J . Phys. Chem. 1989, 93, 3130-3135
3130
Theoretical Study of Nitro-Nitrite Rearrangement of NH2N02 Roberta P. Saxon* Molecular Physics Laboratory, SRI International, Menlo Park, California 94025
and Megumu Yoshimine IBM AImaden Research Center, San Jose, California 95120-6099 (Received: July 26, 1988)
Calculations designed to determine the barrier height for nitro-nitrite rearrangement in N-NO, compounds are reported. Structures of NH2N02,the four isomers of N H 2 0 N 0 , dissociation products, and the transition state for nitro-nitrite rearrangement have been optimized at the MCSCF/4-31G level. The wave function of the transition state is characterized by two singly occupied orbitals and the geometry may be approximately described as separated NH2 and NO2 species with an N-N bond length of 2.845 A. Energies have been obtained by large-scale multireference single- and double-excitation CI calculations (6-31G* basis). The transition state is predicted to lie with (without) zero-point energy 40.70 (46.68) kcal/mol above NH2N02,0.15 kcal/mol above (0.87 kcal/mol below) the NH2 + NO2 asymptote and 22.03 (26.71) kcal/mol above the H-trans, NONO-cis NHzONO isomer, to which it leads. From these results, isomerization is expected to be competitive with N-N02 bond scission, as observed in recent experiments on thermal decomposition of dimethylnitramine [Stewart, Jeffries, Zellweger, McMillen, and Golden, J . Phys. Chem., in press].
Introduction The properties and decomposition kinetics of compounds containing the NO2 group have been extensively studied both theoretically1-8and e~perimentally~-”~ in recent years because of the high energy content of such molecules, interest in unimolecular bond cleavage to form radical pairs, and the serious theoretical challenges posed by such systems. In particular, a recent experimental investigationt0 of the thermal decomposition of dimethylnitramine (DMNA) (CH3)2NN02has determined the rate constant for DMNA disappearance, log k (s-l) = (13.5 f 0.6) - (37.7 f 1.5)/2.3RT. This temperature dependence is not consistent with the expected primary decomposition process, N-NO2 bond scission, which has both a larger A factor and a higher activation energy. Numerical modeling satisfactorily reproduces the observed temperature dependence and the observation of high yields of dimethylnitrosamine (DMNO) (CH3)*NN0 as the primary product only when rearrangement to give the nitrite form, (CH3)2NON0,is included as a competitive pathway. Furthermore, a subsequent e ~ p e r i m e n t in ’ ~which a molecular beam sampling system was used to examine directly the products of dimethylnitramine decomposition found that the initial products ( I ) Dewar, M. J. S.;Ritchie, J. P.; Alster, J. J . Org. chem. 1985, 50, 1031. (2) Turner, A. G.; Davis, L. P. J . Am. Chem. SOC.1984, 106, 5447. (3) McKee, M. L. J . Am. Chem. SOC.1986, 108, 5784 and references quoted therein. (4) Melius, C. F.; Binkley, J. S. Thermochemistry of the Decomposition of Nitramines in the Gas Phase. Presented at the 21st International Symposium on Combustion, Munich, Germany (August 1986). ( 5 ) Rodgers, S., personal communication. (6) Sumater. B. G.: ThomDson. D. L. J . Chem. Phvs. 1987. 86. 3301. (7j Ritciie, J. P. J . Am. Chem. SOC.1985, 107, lSi9. (8) Marynick, D. S.,Ray, A. K.; Fry, J L. Chem. Phys. Lett 1985, 116, 429 (9) Gonzalez, A. C.; Larson, C. W.; McMillen, D. F.; Golden, D. M. J . Phys. Chem. 1985, 89, 4809. (IO) Nigenda, S . E.; McMillen, D. F.; Golden, D. M. J . Phys. Chem., in press. (1 1) Lloyd, S. A,; Umstead, M. E.; Lin, M. E. J . Energetic Mater. 1985, 3, 187. (12) Wodtke, A. M.; Hintsa, E. J.; Lee, Y . T. J . Phys. Chem. 1986, 90, 3549. (13) Zhao, X.;Hintsa, E. J.; Lee, Y . T. J. Chem. Phys. 1988, 88, 801. (14) Stewart, P. H.; Jeffries, J. B.; Zellweger, J.-M.; Golden, D. M.; McMillen, D. J . Phys. Chem., in press. (15) Schroeder, M. A. Critical Analysis of Nitramine Decomposition Results: Some Comments on Chemical Mechanisms. Proc. 16th JANNAF Comb. Mtg., 1979, 2, 17. (16) Tsang, W.; Robaugh, D.; Mallard, W. G. J . Phys. Chem. 1986, 90, 5968.
