Theoretical studies of a series of azaoxaisowurtzitane cage compounds with high explosive performance and low sensitivity

Computational and Theoretical Chemistry 1114 (2017) 77–86

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Theoretical studies of a series of azaoxaisowurtzitane cage compounds with high explosive performance and low sensitivity Yong Pan a,b, Weihua Zhu a,⇑, Heming Xiao a a b

Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, China School of Chemical Engineering and Materials Science, Nanjing Polytechnic Institute, Nanjing, 210048, China

a r t i c l e

i n f o

Article history: Received 22 April 2017 Received in revised form 17 May 2017 Accepted 17 May 2017 Available online 20 May 2017 Keywords: Azaoxaisowurtzitane derivatives Density functional theory Detonation properties Thermal stability Impact sensitivity

a b s t r a c t Ten novel azaoxaisowurtzitane cage compounds were designed by introducing the oxygen atoms into the azaisowurtzitane cage to replace the N-NO2 groups. Then, their heats of formation (HOFs), energetic properties, strain energies, thermal stability, and impact sensitivity were studied by using density functional theory. The introduction of the oxygen atom in the cage is not helpful for increasing the HOFs, densities, and energetic properties of parent compound CL-20. But all the title compounds exhibit remarkable detonation properties superior to or very close to HMX. All the azaoxaisowurtzitane cage compounds exhibit higher thermal stability than parent compound CL-20. The introduction of the oxygen atom in the cage effectively decreases the sensitivity of parent compound CL-20. Considered the detonation performance, thermal stability, and impact sensitivity, six compounds can be regarded as the potential candidates of HEDC because these azaoxaisowurtzitane cage compounds not only exhibit excellent energetic properties comparable with CL-20, but also have higher thermal stability and lower sensitivity than CL-20. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction In recent years, cage energetic compounds have been attracting considerable attention due to their potential applications in high energy density compounds (HEDCs). As an important category of HEDCs, the cage compounds with compact structure usually combine high crystal density with large strain energies, which makes them have superior detonation performance over conventional energetic compounds [1–8]. Among them, 2,4,6,8,10,12-hexani tro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20, see Fig. 1), containing an isowurtzitane cage with six nitramine moieties in the molecule, is considered as one of the most powerful HEDC, being a hotspot for several years [9–15]. However, its high sensitivity (reported as h50 = 12–21 cm/2.5 kg [16]) restricted to some extent the explosive application. This is because CL-20 as a nitramine compound with the nitro groups being bonded to cage nitrogen atoms are less tolerant to shock. Therefore, to obtain potential HEDCs with improved energetic properties and reduced sensitivity, much research has concentrated on the design and synthesis of novel energetic compounds based on the isowurtzitane cage skeleton. In the process, many studies [8,17–20] pay more attention to replacing the NO2 groups in the molecule by introducing different

⇑ Corresponding author. E-mail address: [email protected] (W. Zhu). http://dx.doi.org/10.1016/j.comptc.2017.05.021 2210-271X/Ó 2017 Elsevier B.V. All rights reserved.

substituents such as nitrotriazole, nitrotetrazole, dinitromethyl groups etc. But an alternative strategy by introducing the oxygen atoms into the isowurtzitane cage is more and less ignored. 4,10-Dinitro-2,6,8,12-tetraoxa-4,10-diazatetracyclo[5.5.0.05,903,11]dodecane (TEX, see Fig. 1), constructed by introducing four oxygen atoms into the isowurtzitane cage to replace four nitramine moieties, is an insensitive highly energetic compound first reported by Ramakrishnan and co-workers in 1990 [2]. Although TEX has moderate detonation properties (detonation velocity: 8.17 km/s and detonation pressure: 31.4 GP), good thermal stability (mp > 250 °C), it has low sensitivity toward shock, friction, and impact stimuli, which is attributed to the azaoxaisowurtzitane cage in the TEX molecule [1,21–23]. Therefore, it is believed that properly introducing the oxygen atom into the isowurtzitane cage may obtain novel energetic compounds with both high explosive performance (comparable with CL-20) and reduced sensitivity. However, the design or synthesis of new energetic compounds based on the azaoxaisowurtzitane cage skeleton by replacing the N-NO2 group with the oxygen atom have not been reported till now apart from TEX. In addition, there is lack of comprehensive understanding on the structure-property relationships for energetic azaoxaisowurtzitane compounds. In this work, ten azaoxaisowurtzitane cage compounds (see Fig. 2) were designed on the basis of the CL-20 structure by introducing one or more oxygen atoms into the azaisowurtzitane cage

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7 O2N O2N

N

N

N

N

NO2 NO2 N

N

O

8

O

O

12 N

N

NO2 O2N

O2N

O

NO2

CL-20

TEX

6

1

2

5

9

11 3 4 10 azaoxaisowurtzitane cage skeleton

Fig. 1. Molecular structure of CL-20, TEX, and azaoxaisowurtzitane cage skeleton with atomic position numbering (hydrogen atoms are omitted).

O2N O2N

NO2

N

N

N

N

O2 N

NO2 O

O2 N

N

N

N

N

NO2

O2N

NO2

N

N CL-20

O2 N O

N

N

N

O

O

N

O

O N

B3

N

O

N

O

N

O2 N

NO2

N

O

O

O N

N O2 N

O

N

NO2

O

N

NO2 O

N O2N

NO2

C2

C1

O

NO2

B4

NO2 O

O

NO2

N

N

NO2

N

NO2

O

NO2 O2N

N

NO2

N

B2

NO2 N

N

NO2

N

O2 N

B1

O2 N

N

N

O

N

NO2

A2

NO2

O

O2N

N

O2 N

NO2

N

O2N

O

NO2 O2N

A1

O2N

N

N

N

O

NO2

O2N

NO2

N

O

N

O

N

NO2 N

O

C3

NO2

C4

NO2

Fig. 2. Molecular frameworks of designed azaoxaisowurtzitane cage compounds.

