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An ab initio study of some nitramine molecules
Journal of Molecular
Structure
Elsevier Science Publishers
(Theochem),
279 (1993) 291-297
291
B.V., Amsterdam
An ab initio study of some nitramine molecules David M. Zirl and Theodore Vladimiroff US Army Armament,
Research,
Development
and Engineering
Center, Picatinny Arsenal, NJ 07806
(USA)
(Received 4 June 1992)
Abstract Ab initio self-consistent field (SCF) molecular orbital calculations have been performed for a series of nitramine molecules. Calculations were conducted on trinitramine, methyldinitramine, methylchloronitramine and trimethylamine using Pople’s 6-31G and 6-31G* basis sets. Gas phase geometries for these molecules were determined by a minimum energy criterion using gradient techniques. The results are in qualitative agreement with the geometries derived from electron diffraction studies and microwave spectroscopy. The extra-long N-N bonds in methyldinitramine and methylchloronitramine were not computed accurately at the SCF level of theory and it was shown that these bonds become longer if electron correlation is included at the second-order Moller-Plesset level. Computations were performed for the heat of formation for trinitramine using Pople’s isodesmic reaction concept and compared with a value obtained using an additivity rule.
Introduction
As has been pointed out [ 11,nitramine structures are interesting because they contain adjacent electron donor and electron acceptor groups. The molecular geometry around the central nitrogen atom can be either planar or pyramidal. Several structures of this type of molecule have been determined in the gas phase using electron diffraction techniques [l-4] and microwave spectroscopy [5]. The N-N bond becomes particularly long as electronegative substituents are added to the central nitrogen atom [4]. The structures of nitramine molecules have been extensively studied using both the semiempirical [6-91 and ab initio [lo-151 methods. However, as the molecules become larger, it becomes more expensive to perform ab initio calculations using large basis sets so there is a sharp decline in studies using 6-3 1G and 6-3 lG* basis sets. The present study was undertaken in order to Correspondence to: T. Vladimiroff, U.S. Army Armament, Research, Development and Engineering Center, Picatinny Arsenal, NJ 07806, USA.
determine if basis sets of this size could predict the structure of nitramine compounds and shed some light on the structure and stability of the hypothetical trinitramine molecule.
Method
The GAMES [16] program was used to compute ab initio self-consistent field (SCF) molecular orbital wavefunctions for some nitramine-based molecules. Minimum energy configurations were determined for trinitramine N40,, methyldinitramine (MDN), methylchloronitramine (MCN) and trimethylamine (TMA) using 6-3 1G and 6-3 lG* basis sets with the restricted Hartree-Fock (RHF) method. The structures for N40, and MCN were further refined by including the second-order Moller-Plesset (MP2) many-body perturbation energy at the 6-31G* level. Because GAMES will not calculate gradients at this level of theory, only the N-N bond lengths were varied, leaving the rest of the molecular geometry as determined at the SCF 6-3 1G* level.
0166-1280/93/$06.000 1993 Elsevier Science Publishers B.V. All rights reserved.
292
D.M. Zirl and T. VladimirofflJ.
Mol. Strut.
(Theochem)
279 (1993) 291-297
TABLE 1 Minimum energy configurations
6-31G
Parameter N-C
1.452 1.094 1.082 1.762
C-H C-H H-H C-N-C H-C-N H-C-N H-C-H H-C-H C-N/C-N-C Sumb
for trimethylamine”
plane
Energy (au.)
6-31G* 1.445 1.095 1.084 1.764
Experimental 1.451 1.109 1.088 1.767
114.2 113.0 109.7 108.1 108.0
111.9 113.0 109.8 108.1 107.9
110.9 111.7 110.1 108.1 108.6
40.9 334.7
48.1 335.8
50.9 332.8
- 173.190
- 173.269
[3]
_t 0.003 _t 0.008 + 0.008 (assumed)
& 0.6 + 0.7 * 0.5 f 0.5 c 0.8
a Bond lengths in angstroms; bond angles in degrees. b Sum of angles around the central nitrogen atom.
