Ab Initio Calculation of BN Generation from Boron and NitrogenOxides

Zhong Wang, Shu Fen Li, Li Min Zhang

Laboratory of Bond-Selective Chemistry, Department of Chemical Physics, University of Science and Technology ofChina, Hefei 230026 (P. R. of China)

Zhen Yu Sheng, Shu Qin Yu*

Abdus Salam International Centre for Theoretical Physics, 34014 Trieste (Italy) Laboratory of Bond-Selective Chemistry,Department of Chemical Physics, University of Science and Technology of China, Hefei 230026 (P. R. of China)

Abstract

Boron Nitride (BN) is one of the products produced in theburning of boron-containing propellant. A possible reactionmechanism for the reactions of boron and nitrogen oxides (NO,NO2, N2O) has been studied using the G2MP2 method. The BNproduct can be formed in the reactions of B(4P) with NO, NO2 andN2O. Among these three reactions, B(

4P)þNO2 and B(4P)þN2Oare 181.42 kJ/mol and 160.92 kJ/mol more-exothermic than theB(4P)þNO reaction. The barrier heights from intermediates totransition states are 64.85 kJ/mol and 111.75 kJ/mol for B(4P)þNO2 and B(

4P)þN2O, respectively. However, in the reactionB(4P)þNO , the transition from intermediate to product (IM3!BNþO) is very endothermic by 420.70 kJ/mol. So B(4P)þN2O!BNþNO and B(4P)þNO2!BNþO2 are more likelyreactions to generate BN than B(4P)þNO!BNþO.

Keywords: Boron, Nitrogen Oxides, Reaction Mechanism,G2MP2, Ab Initio Calculation

1 Introduction

As an improvement to solid propellants, the use of highcombustion-heat metal powder in propellants is an effectivemethod to adjust the burning characteristics of propellants.It is well known that boron has the highest energetic densityamongmanykinds of propellant additives. Therefore, boronhas potential applications as an advanced fuel in propulsionsystems [1].During the burning of boron-containing propellant, some

portions of boron are oxidized to boron oxide by releasing alot of energy, while some are taken into reaction by formingboron nitride (BN) [2, 3]. From a thermodynamic point ofview, the formation reactions of both BN and B2O3 areexothermic.The valueof the standard formation enthalpy ofBN and B2O3 can be estimated [4] They are DfHm(BN)¼�250 KJ/mol and DfHm(B2O3)¼�1276 KJ/mol, respec-tively. It is obvious that the formation heat of BN is farless than that of B2O3. So the BN product is not beneficial to

propellant burning. It is interesting to investigate BNgeneration in propellant combustion.Ammonium perchlorate (AP) or cyclic nitramines octa-

hydro-1,3,5,7 tetranitro-1,3,5,7-tetrazocine (HMX) are themain energetic ingredients used in various propellants.Many experiments indicate that nitrogen oxides (NO, NO2,N2O) are important products in the thermal decompositionof APor HMX [5, 6]. The possibility of BN generation fromthe reaction of boron and nitrogen oxides is an interestingtopic. In this paper, we studied the reaction of boron andnitrogen oxides (NO, NO2, N2O) using ab initio calculation.It is a reliable method for calculating the reaction channels.The precision of the calculated results is consistently in theaccepted error range. This is the first electronic structurestudy of boron and nitrogen oxides (NO, NO2 and N2O)systems in theory.

2 Methods of Calculation

Gaussian-2 (G2) theory [7] is a general procedure to getthe total energies of molecules at their equilibrium geo-metries. This method can achieve high accuracy by combin-ing the results of several different calculations as anapproximation to a single, very high level computation,which is much too expensive to be practical. Here a reliableG2MP2 theory was used to explore the potential energysurface for the reactions of boron with N2O, NO and NO2.The geometries of reactants, products, intermediates (IM)and transition states (TS) were optimized at the MP2(full)/6-31G(d, p) level. The vibrational frequencies were ob-tained at theHF/6-31G(d, p) level, in order to determine thenature of different stationary points and the zero-point-energy (ZPE) corrections. To eliminate the systemerror, thefrequency and theZPEquantity are scaled by the factor 0.95and 0.8929, respectively [7]. For the reaction of BþN2O,calculations following the minimum energy path (MEP)down from the transition state in both directions (known asthe IRC option in GAUSSIAN program [8]) were also* Corresponding author; e-mail: sqyu@ustc.edu.cn

