J. Phys. Chem. 1996, 100, 4701-4712
4701
ARTICLES Molecular Dynamics Simulations of Initial Decomposition Process on the Unique N-N Bond in Nitramines in the Crystalline State Yuji Kohno Chugoku Kayaku Co., Ltd., Etajima-cho, Aki-gun, Hiroshima 737-21, Japan
Kazuyoshi Ueda Department of Chemistry, Faculty of Science, Hiroshima UniVersity, Kagamiyama, 1-3-1, Higashi Hiroshima-City 724, Japan
Akira Imamura* Department of Chemistry, Faculty of Science, Hiroshima UniVersity, Kagamiyama, 1-3-1, Higashi Hiroshima-City 724, Japan, and PRESTO, Research DeVelopment Corporation of Japan, Research Consortium, Tsukuba 300-26, Japan ReceiVed: January 31, 1995; In Final Form: July 24, 1995X
Molecular dynamics (MD) calculations have been carried out by using the CHARMM program to study initial decomposition processes in nitramines (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) polymorphs and related nitramines) in the crystalline state. Three types of simulations with different conditions were performed to investigate the effect of the crystalline state on the decomposition processes of the molecule. When the simulation was performed with the gas phase value of the equilibrium N-N bond length but started from the crystallographic structure as an initial conformation, which mimics the course of the trajectory from the crystal state to the gas phase, large amplitude oscillations of the N-N bond lengths were observed in the trajectories. Another simulation, which takes the crystal effects into account by adjusting the equilibrium N-N bond length in CHARMM, also showed the large amplitude oscillations of the N-N bond. In this case, it was also observed that excess vibrational energy of N-NO2 is transferred to another N-NO2 moiety. These results indicate the importance of compressed N-N bonds in the crystal for bringing about the initial decomposition process of nitramines.
1. Introduction Recent attention has been focused on the high performance of nitramines as energetic materials for the new generation of propellants and explosives. The molecular design of new energetic materials with lower sensitivity and higher performance requires an understanding of the mechanisms of the explosion reactions of nitramines. These mechanisms are still not known. In recent work, much effort has been focused on the identification of the factors which are responsible for the sensitivity of energetic molecules to physical stimuli such as impact.1-6 Especially the relationship between the impact sensitivity and the electronic structure of nitramines has become an important subject in this area. It is widely known that the impact sensitivities of the octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) polymorphs (see Figure 1) differ appreciably from each other. HMX is one of the most important energetic ingredients of nitramines that are used in various propellants and explosives. HMX exists in four polymorphic modifications known as the R, β, γ, and δ forms. The β form is stable at room temperature and is used in the general applications. The impact sensitivities of the HMX polymorphs have been studied using the drop weight apparatus and were reported to the order of β , R < γ X
Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-4701$12.00/0
< δ7,8 (Table 1). The conformation of the HMX polymorphs has been determined by diffraction methods9-13 (Table 2). The β form has a chair ring conformation, while the R, γ, and δ forms have a boat conformation, as shown in Figure 1. The molecular structures of the R, γ, and δ forms of the HMX polymorphs in the crystalline state are only slightly different from each other, but the relative orientations of the molecules in the crystal are considerably different from each other. However, the factors which are responsible for the sensitivities of the HMX polymorphs are still not clear. In our previous paper,13-15 ab initio calculations (at the MP2/ 4-31G level) were reported for the molecular structures of the HMX (R, β, γ, and δ) polymorphs in the crystalline states. In this paper, we clarified that there is an intimate relation between the impact sensitivity (β , R < γ < δ) and the total energy of the polymorph which has the crystallographic conformation(β < R < γ < δ). Oyumi and Brill16 and some other researchers17-21 pointed out that the rupture of the N-NO2 bond is the key step in the decomposition process of HMX. Therefore, in order to shed light on the quantum chemical characteristics of the N-N bond of the HMX polymorphs in the crystalline state, we plotted the total energy (the MP2/431G level) as a function of the N-N bond length (Figures 4 and 5 in ref 15). A new parameter δD was then introduced.15 © 1996 American Chemical Society
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δD ) (optimized N-N bond length) (N-N bond length in the crystal) (1)
Figure 1. Molecular structures and nomenclature of HMX polymorphs (R, β, γ, and δ) in the crystalline state.
