) 3 )] . V0 V0 V0 2

(6)

The Birch-Murnaghan EOS is given by: 7

P(V ) =

5

2

3B0 V0 3 V0 3 V 3 [( ) − ( ) ][1 + ( B0′ − 4)(( 0 ) 3 − 1)] . 2 V V 4 V

(7)

Here, B0 and B′0 are isothermal bulk modulus and their pressure derivative, respectively. V0 is equilibrium volume. These parameters are defined at zero pressure. The parameters which were fitted for the both isothermal EOS are given in Table 5. Thus, PETN bulk modulus approximately 50-60% more than the ETN. Table 5. The PETN and ETN bulk modulus B0 and its pressure derivative B′0 obtained by the equation of state. Birch-Murnaghan

Vinet

B0

B0′

B0

B0′

PETN

14.96

8.05

15.23

7.64

ETN

9.39

10.12

10.26

8.44

11



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D. Electron densities. Figure 8 shows the distribution of electron densities on the plane. We selected plane passing through N1, O1 and O2 atoms. We used Mulliken population analysis to determine the crystal atomic charges (Table S3 and S4 of the Supporting Information section). Despite the absence of a clear physical sense in the given schemes, it is possible to establish the atom charge change.

Figure 8. Total electron density maps of PETN and ETN at ambient and 20 GPa hydrostatic pressure (in logarithmic scale).

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It is evident that the distances between molecules reduce under pressure. The pressure of 20 GPa causes only a slight change for the atomic charges. The C1 in the PETN is bonded to four carbon atoms (Fig. 1) and has a negative charge. Other carbon atoms in the PETN and ETN have a positive charge is less than 0.1 |e|. E. Detonation properties. We used the Kamlet-Jacobs formula:65

D = 1.01( NM 1 / 2 Q1/ 2 )1 / 2 (1 + 1.3ρ ) (8) P = 1.558ρ 2 NM 1 / 2Q1 / 2 (9)

Here, D and P are detonation velocity (km/s) and pressure (GPa), respectively. ρ denotes density of the compound (g/cm3). N and M denote number of moles per gram of explosive and average molecular weight of gaseous detonation products, respectively. Q is chemical energy of detonation (kJ/g), which is determined as the difference in enthalpy of the explosive and gaseous reaction products. ETN decomposes to: 2C5 H 8 N 4O12 → 6CO2 + 8 H 2O + 4 N 2 + 4CO .

(9)

Whereas ETN decomposes to: 2C5 H 6 N 4O12 → 8CO2 + 6 H 2O + 4 N 2 + O2 .

(10)

ETN has, that PETN does not, is a positive oxygen balance. Enthalpy calculated as the sum of the total electron energy system and the zero point vibrational energy. Calculated detonation velocity and pressure for the PETN and ETN are given in Table 8. Parameters for Kamlet-Jacobs formula are also listed. Table 8. Comparison of parameters determined from the Kamlet-Jacobs formula of PETN and ETN. Crystal PETN ETN

N (mol/g) 0.035 0.031

3

M (g/cm )

28.7 31.8

Q (kJ/g) 1036.4 1159.7

ρ (g/cm3). 1.784 1.711

D (km/s) 8.214 8.004

P (GPa) 30.3 28.0

The calculated detonation velocity for PETN is 8.214 km/s (ρ= 1.784 g/cm3), which agrees well with the experimental value of 8.266 km/s (ρ= 1.764 g/cm3).66 The calculated detonation velocity for ETN is 8.004 km/s (ρ= 1.711 g/cm3), while experimental value is 7.940 km/s (ρ= 1.69 g/cm3).41 The predicted value of 8.206 km/s (ρ= 1.7219 g/cm3) was calculated by Cheetah 6.0.67 It is obvious that both theoretical and experimental values are in good agreement. The theoretical values are obtained for single crystals with higher density than that of the experimental samples (polycrystals or powders). The experimental value detonation pressure is 30.3 GPa (ρ= 1.784 g/cm3) for PETN.66 The calculated detonation pressure for the PETN and ETN equal 30.4 and 28.0 GPa, respectively. 13



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4. CONCLUSION The crystalline PETN and ETN have been studied within ab initio calculations. For the first time calculated the lattice parameters and energy, band structure, bulk modulus and its pressurederivative of the ETN. The calculated lattice energy of ETN is 1.27 (DFT-D3(BJ)) and 1.61 (revvdW-DF2) eV. Currently the study of pressure effect on electronic and structural properties of crystalline ETN is not presented in the literature. Computer simulation predicts that the bulk modulus and its first derivative are 9.39 GPa and 10.12, respectively. Using the Kamlet-Jacobs formula, the detonation velocity and pressure for PETN (D= 8.214 km/s, P= 30.3 GPa) and ETN (D= 8.004 km/s, P= 28.0 GPa) are calculated.