160 Propellants, Explosives, Pyrotechnics 29 (2004), No. 3

¹ 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim DOI: 10.1002/prep.200400040

performed at the MP2(full)/6-31G(d, p) level. The resultconfirmed that the transition state links the desired reactantand product. Then, a series of high-level single point energycalculations, MP2/6-311G(d, p), MP2/6-311þG(3df,2p)and QCISD(T)/6-311G(d, p), were carried out with theoptimized geometries, and the barrier heights and reactionheats were obtained at the G2MP2 level. The formula ofG2MP2 total energy is the following:

E(G2MP2)¼E(QCISD(T)/6-311G(d, p))�E(MP2/6-311G(d, p))þE(MP2/6-311þG(3df,2p))þHLCþZPE

HereHLC(high-level correction)¼�0.19NOA�4.81NOB,NOA and NOB represent the numbers of a and b valenceelectrons, respectively.All calculations were carried out using the Gaussian 98

program on a personal computer (CPU: AMDAthlon(tm)processor 1000 MHz; EMS memory: 256 MB).In our calculations, the absolute energies are in units of

hartrees and the relative ones are in kJ/mol. But for theoverall profile of the potential energy surface for thereaction, in general, the energies of reactants are regardedas the starting point. So energies of other species in kJ/molare relative.

3 Results and Discussion

To understand how BN is produced by the reactionbetween boron and the nitrogen-containing compounds, wemade some theoretical calculations. As we know, there arethree main compounds containing N in the thermal decom-position products of AP or HMX, i.e. N2O, NO and NO2.Aiming at every compound, calculations were made re-spectively in two different potential energy surfaces (PES):doublet PES and quartet PES. In Table 1, it is obvious thatonly reactions in the quartet PES, B(4P)þNO, B(4P)þNO2and B(4P)þN2O, are exothermic, while reactions in thedoublet PES are all endothermic.The probability of the endothermic reactions producing

BN in the doublet PES is very small. So we focused on those

reactions in the quartet PES. The optimized geometries ofthe reactants, products, intermediates and transition statesfor all reactions in the quartet PES are shown in Fig. 1.The geometries of the reactants and products optimized at

the MP2(full)/6-31G(d, p) level are of a good quality,although the bond distance has slight deviation with respectto experiment [10 ± 13]. The harmonic vibrational frequen-cies for these species are summarized in Table 2. In general,the calculated frequency and available experimental data[11, 13 ± 16] are in good agreement except for NO and NO2.Therefore, the frequencies of NO and NO2 were calculatedby the density functional theory too as listed in Table 2,which are in good agreement with the experimental data.For both species, the contribution of electronic correlativeenergy was overvalued at theMP2(full)/6-31G(d, p) level. Itmakes the calculated total energies higher, while thefrequencies are the second derivative of the energies. Sothere are higher errors for frequencies ofNOandNO2 at theMP2(full)/6-31G(d, p) level. The frequencies and energieswith higher precision can be gotten by the density functiontheory (DFT)methods [17, 18]. So theDFTmodel is used tocalculate NO and NO2 at the B3LYP/6-31G(d) level.

3.1 Calculation for B(4P)þN2O Reaction

We assume the reactant N2O is in the singlet state with alinear structure [8]. Table 3 shows their total energies at theG2MP2 level calculated with the MP2(full)/6-31G(d, p)optimized geometries. The corresponding relative energiesare also listed. The overall energetic profile based on theG2MP2 energies for the reaction B(4P)þN2O!BNþNOis shown in Fig. 2. The two channels shown in the presentcalculation will be discussed respectively.As shown in Figure 2, the boron atom can follow either a

cis- or a trans- approach to the N2O molecule. The totalreaction pathway, B(4P)þN2O!BNþNO, is exothermicby 309.07 kJ/mol at the G2MP2 level.Following the cis-path, the intermediate, cis-BNNO(IM1)

is 362.92 kJ/mol more stable than the reactant B(4P)þN2O,at the G2MP2 level. The IM1 has Cs symmetry, in which theB-N bond is 0.1442 nm and N-O bond is 0.1522 nm at the

Table 1. Total energies (Hartrees) and relative energies (in kJ/mol) of various species for several reactions.