TABLE 1: Impact Sensitivity of the HMX Polymorphs polymorph form
weight/falling height (kg/cm)
impact energy (kg/cm2)
β R γ δ
5/15 1/20 1/20 1/10
0.75 0.20 0.20 0.10
N-NO2 moieties were different in the various HMX polymorphs.15 These molecular orbital studies showed that the compressed N-N bonds in the crystals play an important role in the initial decomposition processes of the nitramines which is induced by strong physical stimuli such as impact. The object of the present study was to investigate the dynamic mechanism of the impact-induced decomposition. To this end, molecular dynamics simulations for the initial decomposition process in the crystalline state were carried out on the abovementioned nitramines and related nitramines. Molecular dynamics simulations have been shown to be a valuable tool for revealing the mechanisms of various kinds of reactions. Concerning the molecular dynamics study of nitramines, the intramolecular vibrational energy transfer in dimethylnitramine (DMN) was studied by Sumpter et al.22 Sewell et al. investigated the unimolecular dissociation of the hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) molecule in the gas phase (1991).23 Recently, conformational changes in RDX in the isolated state and in dense Xe gas were also studied by molecular dynamics simulations.24 However, there have been no detailed molecular dynamics studies which would clarify the dynamic mechanism of the initial step of the impact-induced decomposition of nitramines. Especially there has been no study of the dynamics of the N-N bonds in the process of the impactinduced decomposition of nitramines. Therefore, we carried out molecular dynamics simulations with a crystal effect model on the femtosecond time scale to study the initial decomposition process in connection with the intramolecular vibrational energy transfer for the HMX polymorphs (four-unit moieties) and the family of the HMX compounds, as shown in Figure 2, that is, DMN (dimethylnitramine, a unit moiety of the HMX molecule), RDX (three-unit moieties), and OHMX (1,7-dimethyl-1,3,5,7tetranitrotrimethylenetetramine, four-unit linear moieties) in the crystalline state. From calculations for these molecules, the effect of the ring structure and the size of the ring on the energy transfer may be estimated. 2. Methods and Procedures
This parameter δD can be considered as a measure of the compression of the N-N bond in a crystal environment relative to the gas phase; that is, δD can be referred to as a crystal effect parameter. The δD values of the HMX polymorphs are about 0.06-0.08 Å for all crystal forms. A good correlation between the impact sensitivity and the maximum δD (δDmax) or the average value of the δD’s (δD h ) of each HMX molecule was found. In the calculation of δD, we also found that the δD values depend significantly on the electronic correlation. In the previous study,14 we investigated the influence of electron correlation on the characteristic N-NO2 bond length in comparison with other types of bonds such as the N-NH2 bond in DMH (1,1-dimethylhydrazine), where the oxygen atoms of DMN (N,N-dimethylnitramine, as shown in Figure 2a) are substituted by two hydrogen atoms, and the C-C bond of ethane, and we found that only the N-NO2 bond was lengthened significantly by the electronic correlation effect. This unique property of the N-N bond in nitramines is ascribed to the antibonding character of the N-NO2 bond in the LUMO (lowest unoccupied molecular orbital). In addition, we calculated the magnitude of the force vector acting on each atom of the HMX polymorphs with the geometry in the crystalline state and found that larger vectors were concentrated around the N-NO2 moiety. In other words, the strain energy is stored mainly around the N-NO2 moiety. Furthermore, those strain energies around the
A. Total Potential Energy. In the present study, several molecular dynamics simulations were performed for nitramines using the program CHARMM22.25 We performed calculations for several nitramines [DMN (one-unit nitramine), RDX (threeunit cyclic nitramine), the HMX polymorphs (four-unit cyclic nitramine), and OHMX (four-unit linear nitramine)] with crystallographic geometries9-13,26-29 as shown in Figures 1 and 2 and Table 2. All these molecules include the C2N-NO2 unit. The CHARMM22 potential energy function is expressed as follows.
E ) Eb + Eθ + Eφ + Eω + EVDW + Eel
(2)
where the formulas for each of these terms are presented below. (1) Internal Potential Energy Terms.
Bond potential: Eb ) ∑kb(l - l0)2
(3)
Bond angle potential: Eθ ) ∑kθ(θ - θ0)2 Dihedral angle (torsion) potential:
(4)
N-N Bond in Nitramines in the Crystalline State
J. Phys. Chem., Vol. 100, No. 12, 1996 4703
TABLE 2: Crystal Parameters of Nitraminesa cell parameters nitramine
space group
R (%)
a (Å)
b (Å)
c (Å)
HMX R β γ δ DMN RDX OHMX
Fdd2 P21/n Pn P61 or P65 P21/m Pbca P21/c
3.5 3.2 4.6 11.5 4.6 3.9 3.84
15.140(0) 6.5347(4) 13.27(1) 7.711(2) 6.129(1) 13.182(2) 20.952(7)
23.890(0) 11.0296(6) 7.90(1) 7.711(2) 6.501(1) 11.574(2) 9.477(2)
5.913(0) 7.3549(5) 10.95(1) 32.553(6) 6.060(1) 10.709(2) 6.571(2)
a
β (deg) 102.689(5) 106.8(1) 114.66(2) 96.29(3)
Z
Dabs (g/cm3)
Dcalc (g/cm3)
ref
8 2 2 6 2 8 4
1.84 1.90 1.78 1.58 1.36 1.816
1.839 1.902 1.82 1.586 1.36 1.806 1.598
9 13 12 11 26 28 29
Values in parentheses are estimated standard deviations.
kφ Eφ ) ∑ [1 + cos(nφ - δ)] 2
(5)
Improper torsions: Eω ) ∑kω(ω - ω0)2
(6)
The improper torsional term has been designed both to maintain chirality about a tetrahedrally extended heavy atom and to maintain planarity about certain planar atoms with a quadratic distortion potential. Therefore, in our calculations, internal potential energy terms do not include this improper torsional term. Internal potential energy terms except for dihedral angle potential are represented with the harmonic potential energy function. (2) Nonbonded Interaction Terms. Nonbonded interaction terms are van der Waals interactions and Coulombic interactions between the partial charges on the individual atoms. The parameters for nonbonded interaction terms are those used in the program CHARMM22. Long-range interactions were cut off between 10.0 and 12.0 Å by use of a switching function.25 The formulas for each of the two terms are indicated below.
Van der Waals interactions: EVDW )
∑
[( ) ( ) ] 12 r* ij
*ij
excl(i,j))1
rij
-2
6 r* ij
rij
2 SW(rij2 ,r2on,roff ) (7)
Figure 2. Molecular structure and nomenclature of DMN (a), RDX (b), and OHMX (c) in the crystalline state.