0022-3654/89/2093-3130$01 SO10
include not only dimethylamino radical, (CH3)2N,and NO2, but also comparable amounts of NO and various fragment ions of the nitroxyl radical, (CH3),N0. The latter two are taken as direct evidence of nitro-nitrite rearrangement since the bond energy to release N O from the nitrite is expected to be small on the basis of previous calculation^^^^^ and present work, and by analogy to known C-ON0 compounds.’8 Experimental evidence for nitro-nitrite rearrangement in Cnitro compounds is provided by the work of Wodtke, Hintsa, and Lee’2 who applied RRKM theory to the data for C H 3 N 0 2to estimate a barrier height for isomerization to C H 3 0 N 0 slightly below the H3C-N02 bond dissociation energy. Evidence for nitro-nitrite rearrangement in nitrobenzene, Le., detection of C 6 H 5 0 H in the presence of a radical scavenger, has also been reported by two g r o ~ p s . ~ J ~ There is, to our knowledge, little theoretical study in the literature of nitro-nitrite rearrangement of nitramines. Melius has reported a barrier4 for rearrangement of N H 2 N 0 2that is higher in energy than the N H 2 NO2 dissociation limit but has cautioned” that the R H F model used may not be valid for the transition state. For methyl nitrate, McKee3 has optimized a transition state for rearrangement at the H F level, which produces a barrier significantly higher than the bond dissociation energy. He conjectures in this case, as well, that use of a multiconfigurational approach could affect the reported results. Although much of the published, ab initio work on NO,-containing molecules has relied on Hartree-Fock-based methods, it has been pointed 0 u t ~ 9that ~ proper description even of the ground state of the stable molecules requires including more than one configuration. The use of a multiconfigurational approach should have an even greater effect on the description of a transition state. In view of the experimental interest in decomposition of nitramines and evidence for isomerization as well as the lack of multiconfigurational treatments for this important class of compounds, we have undertaken ab initio calculations of nitro-nitrite rearrangement of N H 2 N 0 2 , the unsubstituted analogue of dimethylnitramine. Structures of the stable isomers as well as that of the transition state have been optimized at the MCSCF level by using analytic second derivatives. Large-scale configuration interaction (CI) calculations were performed at the optimized geometries for determinations of energy differences. In the next
+
(17) Melius, C. F., personal communication. (18) Batt, L.; Robinson, G. N. Thermochemistry of Nitro Compounds, Amines, and Nitroso Compounds. In Chemistry of Functional Groups: Supplement F , Patai, S . , Ed.; Wiley: Chichester, U.K., 1981; p 1035.
0 1989 American Chemical Society
Nitro-Nitrite Rearrangement of N H 2 N 0 2
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 3131
TABLE I: Optimized Geometrical Parameters for NH2N02 (in angstroms and degrees) MCSCF/ 4-31G' 1.418 1.227 0.991 123.3 126.6 113.8 116.7 178.1 16.8 164.9 3 1.9
RHF/
experimentc
6-31G*b 1.356 1.191 0.998 116.8 127.0 110.5 116.5 177.6 25.6 156.5 48.0
ref 25' ref 26 1.427 f 0.002 1.381 1.206 (assumed) 1.232 1.005 f 0.010 1.007 115.2 f 2 120.9 130.1 f 0.3 132.7 109.7 113.6 180.0
Nl-N2 N2-01 N1-H LH-N-H LOI-N2-02 LH-N 1-N2 LNl-N2-0 L02-N2-01-Nld LHI -N 1-N2-0Id ,!H2-N1-N2-01d (NHz)("Y energy, hartrees MCSCF/6-31G* -259.71268 -259.71665
51.8 f 1
TABLE 11: Optimized Geometrical Parameters of NH20N0 Isomers (in angstroms and degrees) H-cis," NONO-cis
46.9
'Eight-orbital active space, including one additional 0 lone pair orbital, was used for this optimization. bMelius, ref 17. 'Tyler, ref 25. "0, assumed coplanar. dTorsion angles. (Angle between NH, plane and N N bond.
section, the design of appropriate MCSCF and subsequent CI calculations is described. Results and Discussion are presented in the following section.