Species Energy (Hartrees) Reactions Reaction Heats (kJ/mol)

B(2P)þNO �154.33892 B(2P)þNO!BNþO 210.08BNþO �154.25890B(4P)þNO �154.20247 B(4P)þNO!BNþO �148.16BNþO �154.25890B(2P)þNO2 �229.43321 B(2P)þNO2!BNþO2 28.66BNþO2 �229.42229B(4P)þNO2 �229.29676 B(4P)þNO2!BNþO2 �329.57BNþO2 �229.42229B(2P)þN2O �209.03517 B(2P)þN2O!BNþNO 49.16BNþNO �209.01644B(4P)þN2O �208.89872 B(4P)þN2O!BNþNO �309.07BNþNO �209.01644

Ab Initio Calculation of BN Generation from Boron and Nitrogen Oxides 161

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MP2/6-31G(d, p) level. The energetically favorable path isIM1!BNþNO, via a TS1 and barrier of 111.75 kJ/molheight at the G2MP2 level. The N-N bond cleavage barrierTS1 has Cs symmetry too with an imaginary frequency788.71 cm�1. The breaking N-N bond is elongated from0.1292 nm in IM1 to 0.1749 nm. The other two bonds, B-Nand N-O are shortened by about 0.0134 nm and 0.0332 nm,respectively. They are close to those of the equilibriumvalueof the products BN and NO, 0.1316 nm and 0.1143 nm. At

the same time, bond angles increase from 97.878 and 87.528in IM1 to 125.208 and 98.768 in TS1 for aB-N-N andaN-N-O respectively. These four atoms all lie in the sameplane both in IM1 and TS1. The products, BN and NO, areformed by the simple N-N bond scission of TS1.On the other hand, trans-BNNO(IM2) is 371.75 kJ/mol

more stable than the reactants B(4P)þN2O. It ismore stablethan IM1. The energetically favorable channel is the simpleN-N bond scission channel of IM2 to BNþNO, via a barrier

Figure 1. Optimized structures of reactants, products, intermediates and transition states for all reactions at MP2(full)/6-31G(d, p)level. Bond lengths are in (nm), and bond angles are in (8). (*Reactants are devoted as R; Products are devoted as P. Values inparentheses indicate experimental data taken from [9 ± 12]).

Table 2. Scaled MP2(full)/6-31G (d, p) harmonic vibrational frequencies of the reactants, products, intermediate and transition states inall reactions

Species Frequencies (cm�1)

N2O 554.63 (588.8)a, 1228.04 (1284.9), 2143.55 (2223.8)BN 1714.46 (1514.6)NO 3700.47 (1904.2)b

NO2 715.13 (648.0), 1312.45 (1320.0), 2171.61 (1621.0)b

O2 1341.69(1580.36)cis-BNNO (IM1) 174.75, 772.60, 850.33, 1011.09, 1136.60, 1223.80trans-BNNO (IM2) 216.13, 302.77, 676.50, 1029.74, 1797.00, 1906.60BNO (IM3) 202.30, 920.06, 2049.87BNOO (IM4) 259.15, 437.79, 771.57, 803.02, 1040.17, 1673.79trans-BNOO (IM5) 170.13, 281.20, 598.17, 912.86, 1112.04, 2128.49cis-BNNO (TS1) 788.71ic, 89.97, 210.35, 280.51, 1693.94, 1794.44trans-BNNO (TS2) 688.19ic, 91.42, 243.95, 365.24, 1746.24, 2016.89trans-BNOO (TS3) 990.81ic, 296.13, 402.54, 912.73, 1671.42, 2359.81

a Values in parentheses indicate experimental data taken from [10 ± 14]b 2004.975, 1530.36 are the calculated frequencies at the B3LYP/6-31G(d) level for NO and NO2, respectively.c i represents imaginary frequency.

162 Zhong Wang, Shu Fen Li, Li Min Zhang, Zhen Yu Sheng and Shu Qin Yu

Propellants, Explosives, Pyrotechnics 29 (2004), No. 3 ¹ 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim

TS2 with 98.45 kJ/mol in height. The TS2 also has Cssymmetry with an imaginary frequency 688.19 cm�1. Atthe MP2(full)/6-31G(d, p) level, the breaking N-N bond inTS2 is elongated by about 0.0497 nm compared with IM2.The N-O bond is shortened by about 0.0056 nm, while theB-N bond is elongated by about 0.0045 nm, and is close tothat of the product BN(3<P), 0.1316 nm. The path, IM2!BNþNO, is endothermic by 98.45 kJ/mol, while the totalreaction pathway B(4P)þN2O!BNþNO is still exother-mic as mentioned above.To further illustrate the detailed mechanism for the

reactions, the intrinsic reaction coordinate (denoted as IRC)calculations were performed starting from the intermedi-ates toward the products at the MP2(full)/6-31G(d, p) levelto obtain the minimum energy path (MEP). The potentialenergy of each reaction path drops rapidly to approach theenergy of products after the intermediates pass throughtheir transition states. It is confirmed that the IM andproducts are linked by TS, and the reactions are carried outalong these two reaction paths.In summary, we have investigated the mechanism of the

reaction B(4P)þN2O!BNþNOat theG2MP2 level. Tworeaction paths are encountered, having cis- and trans-BNNO arrangements. The calculated heat of reaction is�309.07 kJ/mol. In light of the above calculation, it isconcluded that BN can be produced by the reaction B(4P)with N2O via two reaction channels.

