J. Phys. Chem. 1082, 86, 459-462
model. A conclusion of this study is that the higher order shells surrounding hydrate cavities do have an effect on the stability of the hydrate, and these higher order potentials should be taken into account in determinations of hydrate
459
equilibria.
Acknowledgment. This work was supported by the National Science Foundation under NSF Grant No. Eng. 79-21022.
Molecular Structure of 2,4,6-Trlnltrotoluene W. Robert Carper, Larry P. Davis,' The Frank J. Selk Research LaLwatory, united States Air Force Academy, Colorado 80840
and Michael W. Extlne Moleculer Structure Ccfporatbn, College Station, Texas 77840 (Received: July 13, 1981; I n Final Form: September 18, 1981)
Crystals of 2,4,64rinitrotoluene are orthorhombic, a = 14.991 (1)A, b = 6.077 (1)A, c = 20.017 (2) A, 2 = 8, R = 0.057 for 1461 reflections. 2,4,6-Trinitrotoluene exists as two unique molecules (A and B) within the unit cell. In the A form the 2,4, and 6 nitro groups are twisted out of the benzene ring plane by 51', 24', and 43'. The B-form nitro groups are twisted out of the plane by 60', 30', and 45' in the 2,4, and 6 positions. The structural properties of the two forms of 2,4,6-trinitrotolueneare compared with those determined from MIND0/3 and MNDO methods.
Introduction The thermochemical decomposition of 2,4,&trinitrotoluene (TNT) and other nitroaromatica has been studied for more than 50 years. Despite this fact, the initial decomposition steps have not been clearly identified either for slow decomposition at relatively low temperatures or for conditions under which the thermochemical decomposition reaction is self-sustaining. This laboratory has recently undertaken various studi e ~ ' -in ~ an effort to elucidate the kinetics and the mechanism of the thermochemical decomposition reactions of TNT. We have determined that structural information pertaining to 2,4,6-trinitrotoluene would prove useful to us in determining its mechanism of thermochemical decomposition. Consequently, we undertook X-ray and theoretical studies of TNT, both of which are contained in this report. Experimental Section The sample of 2,4,6-trinitrotoluene was recrystallized from ethanol. TNT crystals show a propensity for twinning. Numerous crystals were examined which showed twinning along the crystallographic c axis. The twinning usually doubled the length of the c axis. It was noted that the reflections which doubled the length of the c axis varied 2 orders of magnitude in relative intensity from crystal to crystal. A crystal was chosen which was only slightly twinned, and the reflections which doubled the c axis length were ignored. X-Ray Data Collection A colorless prismatic crystal having approximate dimensions of 0.20 X 0.25 X 0.10 mm was mounted on a glass fiber with ita long axis roughly parallel to the 4 axis of the (1)S. A. Shackelford, J. W. Beckmann, and J. S. Wilkee, J. Org. Chem.. 42. 4201 (1977). (2)J. W. Beckkann, J. S. Wilkee, and R. R. McGuire, Thermochim. Acta, 19, 111 (1977). (3) R. M. Guidry and L. P. Davie, Thermochim. Acta, 32, 1 (1979).
goniometer. Preliminary examination and data collection were performed with Cu K a radiation (A = 1.54184 A) on an Enraf-Nonius CAD4 computer-controlled K axis diffractometer equipped with a graphite crystal, incident beam monochomator. Cell constants and an orientation matrix for data collection were obtained from least-squares refinement, using the setting angles of 25 reflections in the range 16' < 8 < 45O, measured by the computer-controlled diagonal slit method of centering. The orthorhombic cell parameters and calculated volume are as follows: a = 14.991 (1)A, b = 6.077 (1) A, c = 20.017 (2) A, V = 1823.6 A3. For 2 = 8 and F W = 227.13 the calculated density is 1.65 g/cm3. The previously determined density by McCrone4 for orthorhombic 2,4,6-trinitrotoluene is 1.654 g/cm3. As a check on crystal quality, o scans of several intense reflections were measured; the width at half-height was 0.20' with a takeoff angle of 2.8', indicating good crystal quality. From systematically absent reflections, and from subsequent least-squares refinement, the space group was determined to be Pcael. The data were collected at a temperature of 23 f 1 'C by using the u-19 scan technique. The scan rate varied from 2' to 20°/min (in u). Data were collected to a maximum 28 of 150.0'. The scan range (degrees) was determined as a function of 6 from: Au = 0.7 + 0.300 tan 0. Movingcrystal, moving-counter background counts were made by scanning an additional 25% above and below this range. Thus, the ratio of peak counting time to background counting time was 2:l. The horizontal counter aperture width ranged 2.0 to 5.7 mm; the vertical aperture was set at 2.0 mm. The diameter of the incident beam collimator was 0.7 mm, and the crystal-to-detector distance was 21 cm. A total of 2302 reflections were collected, of which 1942 were unique and not systematically absent. As a check on crystal and electronic stability, three representative re(4)W.C. McCrone, Anal. Chem., 21, 1582 (1949).