Calculations Geometries of the stable isomers, the dissociation products, and the transition state have been optimized at the MCSCF level by using analytic second derivatives with a standard 4-3 1G Gaussian basis set.Ig The active space of the MCSCF calculation was carefully chosen to include all the bonds involved in the rearrangement of NH2NOzto N H 2 0 N 0 . Following the discussion of Bauschlicher et aLzoon the design of MCSCF calculations for N204,two N-O bonds, two N-O antibonds, and analogously, four N-H bonding and antibonding orbitals were excluded from the active space. For the NH2N02isomer, for example, which has the four heavy atoms nearly coplanar, this leads to an eight-orbital active space consisting of the four 7 orbitals formed from the out-of-plane p orbitals on the heavy atoms and the following four u orbitals: two combinations of the in-plane lone pair p orbitals on the 0 ' s and the N-N bond and antibond pair. The eight-orbital MCSCF was used in the geometry optimization of the NHzN02 species. However, for MCSCF calculations on the NHzONO isomers, a seven-orbital active space converged far more readily. Furthermore, use of a seven-orbital active space does not change the description of N H 2 N 0 2because the lowest lying orbital in the original active space, one of the oxygen lone pairs, had an occupation number extremely close to 2.0. Therefore, geometry optimizations of N H 2 0 N 0 and the transition state were performed with the seven-orbital active space. Taking all possible distributions of 10 electrons within seven orbitals results in 196 configurations when no symmetry is considered. Energies were determined by multireference single- and double-excitation CI calculations with the standard 6-3 lG* basis set2] using MCSCF molecular orbitals. In constructing the CI expansions, the orbitals were divided into four spaces: frozen, inactive, composed of four orbitals, active, composed of seven orbitals as for the MCSCF, and external. The seven lowest occupied orbitals were kept doubly occupied. For the stable isomers, which have C, symmetry, test calculations in which only the four 1s orbitals were frozen, Le., in which the three highest frozen orbitals were transferred to the inactive space, were performed. For all CI calculations, the configuration list included all single and double excitations from the inactive and active spaces with at most one electron in the external space and all double excitations from the inactive and active spaces to the external space which differed by no more than two electrons from a set of reference configu-
MCSCF/ 4-31G 1.384 1.750 1.167 0.994 113.2 109.9 110.8 117.0 68.1 0 .O
N1-01 01-N2 N2-02 N1-H LH-N 1-01 LN 1-01-N2 LO 1-N2-02 LH 1-N 1-H2 LH-N 1-0 1-N2' L02-N 2-0 1-N 2' energy, hartrees MCSCF/6-31G* -259.70284 relative energy: 2.3 kcal/mol
-259.70225 2.6
H-trans, NONO-cis MCSCFJ4-31G N1-01 01-N2 N2-02 N1-H LH-N 1-01 LN 1-0 1-N2 LO 1-N2-02 LH1-Nl-H2 LH-N1-01-N2' L02-N2-01-N2' energy, hartrees MCSCF/6-3 l G * relative energy, kcal/mol
H-cis, NONO-trans MCSCF/4-31G 1.398 1.720 1.164 0.995 111.2 108.0 109.6 115.6 65.2 180.0
RHF/ RHF/ 4-31G 6-31G" 1.418 1.391 1.416 1.342 1.171 1.159 0.997 1.003 110.2 107.0 117.1 117.5 114.7 115.3 114.8 57.4 63.8 0.0 0.0
H-trans, NONO-trans MCSCF/ 4-31G'
1.403 1.714 1.159 0.996 109.5 107.6 113.0 115.2 116.4 0.0
1.413 1.675 1.164 0.996 108.1 105.5 109.1 114.3 117.9 180.0
-259.70644
-259.70584 0.4
0.0
RHF/ 6-31G'*b 1.393 1.356 1.153 1.002 104.5 108.7 110.2 123.5 180.0
"Orientation of H's with respect to N1-01 bond. *Melius, ref 17. CTorsionangles. With respect to H-(runs NONO-cis.
TABLE III: Optimized Geometrical Parameters for Dissociation Products (in angstroms and degrees) (MCSCF/4-31G) NH, MCSCF/ 4-31G
expt'
1.014 108.4
1.024 103.4
N-H LH-N-H
ref 29.
