J . Phys. Chem. 1990, 94, 5689-5694
5689
Is N8 Cubane Stable?’ Ray Engelke* and James R. Stine Los Alamos National Laboratory, M S P952, Los Alamos, New Mexico 87545 (Received: July 28, 1989; In Final Form: February 26, 1990)
The question of N8 cubane’s stability is addressed via ab initio calculations. An 0,symmetry stationary point is found on the energy hypersurface for all three levels of theory used; these were restricted Hartree-Fock (RHF) self-consistent-field theory using STO-3G, 4-31G, and 4-31G* basis sets. Vibrational frequency calculations, at the same three levels of theory, all indicate that the cubic structure is stable. The effect of correlation on the stable structure energies is examined with Maller-Plesset perturbation theory up to fourth order; these post-Hartree-Fock calculations were performed at the RHF optimized geometries. The calculations indicate that, if it could be synthesized, N8cubane would be a highly energetic material, metastable to dissociation to four N, molecules; the energy release for this reaction is predicted to be 530 f 50 kcal/mol. The energy barrier to dissociation is estimated via reaction coordinate calculations. The [4+4+4+4] symmetry-forbidden NB 4N2 concerted reaction has an activation barrier of about 162 kcal/mol at the RHF/4-31G* level. This dissociation could also take place as a sequence of four [2+2] symmetry-forbidden reactions. Each of these [2+2] reactions would probably have a reaction barrier of roughly 40 kcal/mol-this suggests that N8 cubane may be a reasonably stable structure. Estimates are given of the mass density of condensed-phase Ns, along with predicted values of its Chapman-Jouguet detonation velocity and pressure. It appears that condensed-phase N8 would be a very powerful chemical explosive.
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I. Introduction We report a b initio calculations of the stability of N8 cubane. N8 cubane is isoelectric with the experimentally known [(CH),] carbon cubane.* One reason such structures are interesting is their high strain energy. To quote Eaton and Castaldi,’ “.,, (carbon) cubane has the highest strain energy (166 kcal/mol) of any stable organic compound available in multigram amounts.” The complete replacement of the C H groups in the cubane structure by nitrogen atoms (with their associated lone-pair interactions) should produce an even higher energy structure. This suggestion is consistent with the fact that a nitrogen single bond is much weaker than the analogous bond of the C H group. The high thermal stability‘ of carbon cubane (it decomposes slowly at 200 “C)is suggestive that N8 cubsne might also be a stable structure. To our knowledge there has never been an experimental observation of N8 cubane. In the light of these observations, ab initio calculations on the N8 structure were performed using the GAUSSIAN-82and C A D P A C ~ program^.^ In an earlier work, similar calculations were reported for four valence isomers of hexaazabenzeneS6 The calculations reported here indicate that N, cubane is a stable molecule, metastable to dissociation into four N2 molecules with the liberation of significant amounts of energy (530 f 50 kcal/mol). The activation barrier to its dissociation is estimated, by RHF/4-31 G* reaction coordinate calculations, to be quite large (ca. 40 kcal/mol). Because of the high energy content of NBcubane, some of its properties as a condensed-phase material have also been calculated and are reported here. First a mass density prediction is given. Then, by use of the predicted density and heat of formation, the Chapman-Jouguet detonation velocity and pressure are obtained. These calculations indicate that N8 cubane would be a very powerful chemical explosive, if it could be synthesized. 11. Ab Initio Calculations and Results A . Background and Methods. A computer search of Chemical Abstracts (from 1967 to February 1989) turned up only one ( I ) This work was supported by the US.Department of Energy. (2) Eaton, P. E.; Cole, T. W. J . Am. Chem. Soc. 1964,86, 3157. (3) Eaton, P. E.; Castaldi, G. J. Am. Chem.
[email protected], 107, 784, and references therein. (4) Eaton, P. E.; Ravi Shankar, B. K.; Price, G. D.; Pluth, J. J.; Gilbert, E. E.; Alster, J.; Sandus, 0. J . Org. Chem. 1984, 49, 185. (5) (a) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Rahgavachari, K.; Whiteside, R. A.; Schlegel, H.B.; Fluder, E. M.; Pople, J. A. Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA. (b) Amos, R. D.; Rice, J. E. CADPAC, The Cambridge Analytic Derivative Package, Issue 4.0, Cambridge, 1987. (6) Engelke, R. J . Phys. Chem. 1989, 93, 5722.