Results and discussion The structure of TMA was determined by Wollrab and Laurie [17] using microwave spectroscopy. Ab initio geometry calculations using smaller basis sets have been conducted [ 18,191 for this molecule, but no geometry calculations using larger basis sets were found in the literature. Atomic coordinates derived from experiment were used as the initial geometry and all geometric parameters were optimized using the 6-31G and 63 lG* basis sets. The results are reported in Table 1. The smaller basis set produced satisfactory bond lengths, but the geometry around the central nitrogen atom was not quite right. The C-N-C angle was too large and the third methyl group protruded from the C-N-C plane by 40.9”, rather than the experimental value of 50.9’. The minimum energy configuration at the 6-31G* level was in close agreement with the experimental data. The bond distances were within 0.01 A and the bond angles within lo. The C-N-C angle was slightly larger than the experimental value and the methyl groups protruded at an angle of 48.1” from the C-N-C plane, compared to the 50.9” observed in the experimental data. The assumed
H-H distance was well reproduced at both levels of theory. Dimethylnitramine (DMN) has been extensively studied by Cordell [111.Calculations were reported using 4-2 1NO* and 6-31G* basis sets. The molecule was found to be non-planar. The MDN structure was determined by Tarasenko et al. [4], using electron diffraction. It was found that this molecule is also non-planar with N-N bonds which are 0.1 A longer than in dimethylnitramine [2]. The MDN molecule was studied at both the semiempirical [6] and ab initio [14] levels, although complete structures were not published. The current calculations for MDN are reported in Table 2. MDN was found to be almost planar using the smaller basis set and a little less planar using the 6-31G* basis set. The bond angles around the central nitrogen atom total 359.36” and 355.42” respectively. At the 6-3 1G* level the angle between the C-N bond and the N-N-N plane was 22”. This angle was less than the value derived from diffraction experiments [4] and less than the 55” computed using the semiempirical MIND0 and CNDO-BW techniques [6] (Boyd-Whitehead (BW) as defined in ref. 6). The bond lengths and other geometric parameters from the 6-31G* computations also
293
D.M. Zirl and T. VladimiroffjJ. Mol. Struct. (Theochem) 279 (1993) 291-297 TABLE 2 Minimum energy configurations Parameter
6-31G*
1.383 1.484 1.230/1.210’ 1.072/1.078’
N-N-N N-N-C O-N-O N-N-O N-N-O N-C-H H-C-H
Energy (a.u.)
:
6-31G
N-N N-C N-O C-H
C-N/N-N-N Sumb
for methyldinitramine”
plane
Experimental
1.395 1.416 1.177/1.189’ 1.073/1.081’
122.0 118.7 125.1 114.0 120.8 110.3/107.4’ 110.5/l 10.7
121.8 116.8 126.6 112.8 120.6 110.3/106.5” 110.8/l 11.3’
8.1 359.4
21.9 355.4
- 501.783
- 502.075
[4]
1.480 ) 0.005 1.494 & 0.006 1.231 k 0.003 117.0 + 1.1 107.5 & 1.5 132.0 f 1.0
42.2 f 2.0
aBond lengths in angstroms; bond angles in degrees. bSum of angles around the central nitrogen atom. “Different values of this geometric parameter
were found to
approach those inferred from electron diffraction studies [4]. The N-N bonds were found to be shorter than the experimental values although there was a slight improvement on going to the larger basis set. The effect of the addition of an electronegative substituent does not seem to be well described at this level of theory. The structure of MCN was otained from electron diffraction by Sadova et al. [3]. The results are reported in Table 3. The substitution of Cl for the NO, group in MDN to form MCN resulted in an almost planar molecule at the 6-31G level, but a puckered molecule at the 6-3 lG* level. In the latter case, the angles subtended at the central nitrogen atom added to 344”, which was in fair agreement with the 335” derived from the electron diffraction study [3]. The CH3 group protruded with an angle of 38.8“from the N-N-Cl plane, compared to 46.1” from the electron diffraction work. The long N-N bond observed in MCN was not calculated accurately at this level of theory. The N406 molecule was considered next. To our knowledge there has not been much work reported
occur in this molecule. on this substance, which would constitute another possible oxide of nitrogen, although there has been some speculation as to its heat of formation [20]. The structure of this molecule is not known. As noted in Table 4, our calculations indicate that this molecule is planar at both levels of theory. The addition of the d polarization functions at the 631G* level resulted in longer N-N bonds than at the 6-3 1G level, but planarity was still maintained. The ab initio energy values (see Tables l-4) were used to estimate the heat of formation for N.,06 using Pople’s isodesmic reaction principle [21]. An isodesmic reaction is one in which the number of formal chemical bonds and the number of electron pairs are conserved despite transformations where the relationships among the bonds are altered. For the current computations the isodesmic reaction took the form N-(NO&
+ N-(CH,),
+ (CHs L-N-(NO,
+ (CH,)-N-(NO,), )
(1)
There are three N-N bonds and three C-N on each side of eqn. (l), but from the left side to the
294
D.M. Zirl and T. Vladimiroff/J.
Mol. Struct.