This article not subject to US. Copyright. Published 1982 by the American Chemical Society
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The Journal of Physical Chemistry, Vol. 86, No. 4, 1982
Carper et al.
flections were measured every 41 min. The intensities of these standards remained constant within experimental error throughout data collection. No decay correction was applied. Lorentz and polarization corrections were applied to the data. The linear absorption coefficient is 13.2 cm-l for Cu Ka!radiation. No absorption correction was made. A secondary extinction correction was applied.6 The final coefficient, refined in least-squares, was 15 X (in absolute units).
Structure Solution and Refinement The structure was solved by direct methods. Using 228 reflections (minimum E of 1.52) and 2916 relationships, we produced a total of 40 phase sets. The 32 nonhydrogen atoms were located from an E map prepared from the phase set with probability statistics: absolute figure of merit = 1.29, residual = 0.21, and $o = 1.080. Hydrogen atoms were located and their positions and isotropicthermal parameters were refined. The structure was refined in full-matrix least squares where the function minimized was Cw(lFol - IF,l)Zand the weight w is defined as 4F-2/a2(F-2). .-", The standard deviation on intensities, u(F,2),is defined as follows: "
I
a2(F,2)= [S2(C + R2B) + (pF,2)']L,2
Flgure 1. Molecular form A of TNT containing 50% probability elipIntramolecular and intermolecular hydrogen bonds are indicated by dashed lines and arrows.
so&.
where S is the scan rate, C is the total integrated peak count, R is the ratio of scan time to background counting time, B is the total background count, L, is the Lorentzpolarization factor, and the parameter p (=0.05) is a factor introduced to downweight intense reflections. Scattering factors were taken from Cromer and Waber.6 Anomalous dispersion effects were included in F,; the values for Af' and Af" were those of Cromer.8 The 1461 reflections having intensities greater than 3a were wed in the refinements. The final cycle of refinement included 329 variable parameters (largest parameter shift was 0.34 times its esd) with unweighted and weighted agreement factors of
R1 = C llFol - ~ F c ~ ~ / E=~0.043 Fo[ R2 = SQRT(Cw(lF0I - IF,I)2//C~Fo2) = 0.057 The standard deviation of an observation of unit weight was 1.62. The highest peak in the final difference Fourier had a height of 0.28 e/A3 with an estimated error9 based on AF of 0.05. Plots of Cw(lFol - lFc1)2vs lFol, reflection order in data collection, sin 8/A, and various classes of indices showed no unusual trends. The fact that the structure was so well-behaved, with hydrogens refining quite well, supports our conclusions with regard to the twinning. All crystallographic calculations were performed on linked PDP-11/45-11/60 computers using the EnrafNonius Structure Determination Packagelo as well as private programs of Molecular Structure Corp. The final positional parameters are available as supplementary ( 5 ) W. H. Zachariasen, Acta Crystallogr., 16, 1139 (1963). (6)D. T. Cromer and J. T. Waber, "International Tables for X-ray Crystallography", Vol. IV, Kynoch Press, Birmingham, England, 1974, P 99. (7) J. A. Ibers and W. C . Hamilton, Acta Crystallogr.,17, 781 (1964). (8) Reference 6, pp 149-50. (9) D. W. J. Cruichskank, Acta Crystallogr.,2, 154 (1949). (10) B. A. Frenz, in "Computing in Crystallography", H. Schenk, R. Olthof-Hazelkamp, H. vanKonigsveld, and G. C. Bassi, Eds., Delft University Press, Delft, Holland, 1978, pp 64-71.
I I
Flgure 2. Molecular form B of TNT containing 50% probability ellipsoids. Intramolecular and intermolecular hydrogen bonds are indicated by dashed lines and arrows.
material. (See paragraph at end of text regarding supplementary material.)
Molecular Structure Unlike p-nitrotoluene," 2,4,6-trinitrotol~ene(TNT)~~ exists in two forms (A and B) in the unit cell, each of which contains different bond lengths in a number of interatomic positions. Each unit contains four molecules of both A and B, for a value of 2 = 8. (11) J. V. Barve and L. M. Pant, Acta Crystallogr., Sect. B , 27, 1158
(1971).
(12) Throughout this paper, we will use the following abbreviations: TNT for 2,4,6-trinitrotoluene, TNA for 2,4,6-trinitroaniline, and TENA for 2,3,4,6-tetranitroaniline.