0022-3654/90/2094-5689$02.50/0
previous calculation of cubic Ng.7 This earlier work was a valence-shell-only self-consistent-field (SCF) calculation using a double-{basis set. In this calculation, the cubic (4point group symmetry) structure was assumed to correspond to an energy minimum. That is, only the N-N distance was varied in the optimization and second energy derivatives at the stationary point were not evaluated. The current calculations are improvements in a number of respects. These include (1) the cubic N,, structure is shown to be a stable point on the energy hypersurface at three levels of calculation via frequency calculations (these calculations used increasingly more complete basis sets), ( 2 ) the core orbitals are optimized in all the S C F calculations, (3) the highest level S C F and frequency calculations used a basis set (4-3 1G*) that includes d-shell polarization functions, and (4) the effect of electron correlation on the energy is examined by use of Maller-Plesset perturbation theory up to fourth order; these correlated calculations utilized models up to the MP4=FC/4-31G//RHF/4-3 IG and MP2=FC/4-3 lG*//RHF/4-3 lG* levels. ( i ) GAUSSIAN-82 Calculations. In all the R H F calculations, the condition for a self-consistent field was that the maximum change in any density matrix element between cycles must be S10-7. Integrals were neglected if their magnitude was Ilo-’*. An INDO guess was used to begin an S C F calculation. The following four criteria were required at a stationary point on the energy hypersurface: (1) the maximum force along a spatial or angular displacement is 14.5 X lo4 h/bohr or h/rad, ( 2 ) the rms force is S 3 X lo4 h/bohr or h/rad, (3) the maximum displacement is S1.8 X IO-3 bohr or rad, and (4) the rms displacement is 51.2 X bohr or rad. The STO-3G and 4-31G frequencies were calculated by using energy second derivatives computed numerically from analytically calculated first derivatives. The step size in the second-derivative calculations was 0.0025 A. The same S C F and integral criteria used in the optimizations were maintained in the frequency calculations. The Maller-Plesset energy calculations used the Fock Hamiltonian and the R H F wave function obtained using the above-listed S C F criteria; the cores were frozen in all the correlated calculations. The MP4 calculations included single, double, and quadruple substitutions. (ii) The C A D P A C ~Calculations. Because RHF/4-3 lG* calculations of N, cubane’s vibrational frequencies are computationally quite demanding, we switched to use of the CADPAC4 program for this work and computed the first and second energy derivatives analytically. Before doing the frequency calculations, we checked the GAUSSIAN-82 RHF/4-3 lG* N, optimum structure , the N-N bond lengths were found to differ using C A D P A C ~ and ~~
(7) Trinquier, G.;Malrieu, J.; Daudey, J. Chem. Phys. Leu. 1981,80, 552.
0 1990 American Chemical Society
5690
Engelke and Stine
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
TABLE I: N-N Structural Parameters (A)” model Ngb N2H4 rrans-N2H2 RHF/4-31G 1.539 1.401 1.226 RHF/4-31G* 1.468 1.413 1.214 1.252 I .50Sc 1.449 experimental
I
N, 4.0
1.076 1.094
‘At all levels of calculation, the ground electronic state has IA,, symmetry. bThe RHF/STO-3G model predicts a stable structure with N-N bond length of 1.537 A. CEstimated;see section JIB.
(8) Hehre, W. J.; Radom, L.;Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1988; pp 246-250.
,
’
,
1135 R
1 ,085
by less than 0.001 A. In the CADPAC4 calculations, integrals with magntitude S10-Iowere neglected. The S C F convergence criteria for an acceptable change in density matrix elements from cycle to cycle were IO” and IO-’ for gradients and second-derivative work, respectively. S C F calculations were started by use of the one-electron Hamiltonian. The CADPAC~ criterion for having located a stationary point on the energy surface was that the largest component of the (Cartesian coordinate) energy gradient be less than h/bohr. 8. Stability and Structure Results. In Tables I and I1 we give calculated bond lengths and frequencies for N8 cubane. The calculations were begun by optimizing N, cubane at the lowest level of theory (RHF/STO-3G). The 0,point group symmetry assumption was built into the geometry file used in the optimization. However, after finding the stationary point, its character was determined by RHF/STO-3G vibrational frequency calculations. All the RHF/STO-3G vibrational frequencies were found to be real, and in fact, the lowest frequency is quite large (747 cm-I), indicating a structure fairly resistant to deformation. Next, similar calculations were carried out at the RHF/4-31G and RHF/4-3 1 G* levels of theory; these calculations also yielded stationary points. The character of both the RHF/4-3 1G and RHF/4-3 1 G* stationary points was checked by frequency calculations, and they were found to be stable points. The lowest frequency found at the RHF/4-31G level (704 cm-l) indicates that NE cubane is not easily deformable. A similar statement applies to the RHF/4-31G* structure for which the lowest vibrational frequency is 728 cm-’. One notes, from Table I, that the addition of polarization functions to the 4-31G basis set causes a marked decrease in the predicted N8 N-N bond length (by ca. 0.07 A). One expects that the RHF/4-31GS model gives the most accurate N-N bond length of the three models used. It is useful to calibrate the RHF/4-31G* bond length in order to try to get an improved estimate of the experimental N E N-N bond length. In Table I, we give N-N distances for N2, rrans-N2H2, and N2H4. One notes that both the RHF/4-31G* and RHF/4-31G theoretical models give N-N bond distances smaller than the experimental values; the errors in the computed bond lengths are about -3%, -2.5%, and -1% depending on whether the N-N bond is single, double, or triple. This indicates that the predicted N, cubane RHF/4-31G* bond length is probably also too short and should be corrected. Using the RHF/4-31G* and experimental values for the N-N bond length of (sp3) hybridized N2H4, one obtains [( 1.449/ 1.41311.4681 = 1.505 A as a ‘corrected” estimate of NEcubane’s experimental bond length. From earlier work,s it might be expected that the frequencies in Table I1 could be calibrated by use of calculated and experimental results from smaller (nitrogen containing) molecules. Usually, for example, hydrocarbon frequencies calculated at the RHF/4-31G level are uniformly high by ca. 10-15%. If we use hydrazine (see ref 6) as a prototype for obtaining a frequency calibration for an sp3 hybridized nitrogen structure, it is found that such a simple correction is not possible. For the lowest three vibrational modes of hydrazine, two frequencies are significantly underestimated by the RHF/4-3 IG theory. Above the third vibrational level, the frequencies are overestimated by 8-1 8%. Thus, before making a vibrational frequency correction on N8 cubane, more information about the character of the particular
.