(Theochem)
279 (1993) 291-297
TABLE 3 Minimum energy configurations
for methylchloronitramine”
Parameter
6-31G
N-N N-N (MP2) N-Cl N-C N-O
1.335 1.749 1.466 1.239/1.223’ 1.223 1.078/l .075/l .079
C-H N-N-C N-N-Cl C-N-Cl O-N-O N-N-O N-N-O N-C-H H-C-H C-N/N-N-Cl Sum’
6-31G*
120.7 118.2 121.1 125.1 115.5 119.4 109.7/107.0/110.1d 110.1/109.7/110.2d
1.72 _+0.004 1.478 + 0.005 1.209 f 0.002
1.076/1.078/1.083d 112.9 108.4 115.0 128.5
.360.0
38.8 344.2
46.1 + 1.3b 336.3 * 4.0
- 757.320
- 757.519
1.5
[3]
1.469 + 0.005
1.380 1.440 1.698 1.472 1.193/1.183d
115.9 113.9 114.5 126.7 115.0 118.1 108.5/106.3/111.7d 109.7/l 10.3/l 10.2d
plane
Energy (a.u.)
Experimental
+ + * +
1.5 1.3 1.2 0.9b
a Bond lengths in angstroms; bond angles in degrees. bRef. 4. ‘Sum of angles around the central nitrogen atom. dDifferent values of this geometric parameter were found to occur in this molecule.
right side of eqn. (l), there is a change in the number of each type of bond within each molecule. The energy difference between the two sides of the equation can be used to compute the heat of formation of an unknown component by formulating an TABLE 4 Minimum energy configuration
for N40ea
6-31G N-N N-N (MP2) N-O N-N-N O-N-O N-N-O Sumb Energy (a.u.)
6-31G*
1.464 1.540 1.205
1.466 1.169
120.0 125.8 117.1 360.0
120.0 127.7 116.1 360.0
- 665.985
- 666.405
a Bond lengths in angstroms; bond angles in degrees. b Sum of angles around the central nitrogen atom.
equation similar to eqn. (l), but with heats of formation instead of the SCF energies. Table 5 shows the calculation for the heat of formation of the unknown N406 based on this isodesmic reaction. The heats of formation for MDN, DMN and TMA were obtained from refs, 20,22 and 23 respectively. The heat of formation for N,O, is estimated to be 96 kcalmol-’ at the 6-31G level and 80 kcal mol-’ at the 6-31G* level. Leroy et al. [14] have suggested a correction be applied to the semiempirical heat of formation obtained with the smaller basis set: AH(exp) = - 2.111 + 0.942AH(sem)
(2)
where AH(exp) and AH(sem) are the experimental and semiempirical heats of formation respectively. The use of eqn. (2) reduces the 96 kcalmol-’ to 88 kcal mol-’ , bringing this value into closer agreement with the value obtained using the larger basis set. Miroshnichenko et al. used additivity rules to obtain an estimate of 38 kcalmol-’ [20].
D.M. Zirl and T. VladimirofsIJ. Mol. Struct. (Theochem) 279 (1993) 291-297 TABLE 5 Heat of formation
computation
Isodesmic equation N-(NO,), + N-(CH,), + (CH,),-N-NO2
for trinitraminea
+ H,C-N-(NO,),
Energy difference X = E(N406) + E(TMA) - [E(MDN) + E(DMN)] X (6-3 1G) = 79 kcal mol- ’ X (6-3 1G*) = 63 kcal mol-’ Heat of formationb H(N406) = X - H(TMA) + [H(MDN) + H(DMN)] H(N406) = X- (-5.66) + [12.78 + (- 1.79)] H(N406) (6-31G) = 96 kcalmol-’ H(N406) (6-31G*) = 80 kcalmol-’ aX, energy difference; E, minimum energy (see Tables l-4); H, heat of formation. bSee text for references for heats of formation.