to replace the N-NO2 group. Then their molecular structure, heats of formation (HOFs), density, energetic properties, strain energy, thermal stability, and impact sensitivity were systematically investigated by density functional theory (DFT) method. Our study will be helpful to understand the structure-property relationship of energetic azaoxaisowurtzitane-based HEDCs and provide useful information for experiments. The remainder of this paper is organized as follows. A 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 hybrid DFT-B3LYP method with the 6-311G(d, p) basis set were adopted to optimize the molecular structures and to predict their HOFs. Previous studies have shown that the basis set 6-311G(d, p) is able to precisely figure out molecular structure and energies of energetic organic compounds [24–27]. The gas-phase HOFs were estimated using isodesmic reaction method, which has been demonstrated to evaluate reliably the gas-phase HOFs of many organic systems [17,24–28]. To obtain better calculation accuracy, the basic cage skeleton of the title

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compounds is kept invariable in the designed isodesmic reactions, and CL-20 was elected as a reference compound. The isodesmic reactions adopted to obtain the gas-phase HOFs of the title compounds at 298 K are as follows:

where A is the surface area of the 0.001 electrons/bohr3 isosurface of electronic density of the molecule, m describes the degree of balance between positive and negative potential on the isosurface, and r2tot is a measure of variability of the electrostatic potential on the

For the isodesmic reaction, the heat of reaction DH298K at 298 K can be calculated from the following equation:

molecular surface. The descriptors A, m, and r2tot were calculated using the computational procedures proposed by Bulat et al. [34]. The coefficients a, b, and c were determined by Rice et al.: a = 2.670  104 kcal/mol/Å4, b = 1.650 kcal/mol, and c = 2.966 kcal/mol [35]. This approach has been proved to predict reliably the DHsub of many energetic compounds [35–37]. The detonation velocity and detonation pressure of the were estimated by the Kamlet-Jacobs equations [38] as

DH298K ¼

X

DHf ;P 

X

DHf ;R

ð4Þ

where DHf,R and DHf,P are the HOFs of reactants and products at 298 K, respectively. As the experimental HOFs of NH2NO2 and (CH3)2NNO2 are unavailable, additional calculations were carried out for the atomization reaction: CaHbNc ? aC(g) + bH(g) + cN(g) to obtain their HOFs at the G3 level. The G3 theory [29,30] has been verified to be able to predict the HOFs of small molecules accurately. Therefore, the DH298K can be evaluated using the following expression:

DH298K ¼ DE298K þ DðPVÞ ¼ DE0 þ DZPE þ DHT þ DnRT

ð5Þ

where DE0 is the change in total energy between the products and the reactants at 0 K; DZPE is the difference between the zero-point energies (ZPE) of the products and the reactants at 0 K; DHT is thermal correction from 0 to 298 K. The D(PV) value equals DnRT for the reactions of ideal gas. For the isodesmic reactions in this work, Dn = 0, so D(PV) = 0. Since the condensed phase for most energetic compounds is solid, the calculation of detonation properties requires solidphase HOF (DHf,solid). According to Hess’s law of constant heat summation [31], the gas-phase HOF (DHf,gas) and heat of sublimation (DHsub) can be used to evaluate their solid-phase HOF:

DHf ;solid ¼ DHf ;gas  DHsub

ð6Þ

Politzer et al. [32,33] found that the heats of sublimation can correlate well with the molecular surface area and electrostatic interaction index mr2tot of energetic compounds. The empirical expression of the approach is as follows:

DHsub ¼ aA2 þ bðmr2tot Þ

0:5

þc

ð7Þ

D ¼ 1:01ðNM1=2 Q 1=2 Þ

1=2

ð1 þ 1:30qÞ

P ¼ 1:558q2 NM1=2 Q 1=2

ð8Þ ð9Þ

where q is the density of explosives (g/cm3), D is the detonation velocity (km/s), P is the detonation pressure (GPa), N is the moles of detonation gases per gram explosive, M is the average molecular weight of these gases, and Q is the heat of detonation (cal/g). As the Q and q of some compounds cannot be evaluated from experimental measures, their Q and q need be firstly calculated. For the title compounds, the theoretical density was determined based on an improved approach developed by Politzer et al. [39], which added corrections for electrostatic interactions in order to better represent the intermolecular interactions. So the crystal density can be corrected by introducing the interaction index mr2tot :

q ¼ b1



 M þ b2 ðmr2tot Þ þ b3 Vð0:001Þ

ð10Þ

where M is the molecular mass (g/mol) and V(0.001) is the volume of the 0.001 electrons/bohr3 contour of electronic density of the molecule (cm3/molecule). The coefficients b1, b2, and b3 are 1.0462, 0.0021, and 0.1586, respectively [40].

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The heat of detonation Q was evaluated by the HOF difference between products and explosives according to the principle of exothermic reactions. For the title compounds, all the N atoms turn into N2 and oxygen atoms go to H2O before CO2. The detonation products are supposed to be CO2 (or C), H2O, and N2, so released energy in the decomposition reaction reaches its maximum. On the basis of the q and Q values, the corresponding D and P values can be evaluated. Strain energy (SE) can be regarded as an index to correlating the structure with the stability and reactivity of a molecule. The approach of homodesmotic reaction has been employed successfully to calculate strain energy from total energies (E0) with zeropoint energies (ZPE) based on ab initio calculations [41–45]. In this work, in order to investigate the strain energy of the azaoxaisowurtzitane cage to understand the stability of the title compounds, the corresponding homodesmotic reactions are designed as follows:

The change of energies with correction of the zero-point vibrational energy in the homodesmotic reactions can be obtained from Eq. (11):

DH298K ¼

X

Eproduct 

X

Ereactant þ DZPE

ð11Þ

The strength of bonding, which could be evaluated by bond dissociation energy, is fundamental to understand chemical processes [46]. The energy required for bond homolysis at 298 K and 1 atm corresponds to the enthalpy of reaction A-B(g) ? A(g) + B(g), which is the bond dissociation enthalpy of the molecule A-B by definition [47]. For many organic molecules, the terms ‘‘bond dissociation energy” (BDE) and ‘‘bond dissociation enthalpy” often appear interchangeably in the literature [48]. Therefore, at 0 K, the homolytic bond dissociation energy can be given in terms of Eq. (12):