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2.0
1
1
z l 1.0
900
lo00
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no0
1300
“CY (CM-’) Figure 1. Raman and infrared RHF/4-31G* N8 cubane vibrational intensities.
mode of interest would need to be specified. One notes from Table I1 that increasing basis set quality from STO-3G to 4-3 1G decreases all the predicted N8 cubane vibrational frequencies. If the lowest mode is neglected, the mean difference and standard deviation of the mean for the two sets of frequencies are -21.4 f 4.3%. In contrast, increasing basis set quality further from 4-31G to 4-31G* increases all the frequencies. In this case, if the lowest frequency mode is neglected, the mean difference and standard deviation of the mean between the two sets of frequencies is -18.9 f 5.2%. Consequently, the STO-3G and 4-31G* frequencies are in better agreement with each other than either are with the 4-31G results. Note that hydrazine’s vibrational frequencies show a similar pattern when calculated with these three basis sets. That is, there is a strong frequency decrease when going from STO-3G to 4-3 1G and a strong increase in going from 4-31G to 4-31G*. Examples of this are hydrazine’s second and third normal modes which show the pattern 1120 607 978 cm-l and 1212 750 11 16 cm-’ as basis set quality is incremented. In order to make this comparison, hydrazine’s normal modes 1 and 7-12 should be ignored, as they correspond to a torsion and to vibrations that strongly invovle the hydrogen nuclei, respectively; NEcubane has no corresponding motions. In Figure 1, we have plotted the RHF/4-31G* infrared and Raman intensities for N8 cubane; of the eight nondegenerate vibrational modes four are predicted to be Raman-active and one IR-active. C. Energies. The calculated energies involved in the N8 4N2 reaction are given in Table 111. All the E(NE)-E(4N2) energies (independent of model) show that N E cubane is very energetic relative to four N2 molecules. The RHF/STO-3G calculations give a reaction energy of about 300 kcal/mol, while the R H F calculations with the 4-31G and 4-31G* basis sets suggest that this value is more likely about 530 kcal/mol. Which of these energies of reaction is more trustworthy? It is known that calculations using the RHF/STO-3G basis set significantly overestimate the stability of strained four-member rings (e.g., cyclobutane); see Table IV of ref 9. The STO-3G basis set is also known to have difficulties in predicting energies of reaction even when small rings are not involved. For example, an RHF/STO-3G calculation of the reaction N, + 4NH3 3NH2-NH2 gives a reaction energy too low by ca. 54%. In comparison, RHF c’alculations with 3-21G and 6-31G* basis sets, for the same reaction, are in error by -18% and +2% (see ref 8, p 291). Due to these considerations, one concludes that the R H F reaction energies obtained with the 4-31G and 4-31G* basis sets are, no doubt, significantly more accurate than the STO-3G ones.
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(9) Engelke, R.;Hay, P. J.; Kleier, D. A,; Wadt, W. R. J . Am. Chem. Soc. 1984. 106. 5439
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 5691
Is NE Cubane Stable? TABLE 11: N8 Cubane Frequencies (cm-') model 1 2 951" (T2 ) RHF/STO-3G 747 (E,)' RHF/4-31G 704 (E,)' 775 (T4f RHF/4-31G* 728 (E,)C 961" (T2,)
3 1155' (TI,) 821' (TI,) 1044' (TI")
4 1206 (T2,) 956 (Tzu) 1071" (T2,)
5
6
7
8
1229" (AI,) 960 (T2J 1135.4" (Al,)
1292 (AZu) 969 (AI 1 1135.8 (T2u)
1294 (T2J 1064 (E,) 1223" (E,)
1348" (E,) 1 I26 (A2,) 1336 (Azu)
a Raman-active mode; intensities are (951 cm-I) 0.13, (1 229 cm-I) 0.85, and (1 348 cm-I) 0.30 in D2/(amu.A2); also see Figure intensities are 0.44 (4-31G) and 0.88 (STO-3G) in D2/(amd2);also see Figure I . CSymmetryof the vibration.
1.