There are a number of sources of error in these heat of formation computations. The isodesmic procedure assumes the approximate cancellation of not only the basis set effects and correlation effects, but also of the zero-point energy and thermal corrections. Better overall agreement between the heat of formation calculations and the 6-3 1G and 631G* basis set calculations has previously been attained [ 141,but only smaller molecules were considered. The fact that the N-N bond is not calculated accurately in this work may also be a source of error. The larger basis set should result in overall smaller errors, but not necessarily more complete cancellation of errors. Finally the computations for DMN at the 6-31G* level [l l] employed “d” functions which were composed of two displaced “p” functions rather than the more conventional type of “d” polarization basis sets, which may lead to a less constant error. The estimation of the heats of formation based on the additivity rules may not be very accurate because the system is not very linear and a rather large interaction term between the nitro groups had to be assumed. Using the computed heats of formation for N,O,, an estimate of the N-N bond strength can be
295
made. The molecule has only two types of bond: N-N and N-O. The energy of formation of the dissociated atoms is 809 kcal mol-’ , based on the energy of the gaseous atoms found in ref. 22. Subtracting the estimates for the heats of formation and for the strength of the six N-O bonds (113 kcal mol-’ each [24]), results in the bond strength for the three N-N bonds. This computation produces an estimate of the N-N bond strength in N406 of 14 kcalmoll’ with the 6-31G basis set and 17 kcal mol-’ with the 6-31G* basis set. This compares with the estimate of 17 kcal mol-’ obtained by Miroshnichenko et al. 1201.In order for these authors to obtain this value based on their estimation of the heat of formation, they must have assumed an unreasonably high value for the N-O bond strength. There seems to be a fundamental difference between the C-N bonds in trimethylamine, which are well described at the 6-3 lG* level of theory, and the N-N bonds which are not. The two possible sources of error are that the basis set is not large enough or that electron correlation effects are not included. To investigate the latter possibility, many-body perturbation theory was used at the MP2 level. Since GAMES will not optimize geometries at this level of theory, the molecular geometry was frozen at the 6-31G* level and only the N-N bond lengths were varied. Figure 1 shows the total energy of MCN as a function of the N-N distance for the MP2/6-31G* calculation. The minimum occurs at 1.44A, which is closer to the experimental value of 1.469 A than the SCF N-N bond length. Figure 2 illustrates the energy of the N406 molecule as a function of the N-N bond lengths at the MP2/ 6-31G* level. The minimum energy in this curve corresponds to an N-N distance of 1.556 A. At the MP2 level, two-thirds of the difference between the SCF and experimental bond lengths is recovered for MCN. If the same percentage of recovery is assumed for N406 then the N-N bond length for this molecule can be estimated to be 1.601 A. This value can be compared with the N-N bond length of 1.76A [24] in dinitrogen tetroxide.
D.M. Zirl and T. VladimiroffjJ. Mol. Struct. (Theochem)
296
279 (1993) 291-297
Conclusions
1
-758.4755 t. 1.40
1.42
1.44 N-N distance
1
1.46
1.41
(A)
Fig. 1. Energy for methylchloronitramine 31G* level as a function of N-N distance.
at the MP2/6-
The structure of trimethylamine, methyldinitramine, methylchloronitramine and trinitramine were investigated using the 6-3 1G and 6-3 1G* basis sets. Although the structure of trimethylamine is well described at the SCF level of theory, the same cannot be said for the nitramines considered in this study. The calculated N-N bonds are too short and the geometry around the central nitrogen atom has a tendency to be too flat when compared with the experimental structures. Many-body perturbation theory at the MP2 level had to be used to recover about two-thirds of the difference between the SCF and experimental N-N bond lengths. However, when the results were combined with experimental values, reasonable estimates could be made for the N-N bond length and strength and for the heat of formation in N406. Acknowledgments
This research was partly funded by the Army High Performance Computing Research Center at the University of Minnesota under the Army Research Office contract number DAAL03-89-C0038. The authors are grateful for the generous use of computer time on the Cray Y-MP/6128 at the US Army Waterways Experiment Station, Vicksburg, MS, and on the Cray X-MP/48 at the US Army Ballistic Research Laboratory, Aberdeen Proving Grounds, MD. References
-668.2071 A 1.52
1.53
1.54
1.55
1.56
1.57
I I.58
N-N distance (A)
Fig. 2. Energy for N,O, at the MP2/6-31G* function of N-N distance.
level as a
I.F. Shishkov, L.V. Vilkov and I. Hargittai, J. Mol. Struct., 248 (1991) 125. R. Stolevik and P. Rademacher, Acta Chem. Stand., 23 (1969) 672 N.I. Sadova, G.E. Slepnev, N.A. Tarasenko, A.A. Zenkin, L.V. Vilkov, I.F. Shishkov and Yu.A. Pankrushev, Zh. Strukt. Khim., 18 (1977) 865. N.A. Tarasenko, L.V. Vilkov, G.E. Slepnev and Yu.A. Pankrushev, Zh. Strukt. Khim., 18 (1977) 953. J.K. Tyler, J. Mol. Spectrosc., 11 (1963) 39. K.Ya. Burshtein and I.N. Fundyler, Izv. Akad. Nauk, (1974) 892. A.R. Farminer and G.A. Webb, J. Mol. Struct., 27
D.M. Zirl and T. Vladimiroff/J.
12 13 14
15 16
Mol. Struct.