1.193 134.1
NO MCSCF/ 4-31G
'Herzberg
expt'
1.210 133.1
N-0 LO-N-0
NH2O
N-H N-0 LH-N-H LO-N-H-HE
NO2 MCSCF/ 4-31G
0.988 1.307 122.4 175.8
N-0
MCSCF/ 4-31G
exptb
1.166
1.151
* Huber and Herzberg, ref 30.
Torsion angle.
rations. Interacting space restrictions on the coupling were imposed for double excitations from the inactive space. The weight of the reference configurations in the C I wavefunctions was approximately 0.88 for all calculations. This resulted in C I expansions of 500000-900 000 configurations in C, symmetry and 1.8 million in C1symmetry. Calculations with the larger inactive space totalled 1-1.4 million configurations in C, symmetry. Preliminary geometry optimizations were carried out with the G A M E S S ~program; ~ final geometry determination^^^ and all other calculations used the ALCHEMY 1P4program system.
-
(22) Dupuis, M.; Wendoloski, J. J.; Spangler, D. Natl. Res. Comput. (19) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. (20) Bauschlicher, C. W.; Komornicki, A,; Roos, B. J . Am. Chem. SOC. 1983, 105, 745. (21) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acra 1973, 28, 213.
Chem. SoJtware Cur. 1980, 1 , QGOl.
(23) Page, M.; Saxe, P.; Adams, G. E.; Lengsfield 111, B. H. J . Chem. Phys. 1984, 81, 434. (24) Lengsfield 111, B. H . J . Chem. Phys. 1980, 73, 382. Lengsficld, B. H.; Liu, B. J . Chem. Phys. 1981, 75, 478. Liu, B.; Yoshimine, M. J . Chem. Phys. 1981, 74, 612.
Saxon and Yoshimine
3132 The Journal of Physical Chemistry, Vol. 93, No. 8, 1989
TABLE IV: Calculated Frequencies (cm-I) (MCSCF/C31G) and Zero-Point Energies (kcal/mol) for NHZNO2,NH20N0, and Dissociation Products
NH20NO‘ (H-trans, NONO-cis)
N H , N O ~ exptC
348.6
a’ a”
411.5
534.2 700.1 741.9 949.2
a”
a’ a’ a’
a”
b’
NONO-CIS
NH20No
692.5 797.9
950.9 1226.7 1344.6 1349.6 NO2 sym 1738.8 1558.1 NH2 bend 1748.5 1612.8 NO2 asym 3798.9 3359.3 NH2 sym 3981.9 3478.0 NH2 asym zero-pt energy 25.08
a’ a‘ a’ a”
NH2“
exptd
a’ a’
1663.1 1497 bend 3541.6 3219 sym a” 3661.7 3302 asvm zero-pt energy 12.68 ~~~
H-trans NONO-trans
a’
NO,” 746.8
a’ a” a’ a’ a’ a’
a’
227.9 1281.9 a” 1365.3 a’ 1833.7 NH2 bend a’ 3813.0 NH2 sym a“ 3989.7 NH; asym zero-pt energy 17.89 a’
expte
749.8
200.0 301.8 376.3 383.9 724.8 836.2 1132.3 a” 1386.3 NH20 a’ 1805.6 a’ 1856.0 a’ 3743.2 NH2 sym a” 3886.9 NH2 asym zero-pt energy 23.78 NH2O” a”
1239.8
a”
H-trans
628.5 401.5 484.5
bend
NO 1890.3
exptf 1904.2
(C)
Figure 1. MCSCF/4-31G optimized equilibrium geometry of NH2N02 and two NH20N0 isomers. (a) NH2N0,: N1, N2, 01, 0 2 are nearly coplanar. NH20NO: cis and trans are designated with respect to N101 bond. N1, N2, 01, 0 2 are strictly coplanar and bisect LHlNIH2. (b) H-trans NONO-cis. (c) H-trans NONO-trans.
