First-Principles Study of Electronic, Absorption, and Thermodynamic

First-Principles Study of Electronic, Absorption, and Thermodynamic Properties of Crystalline Styphnic Acid and Its Metal Salts ... Fax: +86-25-843039...
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J. Phys. Chem. B 2009, 113, 10315–10321

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First-Principles Study of Electronic, Absorption, and Thermodynamic Properties of Crystalline Styphnic Acid and Its Metal Salts Weihua Zhu* and Heming Xiao* Institute for Computation in Molecular and Materials Science, and Department of Chemistry, Nanjing UniVersity of Science and Technology, Nanjing 210094, China ReceiVed: April 30, 2009; ReVised Manuscript ReceiVed: June 10, 2009

The electronic structure, absorption spectra, and thermodynamic properties of crystalline styphnic acid and its metal salts (potassium, barium, and lead styphnates) have been studied using density functional theory within the local density approximation. The results show that the metal states affect the electronic structure of styphnic acid by modifying the density of states of the O atoms of hydroxyls. The C-O bond fission may be favorable in the decomposition of styphnic acid and its metal salts. The absorption spectra of the four crystals display a few strong bands in the fundamental absorption region. Compared with styphnic acid, potassium, barium, and lead styphnates decrease its enthalpy, entropy, free energy, and heat capacity as the temperature increases. However, the differences of the thermodynamic functions between each metal salt are very small. As the temperature increases, the decomposition reactions of the four crystals are more and more favorable thermodynamically. It is also found that there is a relationship between the band gap and impact sensitivity for the four crystals. 1. Introduction Styphnic acid (2,4,6-trinitroresorcinol) is one of several polyhydric phenols of industrial importance, especially to the explosives industry. Its metal salts, particularly lead styphnate, have been extensively used as primary explosives for several decades.1,2 Therefore, their structure, properties, and decomposition mechanism are extensively investigated and compared.3-13 Unfortunately, many fundamental and practical problems of these compounds are still not well understood because they possess a complex chemical behavior. For crystalline styphnic acid and its metal salts, there is a variation in the stability to impact, light, and shock. Therefore, understanding the differences between the structure and fundamental properties of the solids is important for the development of new energetic materials. Materials such as propellants and explosives contain tightly bonded groups of atoms that retain their molecular character until a sufficient stimulus is applied to cause exothermic dissociation. This in turn triggers further dissociation, leading to initiation or ignition. The macroscopic behavior is ultimately controlled by microscopic properties such as the electronic structure and interatomic forces. Thus, a desire to probe more fundamental questions relating to the basic properties of the styphnates as solid energetic materials is generating significant interest in the basic solid-state properties of such energetic systems. Although the detailed decomposition mechanisms by which energetic materials release energy under mechanical shock are still not well understood, it has been suggested that these decompositions may result from transferring thermal and mechanical energy into the internal degrees of freedom of the molecules in energetic solids.14-16 Thus, the knowledge of their electronic and thermodynamic properties appears to be very important in understanding the reasons of their high instability and in developing models that adequately describe their * To whom correspondence should be addressed. Fax: +86-25-84303919. E-mail: [email protected] (W.Z.); [email protected]. (H.X.).

behavior. Since their basic solid-state properties are not systematically investigated and compared, there is a clear need to gain an understanding of those at the atomic level. The investigation of the microscopic properties of energetic materials remains to be a challenging task. Theoretical calculations can play an important role in investigating the physical and chemical properties of complex solids at the atomic level and the establishment of the relationships between their structure and properties. In this study, we report a systematic study of the electronic structure, absorption spectra, and thermodynamic properties of crystalline styphnic acid and its metal salts (potassium styphnate, barium styphnate, and lead styphnate) from density functional theory (DFT). Our main purpose here is to examine the differences in the microscopic properties of the solids and to understand their structurefunction relationships. The remainder of this paper is organized as follows. A brief description of our Computational Method is given in section 2. The Results and Discussion are presented in section 3, followed by a summary of our conclusions in section 4. 2. Computational Method The calculations were performed in this study by using the DFT method with Vanderbilt-type ultrasoft pseudopotentials17 and a plane wave expansion of the wave functions as implemented in the CASTEP code.18 The self-consistent ground state of the system was determined by using a band-by-band conjugate gradient technique to minimize the total energy of the system with respect to the plane wave coefficients. The electronic wave functions were obtained by a density-mixing scheme,19 and the structures were relaxed by using the Broyden, Fletcher, Goldfarb, and Shannon (BFGS) method.20 The LDA functional proposed by Ceperley and Alder21 and parametrized by Perdew and Zunder,22 named CA-PZ, was employed. The cutoff energy of plane waves was set to 400.0 eV. Brillouin zone sampling was performed by using the Monkhost-Pack