3.2 Calculation for B(4P)þNO Reaction

No transition state is found in the path producing BNthrough B(4P)þNO reaction as shown in Figure 3. In thisreaction, two reactants, boron and NO can bind directly toproduce the intermediate BNO radical. The extra energycan make the N-O bond of BNO become longer and longer,and then finally break.This process canbe called singlebonddissociation. BNO (IM3) is 568.86 kJ/mol more stable thanthe reactants B(4P) andNO.Table 4 shows the total energiesof reactants, products and the intermediate at the G2MP2level calculated with the MP2(full)/6-31G(d, p) optimizedgeometries. From the energy chart, the overall reaction isexothermic. But IM3!BNþO is very endothermic by420.70 kJ/mol, and hence unlikely to be significant.

3.3 Calculation for B(4P)þNO2 Reaction

The reaction path producing BN can be drawn fromFigure 4. The exclusive transition state connects two differ-ent intermediates. At the beginning of this reaction, whenthe reactant B is approaching to the atom N of NO2, the O-N-O bond angle reduces from 133.738 to 66.438. Subse-quently, the intermediate BNOO with a three-memberedring is formed. The path BNOO(IM4)! trans-BNOO(IM5) is via a barrier over TS3 trans-BNOO of64.85 kJ/mol. From 67.798 in TS3 to 112.108 in IM5, there is

Figure 2. The overall profile of the potential energy surface for the reaction B(4P)þN2O, calculated at the G2MP2 level.

Table 3. Total energies (Hartrees) and relative energies (in kJ/mol) of various species for the reaction BþN2O

Species MP2/ MP2/ QCISD(T)/ G2MP2 DE6-311G(d, p) 6-311þG(3df,2p) 6-311G(d, p) (Hartree) (kJ/mol)

B(4P)þN2O �208.74186 �208.85539 �208.75563 �208.89872 0.00B(2P)þN2O �208.85216 �208.96894 �208.88420 �209.03517 �358.23BNþNO �208.81445 �208.92976 �208.86867 �209.01644 �309.07cis-BNNO (IM1) �208.82830 �208.95303 �208.88251 �209.03695 �362.92trans-BNNO (IM2) �208.84030 �208.96321 �208.88759 �209.04032 �371.75cis-BNNO (TS1) �208.77888 �208.89768 �208.84262 �208.99438 �251.17trans-BNNO (TS2) �208.79770 �208.91547 �208.85311 �209.00282 �273.30

Ab Initio Calculation of BN Generation from Boron and Nitrogen Oxides 163

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severe change in the N-O-O bond angle. In the final step, notransition state canbediscovered andBN is produced fromasingle bond dissociation, which is endothermic by 60.38 kJ/mol. In Figure 4, by scanning the potential energy surfacewith different lengths of the N-O bond, it is confirmed thatthe dissociation channel has no distinct transition state.The total energies at the G2MP2 level are shown in

Table 5. From the energy chart, we can see that it is astrongly exothermic reaction, which could easily pro-ceed.

Comparing the above three reactions, B(4P)þNO2, (N2O,NO) are exothermic by 329.57 kJ/mol, 309.07 kJ/mol and148.16 kJ/mol, respectively. It is obvious that the first tworeactions are more exothermic than the B(4P)þNO reac-tion. Furthermore, the B(4P)þNO2 and B(4P)þN2O reac-tions have barrier heights of only 64.85 kJ/mol and111.75 kJ/mol. But for the B(4P)þNO reaction, the N-Obond scission of IM3 needs 420.70 kJ/mol energy. So theenergetically favorable paths are B(4P)þNO2!BNþO2and B(4P)þN2O!BNþNO. It is worth pointing out that

Figure 3. The overall profile of the potential energy surface for the reaction B(4P)þNO, calculated at the G2MP2 level.

Table 4. Total energies (Hartrees) and relative energies (in kJ/mol) of various species for the reaction BþNO

Species MP2/ MP2/ QCISD(T)/ G2MP2 DE6-311G(d, p) 6-311þG(3df,2p) 6-311G(d, p) (Hartree) (kJ/mol)

B(4P)þNO �154.07804 �154.1552 �154.10408 �154.20247 0.00B(2P)þNO �154.18834 �154.26875 �154.23265 �154.33892 �358.23BNþO �154.11359 �154.18850 �154.16181 �154.25890 �148.16BNO (IM3) �154.26222 �154.34826 �154.30951 �154.41914 �568.86

Figure 4. The overall profile of the potential energy surface for the reaction B(4P)þNO2, calculated at the G2MP2 level.