* IR-active mode;
TABLE III: N, Cubane Energies"
theoretical model
N 8 cubane abs energies, hartrees
4N2 abs energies, hartrees
E(N8)-4E(N2) re1
RH F/STO-3G//RH F/STO-3Gb MP2/STO-3G//RHF/STO-3G MP3/STO-3G//RI4F/STO-3G MP4/STO-3G//RHF/STO-3G RHF/4-3 IG//RHF/4-31Gb MP2/4-31G//RHF/4-3 IG MP3/4-3 1G//RHF/4-3 IG MP4/4-31G//RHF/4-31G RHF/4-31G*//RHF/4-3 lG* M P2/4- 3 1G *// R H F/4-3 1G *
-429.590 870 6 -430.073 963 9 -430.158 479 3 -430.1690638 -434.119451 2 -435.076 224 6 -435.063 8346 -435.085 771 5 -434.522 976 5 -435.825 6524
-430.002 61 7 2 -430.67 1 5 13 2 -430.632 61 5 2 -430.648 440 8 -435.0168780 -435.953 859 6 -435.866 392 4 -435.923 152 4 -435.357 302 8 -436.572 680 0
258 375 298 301 563 551 504 525 524 469
'
energies, - kcal/mol
"All the correlated calculations were done with the cores frozen and at the mean field geometry. The MP4 calculations included single, double, and quadruple substitutions. 'The N, cubane zero-point energies (ZPE) are 29.4, 23.1, and 27.2 kcal/mol at the RHF/STO-3G, RHF/4-31G, and RHF/4-31G* levels, respectively. The corresponding N2 ZPE's are 3.8, 3.8, and 4.0 kcal/mol, respectively.
+
-
The N, 4NH3 3NH,-NH2 reaction is an interesting comparison case, since it involves an N2 molecule in which A bonds are being transformed into u bonds-with the possibly significant, concomitant, change in the electron correlation energy. The size of the energy errors for this case (see above) suggests we might expect the NE cubane RHF/4-31G and RHF/4-31G* reaction energies to be within &20% or less of the experimental value. Interestingly, the N8 4N2 energies obtained here at the two highest levels of R H F calculation used (Le. RHF/4-31G// RHF/4-31G and RHF/4-31G*//RHF/4-31G*) agree to within about 7% and predict that the reaction should be exothermic by ca. 530 kcal/mol. Since the number of A and u bonds changes markedly in the N E 4N2 reaction ( 8 u bonds are replaced by 8~ bonds), one expects the electron correlation energy to be significantly different between reactants and products. Therefore, correlated calculations were carried out and the results are given in Table 111. Because of the inherent inaccuracies associated with the RHF/STO-3G Slater determinant description, discussed above, only the 4-3 1G and 4-3 1G* post-Hartree-Fock results are discussed. One sees that the 4-31G MP2, MP3, and MP4(S,D,Q) correlation energy corrections all reduce the energy of reaction. The MP4 reduction is intermediate to the MP2 and MP3 ones. The MP4=FC/431G//RHF/4-31G reaction energy (525 kcal/mol) is 38 kcal/mol lower than the analogous mean-field result. The MP2=FC/431G*//RHF/4-31G* calculation reduces the reaction energy by 55 kcal/mol from the corresponding S C F result. There is a significant zero-point-energy correction (ZPC) for the N8 4N2 reaction. For the RHF/4-31G//RHF/4-31G and RHF/4-31G*//RHF/4-31G* models, these are +7.8 and +11.3 kcal/mol, respectively. These substantial corrections are, partially, due to replacement of vibrational modes by translational and rotational ones upon dissociation. NEcubane has 18 vibrational modes, while four N2 molecules have four. If the R H F ZPCs are added to the MP2/4-3lG*//RHF/4-31G* and MP4/4-31G// RHF/4-3 1G reaction energies, one obtains corrected estimates of 480 and 533 kcal/mol. In view of these comments, we predict that the N8 4N2 experimental energy of reaction is covered by the values 530 f 50 kcal/mol. The calculations also yield predictions of the first vertical ionization potential (via Koopman's theorem) and rotational constants of N8 cubane. The RHF/4-31G and RHF/4-31G* ionization potentials are 306 and 280 kcal/mol, respectively. The rotational constants ( A = B = C ) are 3.81 and 4.19 (GHz) at the RHF/4-31G and RHF/4-31G* levels, respectively. D. Reaction Coordinate ResuIts. Since N8 cubane is a highly strained species, arguments in favor of its possible stability are
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of interest. Formation of N, cubane from four N 2 molecules in a one-step [4+4+4+4] cycloaddition process is highly symmetry forbidden.1° (We note that the notations [4+4+4+4] and [2+2] are shorthand for the number of A electrons, in each reacting molecule, that participate in the reaction process.) Conversely, the cycloreversion of N8 cubane into four N2 molecules is symmetry forbidden; Le., there will be a barrier to its (thermal) dissociation due to the required molecular orbital crossings. This will tend to stabilize the NEstructure. Such arguments have been used to rationalize the experimental stability of other highly strained species (e.g., [CHI, prismane).I0 To examine the form of the N8 4N2 barrier quantitatively, we have done reaction coordinate calculations. The reaction coordinate (RC) had the following form. N8 cubane was visualized as being composed of two square, parallel N4 structures separated by some distance. An excursion along the R C was made by changing the size of the N4 squares, the intersquare distance being optimized at each RC value. This motion corresponds to the 16th vibrational mode of the RHF/4-31G model of the N, cubane. The point group