10.1021/jp903982w CCC: $40.75  2009 American Chemical Society Published on Web 07/02/2009

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Figure 1. Unit cells for (a) styphnic acid, (b) potassium styphnate, (c) barium styphnate, and (d) lead styphnate. Gray, blue, red, white, purple, green, and dark gray spheres stand for C, N, O, H, K, Ba, and Pb atoms, respectively.

3. Results and Discussion

Figure 2. Conformation and atomic numbering of the C6N3O8H3 molecule in styphnic acid.

scheme with a k-point grid of 2 × 2 × 2, 3 × 2 × 3, 3 × 2 × 2, and 3 × 2 × 2 for styphnic acid, potassium styphnate, barium styphnate, and lead styphnate, respectively. The values of the kinetic energy cutoff and the k-point grid were determined to ensure the convergence of total energies. Styphnic acid crystallizes in a triclinic P-3c1 space group and contains six H3C6N3O8 · 4H2O molecules per unit cell.23 Potassium styphnate contains two HC6N3O8K2 · H2O molecules per unit cell in a triclinic lattice with space group P-1.24 Barium styphnate crystallizes in a monoclinic P2/c space group with two HC6N3O8Ba · 2H2O molecules per unit cell.25 Lead styphnate contains two HC6N3O8Pb · H2O molecules per unit cell in a monoclinic lattice with space group P2/c.26 Figure 1 displays the unit cells of the four crystals, and conformation and atomic numbering of H3C6N3O8 molecule in the styphnic acid are shown in Figure 2. Starting from the above-mentioned experimental structures, the geometry relaxation was performed to allow the ionic configurations, cell shape, and volume to change. In the geometry relaxation, the total energy of the system was converged less than 2.0 × 10-5 eV, the residual force less than 0.05 eV/Å, the displacement of atoms less than 0.002 Å, and the residual bulk stress less than 0.1 GPa. The Mulliken charges and bond populations were investigated using a projection of the plane wave states onto a linear combination of atomic orbitals (LCAO) basis set,27,28 which is widely used to perform charge transfers and population analyses. The phonon frequencies at the gamma point have been calculated from the response to small atomic displacements.29

3.1. Bulk Properties. As a base for studying other crystals and as a well-studied benchmark, we apply three different functionals to bulk lead styphnate as a test. The LDA (CA-PZ) and generalized gradient approximation (GGA) (PBE30 and PW9131) functionals were selected to fully relax lead styphnate without any constraint. The calculated lattice parameters are given in Table 1 together with the experimental values.26 It is found that the errors in the LDA (CA-PZ) results are slightly smaller than those in the GGA (PBE and PW91) results in comparison with the experimental values. This shows that the accuracy of LDA is better than that of the GGA functionals. Table 1 also presents the calculated lattice constants of crystalline styphnic acid, potassium styphnate, and barium styphnate by LDA along with corresponding experimental data. It is seen that the lattice constants compare well with experimental values. The comparisons confirm that our computational parameters are reasonably satisfactory. We thus used LDA in all subsequent calculations. 3.2. Electronic Structure. The calculated total density of states (DOS) and partial DOS (PDOS) for styphnic acid and its metal salts are displayed in Figures 3-6. The general shapes of the DOS in the four crystals are very similar, both in the valence band region and in the conduction band region, showing that the fundamental bonding pictures in the four crystals are the same. The DOS of the four crystals are finite at the Fermi energy level. This is because the DOS contain some form of broadening effect. In the upper valence band, all four crystals have a sharp peak near the Fermi level, which indicates that the top valence bands of their band structures are flat. The top of the DOS valence band shows three main peaks for the four crystals. These peaks are predominately from the p states. After that, several main peaks in the upper valence band are superimposed by the s and p states. The conduction band of each crystal is dominated by the p states. This indicates that the p states for the four crystals play a very important role in their chemical reactions. Compared to the DOS of styphnic acid, the DOS of potassium styphnate presents a peak at -11.01 eV from the K states. Similarly, the DOS of barium styphnate shows a peak at -10.12 eV from the Ba states, and the DOS of lead styphnate shows a peak at -15.22 eV from the Pb states. Since these peaks are far from the upper valence band, the metal states indirectly affect the top DOS of styphnic acid. This will be further discussed below. Note that several DOS peaks in the