BDE0 ðA  BÞ ! E0 ðAÞ þ E0 ðBÞ  E0 ðA  BÞ

ð12Þ

The bond dissociation energy with ZPE correction can be calculated by Eq. (14)

BDEðA  BÞZPE ¼ BDE0 ðA  BÞ þ DEZPE

ð13Þ

where DEZPE is the difference between the ZPEs of the products and the reactants. Impact sensitivity is generally characterized through a drop weight test and reported as the height in cm, designated as h50. h50 is the height from which the sample is impacted by a 2.5 kg dropping mass and there is a 50% probability of causing an explosion [49,50]. The higher h50 is, the more insensitive the explosive is. For the title compound, impact sensitivity (h50) was predicted by a simple method suggested by Pospíšil et al. [51,52]

h50 ¼ ar2þ þ bm þ c

ð14Þ

where r2þ indicates the strength and variability of the positive surface potentials, m is the balance of charges between positive potential and negative potential on the molecular surface, and the coefficients a, b, and c are 0.0064, 241.42, and 3.43, respectively.

In addition, the free space per molecule in the unit cell, designated DV, is also calculated to estimate the general tendency of impact sensitivity for these cage compounds [51]. Generally, the sensitive of energetic compounds increases as the value of DV becomes large [53]. DV can be represented as the difference between the effective volume per molecule that would be required to completely fill the unit cell, Veff, and the intrinsic gas phase molecular volume, Vint:

DV ¼ V eff  V int ¼ ðM=qÞ  V int

ð15Þ

where Vint is defined as the volume enclosed by the 0.003 electrons/ bohr3 contour of the molecule’s electronic density. M is the molecular mass and q is the crystal density. The calculations were performed with the Gaussian 09 package [54]. The optimizations were performed without any symmetry restrictions using the default convergence criteria in the program. All of the optimized structures were characterized to be true local energy minima on the potential energy surfaces without imaginary frequencies.

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3. Results and discussion

800 Gas-phase HOF Solid-phase HOF

3.1. Gas- and solid-phase heats of formation

600

400

HOF(kJ/mol)

The solid-phase HOF, DHf,solid, is an important property to predict the detonation properties of the energetic materials. Here we investigate the effects of different azaoxaisowurtzitane cages on the gas-phase HOF (DHf,gas) and solid-phase HOFs (DHf,solid) of the title compounds. Table 1 lists the total energies, ZPEs, thermal corrections, and HOFs for 8 reference compounds in the isodesmic reactions. The experimental gas-phase HOFs of CH4, NH3, CH3CH3, CH3NH2, and CH3OCH3 were taken from Ref. [55]. The gas-phase HOF values of NH2NO2 and (CH3)2NNO2 were obtained from the atomization reaction using the G3 theory. Table 2 presents the total energies, ZPEs, thermal corrections, DHf,gas, and DHf,solid of the title compounds. It is found that our calculated DHf,gas and DHf,solid of CL-20 are in agreement with available calculated values [17,19], which indicates that the predicted method chosen here are credible. As seen in Table 2, when the N-NO2 group of the isowurtzitane cage is replaced by the oxygen atom, the DHf,gas and DHf,solid of the cage compounds decrease markedly. For examples, A1 and A2 exhibit high positive DHf,gas and DHf,solid, whereas the HOFs of C2, C3, and C4 are negative. To illustrate the effects of the oxygen atom in the cage on the HOFs, the variation of the calculated HOFs with the number (n) of the oxygen atom in the azaoxaisowurtzitane cage are presented in Fig. 3, in which the average HOFs of isomers with the same n are used. Obviously, each curve has a linear relationship with good correlation coefficients (R) in Fig. 3. According to the established equations, the gas- or solid-phase HOFs of the azaoxaisowurtzitane

Y =717.066-248.103 X R=0.9991,SD=13.875

200

Y =568.608-235.488 X R=0.9990,SD=13.725

0

-200

-400 0

1

2

3

4

oxygen atom numbers (n) in the cage skeleton Fig. 3. The linear relationship between the number (n) of the oxygen atom and HOFs of the title compounds (the average HOFs of isomers with the same n are used).

cage compounds decrease by 248.103 kJ/mol or 235.488 kJ/mol on average, respectively, when one oxygen atom is introduced into the azaisowurtzitane cage to replace the N-NO2 group. In addition, the space orientations of oxygen atom also affect the HOFs of the title compounds. Generally, the more oxygen atom orients to the 4 or 10 position of the azaisowurtzitane cage, the higher the HOF of the isomer is. For example, A1 has a somewhat higher HOF than A2, and B1 has higher HOF than B2, B3 or B4. 3.2. Energetic properties

Table 1 Calculated total energies (E0), zero-point energies (ZPE), thermal corrections (HT), and HOFs for the reference compounds.a Compd.

E0

ZPE

HT

HOF

NH3 CH4 CH3NH2 CH3CH3 CH3NHCH3 NH2NO2 (CH3)2NNO2

56.5760 40.5337 95.8884 79.8563 135.2054 261.1138 339.7534

0.0343 0.0446 0.0638 0.0744 0.0920 0.0394 0.0948

10.00 10.03 11.56 11.76 14.21 12.28 20.41

45.94b 74.60b 22.50b 84.00b 18.50b 8.16c (8.00d) 5.25c

a E0 and ZPE are in a.u.; HT and HOF are in kJ/mol. The scaling factor is 0.98 for ZPE [25]. b The experimental HOFs were taken from Ref. [55]. c The value were calculated at the G3 level from the atomization reaction. d The calculated value was taken from Ref. [17].