symmetry is D4h along the reaction path. Since the N8 4N2 dissociation is symmetry forbidden, a single Slater determinant wave function is not capable of describing the system over the complete course of the reaction, because of molecular orbital crossings between filled and unfilled orbitals and the consequent configuration change. Each orbital crossing manifests itself as a slope discontinuity on the energy hypersurface. To deal with this, we did computations along the R C in two directions: first by compressing 4N2 molecules (an inward excursion) and second by expanding N8 cubane (an outward excursion). The energy value at the crossing of these two types of energy vs RC curves was taken as the barrier to dissociation. This approach probably overestimates the reaction barrier somewhat. However, it has been found to give acceptable estimates (as compared with multiconfiguration SCF calculations) for a similar symmetry-forbidden r e a ~ t i o n . ~ Figure 2 shows the results of reaction path calculations for the (concerted) N8 4N2 reaction. The RHF/4-31G and RHF/ 4-31G* barriers to reaction are respectively 100 and 162 kcal/mol. One expects the RHF/4-3 1G* value to be the more credible. Along the concerted path, a highly symmetry-forbidden [4+4+ 4+4] reaction occurs, as all the orbital crossings take place simultaneously. Clearly, there are lower symmetry reaction paths along which the orbital crossings would occur in sequence rather than simultaneously. That is, one could construct a reaction path
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( 1 0) Woodward, R. 8.; Hoffmann, R. The Conservation of Orbital Symmetry; Academic: New York, 1970.
5692
The Journal of Physical Chemistry. Vol. 94, No. 15, 1990 220 0
7
-
,
-
1
RHF/4-31G* TS
1 \ \ /
8 4
20.0 -200
/ ’
’\
0
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c --
00
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-
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,iL+, :
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0.2
1 i
\$,
1
\
,
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04
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REACTION COORDINATE(A) Figure 2. Energy vs reaction coordinate (RC) results for the concerted dissocation of N, cubane to four N2 molecules. See section IID for a description of the RC. At R C = 0, the molecule is a t the NBcubane equilibrium configuration. The horizontal dashed line that intercepts the RHF/4-31G curve shows the zero-point vibrational energy for that model
on which the [4+4+4+4] concerted reaction is replaced by one in which four [2+2] (symmetry forbidden) reactions occur in sequence. A rough estimate of the reaction barrier height of each of the sequential [2+2] reactions is ca.162/4 = 40 kcal/mol. We note that 40 kcal/mol is a substantial barrier to decomposition and is support for the possibility of an experimental synthesis of N8.
-
It would be desirable to have a multiconfiguration S C F calculation, using a high-quality basis set, of the [4+4+4+4] Ns 4N2 reaction path in order to improve our knowledge of the energy barrier and shape.
111. Predicted Condensed-Phase Properties Because of the very large energy stored in the Ns cubane molecule, we decided to examine its potential properties as an energetic material. First, the mass denisty of crystal phase N8 cubane is predicted. Then two important detonation properties of N8 are predicted; these are its Chapman-Jouguet detonation velocity and detonation pressure. A. Density. One important property of an energetic material is its density. Hence, we wish to estimate the crystal density of N8 cubane. This value, along with the estimated heat of formation, will then be used to estimate Ns’s detonation properties. Stinell has developed an empirical method of estimating the density of any compound containing carbon, hydrogen, nitrogen, oxygen, and/or fluorine, given the structural formula of the molecule. In this method, an atom in a particular bonding environment is assumed (1) to have a particular volume and (2) the molar volume is a sum of such atomic constituent volumes. For the elements considered, a total of 34 different types of “atoms” in different bonding environments were defined. These represent all the atom types needed to describe most neutral organic molecules. Examples of these atoms in particular bonding environments are a carbon atom with four single bonds (denoted as C(l,l,l,l), if the four bonds are not part of any ring systems, and as C(l,l,-l,-l), C( 1,-1,-1,-I), and C(-1,-l,-l,-l) if two, three, or all four of the bonds are part of ring systems). Values for these constituent volumes that correspond to the 34 types of constituents were obtained by a least-squares analysis of over 2000 organic compounds that have known crystal structures and hence known molar volumes. Of course, some of these constituents (such as C ( l , l , l , l ) ) are much more common than some of the others (such as C(-l,-l,-l,-l)). The constituent of ( 1 I ) Stine, J. R. Prediction of Crystal Densities of Organic Explosives by Group Additivity. Los Alamos Report LA-8920, 1981.