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TABLE 1: Experimental and Relaxed Lattice Constants (Å) for Lead Styphnate, Styphnic Acid, Potassium Styphnate, and Barium Styphnate lead styphnate a b c R β γ

styphnic acid

potassium styphnate

barium styphnate

LDA

PBE

PW91

expt26

LDA

expt23

LDA

expt24

LDA

expt25

7.826 8.074 8.368 89.34° 106.75° 89.86°

8.703 8.287 10.823 84.07° 124.44° 93.32°

8.385 8.173 9.772 83.59° 121.56° 92.70°

7.519 8.004 8.413 90° 107.22° 90°

12.434 12.391 9.828 89.75° 90.17° 120.1°

12.607 12.607 10.114 90° 90° 120°

7.307 9.214 9.653 114.86° 109.32° 95.58°

6.993 9.474 9.791 115.28° 107.86° 95.94°

7.595 8.035 8.771 90.01° 108.08° 89.91°

7.546 8.082 8.756 90° 106.52° 90°

upper valence band merge together, indicating that there is good electronic delocalization in the systems. The atom-resolved DOS and PDOS of the four crystals are also shown in Figures 3-6. The main features can be summarized as follows. (i) In the upper valence band, the PDOS of the states of C and O of hydroxyls are far larger than those of the states of N of NO2. It is expected that the states of C and O

of hydroxyls make more important contributions to the valence bands than those of N of NO2. This shows that the O of hydroxyl acts as an active center. (ii) Some strong peaks occur at the same energy in the PDOS of a particular C atom and a particular N atom. It can be inferred that the two atoms are strongly bonded. Similarly, a particular O atom of hydroxyl and a particular C atom are strongly bonded. The same is true of a

Figure 3. Total and partial density of states (DOS) of O of OH states, C states, N states, O of NO2 states, O of H2O states, and styphnic acid. The Fermi energy is shown as a dashed vertical line.

Figure 5. Total and partial density of states (DOS) of Ba states, O of OH states, C states, N states, O of NO2 states, O of H2O states, and barium styphnate.

Figure 4. Total and partial density of states (DOS) of K states, O of OH states, C states, N states, O of NO2 states, O of H2O states, and potassium styphnate.

Figure 6. Total and partial density of states (DOS) of Pb states, O of OH states, C states, N states, O of NO2 states, O of H2O states, and lead styphnate.

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TABLE 2: Calculated Charges (e) and Bond Orders for Styphnic Acid, Potassium Styphnate, Barium Styphnate, and Lead Styphnate styphnic acid