The Journal of Physical Chemistry, Vol. 86, No. 4, 1982 461
Molecular Structure of 2,4,6-Trinltrotoiuene
Figure 1contains form A of TNT viewed perpendicular to the least-squares plane of the benzene ring.13 The equation of this plane is -0.1605~- 0.612143, - 0.76692 3.5904 = 0 where x, y, and z are orthogonalized coordinates. Figure 2 contains a similar diagram of form B. The equation of its plane is 0.1477~- 0.6064~- 0.78132 - 2.2596 = 0 As is the case for other nitroaromatic compounds, the interior angles of T N T reflect distortion of the benzene ring. Those carbon atoms carrying nitro groups all have interior angles greater than 120O. Similarly, the exterior bond angles reflect crowding between the o-nitro groups and the methyl group. Despite these and other effects, the benzene rings are reasonably planar in both forms of TNT. The methyl and nitro groups are somewhat displaced from the ring planes. The variations in bond lengths and angles of T N T are similar to those found in substituted nitrobenzenes such as 2,4,6-trhitro&e (TNA)14and 2,3,4,6-tetranitroaniline (TENA).lS In TNA and TENA, there is considerable variation in ring bond angles and bond lengths from those found in benzene. The differences in the bond lengths and bond angles of TNA and TENA are considerably more than those found in 4-nitroaniline,16 whose measured density of 1.422 g/cm is less than that of either TNA (1.762 g/cm) or TENA (1.87 g/cm). Furthermore, in TNA, the 2, 4, and 6 nitro groups are twisted out of the plane by 22.5O, 4.0°, and 8.5', respectively. In the case of TENA, the 2,3,4, and 6 nitro groups are twisted out of the plane by 45O, 6 4 O , 19O, and 3 O . Holden et al.14 argue that twisting of the nitro groups is required by packing due to crowding between groups. It seems likely that the same argument holds true in the case of 2,4,6-trinitrotoluene, whose calculated density is 1.65 g/cm3, compared with 4-nitrotoluene,l' whose density is 1.287 g/cm3. A similar comparison can be made between T N T and 4-nitrotoluene. The C-C bond distances between the methyl group and the ring carbon is lengthened from 1.482 (7) A in 4-nitrotoluene to an average of 1.506 (6) A in the two forms of TNT. The average C-N bond distance in the two forms of TNT is 1.471 ( 5 ) A compared with 1.482 (7) A found in 4-nitrotoluene. Unlike the nitro group in 4nitrotoluene, all of those in T N T form nonzero dihedral angles with the plane of the benzene ring as shown in Figures 1 and 2. An increase in hydrogen bonding is exhibited in TNT vs. 4-nitrotoluene where there is less opportunity for such interactions. Figures 1and 2 contain a number of interatomic distances which are less than the sum of the van der Waal's radii" and may be classified as hydrogen bonds under this formulation.l* The intramolecular hydrogen bonds in T N T are generally longer and probably weaker than those found in such compounds as 2-nitrophenol,lg 2,4-dinitrophen01,~"and
+
(13)Hydrogen atoms were given arbitrary isotropic thermal parameters for clarity in Figures 1-4. (14)J. R. Holden, C. Dickinson, and C. M. Bock, J. Phys. Chem., 76, 3597 .... (1972).
(15)C.Dickinson, J. M. Stewart, and J. R. Holden, Acta Crystallogr., 21,663 (1966). (16)K. N. Trueblood, E. Goldish, and J. Donohue, Acta Crystallogr., 14, 1009 (1961). (17) A. Bondi, J . Phys. Chem., 68,441 (1964). (18)R.D.Green, 'Hydrogen Bonding by C-H Groups", Wiley, New York, 1974. (19)F. Iwasaki and Y. Kawano. Acta Crvstalloar.. - . Sect. B . 34.. 1286 (1978). (20)T. Kagawa, R. Kawai, S. Kashino, and M. Haisa, Acta Crystallogr., Sect. B , 32,3171 (1976).
TABLE I: Intermolecular Hydrogen Bonds and Contacts molecule
distance, A
B
2.38 2.63 2.70 2.61 2.68 2.54 2.62 2.97 2.94 3.00 3.16 3.19 3.13 3.19 3.13 3.09
A
B B B A A A
B B A A
B B B B
Figure 3. Steroview of unit cell using 20% probability ellipsoids. Selected intermolecular hydrogen bonds are indicated by dashed lines.