Engelke and Stine concern for the present system is nitrogen with three single bonds, all of which are part of ring systems (Le., N(-l,-l,-l)). This constituent is found to have a volume, uN, of 8.759 f 0.705 A3. This value yields an estimated density of 2.65 g/cm3 for N8 cubane. This is an extremely large density compared to that of any known or proposed organic compound. Very few known organic (i.e., C, H, N, 0)compounds have a density greater than about 2.0 g/cm3, and only a few of those proposed as energetic materials have predicted densities greater than 2.1-2.2 g/cm3. However, we note that the N(-1,-1,-1) constituent is relatively rare; only 140 such nitrogen atoms were found in the calibration set of over 2000 compounds that in turn contained over 70 000 atoms. Also, because of the high symmetry of N8 cubane and the lone-pair electrons on each nitrogen atom, we would expect that intermolecular repulsion would tend to reduce the crystal density from our estimated value. This latter correction is difficult to estimate by any simple means; we just note that for two similar molecules an overestimate of the crystal density is found to be the case. These are (1) (CH)8 cubane which has an observed density of 1.29 g/cm3 (ref 12) and a density estimated by Stine’s method of 1.37 g/cm3 and (2) the recently synthesized 1,3.5,7tetranitrocubane which has an observed crystal density of 1.814 g/cm3 and an estimated density of 1.92 g/cm3 (ref 12). Therefore, we will consider three N8 cubanes in which each nitrogen atom has a constituent volume given by uN, uN + u, and uN + 2a, where u = 0.705 A3. These values yield densities of 2.65, 2.46, and 2.29 g/cm3, respectively. We note that any of these predicted (very high) crystal densities make N8 cubane an unusual and interesting molecular form for this reason alone. B. Detonation Properties. We now wish to estimate the performance of N8 cubane as an explosive. Two indicators of performance are detonation velocity and detonation pressure. The ideal (Chapman-Jouguet (CJ)) detonation velocity of an explosive is the velocity at which the chemical reaction zone traverses the explosive, assuming there are no energy losses at the boundaries of the material. Although the CJ detonation velocity is a theoretical concept, in fact, observed detonation velocities can be extrapolated to this ideal value without difficulty. Detonation velocities can be measured quite accurately (errors are typically 0.1%). Hence, the CJ detonation velocity serves as an accurately obtained measure of performance. We also consider the Chapman-Jouguet pressure because it is an indicator of the work that an explosive can do on its surroundings. The C J pressure of an explosive is the pressure at the plane behind the shock wave at which the exothermic chemistry is complete. The pressure at this plane is independent of the reaction kinetics (in the simplest form of theory) and therefore is a property of special interest. The C J pressure is not so easily measured as CJ detonation velocity. For a more complete discussion of both C J detonation velocity and pressure see ref 13. One method of calculating these two quanities is with the TIGER computer code.I4 This code is based on the solution of the hydrodynamic (Euler) equations describing the detonation and an equation of state originally proposed by Becker and later modified by Kistiakowsky and Wi1s0n.I~ This code was written by Cowperthwaite and Zwisler. Given the initial density, heat of formation, and molecular formula of an explosive, this code calculates the CJ detonation velocity and pressure. We wish to compare the performance of N8 cubane with that of one of the best performing explosives currently in use, Le., octahydro-l,3,5,7-tetranitro-l,3,5,7-tetrazocine, more commonly known as HMX. This explosive has a heat of formation of + 18 kcal/mol, a heat of detonation of about -1.5 kcal/g, a measured (12) Gilardi, R. Naval Surface Weapons Center (private communication), 1989. (13) Fickett, W.; Davis, W. C. Detonation; University of California Press: Berkeley, 1979. (14) Cowperthwaite, M.; Zwisler, W. H. Stanford Research Institute Publication No. 2106, 1973. (15) Mader, C. L. Numerical Modeling of Detonation; University of California Press: Berkeley, 1979; pp 41 2-448.
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 5693
Is N8 Cubane Stable?