(Theochem)
279 (1993) 291-297
(1975) 417. A.V. Belik, SK. Bakeeva and V.A. Shlyapochnikov, Izv. Akad. Nauk, (1977) 2608. V.P. Ivshin, O.A. Yashukova and V.A. Shlyapochnikov, Izv. Akad. Nauk, (1986) 1295. M Picard, M. Blain, S. Odiot and J.M. Leclercq, J. Mol. Struct. (Theochem), 139 (1986) 221. F.R. Cordell, An ab initio study of dimethyl nitramine, Masters Thesis, The University of Texas at Austin, 1987. P. Politzer, N. Sukumar, K. Jayasuriya and S. Ranganathan, J. Am. Chem. Sot., 110 (1988) 3425. R.P. Saxon and M. Yoshimine, J. Phys. Chem., 93 (1989) 3130. G. Leroy, M. Sana, C. Wilante, D. Peeters and S. Bourasseau, J. Mol. Struct. (Theochem), 187 (1989) 251. D. Habibollahzadeh, J.S. Murray, PC. Redfern and P. Politzer, J. Phys. Chem., 95 (1991) 7702. M.W. Schmidt, K.K. Baldridge, J.A. Boatz, J.H. Jensen, S. Koseki, M.S. Gordon, K.A. Nguyen, T.L. Windus and ST. Elbert, QCPE Bull., 10 (1990) 52-54.
291
J.E. Wollrab and V.W. Laurie, J. Chem. Phys., 51 (1969) 1580. 18 I. Carmichael, J. Phys. Chem., 90 (1986) 2057. 19 W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986, p. 330. L.I. Korchatova, B.L. Kor20 E.A. Miroshnichenko, sunskii, B.S. Fedorov, Yu. D. Orlov, L.T. Eremenko, Yu.A. Lebedev and F.I. Dubovitskii, Dokl. Akad. Nauk SSSR, 295 (1987) 419. 21 Ref. 19, p. 271. 22 J.D. Cox and D. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, New York, 1970, p. 527. 23 D.R. Stull, E.F. Westrum and G.C. Sinke, The Chemical Thermodynamics of Organic Compounds, Wiley, New York, 1969. 24 CODATA recommended key values for thermodynamics, J. Chem. Thermodyn. 8 (1976) 603. 25 A. Kvick, R.K. McMullan and M.D. Newton, J. Chem. Phys., 76 (1982) 3754. 17
Structure
Elsevier Science Publishers
(Theochem),
279 (1993) 291-297
291
B.V., Amsterdam
An ab initio study of some nitramine molecules David M. Zirl and Theodore Vladimiroff US Army Armament,
Research,
Development
and Engineering
Center, Picatinny Arsenal, NJ 07806
(USA)
(Received 4 June 1992)
Abstract Ab initio self-consistent field (SCF) molecular orbital calculations have been performed for a series of nitramine molecules. Calculations were conducted on trinitramine, methyldinitramine, methylchloronitramine and trimethylamine using Pople’s 6-31G and 6-31G* basis sets. Gas phase geometries for these molecules were determined by a minimum energy criterion using gradient techniques. The results are in qualitative agreement with the geometries derived from electron diffraction studies and microwave spectroscopy. The extra-long N-N bonds in methyldinitramine and methylchloronitramine were not computed accurately at the SCF level of theory and it was shown that these bonds become longer if electron correlation is included at the second-order Moller-Plesset level. Computations were performed for the heat of formation for trinitramine using Pople’s isodesmic reaction concept and compared with a value obtained using an additivity rule.
Introduction
As has been pointed out [ 11,nitramine structures are interesting because they contain adjacent electron donor and electron acceptor groups. The molecular geometry around the central nitrogen atom can be either planar or pyramidal. Several structures of this type of molecule have been determined in the gas phase using electron diffraction techniques [l-4] and microwave spectroscopy [5]. The N-N bond becomes particularly long as electronegative substituents are added to the central nitrogen atom [4]. The structures of nitramine molecules have been extensively studied using both the semiempirical [6-91 and ab initio [lo-151 methods. However, as the molecules become larger, it becomes more expensive to perform ab initio calculations using large basis sets so there is a sharp decline in studies using 6-3 1G and 6-3 lG* basis sets. The present study was undertaken in order to Correspondence to: T. Vladimiroff, U.S. Army Armament, Research, Development and Engineering Center, Picatinny Arsenal, NJ 07806, USA.
determine if basis sets of this size could predict the structure of nitramine compounds and shed some light on the structure and stability of the hypothetical trinitramine molecule.
Method
The GAMES [16] program was used to compute ab initio self-consistent field (SCF) molecular orbital wavefunctions for some nitramine-based molecules. Minimum energy configurations were determined for trinitramine N40,, methyldinitramine (MDN), methylchloronitramine (MCN) and trimethylamine (TMA) using 6-3 1G and 6-3 lG* basis sets with the restricted Hartree-Fock (RHF) method. The structures for N40, and MCN were further refined by including the second-order Moller-Plesset (MP2) many-body perturbation energy at the 6-31G* level. Because GAMES will not calculate gradients at this level of theory, only the N-N bond lengths were varied, leaving the rest of the molecular geometry as determined at the SCF 6-3 1G* level.
0166-1280/93/$06.000 1993 Elsevier Science Publishers B.V. All rights reserved.
292
D.M. Zirl and T. VladimirofflJ.
Mol. Strut.