AUTHOR INFORMATION Corresponding Author *I. A. Fedorov. Phone: +7-3842-58-3195. E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT The authors gratefully acknowledge the Center for collective use “High Performance Parallel Computing” of the Kemerovo State University for providing the computational facilities. This work was supported by the Ministry of Education and Science of the Russian Federation (Project no.3.1235.2014К). Supporting Information Available: Comparison of the rev-vdW-DF2 predicted fraction coordinates for PETN and ETN with corresponding experimental data is provided in Tables S1 and

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S2. Tables S3 and S4 present the Mulliken atomic charges for the PETN and ETN. This material is available free of charge via the Internet at http://pubs.acs.org.

REFERENCES (1)

Liu, L.; Liu, Y.; Zybin, S. V.; Sun, H; Goddard, W. A. III. ReaxFF-lg: Correction of the

ReaxFF Reactive Force Field for London Dispersion, with Applications to the Equations of State for Energetic Materials. J. Phys. Chem. A. 2011, 115, 11016-11022. (2)

Zerilli, F. J.; Kuklja, M. M. Ab Initio Equation of State of the Organic Molecular Crystal: β-

Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine. J. Phys. Chem. A. 2010, 114, 5372-5376. (3)

Aluker, E. D.; Krechetov, A.G.; Mitrofanov, A.Y.; Nurmukhametov D. R.; Kuklja, M.M.

Laser Initiation of Energetic Materials: Selective Photoinitiation Regime in Pentaerythritol Tetranitrate. J. Phys. Chem. C. 2011, 115, 6893-6901. (4)

Zhurova, E. A.; Stash, A. I.; Tsirelson, V. G.; Zhurov, V. V.; Bartashevich, E. V.; Potemkin,

V. A.; Pinkerton, A. A. Atoms-in-Molecules Study of Intra- and Intermolecular Bonding in the Pentaerythritol Tetranitrate Crystal. J. Am. Chem. Soc. 2006, 128, 14728-14734. (5)

Hunter, S.; Sutinen, T.; Parker, S. F.; Morrison, C. A.; Williamson, D. M.; Thompson, S.;

Gould P. J.; Pulham C. R. Experimental and DFT-D Studies of the Molecular Organic Energetic Material RDX. J. Phys. Chem. C. 2013, 117, 8062-8071. (6)

Wang, F.; Du, H.; Zhang J.; Gong, X. First-Principle Study on High-Pressure Behavior of

Crystalline Polyazido-1,3,5-triazine. J. Phys. Chem. C. 2012, 116, 6745-6753. (7)

Kimmel, A. V.; Sushko, P. V.; Shluger A. L.; Kuklja, M. M. Effect of Molecular and Lattice

Structure on Hydrogen Transfer in Molecular Crystals of Diamino-dinitroethylene and Triaminotrinitrobenzene. J. Phys. Chem. A. 2008, 112, 4496-4500. 15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(8)

Kuklja, M. M.; Rashkeev, S. N. Molecular Mechanisms of Shear Strain Sensitivity of the

Energetic Crystals DADNE and TATB. Journal of Energetic Materials. 2010, 28, 66-77. (9)