*ij ) x* i* j r* i + r* j (8) 2 where nj is the distance between atoms i and j in a molecule and * and r* are the well depth and the position of the minimum in the Lennard-Jones potential respectively. r* ij )
Electrostatic potential: Eel )
∑
qiqj
2 SW(rij2 ,r2on,roff )
2 excl(i,j))1 4π0rij
(9)
SW is a switching function defined by
(1) SW(χ,χon,χoff) ) 1 (2) SW(χ,χon,χoff) )
when χ e χon
(χoff - χ)2(χoff + 2x - 3χoff)
(3) SW(χ,χon,χoff) ) 0
(χoff - χon)3 when χon < χ < χoff when χ > χoff
excl(i,j) ) 0 if atoms are connected by angles or bonds or igj
) 1 otherwise (unless explicitly specified to be zero) Since there are no appropriate parameters for the N-NO2 moiety of HMX in the program CHARMM22, ab initio calculations have been performed at the MP2(second-order Mφller-Plesset theory30)/4-31G and the MP2/4-31G* levels with the GAUSSIAN 92 program31 in order to determine the potential parameters in question. B. Partial Atomic Charges. For the purpose of estimating partial atomic charges for the DMN molecule in the crystalline state, the ab initio periodic Hartree-Fock Roothan method was applied to DMN by using CRYSTAL 88.32 Thus, partial atomic charges for DMN with the crystallographic geometry together with cell parameters were calculated by using Mulliken population analysis at the 6-21G level. However, at present, it is impossible to calculate partial atomic charges for RDX, HMX polymorphs, and OHMX using CRYSTAL 88 because of the sizes of the molecules. Therefore, partial atomic charges for nitramines except DMN were calculated for a single isolated molecule with crystallographic geometry, followed by Mulliken population analysis at the MP2/4-31G level.
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Figure 3. Molecular structure of axial and equatorial parts of RDX: (a) crystallographic geometry; (b) optimized structure.
C. Force Constants. To determine the harmonic force constants of the internal potential energy terms in the gas phase, we calculated the bond, the angle, and the dihedral potential energy curves of isolated nitramines at the MP2/4-31G level. From these potential energy curves, the force constants kb and kθ could be evaluated by varying the bond length and the bond angle by minute values around the optimized value. The force constant for the dihedral angle (Kφ) was determined from the difference in the potential energy between the minimum and the maximum in the range 0-180°. We calculated the force constants for both DMN and two units of RDX. RDX has the axial and the equatorial N-NO2 moieties as shown in Figure 3a. These two unit moieties may be considered as models of other nitramines (RDX, HMX, and OHMX). The force constants for the two units in RDX thus determined were used for molecules other than DMN. For DMN, a set of values for this particular molecule was used. The equilibrium values of bond lengths and bond angles (l0, θ0), except the N-N bond length, were determined by full geometry optimization based at the MP2/4-31G* level. Because the magnitudes of the optimized N-N bond lengths change from molecule to molecule15 and because these molecules are huge, the equilibrium values of N-N bond length (l0) and the corresponding force constants (Kb) of RDX, HMX, and OHMX were determined by partial optimization at the MP2/4-31G level for the geometry which was determined from the crystallographic data for other parts of the molecule. D. Molecular Dynamics. Dynamical simulations were performed by classical mechanics. Initial velocities for all atoms in these systems were selected at random from a Boltzmann distribution at 300 K. Newton’s equations of motion were then integrated for a microcanonical ensemble by using a Verlet integrator with a step size of 0.1 fs. We calculated at first DMN, followed by RDX, the HMX polymorphs, and OHMX. DMN is of fundamental importance in the study of nitramines because it has the basic N-NO2 moiety. Cyclic RDX, cyclic HMX polymorphs, and linear OHMX were calculated in order to study the effects of the cyclic structure systematically.
Figure 4. Minimized molecular structures of nitramines using CHARMM22: (a) DMN, (b) RDX, and (c) OHMX.
Molecular dynamics calculations were carried out with three different conditions on nitramines at 300 K. In the first condition, the crystallographic conformation was used as a starting geometry at 300 K and the simulation was done by using l0 in vacuum for 10 ps at 300 K. The changes in the N-N, C-N, and O-N bond lengths were plotted as functions of time. In addition, in order to analyze the characteristic wave pattern in the simulations, we calculated the autocorrelation functions and the power spectra by using program packages in CHARMM22. The first 4 ps of all the 10 ps trajectories were used in the calculation of the correlation functions. The power spectra were obtained from the Fourier transform of the correlation function. The spectral resolution is 0.25 ps-1. In the second condition, the crystallographic structure was first minimized in vacuum and then equilibrated for 1 ps (see Figures 4 and 5). After equilibration for 1 ps, a dynamics simulation was performed for 10 ps at 300 K. The third condition is described in the following. First of all, the equilibrium bond length for the N-N bond (the value for l0) was adjusted to reproduce the N-N bond length in the crystalline state at 300 K. Hereafter, the adjusted value for l0 is referred to as ladj. After the structure was equilibrated for 1 ps with the parameter ladj, the molecular dynamics simulation was continued for 10 ps with the same parameter. In this way, we mimicked the crystal effects even though just one molecule is explicitly treated in the simulation. The data for these dynamics were stored in a restarting file, and then a dynamics simulation was restarted using the l0 parameter instead of ladj. That is to say, by changing the value of the equilibrium N-N bond length from ladj to l0, the crystal effect is considered to be suddenly removed. Since the crystal effect should be reduced remarkably at the initial decomposition process for nitramines
N-N Bond in Nitramines in the Crystalline State
J. Phys. Chem., Vol. 100, No. 12, 1996 4705 TABLE 3: Optimized N-N Bond Length and Values of δD of Nitramines (the MP2/4-31G Level) N-N bond length (Å) nitramine
obsa
opt
δDb (Å) δDmaxc
δDd
∑δDe
HMX R axial equatorial
1.354 1.4293 1.367 1.4413
0.075 0.074
0.075 0.075
axial equatorial
1.368 1.4364 1.362 1.4304
0.068 0.068
axial(1) axial(2) equatorial(1) equatorial(2)
1.395 1.361 1.364 1.376
1.4564 1.4428 1.4455 1.4424
0.061 0.082 0.082 0.066
axial(1) axial(2) equatorial(1) equatorial(2)
1.346 1.355 1.392 1.363 1.332
1.4174 1.4302 1.4637 1.4375 1.3925
0.071 0.075 0.072 0.075 0.061
axial(1) axial(2) equatorial
1.392 1.4779 1.398 1.4804 1.351 1.4322
0.086 0.082 0.081
0.086
nm(1) nm(2) nm(3) nm(4)
1.358 1.351 1.364 1.351
0.057 0.056 0.046 0.054
0.057
0.298
β 0.068 0.068 0.272
γ 0.082 0.082 0.073 0.291
δ
DMN RDX
0.075 0.075 0.074 0.293 0.061
0.083 0.249
OHMX 1.4145 1.4068 1.4100 1.4089
0.053 0.213
The observed values are in the bond length in the crystal. b δD ) opt val - obs val. c The maximum δD of the N-N bond of each molecule. d The average δD of each molecule. e Total summation δD in a molecule. a
Figure 5. Minimized molecular structures of the HMX polymorphs (R, β, γ, and δ) using CHARMM22.