Detonation velocity and detonation pressure are two key performance parameters of energetic materials. The semi-empirical Kamlet-Jacobs formula has been proved to be reliable for predicting the explosive properties of energetic high-nitrogen compounds [56,57]. Table 3 presents the calculated q, Q, D, P, and oxygen balance (OB) of the title compounds. For a comparison, the q, D, and P of CL-20, TEX, HMX, and RDX are also tabulated in Table 3. The calculated q, D, and P values of CL-20 (2.004 g/cm3, 9.52 km/s, and 42.4 GPa) and TEX (1.95 g/cm3, 8.31 km/s, and 32.1 GPa) are in good agreement with experimental values and other calculated results [4,17,23,33]. This indicates that our calculated results are reliable. It is seen in Fig. 4 that the variation trends of D and P are basically the same for the title compounds, which are commonly determined by q except for small effects from Q.

Table 2 Calculated total energies (E0), zero-point energies (ZPE), thermal corrections (HT), heats of sublimation (DHsub), and HOFs for the title compounds.a

a b c

Compd.

E0

ZPE

HT

DHf,gas

A

m

r2tot

DHsub

DHf,solid

CL-20 A1 A2 B1 B2 B3 B4 C1 C2 C3 C4 TEX

1791.6614 1607.0036 1607.0073 1422.3444 1422.3529 1422.3509 1422.3504 1237.6883 1237.6965 1237.6908 1237.6911 1053.0388

0.2194 0.2056 0.2057 0.1916 0.1917 0.1917 0.1917 0.1774 0.1775 0.1775 0.1773 0.1634

65.19 57.51 57.55 49.80 49.85 49.83 49.93 42.30 42.38 42.34 42.33 34.91

716.97 (715.93b, 691.30c) 471.02 461.80 228.24 206.45 211.72 212.93 1.56 19.73 4.51 5.87 286.77

313.42 288.13 286.87 263.52 261.78 262.06 263.09 238.42 238.52 237.95 233.90 210.87

0.07 0.09 0.10 0.11 0.13 0.13 0.13 0.15 0.14 0.15 0.18 0.18

224.84 211.85 195.70 202.40 178.38 179.95 183.89 175.62 161.05 170.50 176.01 155.93

149.38 135.10 134.40 123.06 122.30 122.49 123.73 111.54 109.04 110.94 111.98 98.24

567.59 (568.00b) 335.92 327.40 105.19 84.15 89.23 89.20 109.98 128.78 115.45 117.85 385.01

E0 and ZPE are in a.u.; HT, DHsub and HOFs are in kJ/mol; The calculated values were taken from Ref. [19]. The calculated value was taken from Ref. [17].

r2tot is in kcal/mol and A is in Å2. The scaling factor is 0.98 for ZPE [25].

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Table 3 Predicted densities (q), heats of detonation (Q), detonation velocities (D), detonation pressures (P), and oxygen balance (OB) for the title compounds.a Compd. CL-20 A1 A2 B1 B2 B3 B4 C1 C2 C3 C4 TEX HMX RDX a b c d e

Q(cal/g) 1671 1603 1598 1518 1504 1507 1507 1402 1387 1398 1396 1233 1498e 1501e

OB 10.95 16.24 16.24 22.84 22.84 22.84 22.84 31.36 31.36 31.36 31.36 42.72

q(g/cm3)

D(km/s) b

c

2.00(4) (2.04 , 1.97 ) 1.99(4) 2.00 1.98 1.99 1.99 1.99 1.96(4) 1.96 1.96(2) 1.98 1.95 (1.99b) 1.91b 1.82b

P(GPa) b

c

e

9.65(9.40 , 9.73 , 9.62 ) 9.44 9.45 9.16 9.17 9.17 9.17 8.81 8.76 8.80 8.85 8.31 (8.17d) 9.10b 8.75b

43.9(42.0b, 44.64c, 44.1e) 41.9 42.1 39.4 39.5 39.5 39.5 36.2 35.8 36.1 36.7 32.1 (31.4d) 39.0b 34.0b

Oxygen balance (%) for CaHbOcNd: 1600  (c  2a  b/2)/Mw; Mw: molecular weight of the titled compounds. The experimental values were taken from Ref. [4]. The Calculated values were taken from Refs. [17,23,33]. The Calculated values were taken from Refs. [17,23,33]. The Calculated values were taken from Refs. [17,23,33].

Fig. 4. Density, detonation pressure, and detonation velocity of the title compounds.

As shown in Table 3, all the title compounds have lower Q, OB,

q, D, and P values than the parent compound (CL-20). As the N-NO2 group of the azaisowurtzitane cage is replaced by the oxygen atom, its Q, OB, q, D and P values gradually decrease. Fig. 5 depicts the q, D, and P values of the title compounds as a function of the number (n) of the oxygen atom in the cage. For the isomers with the same n, the average value was chosen for analysis. Obviously, the introduction of one oxygen atom in the cage decreases its q, D, or P value by 0.0151 g/cm3, 0.3316 km/s or 2.962 GPa on average, respectively. Thus, it can be concluded that the introduction of the oxygen atom in the cage is not favorable for increasing detonation properties for the parent compound. In addition, previous studies demonstrated that the energetic compound with a low Q often have a relatively low sensitivity [58]. It can be thus inferred the title compounds may exhibit a reduced sensitivity compared with CL-20. Particularly, the C series may have lower sensitivity than HMX or RDX. It is also observed in Table 3 and Fig. 4 that all the title compounds exhibit surprisingly high densities, which are higher than that of TEX. This attributes to the compact azaoxaisowurtzitane

cage in their molecular structure. Among them, the q values of A1 and A2 are approximately equal to 2.00 g/cm3, which is close to that of CL-20. In addition, all the azaoxaisowurtzitane cage compounds have outstanding detonation properties, whose D and P values are superior to or close to those of HMX (9.10 km/ s and 39.0 GPa). Especially, A1 and A2, two pentaazaoxaisowurtzitane cage compounds, present the best detonation properties (D  9.45 km/s and P  42.0 GPa) among the title compounds, which are comparable with those of CL-20. Moreover, although the compounds of B series possess only four nitramine moieties, the caged compounds have better detonation properties than HMX (9.10 km/s and 39.0 GPa), which also contains four nitramine moieties in the molecule. Similarly, the triazatrioxaisowurtzitane compounds (C series) have better detonation properties than RDX (8.75 km/s and 34.0 GPa) as they possess the same number of nitramine moieties in the structure. This shows that the azaoxaisowurtzitane cage compounds have a better combination of heat of detonation, density, and detonation properties than the cyclic compound HMX or RDX. Therefore, it may be inferred that the azaoxaisowurtzitane cage is an effective

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Fig. 5. Density, detonation pressure, and detonation velocity of the title compounds as a function of the oxygen atoms’ number (n).