Appalakondaiah, S.; Vaitheeswaran, G.; Lebègue, S. Structural, vibrational, and

quasiparticle band structure of 1,1-diamino-2,2-dinitroethelene from ab initio calculation. J. Chem. Phys. 2014, 140, 014105. (10) Yedukondalu, N.; Vaitheeswaran, G.; Anees P.; Valsakumar, M. C. Phase stability and lattice dynamics of ammonium azide under hydrostatic compression. Phys. Chem. Chem. Phys. 2015, 17, 29210-29225. (11) Rykounov, A. A. Structural and thermodynamic properties of two polymorphic modifications of the insensitive high explosive 5-nitro-2,4-dihydro-1,2,4-triazol-3-one (NTO) under finite pressures and temperatures from ab initio calculations. CrystEngComm. 2015, 17, 7653-7662. (12) Rykounov, A. A. Investigation of the pressure dependent thermodynamic and elastic properties of 1,3,5-triamino-2,4,6-trinitrobenzene using dispersion corrected density functional theory. J. Appl. Phys. 2015, 117, 215901. (13) Manner, V. W.; Tappan, B. C.; Scott, B. L.; Preston, D. N.; Brown G. W. Crystal Structure, Packing Analysis, and Structural-Sensitivity Correlations of Erythritol Tetranitrate. Cryst. Growth Des. 2014, 14, 6154−6160. (14) Gan, C. K.; Sewell T. D.; Challacombe M. All-electron density-functional studies of hydrostatic compression of pentaerythritol tetranitrate C(CH2ONO2)4. Phys. Rev. B. 2004, 69, 035116. (15) Kuklja, M. M.; Kunz A. B. Electronic structure of molecular crystals containing edge dislocations. J. Appl. Phys. 2001, 89, 4962−4970.

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(16) Landerville, A. C.; Conroy, M. W.; Budzevich, M .M.; Lin, Y.; White C. T.; Oleynik, I. I. Equations of state for energetic materials from density functional theory with van der Waals, thermal, and zero-point energy corrections. Appl. Phys. Lett. 2010, 97, 251908. (17) Tsyshevsky, R. V.; Sharia, O.; Kuklja M. M. Energies of Electronic Transitions of Pentaerythritol Tetranitrate Molecules and Crystals. J. Phys. Chem. C. 2014, 118, 9324−9335. (18) Tsyshevsky, R. V.; Sharia O.; Kuklja M. M. Optical Absorption Energies of Molecular Defects in Pentaerythritol Tetranitrate Crystals: Quantum Chemical Modeling. J. Phys. Chem. C. 2014, 118, 26530–26542. (19) Mukhanov, A. E. Electronic excitation energies in crystals of PETN, RDX and HMX. J. Phys.: Conf. Ser. 2014, 500, 182029. (20) Velizhanin, K. A.; Kilina, S.; Sewell, T. D.; Piryatinski, A. First-Principles-Based Calculations of Vibrational Normal Modes in Polyatomic Materials with Translational Symmetry: Application to PETN Molecular Crystal. J. Phys. Chem. B. 2008, 112, 13252–13257. (21) Olinger, B. W.; Cady, H. H. The Hydrostatic Compression of Explosives and Detonation Products to 10 GPa (100 kbar) and their Calculated Shock Compression: Results for PETN, TATB, CO2 and H2O; Sixth Symposium on Detonation, San Diego, CA, Aug 24-27, 1976; Los Alamos LA-UR-76-1174, pp 1-9. (22) Yoo, C.-S., Cynn, H.; Howard, W. M.; Homes, N. Equations of State of Unreacted High Explosives at High Pressures; Proceedings of the Eleventh International Detonation Symposium, Snowmass Village, CO, August 31, 1998-September 4, 1998; p 951. (23) Lein, M.; Dobson J. F.; Gross, E. K. U. Toward the description of van der Waals interactions within density functional theory. J. Comput. Chem. 1999, 20, 12-22.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(24) Tkatchenko, A.; Romaner, L.; Hofmann, O. T.; Zojer, E.; Ambrosch-Draxl, C.; Scheffler, M. Van der Waals Interactions Between Organic Adsorbates and at Organic/Inorganic Interfaces. MRS Bulletin. 2010, 35, 435-442. (25) Kohn, W.; Meir, Y.; Makarov D. E. van der Waals Energies in Density Functional Theory. Phys. Rev. Lett. 1998, 80, 4153. (26) Dion, M.; Rydberg, H.; Schroder, E.; Langreth D. C.; Lundqvist, B. I. Van der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. (27) Grimme, S. Accurate description of van der Waals complexes by density functional theory including empirical corrections. J. Comput. Chem. 2004, 25, 1463-1473. (28) Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787-1799. (29) Grimme, S.; Antony, J.; Ehrlich S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (30) Civalleri, B.; Zicovich-Wilson, C.M.; Valenzano L.; Ugliengo, P. B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to molecular crystals. CrystEngComm. 2008, 10, 405. (31) Foster M. E.; Sohlberg, K. Empirically corrected DFT and semi-empirical methods for nonbonding interactions. Phys. Chem. Chem. Phys. 2010, 12, 307-322. (32) Dobson J. F.; Gould, T. Calculation of dispersion energies. J. Phys.: Condens. Matter. 2012, 24, 073201. (33) Becke, A. D. Perspective: Fifty years of density-functional theory in chemical physics. J. Chem. Phys. 2014, 140, 18A301. 18