80.0,,'
9 , 0 1 1
50.0
1
I
,
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Figure 3. Calculated Chapman-Jouguet detonation velocities as a function of x , where the value of x defines the molecular structure C,H,NSOk The density in all cases is 1.9 g/cm3. The values 0-500
are the heats of formation for the corresponding curves. The open circle is the measured value for HMX. crystal density of 1.90 g/cm3, and a molecular formula of C4H8N808.i6 The TIGER code calculates a CJ detonation velocity of 9.14 "Ips and a C J pressure of 40.5 GPa for this material at density 1.90 g/cm3. The experimental values for HMX a t density 1.89 g/cm3 are 39.3 GPa and 9.1 1 mm/ps.I6. N8 cubane is unlike most other explosives in that the only detonation product is diatomic nitrogen (N2), whereas the usual products of explosives include, among others, C02and H20. The TIGER code determines the amount of each detonation product, by minimizing the free energy of the products with respect to their concentrations. In the present case, because there is only one product, the code fails. This is probably because the minimum free energy occurs at a composition boundary and hence is not a usual parabolic minimum. We circumvented this numerical difficulty by considering a hypothetical molecule that contains some carbon, oxygen, and hydrogen. Because we are interested in comparing N E cubane with HMX, we chose a molecule with the formula CXHkN8O2,, where if x = 4 we have the formula for HMX and if x = 0 we have the formula for N8 cubane. We calculated the C J detonation velocity and pressure for values of x close to 0 and then graphically extrapolated to 0 in order to obtain N8 cubane's values. In Figures 3 and 4, we give calculated C J detonation velocities and pressures as a function of x ; in these calculations a density (identical with HMX's) of 1.90 g/cm3 was assumed. Six heats of formation (0, 100,200,300,400,and 500 kcal/mol) were used. From Figure 3 one sees that for any value of x the hypothetical molecule will out-perform HMX, provided it has a heat of formation greater than ca. 100 kcal/mol. As one would expect, a molecule with a heat of formation of 0 kcal/mol is only weakly explosive as x approaches 0. One also sees that for heats of formation greater than 100 kcal/mol the curves do not change rapidly as x approaches 0, and hence the extrapolation to x = 0 is easily performed. The extrapolated detonation velocities for N Eare 9.25, 10.39, 11.17, 11.80, and 12.36 mm/ps, for heats of formation of 100-500 kcal/mol, respectively, at density 1.90 g/cm3. Figure 4 is a similar plot for CJ pressure as a function of x . The C J pressure for N8 cubane extrapolated from these curves is 36.4, 50.1, 60.9, 70.2, and 76.3 GPa for heats of formation between 100 and 500 kcal/mol and density 1.90 g/cm3. Now we wish to estimate the performance of N8 cubane using our best estimates of its heat of formation and density as described (16) Dobratz, B. M.;Crawford, P.C. LLNL Explosive Handbook; Lawrence Livermore National Laboratory: Livermore, CA, 1985; pp 19-56.
0
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Figure 4. Calculated Chapman-Jouguet pressure as a function of x ,
where the value of x defines the molecular structure C,HkNs02x. The density in all cases is 1.9 g/cm3. The values 0-500 are the heats of formation for the corresponding curves. The open circle is the measured value for HMX. TABLE IV: N. Estimated Detonation Velocities and Pressures AH,, kcal/mol density, g/cm3 det vel, mm/ps pressure, GPa +480 2.25 13.67 109.2
+530
2.45
14.51
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15.51
130.5 157.2 114.6 136.7 164.3
13.92
14.75 15.73
above. Table IV lists the C J detonation velocities and pressures for various values of the heat of formation and density. It is seen that the TIGER code predicts N8 cubane to be vastly superior to HMX as an explosive. One should exercise caution in accepting these values. The TIGER code contains a number of parameters whose values were derived from experimental data of existing explosives. NEcubane is very different than any of these existing explosives, and thus these calculations represent a large extrapolation from standard cases. In spite of this caveat, the calculated performance of N8 cubane is so much better than that of known explosives that it seems unlikely to us that it would not be much superior to them, if it could be synthesized. These results indicate that explosives containing large amounts of nitrogen are prime candidates as energetic materials; this comment is strengthened, if the nitrogens are in strained rings.
IV. Summary of Discussion Ab initio calculations have been presented that indicate that isolated cubic NEis a stable molecule. Stability of the N8 structure is demonstrated by vibrational frequency calculations (up to the RHF/4-31G* level of theory). The computed vibrational frequencies are all fairly large (i.e., >700 cm-'). This is evidence for a stable structure whose geometry is relatively well-defined by the energy surface. The R H F energy calculations using basis sets of 4-31G and 4-3 1G* quality give energies for the reaction N8 4N2 between 524 and 563 kcal/mol. Inclusion of electron correlation (with a 4-31G basis set) lowers this reaction energy slightly. Inclusion of zero-point vibrational effects raises the energy of reaction by ca. + I O kcal/mol. Our estimate of the N8 4N2 reaction energy is 530 f 50 kcal/mol; this value is based on the MP4/4-31G/ /RHF/4-31G, MP2/4-31G*//RHF/4-31G*, and RHF/431G.*//RHF/4-31G* calculations. The estimate of the error in the N8 reaction energy is based on the results of a b initio calculations of known smaller nitrogen system reactions and on the internal consistency of our N8,cubane results at different levels of theory.