Results and Discussion Structures of Stable Isomers. Geometrical parameters for N H 2 N 0 2 ,for the isomers of NH,ONO, and for the stable dissociation products, optimized at the MCSCF level, are given in Tables 1-111. Comparison with experimentally obtained geometries for the fragments is also given in Table 111. There are four isomers of the nitrite depending on whether the hydrogens and the terminal N O are placed cis or trans with respect to the central N O bond. The numbering of the atoms is illustrated in Figure 1. The four heavy atoms of the nitramine are nearly coplanar while the hydrogens are bent with respect to this plane by approximately 30’. For all four isomers of NH,ONO, the four heavy atoms are strictly coplanar and the hydrogens are symmetric with respect to the plane. There is a double bond between the terminal nitrogen and oxygen with a predicted bond length of 1.16-1.17 A. N H 2 0 N 0 is expected to dissociate readily to N H 2 0 + NO. Comparing 6-31G* MCSCF energies, the maximum energy difference between the isomers is 2.6 kcal/mol. Comparing RHF/6-3 lG* geometries and energies,” the isomers are found in a different order in energy, but the maximum spread is similar. Parameters obtained at the R H F level with the 6-31G* basis as well as those derived from analysis of microwave spectra25for NH2N02are also listed in Table I. A comparison with R H F results with both basis sets is given in Table I1 for the N H 2 0 N 0 isomer which has both the hydrogens and NONO-cis. In all cases, qualitatively similar geometries are predicted by both computational models. Examining the MCSCF and R H F parameters obtained with the same basis set in Table 11, it is clear that the 01-N2 bond is most dramatically affected by the MCSCF model, lengthening from the R H F prediction of 1.416 %I to the MCSCF value of 1.750 A. This is consistent with the dominant correlation in the MCSCF wave function for N H 2 0 N 0 being an excitation to an 01-N2 antibonding orbital. It is possible that the length of the 01-N2 bond is overestimated by the present MCSCF model
zero-pt energy 5.40 ‘Symmetry plane bisects LHNH. 6Symmetryplane bisects LONO. ‘Nonella, Muller, and Huber, ref 27, observed in Ar matrix. dJacox, ref 28. Herzberg, ref 29. fHerzberg, ref 30. which does not correlate all bonds to the same extent. A modest difference in geometry due to basis set in calculations at the R H F level is also illustrated in Table 11; the 6-31G* bond lengths are all shorter. The maximum difference is 0.07 A for the 01-N2 bond. In the nitramine, the MCSCF model has the largest effect on the N-N bond length, which is predicted to be 1.418 A as compared to 1.356 A at the RHF/6-31G* level. For this case, excitation to the N-N antibonding orbital is an important correlation contribution to the MCSCF wave function. In calculations on N H 2 N 0 2 where all atoms were constrained to be coplanar, MCSCF vs RHF optimization with the 4-31G basis set results in lengthening of the N-N bond by 0.07 %.,from 1.327 to 1.400 A. The MCSCF energy of the planar species is only 1.6 kcal/mol higher than that of the optimized geometry in Table I. The optimized geometry for N H 2 N 0 2is also compared in Table I with two ana lyse^^^,^^ of the same microwave data.25 The MCSCF result for the N-N bond length of 1.418 8, lies between the reported values of 1.42725and 1.381 A.26 The remaining geometrical parameters are in reasonable agreement with those derived from experiment. The greatest discrepancy is in the location of the hydrogens. The values derived from experiment for the angle between the NH, plane and the N-N bond are 5 1.8’, assuming N N 0 2 coplanar,25 or 46.9°26as compared with 31.9’ from the MCSCF optimization. As reported previously’ with the 3-21G basis and verified with the 4-31G basis in this work, optimizations at the R H F level with unpolarized basis sets erroneously predict a planar structure for N H 2 N 0 2 while the MCSCF/4-3 1G optimization results in a nonplanar geometry although with a smaller angle than derived from experiment. The position of the hydrogens, however, is expected to have little effect on the rearrangement process under investigation here. (26) Sadova, N. I.; Slepnev, G.E.; Tarasenko, N. A.; Zenkin, A. A,; Vilkov, L. V.; Shishkov, I . F.; Pankrushev, Yu.A. Zh. Strukt. Khim 1977,
( 2 5 ) Tyler, J . K. J. Mol. Spectrosc. 1963,11, 3 9 .
18, 8 6 5 .
The Journal of Physical Chemistry. Vol. 93, No. 8, 1989 3133
Nitro-Nitrite Rearrangement of NHzNOz H2
n
I
I
1
I
I
40
-
0
h
I
1
NHz ON0
NH2 N0-2
Transition state
-
Figure 2. MCSCF/4-3 1G optimized transition state for rearrangement of N H 2 N 0 2 to N H 2 0 N 0 (H-trans, NONO-cis).