Page 18 of 32

Page 19 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(34) Berland, K.; Arter, C. A.; Cooper, V. R.; Lee, K.; Lundqvist, B. I.; Schröder, E.; Thonhauser, T.; Hyldgaard, P. van der Waals density functionals built upon the electron-gas tradition: Facing the challenge of competing interactions. J. Chem. Phys. 2014, 140, 18A539. (35) Sorescu, D.C.; Rice, B.M. Theoretical Predictions of Energetic Molecular Crystals at Ambient and Hydrostatic Compression Conditions Using Dispersion Corrections to Conventional Density Functionals (DFT-D). J. Phys. Chem. C. 2010, 114, 6734-6748. (36) Fedorov, I. A.; Zhuravlev Y. N.; Berveno, V. P. Properties of crystalline coronene: Dispersion forces leading to a larger van der Waals radius for carbon. Phys. Status Solidi B. 2012, 249, 1438-1444. (37) Fedorov, I. A.; Zhuravlev Y. N.; Berveno, V. P. Structural and electronic properties of perylene from first principles calculations. J. Chem. Phys. 2013, 138, 094509. (38) Fedorov, I. A.; Zhuravlev Y. N. Hydrostatic pressure effects on structural and electronic properties of TATB from first principles calculations. Chem. Phys. 2014, 436–437, 1–7. (39) Fedorov, I. A.; Marsusi, F.; Fedorova, T.P.; Zhuravlev, Y.N. First principles study of the electronic structure and phonon dispersion of naphthalene under pressure. Journal of Physics and Chemistry of Solids, 2015, 83, 24–31. (40) Lee, K.; Murray, E. D.; Kong, L.; Lundqvist B .I.; Langreth, D.C. Higher-accuracy van der Waals density functional. Phys. Rev. B. 2010, 82, 081101. (41) Matyáš, R.; Künzel, M.; Růžička, A.; Knotek, P.; Vodochodský, O. Characterization of Erythritol Tetranitrate Physical Properties. Propellants Explos. Pyrotech. 2015, 40, 185–188. (42) Manner, V. W.; Preston, D. N.; Tappan, B. C.; Sanders, V. E.; Brown, G. W.; Hartline, E.; Jensen, B. Explosive Performance Properties of Erythritol Tetranitrate (ETN). Propellants Explos. Pyrotech. 2015, 40, 460–462. 19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(43) Giannozzi, P.; Baroni S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502. (44) http://www.quantum-espresso.org (45) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865–3868. (46) Rappe, A. M.; Rabe, K. M.; Kaxiras, E.; Joannopoulos, J. D. Optimized pseudopotentials Phys. Rev. B 1990, 41, 1227. (47) R. Fletcher, Practical Methods of Optimization, Wiley, New York, 1980, Vol. 1, p. 126. (48) Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations Phys. Rev. B 1976, 13, 5188. (49) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; Zicovich-Wilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; et al. CRYSTAL14 User's Manual, University of Torino, Torino, 2014, p. 382. (50) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: the PBE0 model J. Chem. Phys. 1999, 110, 6158–6170. (51) Gatti, C.; Saunders, V. R.; Roetti, C. Crystal field effects on the topological properties of the electron density in molecular crystals: The case of urea. J. Chem. Phys. 1994, 101, 10686-10696. (52) Hamada, I. Van der Waals density functional made accurate. Phys. Rev. B. 2014, 89, 121103.