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5694
J . Phys. Chem. 1990, 94, 5694-5710
The possible stability of N8 cubane is supported by the fact that its decomposition would involve a strongly symmetry-forbidden [4+4+4+4] cycloreversion reaction. By use of reaction coordinate calculations (at the RHF/4-3lG*//RHF/4-31G* level), we estimate that even lower symmetry [2+2] decomposition pathways, which lead to 4N2 molecules, would have activation barriers of ca. 40 kcal/mol. These results support the possibility of an experimental synthesis of N8 cubane. Due to NEcubane’s very high energy content per molecule, we have predicted some of its properties as a condensed-phase energetic material. It is predicted to have a very high crystal density (ca. 2.65 g/cm3). This density is higher than any energetic material, known to us, that contains only C, H, N, 0,and F atoms. The predicted values of detonation pressure and detonation velocity are very high relative to known chemical explosives. The values we consider our best estimates of these quantities for N8 cubane are 137 GPa (1.37 Mbar) and 14.75 mm/ps, respectively. These values are to be contrasted with those for the most powerful explosives in common use today, e.g., 39 GPa and 9.1 mm/ps for HMX. The potential high performance of N8 cubane as an explosive can be traced to three factors: (1) a high energy per molecule
(Le., a heat of detonation of about -4.7 kcal/g), (2) a high condensed-phase density (>2.25 g/cm3), and (3) in its decomposition, 1 mol of reactants becomes 4 mol of products. A point of interest concerning N, cubane as a condensed-phase explosive is that photoexcitation of it could yield an electronically excited state of the molecule whose decomposition is symmetry allowed; Le., the decomposition in the excited state would occur spontaneously. Therefore, it is possible that explosive decomposition of N8 cubane could be initiated by a small number of photons of the correct frequency. Finally, we note that (CH), and N8 cubanes are the end points of a homologous series of cubane-like structures with formula (CH),-,N, (0 5 n 5 8). The known high stability of (CH), and the predicted high energy of NE cubane suggest that there are probably intermediate mixed carbon-nitrogen cubane-like structures that would be stable high-energy materials. This comment also applies to nitrated carbon cubane structures in which one could replace some or all of the remaining C H groups with nitrogen atoms. Acknowledgment. We thank Jim Ritchie of LANL for use of the C A D P A C ~analytic derivatives computer code.
Accuracy In ab Inltlo Reaction-Energy Computations. 1. Compounds of Flrst-Row Elements John R. Van Wazer,* Vladimh Kello,+ B. Andes Has, Jr., and Carl S. Ewig Department of Chemistry. Vanderbilt University, Nashville, Tennessee 37235 (Received: August I , 1989; In Final Form: February 13, 1990)
Ab initio enthalpy computations were carried out for over 40 gas-phase diamagnetic molecules (including 18 hydrocarbons). All employed optimized geometries, basis sets ranging from 4-3 IG to 6-31 1++G(2df,2pd), and a series of electron-correlation approximations (MP2, MP3, MP4SDQ, and MP4SDTQ, as well as CCD, CCSD, CCSD+T(CCSD), and several CCSDT versions). The energies of forming the various molecules from the nuclei and electrons at 0 K with no nuclear motion were calculated from experimental data and compared with the various ab initio values. The percentage difference between these experimental and ab initio values without correlation was found to be characteristic of each molecule regardless of the size of the basis set. For the hydrocarbons (and hydrides of other first-row atoms) these differences could be quantitatively related to the ratio of the number of hydrogens to the other atoms in each molecule. Electron correlation reduced this percentage difference by roughly a factor of 2. The enthalpies at 298 K of chemical reactions between the molecules were considered in terms of the disagreement between the experimental and theoretical enthalpies, with emphasis on generic classes of reactions, e.g., formation reactions involving (1) dehydrogenation of the common hydrides, or (2) combination of the homonuclear diatomics. Generic reactions showed up regularities in disagreements between experiment and theory. Reasons for occasional large disagreements were probed.
A. Introduction After years of slow progress, the computation of reaction enthalpies and other thermodynamic quantities by purely theoretical, nonempirical methods may soon emerge as a serious competitor not only to empirical and semiempirical approximations but also in many cases to direct experimental measurement. In the study reported herein, we investigate whether the common procedure of obtaining reaction enthalpies from differences in total molecular energies based on single-configuration wave functions, with and without electron correlation, is a useful step in this direction. We also look into the assumption that a plethora of polarization functions and increasingly complicated and time-consuming electron-correlation approximations should assure a small error in the theoretically computed enthalpy for a chemical reaction. For SCF computations and alterations to them that incorporate electron correlation, e.g., multiconfiguration S C F (MCSCF) and ‘Permanent address: Department of Physical Chemistry, Comenius University, 842 1 5 Bratislava. Czechoslovakia.
0022-3654/90/2094-5694$02.50/0
configuration interaction (CI), the variation principle demands that a lower energy corresponds to greater accuracy. However, this does not apply to many correlation techniques, such as the usual many-body perturbation procedure (Maller-Plesset or MP), which can in principle over- as well as underestimate the correct total energy. Of course there is no a priori limit on the size or sign of energy differences among molecules. Although massive computations are thought to be required to achieve a close approach to the exact total energy of a molecule, it is reasonable to expect that, due to cancellation of errors, a rather poor but more easily computed approximation might be sufficient for obtaining consistently acceptable values for the very much smaller energies of chemical reactions. Since even Hartree-Fock limiting energies have been computed only for the atoms and a few diatomics, all meaningful reported ab initio reaction energies involving manyatom molecules are based inferentially on error cancellation. The trick is to find an incomplete mathematical description for the molecular systems of interest in which error cancellation is routinely sufficient to allow trustworthy extension to the ther-
0 1990 American Chemical Society