Table 4 Bond lengths (Å) of several bonds in the cage and strain energies (SE, kJ/mol) of the azaisowurtzitane cage for the title compounds through homodesmotic reactions. Compd. CL-20 A1 A2 B1 B2 B3 B4 C1 C2 C3 C4 TEX a b c

C1-C7

C3-C11 b

1.602 (1.596 ) 1.600 1.598 1.599 1.597 1.592 1.595 1.591 1.591 1.594 1.594 1.584 (1.581c)

C-Na

C5-C9 b

1.589 (1.587 ) 1.583 1.581 1.577 1.571 1.577 1.578 1.577 1.577 1.574 1.580 1.571 (1.563c)

b

1.592 (1.587 ) 1.584 1.589 1.573 1.584 1.579 1.580 1.569 1.570 1.572 1.581 1.571 (1.563c)

1.458 1.459 1.456 1.462 1.458 1.456 1.450 1.464 1.456 1.457 1.459 1.451 (1.451c)

C-Oa

SE

1.413 1.426 1.410 1.418 1.423 1.420 1.413 1.419 1.419 1.412 1.417 (1.420c)

340.40 304.93 295.68 273.67 245.63 257.15 258.35 227.70 206.32 221.59 214.03 164.78

Average bond length values of C-N or C-O in the cage. The calculated values were taken from Ref. [20]. The experimental values were taken from Ref. [21].

structural unit for developing new energetic compounds with excellent detonation properties. It is interesting to note that the space orientations of oxygen atom in the cage skeleton also influences density, detonation velocity and detonation pressure of the title compounds. Generally, except for C1, the more oxygen atom orients to the 4 or 10 position of the azaoxaisowurtzitane cage skeleton, the lower the density, detonation velocity, and detonation pressure of the isomer is.

3.3. Molecular geometry Table 4 lists some bond parameters in the cage of all the title compounds. The calculated bond parameters of CL-20 or TEX are very close to previous calculated [20] or experiment values obtained from X-ray diffraction [21], indicating that our calculated results is reliable. As seen in Table 4, all the C-C bonds in the cage of the title compounds are longer than the normal C-C single bond (1.54 Å) due to the cage strain found in the system. The longest C-C bond in the cage reaches 1.60 Å, which may make the C-C bond break easily. In addition, the bond lengths of C1-C7, C3-C11, and C5-C9 in the

cage of the title compounds are shorter than corresponding ones of CL-20 but longer than corresponding ones of TEX. On the whole, as the N-NO2 group in the azaisowurtzitane or azaoxaisowurtzitane cage is replaced by the oxygen atom, the bond lengths of C1-C7, C3-C11, and C5-C9 in the cage of the title compounds decrease, which may mean that the introduction of oxygen atom (s) weakens the azaisowurtzitane cage strain. Also, as the more the number of oxygen atom orients to the 4 or 10 position of the azaisowurtzitane or azaoxaisowurtzitane cage, the shorter the C-O bond in the cage of the isomers often becomes. e.g., the average bond length of C-O in the cage of A1 is shorter than that of A2, and the average bond length of C-O in the cage of B1 or C1 is shorter than that of other isomers except for C4. Moreover, although the bond length of C-N in the cage of the title compounds is different from that of CL-20 or TEX, these differences are not significant.

3.4. Strain energies The calculated strain energies of the azaoxaisowurtzitane cage skeleton of the title compounds via homodesmotic reactions are

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listed in Table 4. As shown in Table 4, CL-20 has the highest strain energy of the cage skeleton, while TEX has the least one. On average, the strain energy of the azaoxaisowurtzitane cage compound decreases by 43.413 kJ/mol as one N-NO2 group in the cage is replaced by one oxygen atom. Hence, the strain of the azaoxaisowurtzitane cage skeleton weakened when the N-NO2 group is replaced by the oxygen atom, indicating that the introduction of the oxygen atom can improve the stability of the parent cage skeleton. In addition, the space orientations of the oxygen atom in the cage skeleton influence the strain energies of the cage skeletons for the isomers. The isomer with more oxygen atom orients to the 4 or 10 position of the azaoxaisowurtzitane cage has higher strain energy of the cage skeleton than its other isomers. Accordingly, it may be inferred that these isomers possessing a higher strain of the azaoxaisowurtzitane cage have a lower stability. 3.5. Thermal stability BDE can provide useful information for understanding the stability of the investigated molecules. In general, the smaller the energy for breaking a bond is, the weaker the bond is, the easier the bond becomes a trigger bond. For the title compounds, four possible bond dissociations were considered: (1) the N-NO2 bond in the side chain; (2) the C-O, C-N, and C-C bonds in the cage. Table 5 presents the BDEs of the relatively weaker bonds of the title compounds. The calculated BDEs of N-NO2 (156.85 kJ/mol and 190.15 kJ/mol) for CL-20 and TEX are close to the previous results (160.28 kJ/mol [8] and 190.16 [59], respectively). As evident in Table 5, the N-NO2 bonds have lower BDE values than other bonds in the molecule, which means that the N-NO2 bonds are the weakest one and easier to rupture than other bonds in thermal decomposition for all the title compounds. The conclusion is consistent with previous research [18,20,24,57] that nitro groups are often the primary cause for the high initiation reactivity of polynitro compounds. In addition, all the title compounds have higher BDE values than the parent compound CL-20, which means that all the title compounds are more stable than CL-20. By and large, the BDE values of the weakest bonds of these cage compounds increase as the number of the oxygen atom in the azaoxaisowurtzitane cage increases except for A2 and C2. And TEX has the highest BDE value for these cage compounds. Therefore, the introduction of the oxygen atom increases thermal stability of the cage compound, which is agreement with the strain analysis as mentioned above. According to the suggestion of Chung et al. [60] that the molecule to be a viable candidate should have a dissociation barrier larger than 80–120 kJ/mol, all the title compounds are the possible candidates for HEDMs. Table 5 Bond dissociation energies (BDE, kJ/mol) of the relatively weak bonds of the title compounds.

a

Comp.