when a strong impact is applied to crystals of explosives, the above condition of simulation may mimic the initial decomposition process. In this manner the effect of the compressed N-N bond in the crystalline state is assessed through comparison of the results using l0 and ladj. E. Intramolecular Vibrational Energy Transfer. In order to investigate the dynamic mechanism of intramolecular vibrational energy transfer between N-NO2 moieties on nitramines, the third condition was modified as follows. The parameter for only one of the N-N bond lengths was changed from ladj to l0, and then simulations were performed. Following this change, the special N-N bond may transfer to other parts of the molecule the excess vibrational energy which was released by removing the crystal effect. Thus, excess vibrational energy in the characteristic N-NO2 moiety can flow into other N-NO2 moieties. Intramolecular vibrational energy transfer was analyzed by the change in the internal energy given by eq 3. Ab initio MO calculations were carried out on a HITAC M-680H computer at the Hiroshima University Information Processing Center, a HITAC S-820 computer at the Institute for Molecular Science, and an IBM RISC 6000/320, 580. Molecular dynamics calculations were carried out on an IBM RISC 6000/320H and an IRIS INDIGO Elan 400. 3. Results and Discussion A. δD Values and the Impact Sensitivities of Nitramines. The impact sensitivities of nitramines determined in a drop
weight apparatus have been reported to be in the order β-HMX < RDX , R-HMX < γ-HMX < δ-HMX.7,8,33,34 The sensitivity of OHMX has not been reported. However, the OHMX analogous compound, 2,4,7,9-tetranitro-2,4,7,9-tetraazadecane (TNTADEC, four-unit linear moieties) is less sensitive than β-HMX.35 DMN is fundamentally important in the study of energetic materials, although it is not an explosive, since RDX and HMX are cyclic polymers of DMN comprising three and four N-NO2 moieties, respectively. RDX and HMX are excellent secondary explosives.27 The order of the sensitivities of the family of nitramines is summarized as follows: (DMN) , (OHMX, β-HMX) < RDX , (R-HMX < γ-HMX < δ-HMX). Values of δD and δDmax for nitramines are listed in Table 3. The calculated N-N bond lengths of all isolated nitramine molecules are longer by 0.05-0.08 Å than those in the crystalline state. The structure of DMN in the gas phase has been reported with the N-N bond length36 (see Table 4). The calculated values (MP2/4-31G level) are in good agreement with the experimental data when the electronic correlation is taken into account in the calculation. The crystal effect, especially the van der Waals interaction, is known to be related in an intimate way to electron correlation. Thus, the electron correlation effect on the molecular structure can be considered as a measure of the crystal effect on the structure. Chapman et al.37 have carried out MRD-CI calculations for the Me2N-NO2 bond dissociation of DMN in a crystalline model. The calculated equilibrium Me2N-NO2 bond length in this crystalline model is 1.48 Å compared with 1.59 Å in the isolated molecule. Although calculated values are not in good agreement with the observed values, 1.332 Å in the crystal and 1.382 Å in the gas phase, these results indicate that the N-NO2 bond of DMN is compressed in the crystalline state due to electron correlation. Therefore, the molecule in which electron correla-
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TABLE 4: Optimized and Observed Structure of DMN observed value
optimized value
in the gas phasea in the crystalb MP2/4-31G MP2/4-31G* N-N N-O
1.382 1.223
C-N
1.460
C-H
1.120
O-N-N
114.8
O-N-O
130.4
N-C-H
101.9
C-N-C C-N-N
127.6 116.2
a
Distances (Å) 1.332 1.230 1.226 1.453 1.438
Angles (deg) 117.9 124.2
124.3 117.3 117.6
1.400 1.283 1.284 1.476 1.092 1.090 1.098
1.389 1.239 1.238 1.457 1.456 1.089 1.086 1.095
117.319 117.298 125.361 106.821 109.393 111.869 121.733 115.078 115.078
116.844 116.884 126.221 106.921 109.472 112.093 118.288 113.653 113.787
TABLE 5: Harmonic Force Constants of DMN in the Gas Phase bond
Kba (kcal/(mol Å2))
l0b (equil value) (Å)
N-O N-N N-C C-H
639.13 408.37 365.16 401.87
1.239 (1.233)c 1.389 (1.382) 1.457 (1.460) 1.090 (1.120)
bond angle
Kθa (kcal/ (mol rad2))
lθb (equil value) (deg)
(Kθ, lθ)d
N-N-O O-N-O N-C-H H-C-H C-N-C C-N-N
267.76 193.21 83.02 72.98 177.40 124.51
117.29 (114.8)c 125.31 (130.4) 107.45 (101.9) 109.67 124.10 (127.6) 117.34 (116.2)
(283.26, 114.8) (187.21, 130.4) (73.91, 101.9) (76.93, 115.9) (194.11, 127.6) (124.37, 116.2)
dihedral angle
Kφa (kcal/(mol rad2))
n
delta (deg)
O-N-N-C H-C-N-C H-C-N-N
21.57 1.55 2.20
2 3 3
180 0 0
a MP2/4-31G level. b MP2/4-31G* level. c Experimentally determined gas phase values are in parentheses.36 d Reference 22.