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Page 20 of 32

Page 21 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(53) Thonhauser, T.; Cooper, V. R.; Li, S, Puzder, A.; Hyldgaard, P.; Langreth, D. C. Van der Waals density functional: Self-consistent potential and the nature of the van der Waals bond Phys. Rev. B 2007, 76, 125112. (54) Roman-Perez, G.; Soler, J. M. Efficient Implementation of a van der Waals Density Functional: Application to Double-Wall Carbon Nanotubes Phys. Rev. Lett. 2009, 103, 096102. (55) Sabatini, R.; Kucukbenli, E.; Kolb, B.; Thonhauser, T.; de Gironcoli, S. Spectroscopic characterization of van der Waals interactions in a metal organic framework with unsaturated metal centers: MOF-74–Mg J. Phys.: Condens. Matter 2012, 24, 424203. (56) Barone, V.; Casarin, M.; Forrer, D.; Pavone, M.; Sambi, M.; Vittadini, A. Role and effective treatment of dispersive forces in materials: Polyethylene and graphite crystals as test cases J. Comput. Chem. 2009, 30, 934. (57) Grimme, S.; Ehrlich, S.; Goerigk, L. J. Effect of the damping function in dispersion corrected density functional theory Comput. Chem. 2011, 32, 1456. (58) Johnson, E. R.; Becke, A. D. A post-Hartree–Fock model of intermolecular interactions J. Chem. Phys. 2005, 123, 024101. (59) Johnson, E. R.; Becke, A. D. A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections J. Chem. Phys. 2006, 124, 174104. (60) AK

Grimme

Research

Web

Site,

Universität

Münster,

see

http://www.uni-

muenster.de/Chemie.oc/grimme/ (61) Cundall, R. B.; Palmer T. F.; Wood C. E. C. Vapour pressure measurements on some organic high explosives. J. Chem. Soc., Faraday Trans. 1. 1978, 74, 1339-1345. (62) Smit, K. J. Ultraviolet and visible absorption spectroscopy of some energetic molecules in the solid state. Journal of Energetic Materials. 1991, 9, 81-103. 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(63) Vinet, P.; Smith, J. R.; Ferrante, J.; Rose, J. H. A Universal Equation of State for Solids. J. Phys. C 1986, 19, L467. (64) Birch, F. Finite Elastic Strain of Cubic Crystals Phys. Rev. 1947, 71, 809. (65) Kamlet, M. J.; Jacobs, S. J. Chemistry of Detonations. I. A Simple Method for Calculating Detonation Properties of C–H–N–O Explosives. J. Chem. Phys. 1968, 48, 23. (66) Green, L. G.; Lee, E. L. Detonation pressure measurements on PETN. 13th International Detonation Symposium, Norfolk, VA, July 23-28 2006; 503-511. (67) Oxley, J. C.; Smith, J. L.; Brady, J. E.; Brown, A. C. Characterization and Analysis of Tetranitrate Esters. Propellants Explos. Pyrotech. 2012, 37, 24–39.

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TOC Graphic

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Figure 1. The unit cell of PETN (a) and ETN (c,d).The PETN (b) and ETN (e) molecule in the crystal. 75x73mm (300 x 300 DPI)


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Figure 2. The band structure of PETN within PBE0 approximation at 0, 10 and 20 GPa. The dashed line denotes the top of the valence band (Fermi level). 135x104mm (300 x 300 DPI)



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Figure 3. The band structure of ETN within PBE0 approximation at 0, 10 and 20 GPa. The dashed line denotes the top of the valence band (Fermi level). 135x104mm (300 x 300 DPI)


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Figure 4. Total and projected DOS for PETN and ETN at ambient, 10 and 20 GPa hydrostatic pressure. The top of the valence band indicated by the Fermi level (dashed line). 107x71mm (300 x 300 DPI)



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Figure 5. Dependence of the volume and unit cell parameters on the pressure for the PETN from theory and experiment.21 78x94mm (300 x 300 DPI)


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Figure 6. Dependence of the volume and unit cell parameters on the pressure for the ETN from theory. 126x200mm (600 x 600 DPI)



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Figure 7. Dependence of volume compression V/V0 of PETN and ETN. 48x33mm (300 x 300 DPI)


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Figure 8. Total electron density maps of PETN and ETN at ambient and 20 GPa hydrostatic pressure (in logarithmic scale). 176x183mm (300 x 300 DPI)



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TOC Graphic 44x23mm (300 x 300 DPI)


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Hydrostatic Pressure Effects on Structural and Electronic Properties of

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