(Theochem)
279 (1993) 291-297
TABLE 1 Minimum energy configurations
6-31G
Parameter N-C
1.452 1.094 1.082 1.762
C-H C-H H-H C-N-C H-C-N H-C-N H-C-H H-C-H C-N/C-N-C Sumb
for trimethylamine”
plane
Energy (au.)
6-31G* 1.445 1.095 1.084 1.764
Experimental 1.451 1.109 1.088 1.767
114.2 113.0 109.7 108.1 108.0
111.9 113.0 109.8 108.1 107.9
110.9 111.7 110.1 108.1 108.6
40.9 334.7
48.1 335.8
50.9 332.8
- 173.190
- 173.269
[3]
_t 0.003 _t 0.008 + 0.008 (assumed)
& 0.6 + 0.7 * 0.5 f 0.5 c 0.8
a Bond lengths in angstroms; bond angles in degrees. b Sum of angles around the central nitrogen atom.
Results and discussion The structure of TMA was determined by Wollrab and Laurie [17] using microwave spectroscopy. Ab initio geometry calculations using smaller basis sets have been conducted [ 18,191 for this molecule, but no geometry calculations using larger basis sets were found in the literature. Atomic coordinates derived from experiment were used as the initial geometry and all geometric parameters were optimized using the 6-31G and 63 lG* basis sets. The results are reported in Table 1. The smaller basis set produced satisfactory bond lengths, but the geometry around the central nitrogen atom was not quite right. The C-N-C angle was too large and the third methyl group protruded from the C-N-C plane by 40.9”, rather than the experimental value of 50.9’. The minimum energy configuration at the 6-31G* level was in close agreement with the experimental data. The bond distances were within 0.01 A and the bond angles within lo. The C-N-C angle was slightly larger than the experimental value and the methyl groups protruded at an angle of 48.1” from the C-N-C plane, compared to the 50.9” observed in the experimental data. The assumed
H-H distance was well reproduced at both levels of theory. Dimethylnitramine (DMN) has been extensively studied by Cordell [111.Calculations were reported using 4-2 1NO* and 6-31G* basis sets. The molecule was found to be non-planar. The MDN structure was determined by Tarasenko et al. [4], using electron diffraction. It was found that this molecule is also non-planar with N-N bonds which are 0.1 A longer than in dimethylnitramine [2]. The MDN molecule was studied at both the semiempirical [6] and ab initio [14] levels, although complete structures were not published. The current calculations for MDN are reported in Table 2. MDN was found to be almost planar using the smaller basis set and a little less planar using the 6-31G* basis set. The bond angles around the central nitrogen atom total 359.36” and 355.42” respectively. At the 6-3 1G* level the angle between the C-N bond and the N-N-N plane was 22”. This angle was less than the value derived from diffraction experiments [4] and less than the 55” computed using the semiempirical MIND0 and CNDO-BW techniques [6] (Boyd-Whitehead (BW) as defined in ref. 6). The bond lengths and other geometric parameters from the 6-31G* computations also
293
D.M. Zirl and T. VladimiroffjJ. Mol. Struct. (Theochem) 279 (1993) 291-297 TABLE 2 Minimum energy configurations Parameter
6-31G*
1.383 1.484 1.230/1.210’ 1.072/1.078’
N-N-N N-N-C O-N-O N-N-O N-N-O N-C-H H-C-H
Energy (a.u.)
:
6-31G
N-N N-C N-O C-H
C-N/N-N-N Sumb
for methyldinitramine”
plane
Experimental
1.395 1.416 1.177/1.189’ 1.073/1.081’
122.0 118.7 125.1 114.0 120.8 110.3/107.4’ 110.5/l 10.7
121.8 116.8 126.6 112.8 120.6 110.3/106.5” 110.8/l 11.3’
8.1 359.4
21.9 355.4
- 501.783
- 502.075
[4]
1.480 ) 0.005 1.494 & 0.006 1.231 k 0.003 117.0 + 1.1 107.5 & 1.5 132.0 f 1.0
42.2 f 2.0
aBond lengths in angstroms; bond angles in degrees. bSum of angles around the central nitrogen atom. “Different values of this geometric parameter
were found to
approach those inferred from electron diffraction studies [4]. The N-N bonds were found to be shorter than the experimental values although there was a slight improvement on going to the larger basis set. The effect of the addition of an electronegative substituent does not seem to be well described at this level of theory. The structure of MCN was otained from electron diffraction by Sadova et al. [3]. The results are reported in Table 3. The substitution of Cl for the NO, group in MDN to form MCN resulted in an almost planar molecule at the 6-31G level, but a puckered molecule at the 6-3 lG* level. In the latter case, the angles subtended at the central nitrogen atom added to 344”, which was in fair agreement with the 335” derived from the electron diffraction study [3]. The CH3 group protruded with an angle of 38.8“from the N-N-Cl plane, compared to 46.1” from the electron diffraction work. The long N-N bond observed in MCN was not calculated accurately at this level of theory. The N406 molecule was considered next. To our knowledge there has not been much work reported
occur in this molecule. on this substance, which would constitute another possible oxide of nitrogen, although there has been some speculation as to its heat of formation [20]. The structure of this molecule is not known. As noted in Table 4, our calculations indicate that this molecule is planar at both levels of theory. The addition of the d polarization functions at the 631G* level resulted in longer N-N bonds than at the 6-3 1G level, but planarity was still maintained. The ab initio energy values (see Tables l-4) were used to estimate the heat of formation for N.,06 using Pople’s isodesmic reaction principle [21]. An isodesmic reaction is one in which the number of formal chemical bonds and the number of electron pairs are conserved despite transformations where the relationships among the bonds are altered. For the current computations the isodesmic reaction took the form N-(NO&
+ N-(CH,),
+ (CHs L-N-(NO,
+ (CH,)-N-(NO,), )
(1)
There are three N-N bonds and three C-N on each side of eqn. (l), but from the left side to the
294
D.M. Zirl and T. Vladimiroff/J.