Reference 36. b Reference 26.
tion has the largest effect can probably be considered to be the one in which crystal effects on the molecular structure are largest. As is discussed in the previous paper15 concerning the HMX polymorphs, impact sensitivity is intimately related both to δD and δDmax. Furthermore, our concept of δD will be extended to HMX and its related nitramines with different numbers of components. In order to investigate the relationship between the impact sensitivity and the molecular structure of HMX and its related nitramines, we introduce a new parameter ∑δD, the sum of all of the δD’s in a molecule. Thus, ∑δD can be considered as a strain parameter for the N-NO2 bond of a molecule in the crystalline state. The order of ∑δD is summarized as DMN (0.061) , OHMX (0.213) < RDX (0.246) < β-HMX (0.272) , γ-HMX (0.291) < δ-HMX (0.293) < R-HMX (0.298). When this order is compared to the order of the experimentally determined sensitivities, good agreement is found. The ∑δD value of DMN is considerably lower (0.061) than those of other nitramines (0.213∼0.298). The experimentally obtained sensitivity of DMN shows that this molecule is not an explosive among nitramines. Furthermore, this order suggests that the linear nitramine OHMX should be less sensitive than the cyclic nitramine β-HMX and the unstable HMX polymorphic forms (R, γ, and δ). However, the order of ∑δD is not in good agreement with the experimentally determined impact sensitivity of RDX relative to that of β-HMX. Although the ∑δD of RDX is smaller than that of β-HMX, the experimentally obtained sensitivity of RDX is higher than that of β-HMX. In the previous paper,15 we introduced the concept of the δDmax value. The δDmax value of RDX is the largest (0.086) among those of other nitramines (Table 3). δDmax can also be considered to be a measure of the ease of rupture of the N-NO2 bond in the initial decomposition process, since δDmax in an N-N bond corresponds to that of the most compressed N-N bond in a molecule. Therefore, it is necessary to consider not only the total strain energy of N-N bonds in a molecule (∑δD) but also the strain energy of the most compressed N-N bond in a molecule (δDmax) as factors responsible for the sensitivity. Thus, judging from the molecular orbital studies described above, the relationship between δD and the impact sensitivity suggests that the compressed N-N bonds may play two roles in response to physical stimuli such as mechanical impact: (1)
the energy stored moiety for explosion (∑δD) and (2) the “hot spot in a molecule” where initial decomposition takes place (δDmax). In order to resolve this question, we carried out the molecular dynamics simulations with the crystal effect model. B. Force Constants of Nitramines. The fully optimized bond lengths and bond angles of DMN at the MP2/4-31G and MP2/4-31G* levels are listed in Table 4 together with experimental values.26,36 The optimized bond lengths at the MP2/431G* level are in good agreement with experimental values in the gas phase.36 However, there is a little difference in only the N-O bond length at the MP2/4-31G and the MP2/4-31G* levels. The optimized N-O bond length at the MP2/4-31G level is about 0.07 Å longer than the experimental value.36 However, by including polarization functions, the large discrepancy is reduced remarkably. Therefore, we calculated the equilibrium values (l0) for bond lengths at the MP2/4-31G* level. The force constants (Kb, Kθ) and the dihedral parameters for the DMN molecule were determined at the MP2/4-31G level and are listed in Table 5 together with reference values.22 The values of equilibrium bond lengths and angles (l0, θ0) were calculated by full geometry optimization at the MP2/4-31G* level and are also shown in the same table. It is found that the force constants of DMN are in good agreement with the reference values. This indicates that the MP2/4-31G level is adequate for the calculation of the force constants. Table 6 shows the force constants for two units (the axial and equatorial moieties) of RDX, which were calculated in the same manner as shown above (Figure 3b shows the optimized structure for the two units). The equilibrium bond length and force constant for the N-N bond (l0, Kb) in RDX, HMX, and OHMX are also listed in Table 7. These force constants and the equilibrium values were used for the molecular dynamics simulations. C. Influence of l0 of Nitramines on Molecular Dynamics. First of all, we carried out molecular dynamics simulations under two different conditions on nitramines at 300 K. Figure 6 displays the change of N-N, C-N, and N-O bond lengths in DMN as a function of time for the first 100 fs (left column) and 9.9-10 ps (right column) calculated under the first condition, which was from the crystallographic conformation as described in the procedure section. Furthermore, Figure 7 displays the results for the first 100 fs (left column) and 5.05.1 ps (right column) calculated under the second set of conditions, i.e. starting initially from the optimized molecular
N-N Bond in Nitramines in the Crystalline State
J. Phys. Chem., Vol. 100, No. 12, 1996 4707
TABLE 6: Harmonic Force Constants for RDX Two-Unit Parts (Axial and Equatorial Parts) in the Gas Phase bond
Kba (kcal/(mol Å2))
l0b (equil value) (Å)
N-O N-C C-H
731.77 318.19 401.87
1.236 1.450 1.092
bond angle
Kθa (kcal/(mol rad2))
lθb (equil value) (deg)
N-N-O O-N-O N-C-H H-C-H C-N-C C-N-N N-C-N
284.24 205.68 94.94 77.79 327.27 220.51 295.76
116.60 126.70 109.42 109.90 109.50 114.30 109.37
dihedral angle
Kφa (kcal/(mol rad2))
n
delta (deg)
C-N-C-N N-N-C-N O-N-N-C H-C-N-C H-C-N-N-O
56.53 6.79 21.62 1.55 2.20
2 2 2 3 3
0 0 180 0 0
a
MP2/4-31G level. b MP2/4-31G* level.