TABLE V: Optimized Geometrical Parameters for NHzNOz NHzONO Transition State (in angstroms and degrees) (MCSCF/CJlG) and Vibrational Freauencies (cm-') geometry frequencies NI-N2 NI-01 N 2-0 1 N2-02 NI-H LO 1-N2-01 LH2-N I-H I LH2-NI-N2 LH 1-N 1-N2 LNI-N2-OI LNI-N2-02 L02-N2-01-NIn LH I-N l-N2-01" LH2-N 1-N2-0IR
2.845 3.214 1.212 1.207 1.014 133.1 108.3 96.3 110.3 96.4 111.1 126.9 102.5 9.7
(184.7i) 43.7 67.7 91.0 173.7 294.1 752.7 1324.4 1668.9 1728.0 3545.4 3664.1
-
NO2 bend NO2 sym N H 2 bend NO2 asym N H 2 sym N H 2 asym
"Torsion angle. Vibrational frequencies for N H 2 N 0 2 , NHzONO (H-trans, NONO-cis), and the dissociation products are reported in Table IV. Those modes that can be readily identified as motion of portions of the molecule are indicated in the table. In the nitramine, modes corresponding to all three modes of N H 2 and to the two NOz stretches are found, with frequencies from 2 to 8% (30-300 cm-l) larger than predicted for the separated fragments at the same level of calculation. Calculated frequencies for N H Z N O 2are compared with those observed2' in an Ar matrix in Table IV. For the identified modes, there is complete qualitative agreement with the calculated frequencies for the predominantly N H 2 modes larger by 11-14%. In the nitrite, the two N H z stretches and one antisymmetric mode similar to that of NHzO may be identified. The calculated N O and NOz frequencies are in excellent agreement with experiment. Frequencies for N H 2 are larger than experiment by 11%. Transition State. The geometry of the transition state for rearrangement of N H 2 N 0 2to the N H 2 0 N 0 (H-trans, NONOcis) isomer, which is the lowest energy NHzONO isomer in these calculations, is illustrated in Figure 2. The N1, H 2 , 0 1 , and N 2 atoms are nearly coplanar with the 0 2 above the plane and the H 1 extending below the plane. Optimized geometrical parameters and calculated harmonic frequencies are given in Table V. This is a true transition state with one imaginary frequency. The geometry may be approximately described as separated N H 2 and NO2 species with an angle between the planes of the triatomics of 159.5'. The Nl-N2 and N1-01 bonds are extremely long, 2.845 and 3.214 A, respectively, and the remaining relevant parameters have almost exactly the values given for the isolated species at the same level of calculation in Table 111. The average of the N 2 - 0 1 and N 2 - 0 2 bond lengths is the same as (27) Nonella, A.; Muller, R. P.; Huber, J. R.J . Mol. Spectrosc. 1985,112, 142. (28) Jacox, M. E. J . Phys. Chem. Ref.Data 1984, 13, 945. (29) Herzberg, G. Molecular Spectra and Molecular Structure. In Electronic Spectra ofPolvatomic Molecules; Van Nostrand: New York, 1966; ~. Vol. 111: (30) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. In Constants of Diatomic Molecules; Van Nostrand: New York, 1979; Vol. IV.
1.42
L
2.70 2.85
M - N ~(A)
3.20
1.85
2.30
.
2.76
2.30 Ni-01
1.85
1.40
(A)
Figure 3. Energy (kcal/mol) with respect to N H z N 0 2 (MCSCF/63 IG*) for path connecting NH2N02, transition state, and NH2ONO (H-truns, NONO-cis). Left side: For fixed Nl-N2 bond length as the reaction coordinate; all other geometrical parameters were optimized. Right side: N1-01 taken as reaction coordinate.