Mol. Struct.
(Theochem)
279 (1993) 291-297
TABLE 3 Minimum energy configurations
for methylchloronitramine”
Parameter
6-31G
N-N N-N (MP2) N-Cl N-C N-O
1.335 1.749 1.466 1.239/1.223’ 1.223 1.078/l .075/l .079
C-H N-N-C N-N-Cl C-N-Cl O-N-O N-N-O N-N-O N-C-H H-C-H C-N/N-N-Cl Sum’
6-31G*
120.7 118.2 121.1 125.1 115.5 119.4 109.7/107.0/110.1d 110.1/109.7/110.2d
1.72 _+0.004 1.478 + 0.005 1.209 f 0.002
1.076/1.078/1.083d 112.9 108.4 115.0 128.5
.360.0
38.8 344.2
46.1 + 1.3b 336.3 * 4.0
- 757.320
- 757.519
1.5
[3]
1.469 + 0.005
1.380 1.440 1.698 1.472 1.193/1.183d
115.9 113.9 114.5 126.7 115.0 118.1 108.5/106.3/111.7d 109.7/l 10.3/l 10.2d
plane
Energy (a.u.)
Experimental
+ + * +
1.5 1.3 1.2 0.9b
a Bond lengths in angstroms; bond angles in degrees. bRef. 4. ‘Sum of angles around the central nitrogen atom. dDifferent values of this geometric parameter were found to occur in this molecule.
right side of eqn. (l), there is a change in the number of each type of bond within each molecule. The energy difference between the two sides of the equation can be used to compute the heat of formation of an unknown component by formulating an TABLE 4 Minimum energy configuration
for N40ea
6-31G N-N N-N (MP2) N-O N-N-N O-N-O N-N-O Sumb Energy (a.u.)
6-31G*
1.464 1.540 1.205
1.466 1.169
120.0 125.8 117.1 360.0
120.0 127.7 116.1 360.0
- 665.985
- 666.405
a Bond lengths in angstroms; bond angles in degrees. b Sum of angles around the central nitrogen atom.
equation similar to eqn. (l), but with heats of formation instead of the SCF energies. Table 5 shows the calculation for the heat of formation of the unknown N406 based on this isodesmic reaction. The heats of formation for MDN, DMN and TMA were obtained from refs, 20,22 and 23 respectively. The heat of formation for N,O, is estimated to be 96 kcalmol-’ at the 6-31G level and 80 kcal mol-’ at the 6-31G* level. Leroy et al. [14] have suggested a correction be applied to the semiempirical heat of formation obtained with the smaller basis set: AH(exp) = - 2.111 + 0.942AH(sem)
(2)
where AH(exp) and AH(sem) are the experimental and semiempirical heats of formation respectively. The use of eqn. (2) reduces the 96 kcalmol-’ to 88 kcal mol-’ , bringing this value into closer agreement with the value obtained using the larger basis set. Miroshnichenko et al. used additivity rules to obtain an estimate of 38 kcalmol-’ [20].
D.M. Zirl and T. VladimirofsIJ. Mol. Struct. (Theochem) 279 (1993) 291-297 TABLE 5 Heat of formation
computation
Isodesmic equation N-(NO,), + N-(CH,), + (CH,),-N-NO2
for trinitraminea
+ H,C-N-(NO,),
Energy difference X = E(N406) + E(TMA) - [E(MDN) + E(DMN)] X (6-3 1G) = 79 kcal mol- ’ X (6-3 1G*) = 63 kcal mol-’ Heat of formationb H(N406) = X - H(TMA) + [H(MDN) + H(DMN)] H(N406) = X- (-5.66) + [12.78 + (- 1.79)] H(N406) (6-31G) = 96 kcalmol-’ H(N406) (6-31G*) = 80 kcalmol-’ aX, energy difference; E, minimum energy (see Tables l-4); H, heat of formation. bSee text for references for heats of formation.