N-NO2

CL-20 A1 A2 B1 B2 B3 B4 C1 C2 C3 C4 TEX

156.85(160.28a) 160.05 162.03 165.05 160.17 161.39 160.68 173.67 162.95 170.07 166.77 190.10(190.16a)

C-O

C-C

C-N

303.92 287.96 308.24 303.26 285.36 295.68 277.58 288.18 281.60 286.23 283.32

233.67 234.00 254.25 233.71 272.12 275.21 278.02 255.40 291.26 272.96 280.86 307.65

272.99 267.61 286.70 292.46 279.98 291.45 283.99 317.62 282.50 301.89 276.27 353.49

The calculated values in parentheses were from Ref. [8,59].

Table 6 The free space per molecule in the unit cell (DV) and impact sensitivity (h50) of the title compounds.a

a b

Compd.

DV

h50

Compd.

DV

h50

CL-20 A1 A2 B1 B2 B3 B4

77 69 68 62 61 61 61

12(12b) 17 19 23 27 27 27

C1 C2 C3 C4 TEX HMX

55 56 55 53 47

32 30 33 38 38 30(29b)

DV are in Å3; h50 are in cm/2.5 kg. The values were from Ref. [16].

3.6. Impact sensitivity Table 6 lists the free space per molecule (DV) in the unit cell and impact sensitivity (h50) of the title compounds. The calculated h50 values for CL-20 and HMX are quite consistent with the experimental results [16]. It can be seen that all the title compounds have smaller DV values than CL-20 but larger DV values than TEX. On the whole, as the number of the oxygen atom in the azaoxaisowurtzitane cage increases, the DV values of the title compounds markedly decrease and the predicted h50 values of these compounds clearly increase. e.g., the h50 value of CL-20 is only 12 cm, while the h50 value of C1, C2, C3, or C4 exceeds 29 cm, which is higher than that of HMX (h50 = 29 cm). Thus, it can be inferred that the introduction of the oxygen atom by replacing the N-NO2 group in the cage can effectively decrease the sensitivity of parent compound CL-20. In particular, the DV or h50 value of triazatrioxaisowurtzitane cage compound such as C4 is close to these of TEX, respectively, which mean that C4 is very insensitive to external impact.

4. Conclusions In this work, ten novel azaoxaisowurtzitane cage compounds were designed by introducing the oxygen atom into the azaisowurtzitane cage to replace the N-NO2 group. Then, their HOFs, energetic properties, molecule structure, strain energies, thermal stability, and impact sensitivity were investigated using the DFTB3LYP/6-311G(d, p). The results indicate that the introduction of the oxygen atom in the cage is not helpful for increasing the HOFs, densities, and energetic properties of the parent compound CL-20. However, all the title compounds exhibit surprisingly high density superior to TEX and remarkable detonation properties superior to or very close to HMX. And the A1 and A2 present a comparable detonation properties (D  9.45 km/s and P  42.00 GPa) with CL-20. Based on the analysis of molecular structure, strain energy, and BDEs, the introduction of the oxygen atom in the cage weakens the strain of the parent cage and increases thermal stability of the title compounds. All the azaoxaisowurtzitane cage compounds exhibit higher thermal stability than the parent compound CL-20. In addition, the N-NO2 bond in the side chain is the weakest one and the N-NO2 bond homolysis may be the initial step in thermal decomposition. Furthermore, an analysis of the impact sensitivity and free space per molecule in the unit cell indicates that the introduction of the oxygen atom in the cage effectively decreases the sensitivity of these cage compounds. In particular, the triazatrioxaisowurtzitane cage compounds (C series) have relatively high h50 values (close to TEX) and are very insensitive to external impact. Considered the detonation performance, thermal stability, and impact sensitivity, A1, A2, B1, B2, B3, and B4 can be regarded as the potential candidates of HEDC because these azaoxaisowurtzi-

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tane cage compounds not only exhibit excellent energetic properties comparable with CL-20, but also have higher thermal stability and lower sensitivity than CL-20.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 21273115) and was sponsored by Qing Lan Project of Jiangsu Province.