potassium styphnate

barium styphnat

lead styphnate

C1 C2 C3 C4 C5 C6 N1 N2 N3 O1 O2 metal

-0.40 0.08 0.31 0.07 0.30 0.08 0.42 0.43 0.42 -0.72 -0.72

Charge -0.21 0.04 0.23 -0.01 0.26 0.05 0.22 0.23 0.22 -0.57 -0.57 K/1.05

-0.21 0.07 0.31 0.0 0.31 0.07 0.37 0.39 0.37 -0.63 -0.63 Ba/1.50

-0.20 0.05 0.29 0.0 0.30 0.05 0.37 0.38 0.37 -0.60 -0.61 Pb/1.40

C1-C2 C2-C3 C3-C4 C4-C5 C5-C6 C6-C1 C2-N1 C4-N2 C6-N3 C3-O1 C5-O2

1.09 1.09 1.11 1.12 1.09 1.09 0.72 0.66 0.72 0.74 0.74

1.11 0.95 1.03 1.03 0.95 1.11 0.79 0.78 0.80 0.81 0.80

1.10 0.99 1.06 1.03 0.96 1.14 0.81 0.77 0.79 0.88 0.92

Bond Order 1.17 0.95 1.03 1.04 0.96 1.11 0.80 0.81 0.85 1.01 0.96

particular N atom and a particular O atom of NO2. (iii) There are some differences in the PDOS of the O atoms of hydroxyls for styphnic acid and its metal salts. This is due to the differences in their local molecular packing. Therefore, it may be inferred that the metal states affect the electronic structure of styphnic acid by modifying the DOS of the O atoms of hydroxyls. (iv) In the conduction band region, the metal states make the DOS peak of the C states split and hence lead to a division for the DOS peak of styphnic acid. (v) At -11.01 eV, the K-3p states are overlapped by the O states of hydroxyls and NO2 in potassium styphnate, which is generally interpreted as evidence of coordination bonding between the K and O atoms. Similar, there is coordination bonding between the Ba and O atoms in barium styphnate. However, for lead styphnate, the Pb states are superposed by the O states of H2O besides the O states of hydroxyls and NO2 at -15.22 eV. This indicates that the coordination bonding in lead styphnate is stronger than that in potassium and barium styphnate. (vi) In the upper valence band from -5.0 to 0 eV, the DOS of the four crystals are superimposed by the states of C and O of hydroxyl. It is inferred that the C-O bond fission may be favorable in the decomposition of crystalline styphnic acid and its metal salts, which is consistent with the previous report.24 The electronic structure can be further analyzed by examining the charge and bond order in the four crystals. The Mulliken charge and overlap population are useful in evaluating the nature of bonds in a compound. Although the absolute magnitudes of Mulliken populations have little physical meaning, the relative values can still offer some useful information. Table 2 shows the charge and bond order values for the four crystals. The charges of the C2-C6 atoms in styphnic acid are close to those in its metal salts, whereas the charge of C1 in styphnic acid is 0.40e, larger than those of 0.20e-0.21e in its metal salts. This difference can be observed from the PDOS of the C states in Figures 3-6. The charges of C in the three metal salts are slightly different. This similarity can actually be seen from the

PDOS of Figures 4-6 where the C-p peak is at about the same energy. The effective charges of the N atoms in styphnic acid are nearly equal, reflecting that the N atoms are in similar local packing. The same is true of the N atoms in their metal salts. The charge of the O atom of hydroxyl in styphnic acid is 0.72e, while that in its metal salts ranges from 0.57e to 0.63e. This indicates that there is charge transfer between O and metal ions. Compared with styphnic acid, the anions in the metal salts have an electronic delocalization over the aromatic nucleus under the influence of the metal ions. The effective charge of the K ion is 1.05, close to 1, whereas that of the Ba ion is 1.50 and that of the Pb ion is 1.40, smaller than 2. This shows that potassium styphnate has stronger ionic bonding than barium styphnate and lead styphnate. Bond order is a measure of the overall bond strength between two atoms. A high value of the bond order indicates a covalent bond, while a low value shows an ionic nature. The bond orders of the C-C bonds in styphnic acid are nearly equal, indicating that the bonding in the ring is formally aromatic. However, this situation is destroyed in its metal salts. The bond orders of the C1-C2 and C6-C1 bonds in the three metal salts increase, while those of the other C-C bonds decrease compared to styphnic acid. This is because these salts have a better electronic delocalization, except that the additions of the metal ions break the intramolecular hydrogen bonding between the nitro and hydroxyl groups in styphnic acid. Therefore, the bond orders are affected by the presence of other nearby atoms, not just the two atoms that form a bond. The C2-N1 bond of styphnic acid has a bond order value of 0.72, equal to the C6-N3 bond order of 0.72. This shows that the C2-N1 and C6-N3 bonds are in similar local packing and have the same bond strength. However, in its metal salts, this situation is completely different. The bond orders of the C3-O1 and C5-O2 bonds in styphnic acid are smaller than those in its metal salts, reflecting the C-O bonds in the former have weaker bonding than those in the latter. This is because the metal salts have a better electronic delocalization than styphnic acid. This is supported by the PDOS of Figures 4-6. 3.3. Absorption Spectra. In this section, we turn to investigate the optical absorption coefficients of the four crystals. The interaction of a photon with the electrons in the system can result in transitions between occupied and unoccupied states. The spectra resulting from these excitations can be described as a joint density of states between the valence and conduction bands. The imaginary part ε2(ω) of the dielectric function can be obtained from the momentum matrix elements between the occupied and unoccupied wave functions within the selection rules, and the real part ε1(ω) of the dielectric function can be calculated from the imaginary part ε2(ω) by the Kramer-Kronig relationship. The absorption coefficient R(ω) can be evaluated from ε1(ω) and ε2(ω).32

R(ω) ) √2ω(√ε21(ω) + ε22(ω) - ε1(ω))1/2

(1)