There are a number of sources of error in these heat of formation computations. The isodesmic procedure assumes the approximate cancellation of not only the basis set effects and correlation effects, but also of the zero-point energy and thermal corrections. Better overall agreement between the heat of formation calculations and the 6-3 1G and 631G* basis set calculations has previously been attained [ 141,but only smaller molecules were considered. The fact that the N-N bond is not calculated accurately in this work may also be a source of error. The larger basis set should result in overall smaller errors, but not necessarily more complete cancellation of errors. Finally the computations for DMN at the 6-31G* level [l l] employed “d” functions which were composed of two displaced “p” functions rather than the more conventional type of “d” polarization basis sets, which may lead to a less constant error. The estimation of the heats of formation based on the additivity rules may not be very accurate because the system is not very linear and a rather large interaction term between the nitro groups had to be assumed. Using the computed heats of formation for N,O,, an estimate of the N-N bond strength can be
295
made. The molecule has only two types of bond: N-N and N-O. The energy of formation of the dissociated atoms is 809 kcal mol-’ , based on the energy of the gaseous atoms found in ref. 22. Subtracting the estimates for the heats of formation and for the strength of the six N-O bonds (113 kcal mol-’ each [24]), results in the bond strength for the three N-N bonds. This computation produces an estimate of the N-N bond strength in N406 of 14 kcalmoll’ with the 6-31G basis set and 17 kcal mol-’ with the 6-31G* basis set. This compares with the estimate of 17 kcal mol-’ obtained by Miroshnichenko et al. 1201.In order for these authors to obtain this value based on their estimation of the heat of formation, they must have assumed an unreasonably high value for the N-O bond strength. There seems to be a fundamental difference between the C-N bonds in trimethylamine, which are well described at the 6-3 lG* level of theory, and the N-N bonds which are not. The two possible sources of error are that the basis set is not large enough or that electron correlation effects are not included. To investigate the latter possibility, many-body perturbation theory was used at the MP2 level. Since GAMES will not optimize geometries at this level of theory, the molecular geometry was frozen at the 6-31G* level and only the N-N bond lengths were varied. Figure 1 shows the total energy of MCN as a function of the N-N distance for the MP2/6-31G* calculation. The minimum occurs at 1.44A, which is closer to the experimental value of 1.469 A than the SCF N-N bond length. Figure 2 illustrates the energy of the N406 molecule as a function of the N-N bond lengths at the MP2/ 6-31G* level. The minimum energy in this curve corresponds to an N-N distance of 1.556 A. At the MP2 level, two-thirds of the difference between the SCF and experimental bond lengths is recovered for MCN. If the same percentage of recovery is assumed for N406 then the N-N bond length for this molecule can be estimated to be 1.601 A. This value can be compared with the N-N bond length of 1.76A [24] in dinitrogen tetroxide.
D.M. Zirl and T. VladimiroffjJ. Mol. Struct. (Theochem)
296
279 (1993) 291-297
Conclusions
1
-758.4755 t. 1.40
1.42
1.44 N-N distance
1
1.46
1.41
(A)
Fig. 1. Energy for methylchloronitramine 31G* level as a function of N-N distance.
at the MP2/6-
The structure of trimethylamine, methyldinitramine, methylchloronitramine and trinitramine were investigated using the 6-3 1G and 6-3 1G* basis sets. Although the structure of trimethylamine is well described at the SCF level of theory, the same cannot be said for the nitramines considered in this study. The calculated N-N bonds are too short and the geometry around the central nitrogen atom has a tendency to be too flat when compared with the experimental structures. Many-body perturbation theory at the MP2 level had to be used to recover about two-thirds of the difference between the SCF and experimental N-N bond lengths. However, when the results were combined with experimental values, reasonable estimates could be made for the N-N bond length and strength and for the heat of formation in N406. Acknowledgments
This research was partly funded by the Army High Performance Computing Research Center at the University of Minnesota under the Army Research Office contract number DAAL03-89-C0038. The authors are grateful for the generous use of computer time on the Cray Y-MP/6128 at the US Army Waterways Experiment Station, Vicksburg, MS, and on the Cray X-MP/48 at the US Army Ballistic Research Laboratory, Aberdeen Proving Grounds, MD. References
-668.2071 A 1.52
1.53
1.54
1.55
1.56
1.57
I I.58
N-N distance (A)
Fig. 2. Energy for N,O, at the MP2/6-31G* function of N-N distance.
level as a
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