References [1] P.F. Pagoria, G.S. Lee, A.R. Mitchell, R.D. Schmidt, A review of energetic materials synthesis, Thermochim. Acta 384 (2002) 187–204. [2] A.K. Sikder, N. Sikder, A review of advanced high performance, insensitive and thermally stable energetic materials emerging for military and space applications, J. Hazard. Mater. 112 (2004) 1–15. [3] L.E. Fried, M.R. Manaa, P.F. Pagoria, R.L. Simpson, Design and synthesis of energetic materials, Ann. Rev. Mater. Res. 31 (2001) 291–321. [4] M.B. Talawar, R. Sivabalan, T. Mukundan, H. Muthurajan, A.K. Sikder, B.R. Gandhe, A.S. Rao, Environmentally compatible next generation green energetic materials (GEMs), J. Hazard. Mater. 161 (2009) 589–607. [5] X.J. Xu, H.M. Xiao, X.H. Ju, X.D. Gong, W.H. Zhu, Computational studies on polynitrohexaazaadmantanes as potential high energy density materials, J. Phys. Chem. A 110 (2006) 5929–5933. [6] F. Wang, H.C. Du, J.Y. Zhang, X.D. Gong, Computational studies on the crystal structure, thermodynamic properties, detonation performance, and pyrolysis mechanism of 2,4,6,8-tetranitro-1,3,5,7-tetraazacubane as a novel high energy density material, J. Phys. Chem. A 115 (2011) 11788–11795. [7] X.J. Xu, H.M. Xiao, X.D. Gong, X.H. Ju, Z.X. Chen, Theoretical studies on the vibrational spectra, thermodynamic properties, detonation properties, and pyrolysis mechanisms for polynitroadamantanes, J. Phys. Chem. A 109 (2005) 11268–11274. [8] Y. Pan, W.H. Zhu, H.M. Xiao, Comparative theoretical studies of dinitromethylor trinitromethyl-modified derivatives of CL-20, Can. J. Chem. 91 (2013) 1243– 1251. [9] A.T. Nielsen, R.A. Nissan, D.J. Vanderah, C.L. Coon, R.D. Gilardi, C.F. George, J. Flippen-Anderson, Polyazapolycyclics by condensation of aldehydes with amines. 2. Formation of 2,4,6,8,10,12-hexabenzyl-2,4,6,8,10,12hexaazatetracyclo[5.5.0.05.9.03,11]dodecanes from glyoxal and benzylamines, J. Org. Chem. 55 (1990) 1459–1466. [10] X.J. Xu, W.H. Zhu, H.M. Xiao, DFT studies on the four polymorphs of crystalline CL-20 and the influences of hydrostatic pressure on epsilon-CL-20 crystal, J. Phys. Chem. B 111 (2007) 2090–2097. [11] M.F. Foltz, C.L. Coon, F. Garcia, A.L. Nichols, The thermal stability of the polymorphs of hexanitrohexaazaisowurtzitane, Part I, Propell., Explos., Pyrotech. 19 (1994) 19–25. [12] D.G. Patil, T.B. Brill, Thermal decomposition of energetic materials 53. Kinetics and mechanism of thermolysis of hexanitrohexazaisowurtzitane, Combust. Flame 87 (1991) 145–151. [13] R. Turcotte, M. Vachon, Q.S.M. Kwok, R. Wang, D.E.G. Jones, Thermal study of HNIW (CL-20), Thermochim. Acta 433 (2005) 105–115. [14] X.J. Xu, H.M. Xiao, J.J. Xiao, W.H. Zhu, H. Huang, J.S. Li, Molecular dynamics simulations for pure e-CL-20 and e-CL-20-based PBXs, J. Phys. Chem. B 110 (2006) 7203–7207. [15] H. Bazaki, H. Kawabe, H. Miya, Synthesis and sensitivity of hexanitrohexaazaisowurtzitane (HNIW), Propell., Explos., Pyrotech. 23 (1998) 333–336. [16] B.M. Rice, J.J. Hare, A quantum mechanical investigation of the relation between impact sensitivity and the charge distribution in energetic molecules, J. Phys. Chem. A 106 (2002) 1770–1783. [17] V. Ghule, P. Jadhav, R. Patil, S. Radhakrishnan, T. Soman, Quantum-chemical studies on hexaazaisowurtzitanes, J. Phys. Chem. A 114 (2010) 498–503. [18] J.Y. Zhang, H.C. Du, F. Wang, X.D. Gong, Y.S. Huang, Theoretical investigations of a high density cage compound 10-(1-nitro-1, 2, 3, 4-tetraazol-5-yl)) methyl2, 4, 6, 8, 12-hexanitrohexaazaisowurtzitane, J. Mol. Model. 18 (2012) 165– 170. [19] Y. Wang, C. Qi, J.W. Song, X.Q. Zhao, C.H. Sun, S.P. Pang, Trinitromethyl/ trinitroethyl substituted CL-20 derivatives: structurally interesting and remarkably high energy, J. Mol. Model. 19 (2013) 1079–1087. [20] J.Y. Zhang, H.C. Du, F. Wang, X.D. Gong, Y.S. Huang, DFT studies on a high energy density cage compound 4-trinitroethyl-2,6,8,10,12pentanitrohezaazaisowurtzitane, J. Phys. Chem. A 115 (2011) 6617–6621. [21] K. Karaghiosoff, T.M. Klapötke, A. Michailovski, G. Holl, 4,10-Dinitro-2,6,8,12tetraoxa-4,10-diazaisowurtzitane (TEX): a nitramine with an exceptionally high density, Acta Crystallogr. A 58 (2002) o580–o581. [22] J. Vágenknecht, P. Marecˇek, W.A. Trzcin´ski, Sensitivity and performance properties of tex explosives, J. Energ. Mater. 20 (2002) 245–253. [23] J. Vgenknecht, TEX—a LOVA explosive, Chinese J. Energ. Mater. 8 (2000) 56–59. [24] F. Wang, G.X. Wang, H.C. Du, J.Y. Zhang, X.D. Gong, Theoretical studies on the heats of formation, detonation properties, and pyrolysis mechanisms of energetic cyclic nitramines, J. Phys. Chem. A 115 (2011) 13858–13864.