that in NOz with the N2-01 bond longer by 0.002 8, and the N2-02 bond correspondingly shorter. As indicated in Table V, all of the significant frequencies correspond strictly to internal motion of one fragment or the other. Frequencies differ by a t most 10 cm-' from those of the separated fragments listed in Table IV. Motions connecting the two halves of the molecule have extremely low frequencies. As would be expected for this loose combination of two radical species, the MCSCF wave function for the transition state is characterized by two singly occupied orbitals. This transition state could not have been located by a Hartree-Fock-based method. The geometry reported in Table V is identified as a transition state by the calculation of all zero gradients (c0.008 au) and one negative second derivative. The calculations illustrated in Figure 3 verify that this transition state does in fact connect the NH2NOZ and NHzONO (H-trans, NONO-cis) species, as claimed. The Nl-N2 bond distance is taken as the reaction coordinate for the left half of the plot describing the path between NH2NOZ and the transition state. Fixing the Nl-N2 bond length at particular distances between the value for NH2NOzand the transition state, the remaining geometrical parameters were optimized at the MCSCF/4-31G level. The relative energies shown in Figure 3 were obtained by subsequent MCSCF calculations with the 631G* basis. Analogous calculations were performed for the path between the transition state and the nitrite by using the N1-01 bond length as the reaction coordinate. The transition state is found to be the highest energy point between NHzNOzand the H-trans, NONO-cis nitrite isomer and to connect smoothly to both forms. At the geometry of the transition state, as shown in Figure 2, the N O N O may be described as trans with respect to the N1-01 bond. As the N1-01 bond is shortened to 2.76 (the first point to the right of the transition state in Figure 3), the N2-02 bond twists around N2-01 to form cis-NONO. The cis form is retained as the N1-01 bond is further shortened to form N H z O N O (H-trans, NONO-cis). The transition state does not lead to the H-trans, NONO-tram N H 2 0 N 0 isomer. The barrier to formation of that isomer is calculated (MCSCF/4-31G) to be 15 kcal/mol higher than the transition state. (We have considered only N H 2 0 N 0 isomers with the H's trans because they are approximately trans in the transition state.) Energies. Test calculations probing the effect of the size of the inactive mace in thl: C I expansion were performed taking advantage of ;he C, symmetry df the stable species. The energ; difference between one of the NH,ONO isomers (H-trans. NONO-trans) and NH2NOZ obtained with the seven orbital inactive space (denoted cI7)is compared with that from the four orbital inactive space (CI4) in Table VI. The Davidson correction3' for the effect of quadruple excitations, also listed in Table (31) Langhoff, S . R.; Davidson, E. R. Int. J . Quantum Chem. 1974.8, 61.
3134
The Journal of Physical Chemistry, Vol. 93, No. 8, 1989
TABLE VI: Energy Differences between NHZNOzand NHzONO (H-trans, NONO-trans) (6-31G* Basis Except As Noted) NH2NO2 total energy," hartrees MCSCF C17b C17D' C14b C14DC MCSCF C17 C17D
RHFf MP4f
NH2ONO (H-trans, NONO-lrans) total energy: hartrees
50 40
AE, kcal/mol 4.30 18.90 19.04 20.83 21.39
RHF/6-31G* -0.7 16 648 -1.284231 -1.357619 -0.647 174 -0.386 522
5.90 17.34 18.08 20.17 21.56
c
NH2+N02
n I I
I
I
I I
40.55
u -
NH2N02
40.70
T
I
Figure 4. Relative energies in kcal/mol (CI with Davidson correction and zero-point energies) for N H 2 N 0 2 ,N H 2 0 N 0 (H-trans, NONO cis) and dissociation products. The slightly larger zero-point energy of the transition state than of the asymptote accounts for the prediction of a transition-state energy larger than that of separated fragments.
With respect to -259.0 hartrees. bC17 (CI4) denotes CI with 7 (4) orbital inactive space (see text). C N H 2 N 0 2C, symmetry CI7, 1080 501 configurations; CI4, 597 551 configurations. d N H 2 0 N 0 C, symmetry C17, 1 445 944 configurations; C14, 816 400 configurations. FC17D (CI4D) denotes C17 (C14) with Davison correction for quadruple excitations. f6-31G** basis set. Melius, ref 17. I?