The absorption coefficients R(ω) of the four crystals are plotted in Figure 7. The absorption spectra are active over various regions corresponding to the molecular or lattice structures of the individual materials. The evolution pattern of the absorption spectra for the four crystals is qualitatively similar. They have an absorption band covering from 0 to 25.0 eV and stronger optical absorption from 2.0 to 15.0 eV. The magnitude of the absorption coefficients of these peaks allows an optical transition due to excitons. Styphnic acid exhibits a

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Figure 7. Optical absorption spectra of styphnic acid, potassium styphnate, barium styphnate, and lead styphnate.

relatively high absorption coefficient over a relatively few closely spaced bands. The absorption bands from 0 to 3.56 eV and 13.4 to 15.9 eV correspond to the frequency of C-H stretching. The bands in the range from 3.6 to 11.6 eV overlap, forming the strongest absorption region that corresponds to NdO vibration and ring distortion. The peak at 19.5 eV corresponds to O-H stretching. Similarly, these peaks in the absorption spectra of its metal salts reveal their structure and bonding. Their absorption spectra manifest a few widely spaced strong bands. These bands exhibit some overlap. This indicates that the three metal salts have strong ionic bonding. Compared with styphnic acid, potassium and barium styphnates decrease the highest peak, while lead styphnate increases it. It is thus inferred that lead styphnate has relatively high optical activity. In addition, the three metal salts have higher absorption coefficients than styphnic acid in the higher-frequency region, indicating a shift toward higher frequencies in their absorption spectra. In the absorption spectra of the three metal salts, the absorption peak at 13.35 eV corresponds to the breathing frequency of the metal ions, which is not observed in the absorption spectra of styphnic acid. The calculated results here present that the absorption spectra of the four crystals display a few strong bands in the fundamental absorption region. 3.4. Thermodynamic Properties. In this section, the thermodynamic functions including enthalpy, entropy, free energy, and heat capacity for the four crystals are evaluated and presented in Figure 8. With the increase of temperature, the calculated enthalpies of the four crystals monotonically increase. This is because the main contributions to the enthalpy are from the translations and rotations of the molecules at lower temperature, whereas the vibrational motion is intensified and makes more contributions to the enthalpy at higher temperature. Compared with styphnic acid, potassium, barium, and lead styphnates increase the enthalpy less as the temperature increases. However, the difference of the enthalpy between each metal salt is very small. The same is true of the entropy and heat capacity. For the free energy, the case is quite the contrary. As the temperature increases, the free-energy values of the four solids gradually decrease. This indicates that the materials become thermodynamically more stable. From Figure 8, it can be also seen that the decreasing order of the free energy is as follows: styphinc acid > its metal salts; moreover, there is a very small difference between the free energy of each metal salt. The free energy of a material strongly depends on the geometry of the atomic configurations. Since the metal salts of

Figure 8. Entropy (S), heat capacity (Cp), enthalpy (H), and free energy (G) of styphnic acid, potassium styphnate, barium styphnate, and lead styphnate as a function of temperature.

styphnic acid have similar crystal packing, their free energies are very close. On the basis of the calculated thermodynamic functions, we evaluated the enthalpy of formation and the free energy of formation for the decomposition reactions 2-5 of the four crystals.

C6N3O8H3 · 4H2O f 2HCN + 4CO2 + 1/2H2 + 1/2N2 + 4H2O (2) C6N3O8K2H · H2O f 2KCN + 4CO2 + 1/2H2 + 1/2N2 + H2O (3) C6N3O8BaH · 2H2O f Ba(CN)2 + 4CO2 + 1/2H2 + 1/2N2 + 2H2O (4) C6N3O8PbH · H2O f Pb(CN)2 + 4CO2 + 1/2H2 + 1/2N2 + H2O (5) The calculated enthalpy and free energy of formation for the four crystals are shown in Figures 9 and 10, respectively. It can be seen that the enthalpies of formation for the four crystals become more and more positive with increasing temperature. This shows that the primary fission reactions are exothermic. As the temperature increases, the enthalpy of formation for the four crystals increases in the following order: styphnic acid < potassium styphnate < lead styphnate < barium styphnate. It is found from Figure 10 that the free energies of formation for the four crystals gradually decrease with the temperature increasing. Above about 160 K, the free energies of formation for styphnic acid are negative, while those for its metal salts become negative over about 350 K. This shows that the decomposition reactions 2-5 are thermodynamically favorable under high temperature. Additionally, we note that the free energy of formation versus temperature curve of styphnic acid crosses that of barium styphnate at about 785 K, lead styphnate at about 825 K, and potassium styphnate at about 923 K. The free energy of formation for styphnic acid is smaller than that