85

[25] T. Wei, W.H. Zhu, X.W. Zhang, Y.F. Li, H.M. Xiao, Molecular design of 1,2,4,5tetrazine-based high-energy density materials, J. Phys. Chem. A 113 (2009) 9404–9412. [26] Y. Pan, J.S. Li, B.B. Cheng, W.H. Zhu, H.M. Xiao, Computational studies on the heats of formation, energetic properties, and thermal stability of energetic nitrogen-rich furazano[3,4-b]pyrazine-based derivatives, Comput. Theor. Chem. 992 (2012) 110–119. [27] X.W. Fan, X.H. Ju, Theoretical studies on four-membered ring compounds with NF2, ONO2, N3, and NO2 groups, J. Comput. Chem. 29 (2008) 505–513. [28] Y. Pan, W.H. Zhu, H.M. Xiao, Design and selection of nitrogen-rich bridged di1,3,5-triazine derivatives with high energy and reduced sensitivity, J. Mol. Model. 18 (2012) 3125–3138. [29] L.A. Curtiss, K. Raghavachari, P.C. Redfern, V. Rassolov, J.A. Pople, Gaussian-3 (G3) theory for molecules containing first and second-row atoms, J. Chem. Phys. 109 (1998) 7764–7776. [30] T. Wei, J.J. Zhang, W.H. Zhu, X.W. Zhang, H.M. Xiao, A comparison of high-level theoretical methods to predict the heats of formation of azo compounds, J. Mol. Struct. – Theochem. 956 (2010) 55–60. [31] P.W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 1982. [32] P. Politzer, P. Lane, J.S. Murray, Computational characterization of a potential energetic compound: 1,3,5,7-tetranitro-2,4,6,8-tetraazacubane, Cent. Eur. J. Energ. Mater. 8 (2011) 39–52. [33] P. Politzer, J.S. Murray, Some perspectives on estimating detonation properties of C, H, N, O compounds, Cent. Eur. J. Energ. Mater. 8 (2011) 209–220. [34] F.A. Bulat, A. Toro-Labbé, T. Brinck, J.S. Murray, P. Politzer, Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies, J. Mol. Model. 16 (2010) 1679–1691. [35] E.F.C. Byrd, B.M. Rice, Improved prediction of heats of formation of energetic materials using quantum mechanical calculations, J. Phys. Chem. A 110 (2006) 1005–1013. [36] M. Jaidann, S. Roy, H. Abou-Rachid, L.S. Lussier, A DFT theoretical study of heats of formation and detonation properties of nitrogen-rich explosives, J. Hazard. Mater. 176 (2010) 165–173. [37] F. Wang, H.C. Du, J.Y. Zhang, X.D. Gong, Comparative theoretical studies of energetic AZO s-triazines, J. Phys. Chem. A 115 (2011) 11852–11860. [38] M.J. Kamlet, S.J. Jacobs, Chemistry of detonation. I. A simple method for calculation detonation properties of C–H–N–O explosives, J. Chem. Phys. 48 (1968) 23–35. [39] P. Politzer, J. Martinez, J.S. Murray, M.C. Concha, A. Toro-Labbé, An electrostatic interaction correction for improved crystal density prediction, Mol. Phys. 107 (2009) 2095–2101. [40] B.M. Rice, E.F.C. Byrd, Evaluation of electrostatic descriptors for predicting crystalline density, J. Comput. Chem. 34 (2013) 2146–2151. [41] D.H. Magers, S.R. Davis, Ring strain in the oxazetidines, J. Mol. Struct. – Theochem. 487 (1999) 205–210. [42] M. Zhao, B.M. Gimarc, Strain energies in cyclic on, n = 3–8, J. Phys. Chem. 97 (1993) 4023–4030. [43] X.W. Fan, X.H. Ju, Q.Y. Xia, H.M. Xiao, Strain energies of cubane derivatives with different substituent groups, J. Hazard. Mater. 151 (2008) 255–260. [44] X.W. Fan, L. Qiu, X.H. Ju, Cage strain in nitro-substituted 1,3,5,7tetraazacubanes, Struct. Chem. 20 (2009) 1039–1042. [45] Y. Pan, W.H. Zhu, H.M. Xiao, DFT studies on trinitromethyl- or dinitromethylmodified derivatives of RDX and b-HMX, Comput. Theor. Chem. 1019 (2013) 116–124. [46] S.W. Benson, Thermochemical Kinetics, second ed., Wiley-Interscience, New York, 1976. [47] I. Mills, T. Cvitas, K. Homann, N. Kallay, K. Kuchitsu, Quantities, Units, and Symbols in Physical Chemistry, Blackwell Scientific Publications, Oxford, 1988. [48] S.J. Blanksby, G.B. Ellison, Bond dissociation energies of organic molecules, Acc. Chem. Res. 36 (2003) 255–263. [49] M.H. Keshavarz, Simple relationship for predicting impact sensitivity of nitroaromatics, nitramines, and nitroaliphatics, Propell., Explos., Pyrotech. 35 (2010) 175–181. [50] J.S. Li, A multivariate relationship for the impact sensitivities of energetic Nnitrocompounds based on bond dissociation energy, J. Hazard. Mater. 174 (2010) 728–733. [51] M. Pospíšil, P. Vávra, M.C. Concha, J.S. Murray, P. Politzer, Sensitivity and the available free space per molecule in the unit cell, J. Mol. Model. 17 (2011) 2569–2574. [52] M. Pospíšil, P. Vávra, M.C. Concha, J.S. Murray, P. Politzer, A possible crystal volume factor in the impact sensitivities of some energetic compounds, J. Mol. Model. 16 (2010) 895–901. [53] P. Politzer, J.S. Murray, Impact sensitivity and crystal lattice compressibility/ free space, J. Mol. Model. 20 (2014) 2223–2230. [54] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian 09, Revision A.01, Gaussian Inc, Wallingford, CT, 2009.

86

Y. Pan et al. / Computational and Theoretical Chemistry 1114 (2017) 77–86

[55] J.A. Dean, LANGE’S Handbook of Chemistry, 15th ed., McGraw-Hill Book Co., New York, 1999. [56] T. Wei, W.H. Zhu, J.J. Zhang, H.M. Xiao, DFT study on energetic tetrazolo-[1,5b]-1,2,4,5-tetrazine and 1,2,4-triazolo-[4,3-b]-1,2,4,5-tetrazine derivatives, J. Hazard. Mater. 179 (2010) 581–590. [57] L. Qiu, H.M. Xiao, X.D. Gong, X.H. Ju, W.H. Zhu, Theoretical studies on the structures, thermodynamic properties, detonation properties, and pyrolysis mechanisms of spiro nitramines, J. Phys. Chem. A 110 (2006) 3797–3807.

[58] P. Politzer, J.S. Murray, Impact sensitivity and the maximum heat of detonation, J. Mol. Model. 21 (2015) 262–272. [59] H. Lin, S.G. Zhu, L. Zhang, X.H. Peng, P.Y. Chen, H.Z. Li, Theoretical investigation of a novel high density cage compound 4,8,11,14,15-pentanitro-2,6,9,13tetraoxa-4,8,11,14,15-pentaazaheptacyclo[5.5.1.13,11.15,9] pentadecane, J. Mol. Model. 19 (2013) 1019–1026. [60] G.S. Chung, M.W. Schmidt, M.S. Gordon, An ab initio study of potential energy surfaces for N(8) isomers, J. Phys. Chem. A 104 (2000) 5647–5650.