TABLE 7: Harmonic Force Constants of Nitramines (MP2/4-31G Level) nitramine
N-N bond
Kb (kcal/(mol Å2))
l0 (equil value) (Å)
axial(1) axial(2) equatorial axial equatorial axial equatorial axial(1) axial(2) equatorial(1) equatorial(2) axial(1) axial(2) equatorial(1) equatorial(2)
250.28 248.01 306.71 308.58 305.15 302.38 316.58 294.49 242.82 244.77 217.41 318.97 304.37 272.27 301.28
1.477 1.480 1.432 1.429 1.441 1.436 1.430 1.456 1.443 1.446 1.442 1.417 1.430 1.464 1.438
nn(1) nn(2) nn(3) nn(4)
349.62 363.57 430.19 358.14
1.415 1.407 1.410 1.409
RDX
HMX R β γ
δ
Figure 6. History of bond lengths of N-N, C-N, and O-N bonds in DMN under the first condition using molecular geometry in the crystal: (a) for the first 100 fs; (b) for ranging from 9.90 to 10.00 ps of data collection.
OHMX
structure (see Figure 4). As can be seen from Figures 6 and 7, for the first 100 fs, the history of only the N-N bond in DMN is remarkably different between the two conditions. In order to confirm the difference in behavior of the N-N bond under these different conditions, the influence of the selection of the initial velocities on molecular dynamics calculations of DMN under the first set of conditions was checked and the results are shown in Figure 8. In this figure, three different trajectories were run using different sets of initial velocities which were assigned to each atom of the molecule (see Figure 8). Large amplitude oscillations are reproducible and always observed at the same time during the first 100 fs. Therefore, the trajectory was run only once per each condition. These results suggest that the compressed N-NO2 bond of DMN in the crystalline state plays an important role in the initial decomposition process of DMN. It should be pointed out that the bond potential in the program package CHARMM is harmonic in nature, as given by eq 3. Consequently, it cannot lead to bond cleavage. However, it suggests that a larger amplitude oscillation may relate to the N-N bond cleavage in the initial decomposition process when the intramolecular energy transfer occurs, as discussed in a later section.
Figure 7. History of bond lengths of N-N, C-N, and O-N bonds in DMN under the second condition using minimized molecular structure: (a) for the first 100 fs after equilibration; (b) from 5.00 to 5.10 ps of data collection.
Figures 9 and 10 display individual histories of the N-N, C-N, and N-O bond lengths of β-HMX and OHMX for the first 100 fs under the first and the second sets of conditions. As can be seen from these figures, it is only the history of the N-N
4708 J. Phys. Chem., Vol. 100, No. 12, 1996
Kohno et al.
Figure 8. History of N-N bond lengths in DMN under the first condition using molecular geometry in the crystal with three different sets of initial velocities.
Figure 10. History of bond lengths of N-N (N-N(1) and N-N(3)), C-N, and O-N bonds of OHMX: (a) under the first condition for the first 100 fs; (b) under the second condition for the first 100 fs.
Figure 9. History of bond lengths of N-N (axial(1) and equatorial(1) positions), C-N, and O-N bonds of β-HMX: (a) under the first condition for the first 100 fs; (b) under the second condition for the first 100 fs.
bond in the cyclic nitramine β-HMX and the linear nitramine OHMX that differs remarkably under the first set of conditions as compared to the second. Other cyclic nitramines, such as the HMX polymorphs (similarly to R-, γ-, and δ-HMX) and RDX, showed similar results. Therefore, the unique phenomenon appears generally only in the N-N bond of the HMX related nitramines. We attempted to analyze these wave components by the autocorrelation function of an individual bond length. Figure 11 displays individual correlation functions of the N-N, C-N and N-O bond lengths in DMN under the first condition for the first 1 ps and under the second condition for the first 1 ps after equilibrium is reached. As can be seen from the two figures under different conditions, the correlation function of only the N-N bond in DMN under the first condition is remarkably different from that under the second condition. From
the correlation function of the N-N bond under the first condition, we can expect that the characteristic wave pattern consists of components with various periods. Therefore, the power spectra of these correlation functions for DMN were calculated. They are displayed in Figure 12. The peak in the power spectrum of the C-N stretching vibration appears at 750 ps-1 under both conditions, and the peaks for the N-O stretching vibration appear at 750 and 950 ps-1 under both conditions. On the other hand, the strong peak in the power spectrum of the N-N stretching vibration under the second condition is 600 ps-1 (period of the wave (T) is 10.5 fs), while under the first condition the strong peak in the power spectrum is separated into three peaks. The main peak at 600 ps-1 decreases considerably, and two new peaks appear at 500 ps-1 (T is 12.5 fs) and 750 ps-1 (T is 7.9 fs). Thus, we can confirm from these results that the characteristic wave pattern of the N-N bond under the first condition consists of components with various periods. At the next stage, we would like to focus our attention on the unique behavior of the N-N bond in nitramines. As is already pointed out, the value of l0 (equilibrium bond length in eq 3) for the N-N bond increases considerably in comparison with its equilibrium value in the crystalline state (see Table 4). However, the lengths of the other bonds are not much different in the crystal environment from what they are in the gas phase. Therefore, the shift of l0, that is, “the crystal effect”, should be responsible for this unique behavior. In order to confirm “crystal effect”, a molecular dynamics simulation was performed in the third condition. Adjusted l0 parameters (ladj) to obtain the best fitted N-N bond lengths in the crystalline state of
N-N Bond in Nitramines in the Crystalline State
J. Phys. Chem., Vol. 100, No. 12, 1996 4709 TABLE 8: l0 (Equilibrium N-N Bond Length) and ladj (Adjusted l0) Parameters of Nitramines N-N bond length (Å) nitramine
obs
a
opt (l0)c
ladj
HMX R axial equatorial
1.354 1.367
1.4293 1.4413
1.300 1.315
axial equatorial
1.368 1.362
1.4364 1.4304
1.334 1.330
axial(1) axial(2) equatorial(1) equatorial(2)
1.395 1.361 1.364 1.376
1.4564 1.4428 1.4455 1.4424
1.347 1.294 1.300 1.306
axial(1) axial(2) equatorial(1) equatorial(2)
1.346 1.355 1.392 1.363 1.332 (1.382)b
1.4174 1.4302 1.4637 1.4375 1.3886d
1.293 1.300 1.340 1.307 1.245
axial(1) axial(2) equatorial
1.392 1.398 1.351
1.4779 1.4804 1.4322
1.354 1.360 1.315
nn(1) nn(2) nn(3) nn(4)
1.358 1.351 1.364 1.351
1.4145 1.4068 1.4100 1.4089
1.310 1.319 1.338 1.309
β γ
δ
DMN RDX
OHMX
Figure 11. Correlation functions of N-N, C-N, and O-N bond lengths in DMN: (a) under the first condition for the first 1 ps; (b) under the second condition for the first 1 ps after equilibration.