calculated zero-point energies in Table IV, the transition state is predicted to lie 40.70 kcal/mol above N H 2 N 0 2 ,at essentially the same energy as the N H 2 NO2 asymptote, 40.55 and 22.03 kcal/mol above N H 2 0 N 0 . The slightly larger zero-point energy of the transition state (1 1 real frequencies) than of the separated fragments accounts for the predictions of the transition-state energy 0.15 kcal/mol above that of the asymptote. The energy difference is not significant. Including zero-point energy, the energy to break the NH20-NO bond is 11.1 1 kcal/mol. Discussion. In the following discussion, we assume the results obtained here for the unsubstituted nitramine can be applied directly to dimethylnitramine, which has been studied experimentally. This appears to be a reasonable assumption for isomerization and bond dissociation in that the hydrogens remain as spectators in both processes. Because the frequencies of the transition state are very similar to those of the separated products, consideration of zero-point energy will not affect the conclusion that within the uncertainty of the calculation; the barrier to nitro-nitrite rearrangement is the same as the energy to break the N-N02 bond. Furthermore, the A factors for isomerization and bond scission should also be quite similar, leading to the prediction that the two paths should compete quite evenly. This in agreement with the conclusion from the molecular-beam-sampled experimentI4 on DMNA that the rearrangement/N-NO, bond scission branching ratio (at ca. 900 K) is -0.7. While the present results are in qualitative agreement with the inference of the importance of nitro-nitrite rearrangement in explaining the observed temperature dependence in the earlier decomposition study,IOthey do not support the assumption of a small A factor and of an isomerization barrier 15 kcal/mol below the bond dissociation energy required by the kinetic model.10
+
VI, should provide a reasonable estimate in these calculations because the weight of the reference configurations is very similar in all of the wave functions. The energy difference of 21.39 kcal/mol obtained from the CI4 calculations with the Davidson correction is in reasonable agreement with the value of 19.04 kcal/mol from the larger CI, justifying the use of the four-orbital inactive space for the transition state for which there is no symmetry to reduce the size of the CI expansion. A comparison between the energy difference at the MCSCF/4-3 1G and RHF/6-3 lG* optimized geometries is also provided in Table VI. At the same level of calculation (CI7), the difference in energy difference due to geometry is only 1 kcal/mol. In addition, at the R H F geometry, we compare the energy difference from the present CI calculations to that previously obtained by Melius and Binkley4J7 with a perturbation-theory approach (MP4/6-3 1G**). For these closed-shell isomers, a difference in prediction of 3.5 kcal/mol is found. The final results of our study are presented schematically in Figure 4 and numerically in Table VII, which lists C I energies for the transition state, the N H 2 NO2 and N H 2 0 N O asymptotes, and the N H 2 0 N 0 (H-trans, NONO-cis) isomer to which the transition state leads, at MCSCF/4-3 1G optimized geometries. First, comparing calculated total energies, the transition state is predicted to lie 46.68 kcal/mol above NH2N02, 0.87 kcal/mol below the asymptote, and 26.71 kcal/mol above the H-trans, NONO-cis nitrite isomer. The N H 2 0 + N O asymptote is found 14.30 kcal/mol above N H 2 0 N 0 . Including the
+
r
I
MCSCF/4-3 IG Geometry -0.7 12 682 -0.705 836 -1.283 697' -1.253 592d -1.360033 -1.329 993 -1.129360' -1.096 175d -1.177215 -1.143 141 Geometry -0.707 247 -1.256 609 -1.328 820 -0.615038 -0.352 174
Saxon and Yoshimine
+
TABLE VII: Calculated Total Energies (hartrees), Zero-Point Energies (kcal/mol), and Relative Energies (kcal/mol) with Respect to NH2N02 for Transition State, Asymptotes, and NHzONO (6-31G* Basis, MCSCF/4-31G Optimized Geometry) total energies" structure
MCSCF
transition state N H 2 NO2 N H 2 0 N 0 (H-frans, NONO-cis) NHzO N O
-0.658 889 -0.656 990 -0.706 436 -0.693 929
+
+
structure transition state NH2 NO2 N H 2 0 N O (H-trans, NONO-cis) NHlO + NO N H 2 0 + NO (with respect to N H 2 0 N O )
+
MCSCF 33.77 34.96 3.92 1 1.77 7.85
CI4
C14 49.57 50.13 19.49 30.65 11.16
C14Db
zero-pt energy
-1.050 382 -1.102852 19.10 -1.049 494 -1.101 460 18.08 -1.098 305 -1. I45 406 23.78 -1.080531 -1.122 618 20.59 relative energies with zero-pt energies MP4'*d (BAC) C14Db MP4C C14Db MP4 46.68 40.70 47.55 50.74 40.55 42.43 47.91 19.97 20.52 18.67 18.85 19.25 34.27 36.37 29.78 30.70 14.30 15.84 11.11 11.84 14.6
" With respect to -259.0 hartrees. bDefined in Table VI.