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Figure 9. Enthalpy of formation for styphnic acid, potassium styphnate, barium styphnate, and lead styphnate as a function of temperature.

impact sensitivity for the solids. A possible explanation may be that the smaller the band gap, the easier the electron transfers from the valence band to the conduction band and the more the solid decomposes and explodes. It may be thus inferred that the impact sensitivity for the four crystals decreases in the following sequence: lead styphnate > potassium styphnate > barium styphnate > styphnic acid. Previous theoretical studies performed at the semiempirical discrete variational XR (DVXR) and extended Hu¨ckel-crystal orbital (EH-CO) levels34,35 have shown that the band gap in the metal azides can be related to the impact sensitivity. Our recent reports on the heavy-metal azides,36 the nitro anilines,37 the potassium-doped cuprous azides,38 the four octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) phases,39 and the four hexanitrohexaazaisowurtzitane (CL-20) polymorphs40 within the framework of periodic DFT have also confirmed the relationship between the band gap and impact sensitivity. Gilman41-44 has emphasized the role of HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gap closure in the explosion of molecules suffering shear strain. Further investigations45,46 on the excitonic mechanism of detonation initiation show that the pressure inside of the impact wavefront reduces the band gap between valence and conducting bands and promotes the HOMO-LUMO transition within a molecule. These studies have suggested that the HOMO-LUMO gap in gas molecules suffering shear strain, impact wave, or distortion can be directly related to the sensitivity. Therefore, these suggestions support our conclusion here that there is the relationship between the band gap and impact sensitivity. 4. Conclusions

Figure 10. Free energy of formation for styphnic acid, potassium styphnate, barium styphnate, and lead styphnate as a function of temperature.

TABLE 3: Experimental Impact Sensitivity and Calculated Band Gap for Styphnic Acid, Potassium Styphnate, Barium Styphnate, and Lead Styphnate styphnic acid impact sensitivity (N m)2 band gap (eV)

potassium styphnate

barium styphnate

7.4 2.42

lead styphnate 2.5-5

1.84

1.85

1.64

for lead styphnate below about 825 K. This shows that styphnic acid is thermodynamically easier to decompose than lead styphnate in this temperature range. In fact, the decomposition of styphnic acid occurs below approximately 176 °C,2 whereas lead styphnate decomposes at about 222.5 °C.33 3.5. Correlation of Band Gap with Impact Sensitivity. In this section, an attempt is made to correlate the impact sensitivity of the four crystals with their electronic structure. The band gap is an important parameter to characterize the electronic structure of solids. Table 3 presents the energy gaps between valence and conduction bands for the four crystals. It is found that the band gap increases in the sequence of lead styphnate, potassium styphnate, barium styphnate, styphnic acid, while the experimental impact sensitivity (shown in Table 3) decreases in the following order: lead styphnate > styphnic acid.2 Therefore, there is a relationship between the band gap and

In this study, we have performed a detailed density functional theory study of electronic, absorption, and thermodynamic properties of crystalline styphnic acid and its metal salts in the local density approximation. An analysis of electronic structure shows that the metal states affect the electronic structure of styphnic acid by modifying the DOS of the O atoms of hydroxyls. The states of C and O of hydroxyls make more important contributions to the valence bands than those of N of NO2. This shows that the O of hydroxyl acts as an active center. The C-O bond fission may be favorable in the decomposition of crystalline styphnic acid and its metal salts. The absorption spectra of the four crystals display a few strong bands in the fundamental absorption region. The three metal salts have higher absorption coefficients than styphnic acid in the higher-frequency region, indicating a shift toward higher frequencies in their absorption spectra. Compared with styphnic acid, potassium, barium, and lead styphnates decrease its enthalpy, entropy, free energy, and heat capacity as the temperature increases. However, the differences of the thermodynamic functions between each metal salt are very small. As the temperature increases, the decomposition reactions of the four crystals are more and more favorable thermodynamically. It is also found that there is a relationship between the band gap and impact sensitivity for the four crystals. Acknowledgment. This work was supported by the NSAF Foundation of the National Natural Science Foundation of China and China Academy of Engineering Physics (Grant No. 10876013), the Research Fund for the Doctoral Program of Higher Education, and the Project sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

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