Figure 12. Power spectra of correlation functions of N-N, C-N, and O-N bond lengths for DMN: (a) under the first condition; (b) under the second condition after equilibration.
nitramines by using the minimization procedure in CHARMM are listed in Table 8. Figure 13 displays the time histories of bond lengths for DMN using ladj for a period ranging from 9.90 to 10.00 ps (After this time, an equilibrium state is assumed to be reached at 300 K.), and then the molecular dynamics simulation is restarted using the l0 parameter instead of ladj for
a The observed values are the bond length in the crystal. b The observed values are the bond length in the gas. c MP2/4-31G level. d MP2/4-31G* level.
Figure 13. History of bond lengths of N-N, C-N, and O-N bonds in DMN: (a) with the crystallographic geometry and using ladj from 9.90 to 10.00 ps; (b) with the crystallographic geometry and using l0 instead of ladj for a subsequent period of 100 fs.
the first 100 fs. From these simulations, a larger amplitude oscillation was observed only in the N-N bond only when l0 was used. Figure 14 displays individual power spectra of the correlation functions of N-N, C-N, and N-O bond lengths for DMN
4710 J. Phys. Chem., Vol. 100, No. 12, 1996
Kohno et al.
Figure 14. Power spectra of correlation functions of N-N, C-N, and O-N bond lengths in DMN: (a) with crystallographic geometry using ladj; (b) with crystallographic geometry using l0 instead of ladj.
using ladj in dynamics simulations and using l0 after restarting. As can be seen from the two figures for the different conditions, power spectra for the N-N bond of DMN are remarkably different. The strong peak in the power spectrum of the N-N bond with ladj is 650 ps-1. With l0 instead of ladj, the main peak at 650 ps-1 decreases considerably and the small peak at 750 ps-1 increases remarkably. Figure 15 displays the time history of the N-N bond length of the linear nitramine OHMX using ladj in the time range from 9.90 to 10.00 ps and for the first 100 fs after restarting the molecular dynamics simulation with l0 instead of ladj. We observe a larger amplitude oscillation only in the N-N bond with l0, not with ladj. For RDX and other HMX polymorphs, similar results were obtained. D. Intramolecular Vibrational Energy Transfer by the Improved Crystal Effect Model. In order to investigate the effect of the molecular structure on the intramolecular vibrational energy transfer, we carried out similar molecular dynamics simulations for a linear nitramine, OHMX, in comparison with a cyclic nitramine, β-HMX. The parameter for the N-NO2 bond only in a specific N-NO2 moiety was changed to l0 from the ladj that was used for equilibrated N-N bonds in the crystalline state. Figure 16a displays the change in the N-N bond length in OHMX obtained by using l0 instead of ladj for only the terminal N-N(1) bond for first 100 fs (l0(1)) after the equilibrium is reached with ladj. Hereafter, l0(i) is referred to as the parameter l0 in the ith moiety. That is, the value of ladj is used in eq 3 except for the ith moiety in which l0(i) is substituted in eq 3. Similar notation is used for the N-NO2 bond. Thus, N-N(i) means the N-NO2 bond in the ith moiety. With regard to the N-N bond lengths of OHMX, a large amplitude oscillation is observed in the N-N(1) bond at 30 fs and in the nearest neighbor N-N(2) bond at 50 fs. The other remote N-N bonds (N-N(3) and N-N(4)) have no large amplitude oscillations. Therefore, the large amplitude oscillation of the terminal N-N bond influences only the nearest neighbor N-NO2 bond in the
Figure 15. History of bond lengths of an N-N bond in OHMX: (a) with crystallographic geometry using ladj; (b) with crystallographic geometry using l0 instead of ladj.
linear nitramine OHMX. This tendency can be confirmed by the potential energy shift in the N-N bond under the same conditions as shown in Figure 16b. This figure indicates that the N-N bond potential energy of the terminal N-N(1) bond is shifted from the terminal N-N(1) bond to the nearest neighbor N-N(2) bond in approximately 20 fs. Thus, it is likely that intramolecular vibrational energy transfer occurs from the N-N(1) bond to the N-N(2) bond in OHMX. Figure 17a and b displays the change in the N-N bond length and the N-N bond potential of OHMX obtained by using l0 instead of ladj at the terminal N-N(1) bond and the middle N-N(3) bond for first 100 fs (l0(1) and l0(3)), after the simulation is performed for 10 ps by using ladj. From the changes in the N-N bond length and the N-N bond potential, the intramolecular vibrational energy transfer seems to occur from the N-N(1) bond to the N-N(2) bond with a time lag of 20 fs and from the N-N(3) bond to the N-N(2) bond with a time lag of 25 fs. Large amplitude oscillations and large changes in the N-N bond potential were not observed for the N-N(4) bond during the first 100 fs. Therefore, the intramolecular vibrational energy transfer takes place from both the N-N(1) and N-N(3) bonds to the N-N(2) bond in this case. Figure 18 displays the changes in the N-N bond length and the N-N bond potential for β-HMX, which has a boat conformation. The simulation was performed using l0 instead of ladj at two equivalent equatorial positions for the 100 fs following simulation for 10 ps with ladj. From the changes in the N-N bond length and in the N-N bond potential, the intramolecular vibrational energy is found to be transferred from equatorial positions with l0 to axial positions with ladj with a
N-N Bond in Nitramines in the Crystalline State
J. Phys. Chem., Vol. 100, No. 12, 1996 4711
Figure 16. History during the first 100 fs of N-N bond lengths (a) and of N-N bond potentials (b) for OHMX using l0 instead of ladj at only the terminal N-N(1) bond. The black arrow points to the strong change in the potential at the N-N(1) bond. The white arrow points to the strong change in the potential due to intramolecular vibrational transfer from the N-N(1) bond to the N-N(2) bond.