164 Zhong Wang, Shu Fen Li, Li Min Zhang, Zhen Yu Sheng and Shu Qin Yu

Propellants, Explosives, Pyrotechnics 29 (2004), No. 3 ¹ 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim

only homogeneous gas phase reactions were considered inthis calculation. In fact, propellant burnings are morecomplex processes. Therefore, present calculation resultsonly provide a guide for experimentalists.

4 Conclusion

The BN generation is not beneficial to energy character-istics of boron-containing propellant burning. The mecha-nism of BN generation was first studied using ab initiocalculations.Ab initio calculations show that the reactions of ground

state boron atom and nitrogen oxides (N2O, NO, NO2) areendothermic, but B(4P)þNO2 (NO, NO2) reactions areexothermic and the BN product can be formed. In the threeexothermic reactions, B(4P)þNO2 and B(4P)þN2O are181.42 kJ/mol and 160.92 kJ/mol more exothermic thanB(4P)þNO reaction, respectively. But IM3!BNþO isvery endothermic by 420.70 kJ/mol. Therefore, B(4P)þN2O!BNþNO and B(4P)þNO2!BNþO2 are morefavorable reactions to generate BN.The calculated results indicated that the boron atom of

excited state B(4P) with nitrogen oxides (N2O, NO2) caneffectively produce BN. So reducing the excited state ofboron or the additives, which can produce nitrogen oxidesespecially N2O and NO2 by thermolysis, will be beneficial inimproving the energy characteristics of boron containingpropellant burning.

5 References

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[6] T. B. Brill, P. J. Brush, and D. G. Patil, Thermal-Decomposi-tion of Energetic Materials. 60. Major Reaction Stages of ASimulated Burning Surface of NH4ClO4, Combust. Flame1993, 94, 70.

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[8] Gaussian 98, Revision A.7, M. J. Frisch, G. W. Trucks, H. B.Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G.Zakrzewshi, J. A. Montgomery, Jr., 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. Cibslowski, J. V. Ortiz, 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, W., B. G.Johnson, W. Chen, M. W. Wong, J. L. Andres, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian Inc,Pittsburgh, PA., 1998.

[9] J. L. Teffo, A. Chedin, Internuclear Potential and EquilibriumStructure of the Nitrous Oxide olecule from RovibrationalData, J. Mol. Spectrosc. 1989, 135, 389.

[10] H. Bredohl, I. Dubois, Y. Houbrechts, and P. Nzohabonayo,New Analysis of the A3Pi-X

3Pi Transition of BN, J. Mol.Spectrosc. 1985, 112, 430.

[11] K. P. Huber and G. Herzberg, Molecular Spectra and Mo-lecular Structure, Vol. IV, Constants of Diatomic Molecules,Van Nostrand Reinhold, New York, 1979.

[12] J. Yang, Y. Ren, A. Tian, and H. Sun, Compass Force Field for14 Inorganic Molecules, He, Ne, Ar, Kr, Xe, H2, O2, N2, NO,CO, CO2, NO2, CS2, and SO2, in Liquid Phases, J. Phys. Chem.B 2000, 104, 4951.

[13] E. D. Tidwell, E. K. Plyler, and W. S. Benedict, Vibration-Rotation Bands of N2O, J. Opt. Soc. Am. 1960, 50, 1243.

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Acknowledgements

The support from the National Natural Science Foundation ofChina (50176047) is gratefully acknowledged.

(Received September 9, 2003; Ms 2003/117)

Table 5. Total energies (Hartrees) and relative energies (in kJ/mol) of various species for the reaction BþNO2Species MP2/ MP2/ QCISD(T)/ G2MP2 DE

6-311G(d, p) 6-311þG(3df,2p) 6-311G(d, p) (Hartree) (kJ/mol)

B(4P)þNO2 �229.11554 �229.24216 �229.13819 �229.29676 0.00B(2P)þNO2 �229.22584 �204.78064 �229.26676 �229.43321 �358.23BNþO2 �229.21880 �229.34339 �229.26460 �229.42229 �329.57BNOO (IM4) �229.15473 �229.29660 �229.19656 �229.37369 �201.96trans-BNOO (IM5) �229.22167 �229.35890 �229.27398 �229.44528 �389.95trans-BNOO (TS3) �229.14059 �229.28323 �229.19467 �229.34898 �137.11

Ab Initio Calculation of BN Generation from Boron and Nitrogen Oxides 165

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