2-nitro-4-chlorophenolZ1 whose values for the 0-H.. -0-N bond are 1.93 (5), 1.89 (7), and 1.84 (7) A,respectively. The same is true for TENA where typical N-H-a-0-N intramolecular hydrogen bond lengths are 2.04 and 1.92 A. Table I contains a list of the various intermolecular hydrogen bonds between forms A and B both within and between the unit cells. The B form of TNT participates in one more intermolecular hydrogen bond than does the A form; however, the two hydrogen bonds between the A molecules are both shorter than any of the three bonds between the B molecules. This suggests, but does not prove, that the total energy involved may be the same for each case. No distances for O...Hintermolecular hydrogen bonds were included in the analysis of 4-nitrotoluene; however, estimates from the data are ~ 2 . A, 6 similar to those reported for p-toluic acidz2(2.63 A). The intermolecular hydrogen bonds in T N T (2.38-2.70 A) are more typical of those found in other nitrobenzenes such as TNA (2.36 and 2.38 A), TENA (2.36-2.54 A), 4-nitrotoluene (21)R. Kawai, S. Kashino, and M. Haisa, Acta Crystallogr., Sect. B , 32,1972 (1976). (22)M.G. Takwale and L. M. Pant, Acta Crystallogr., Sect. B , 27, 1152 (1971).
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The Journal of Physical Chemistry, Vol. 86, No. 4, 1982
Carper et ai. TABLE 11: Dihedral Angles (deg) between Nitro Groups and Plane of Ring nitro group molecular form
2
4
6
A
B
51 60
24 30
43 45
calcd MIND0/3 MNDO
45 85
0 90
45 84
TABLE 111: Comparison of Experimental and Theoretical Values property
exptl
MIND0/3
MNDO
A Hf, kcal /mol M, D
12.ga 1.16b 1.63'
-11.34 1.5025 1.69
74.86 0.9641 2.44
EA, eV
R. Shaw, J. P h y s . C h e m . , 1 5 , 4047 ( 1 9 7 1 ) . R. C. Cass, H. Spedding, and H. D. Springall, J. C h e m . SOC., 3451 ( 1 9 5 7 ) . E. C. M. Chen and W. E. Wentworth, J. C h e m . P h y s . , 6 3 , 3183 ( 1 9 7 5 ) .
Flgure 4. Rotated stereoview of unit cell using 20% probability ellipsoids.
(-2.6 A), P-p-nitr~phenol~~ (1.89-2.51 A), and 2,4-dinitrophenol (2.23 A). Projections of the crystal structure are shown in Figures 3 and 4. In addition to the various inter- and intramolecular hydrogen bonds that are present, there are a number of interatomic contacts involving carbon and oxygen as listed in Table I. There are no C-C contact distances less than 3.50 A,a fact that emphasizes the lack of simple ring stacking in this structure. The stacking that does occur is enhanced by weak van der Waals forces between the oxygen atoms of nitro groups and the aromatic carbon atoms of adjacent TNT molecules. A limited number of contacts also occur between oxygen atoms of adjacent molecules.
Theoretical Calculations The calculations were carried out by using both the MIND0/324and the MNDOZ5procedures. The number of parameters used in the MNDO approach is fewer than those used in the MIND0/3 method due to the use of atomic instead of bond parameters. The parameters used in these calculations are those previously published by Dewar and co-workers in his development of these metho d ~ These . ~ theoretical ~ ~ ~ approaches have proved to be quite useful in the prediction of molecular ground-state properties, with the MNDO procedure being an im(23)P. Coppens and G. M. J. Schmidt, Acta Crystalogr., 18, 654 119fi.5). ~_.__,.
(24)R.C.Bingham, M. J. S. Dewar, and D. H. Lo, J. Am. Chem. SOC., 97,1286,1294,1302 (1975). (25)M.J. S.Dewar and W. Thiel, J. Am. Chem. SOC.,99,4899,4907 (1977).
provement over MINDO/3 in most cases. The calculated bond distances and bond angles agree well with experimental values. If one averages the nonhydrogen-containing bond lengths for both forms of TNT and then calculates an average deviation between these and the calculated values, average deviations of 0.031 and 0.020 A are obtained for the MIND0/3 and MNDO values, respectively. A comparison of the calculated vs. actual bond angles clearly supports the use of the MNDO method in virtually every example. This result is in contrast with the bondlength comparison where there is little to choose from between the two methods. In view of the inability of these and other methods to properly account for nonbonded interactions such as hydrogen bonding,26it is surprising that the calculated bond angles are reproduced to the extent that they are. Perhaps the best example of this discrepancy is in the comparison between the actual and calculated ring-nitro-group dihedral angles given in Table 11. Other physical properties of TNT are compared with the calculated values in Table 111. Unlike results for other nitrogen-oxygen-containingcompounds,25MIND0/3 gives better results for several properties. Acknowledgment. The expert typing of Mrs. B. J. Darcy is gratefully acknowledged. W.R.C. acknowledges helpful discussions with Mr. Lloyd Pflug. Supplementary Material Available: Five tables listing general temperature factor expressions, final positional parameters, experimental and calculated bond lengths in angstroms, displacements of atoms from weighted leastsquares planes, and bond angles (6 pages). Ordering information is given on any current masthead page. (26)M.J. S. Dewar and G. P. Ford, J. Am. Chem. SOC.,101, 5558 (1979).