Figure 17. History during the first 100 fs of N-N bond lengths (a) and of N-N bond potentials (b) for OHMX using l0 instead of ladj at the terminal N-N(1) and the middle N-N(3) bonds. The black arrows point to the strong change in the potential at the N-N(1) and the N-N(3) bonds. The white arrow points to the strong change in the potential due to intramolecular vibrational transfer from the N-N(1) and N-N(3) bonds to the N-N(2) bond.
time lag of 50-70 fs. These results can be linked with the results mentioned in the previous paragraph. Thus, in the case of the linear nitramine OHMX, although a molecular dynamics simulation was performed under the same conditions with l0(1) and l0(3) as those for β-HMX, the vibrational energy in the middle N-N(3) bond did not transfer into the terminal N-N(4) bond. However, in β-HMX, there are no terminal N-NO2 moieties because of its ring structure. Accordingly, the intramolecular vibrational energy transfer occurs between segments with the relaxed N-N bonds and those with the compressed N-N bonds, but with a greater time lag. These results suggest strongly that the compressed N-N bonds in the crystalline state, particularly in cyclic nitramines, play two roles in the initial decomposition process: they are “hot spots in a molecule”, and they store energy for the explosion. The above-mentioned simulations show that the rate of the intramolecular vibrational energy transfer in OHMX is faster than that in β-HMX. This result is probably connected with the relative orientation of the neighboring N-NO2 bond in the molecules. A more detailed analysis for this result is in progress and will be published in the near future.
the relationship between δD and the impact sensitivity suggests that the compressed N-N bonds can play two roles in physical stimuli: one being the energy storage for the explosion and the other being to serve as “hot spots in a molecule”. In order to investigate the role of the unique N-N bond in crystalline nitramines, a molecular dynamics simulation was done at 300 K. A large amplitude oscillation is observed only in the N-N bond length when the molecular geometry of the crystal is assumed. Moreover, from our study of an improved crystal effect model, it has become apparent that intramolecular vibrational energy is transferred among N-NO2 moieties. The characteristics of intramolecular vibrational energy transfer of nitramines were found to be as follows: (1) The rate of energy transfer in the linear nitramine OHMX is approximately 20 fs. (2) The vibrational energy in the middle N-N(3) bond of the linear nitramine OHMX is not transferred to the equilibrated terminal N-N(4) bond. In other words, the terminal moiety of the linear nitramine has only a small probability of receiving excess energy from the other N-NO2 bond. (3) In the cyclic nitramines, intramolecular vibrational energy transfer from activated N-NO2 bonds to other N-NO2 bonds is observed. (4) The rate of energy transfer in cyclic nitramines is approximately 50-70 fs. Therefore, the rate of energy transfer in the linear nitramine is faster than that for cyclic nitramines. At present, nitramines which are of use because of their performance and lower sensitivity are mostly cyclic compounds
4. Conclusions We carried out a molecular orbital study and molecular dynamics simulations of the initial decomposition of the HMX polymorphs and HMX related nitramines such as is likely to occur on application of a physical stimulus such as impact. From the viewpoint of molecular orbital studies in the crystalline state,
4712 J. Phys. Chem., Vol. 100, No. 12, 1996
Kohno et al. References and Notes
Figure 18. History during the first 100 fs of N-N bond lengths (a) and of N-N bond potentials (b) for β-HMX using l0 instead of ladj at the two equatorial positions. The black arrows point to the strong change in the potential at the two equatorial positions. The white arrows point to the strong change in the potential by intramolecular vibrational transfer from the equatorial position to the axial position.
such as β-HMX, RDX, and the new polycyclic nitramine 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW).38 Zeman has shown that the relationship between the impact sensitivities and 15N chemical shifts of amino nitrogen atoms in the reaction centers of nitramine molecules is different for the cyclic nitramines from what it is for the linear nitramines.35 Therefore, our findings are of interest in connection with the dynamics of the intramolecular vibrational energy transfer, especially with regard to the difference between linear and cyclic nitramines. Acknowledgment. We thank Dr. J. Kimura of First Research Center, Technical Research and Development Institute, Japan Defense Agency; Dr. S. Tsuboyama and Dr. T. Sakurai of Institute of Physical and Chemical Research (RIKEN); Dr. Y. Oyumi of Third Research Center, Technical Research and Development Institute, Japan Defense Agency; Dr. K. Maekawa and Dr. S. Nakagawa of Institute for Fundamental Chemistry; Manager of R&D T. Tsuchioka and Director & General Manager of R&D T. Hashizume of Chugoku Kayaku Co., Ltd.; Professor N. Azuma of Ehime University; and Professor K. Saito of Hiroshima University for helpful discussions. We also thank the reviewers for some comments and kind correction of the syntax of the manuscript toward traditional Western usage. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan.
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