J . Phys. Chem. 1990, 94. 6924-6925
6924
level). Such a difference is large enough, pointing toward a thermodynamic preference for the open-chain structure 2 at low temperatures. Nevertheless, the latter still lies much higher in energy than three free N2 molecules (by 175 f 3 kcal/mol at an approximate MP4/6-31 lG(2df) level; cf. Table 11). Thus, its observability in the gas phase depends on, among other things, the corresponding barrier height for decomposition. Other fragmentation processes such as the homolytic cleavage yielding 2(N3’) may also be important in determining the relative stability of the open-chain structure 2. I n summary, this Comment points out that the open-chain form 2 is significantly more stable than the cyclic form 1. Further appropriate studies exploring the whole N6 potential energy surface are necessary to establish whether 2 is a realistic candidate for an actual preparation in the laboratory.
1
‘Research .4ssociate of the National Fund for Scientific Research (Belgium).
Minh Tho Nguyent
Department of Chemistry University of Leucen 8-3030- Leucen, Belgium
Receiaed: January 8, I990 4
Reply to Comments on the Stable Points on the N, Energy Hypersurface Sir; In the preceding paper in this issue, Nguyen makes a comment related to the paper “Five Stable Points on the N6 Energy Hypersurface ...’’.I He reports a b initio calculations on the thermodynamic stability of the Ci structure (2) relative to the Dsh (hexaazabenzene) structure 1 and finds that 2 is 15-35 kcal/mol more stable that 1. In turn, either 1 or 2 is ca. 200 kcal/mol higher in energy than three N2 molecules. I agree with most of the results he presents. Given this opportunity, 1 would like to make some comments on ( I ) the motivation for the computations presented in ref 1 and (2) the sensitivity of 2 s energy hypersurface to the computational method employed. The latter comments may have value to other workers doing calculations on molecules containing hypervalent first-row atoms. Firstly, the main purpose of the calculations described in ref 1 was to examine N6 structures that are ( I ) possibly kinetically fairly stable to degradation to three N,molecules but (2) thermodynamically very unstable to this reaction. Molecules with these two properties are potentially useful as energetic materials. The five nitrogen structures of ref 1 are interesting in this sense because there exist (isoelectronic) carbon-hydrogen analogue structures that have been experimentally isolated.2 Furthermore, these five nitrogen forms have structures consistent with classical ideas of valence. In contrast, 2 is a highly nonclassical structure-with centers N,and N5being hypervalent. Note that structure 2 can be viewed as the product of a ring-opening reaction of 3, where the N,-N6 and N2-N, bonds are broken. This suggests that 2 may have radical character and, consequently, would have a very transient existence. If this is so, 2 would not be interesting as a possible high-energy material. However, 2’$ hypervalent nature makes it interesting in its own right. Hehre et al. note that -... first row atoms generally obey the classical Octet rule”.3 They further point out that the molecules containing second-row atoms are frequently hypervalent and re~~~~
~
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~
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( 1 ) Engelke, R. J . Phys. Chem. 1989, 93, 5722.
(2) (a) Scott, L. T.; Maitland, Jr., J . Chem. Reu. 1972, 72, 182. (b) Kobayashi, Y.; Kumasaki, I . Top. Curr. Chem. 1984, 123, 103. (3) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbiral Theory: Wiley: New York, 1986; pp 181-186.
0022-3654/90/2094-6924$02.50/0
3 Figure 1. The three N, structures of interest: (1) Dbh hexaazabenzene, (2) Nguyen’s C, structure, and (3) C2hbicyclopropenyl.
TABLE I: Results of Calculations on Open-Chain Ns Nguyen’s C, Ramek‘s C, level of theory structure structure dissociates dissociates AM1 RHF/3-2 1G RHF/6-31G RHF/6-31G*
dissociates becomes C2. stable
dissociates stable stableb
“The C, structure relaxes to Ramek’s C2 structure. bSee the last two paragraphs of the text.
quire basis sets containing functions of d-type symmetry for their proper description. Below calculations are described that indicate d-type functions are also needed for the proper description of the hypervalent first-row structure 2 and for a closely related C2 symmetry structure. As noted by Nguyen, 2 corresponds to a stable structure at the RHF/6-31G* level of theory. Previous workers have found a closely related C, structure to be a stable point using calculations up to the RHF/6-31G leveL4 To systematically examine the dependence of stable structure form on the level of theory used, I have done geometry optimizations (and where necessary frequency calculations) at the AMI, RHF/3-21G, RHF/6-31G, and RHF/6-31G* levels of theory on both the Ci and C? point group structures. Most of these calculations were done with Gaussian 88 on a VAX-8600 c o m p ~ t e r . ~ ( 4 ) Ramek. M J Mol Srrucr (THEOCHEM) 1984, 109, 391
1990 American Chemical Societv
The Journal of Physical Chemistry, Vol. 94, No. 17, 1990 6925
Comments
For the Cistructure, Nguyen’s RHF/6-31G* geometry was always used for the initial guess, and for the C, structure, Ramek’s RHF/6-31G optimized geometry was always used. The results are presented in Table I. One sees that the AMI and RHF/321G calculations, for both structures, lead to dissociation. In all four cases the dissociating structures were tending to three N, molecules and not two N 3 radicals. For the RHF/6-3 1G calculations, Ramek’s C, structure is recovered in both cases; i.e., the Ci guessed structure relaxes to the C, form. Finally, when the basis-set quality is raised to the 6-31G* level, the RHF calculations give the Ciand C, stable points. Clearly, when hypervalent structures such as 2 are studied, it is imprudent to begin searches for a stationary point structure either with a semiempirical method or with an RHF calculation that uses a basis set of less than split valence polarization function quality. For example, a search using the RHF/6-31G model would miss the Ci stable point. As a test of whether 2 has radical character, the stability of the RHF wave function to relaxation to UHF form was examined.6 This was done for the RHF/6-31G* (Ci)and RHF/6-31G (C,) stable forms. It is found that the RHF/6-31G* Cistructure wave function is marginally stable to this relaxation, while that of the
+
( 5 ) Frisch, M . J.; Head-Gordon M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J . S.;Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J . P.; Fluder, E. M.; Topiol, S.;Pople, J. A . Guussiun 88; Gaussian, Inc.: Pittsburgh, PA, 1988. (6) Seeger, R.; Pople, J . A. J . Chem. Phys. 1977, 66, 3045.
RHF/6-3 1 G C2 structure wavefunction is unstable. A point of interest concerning the reactivity of structure 2 is that its various centers carry quite large net charges as determined from a Mulliken population analysis. The RHF/6-31G* wave function for 2 shows net (i.e., nuclear plus electronic) charges of +0.26e (N,),4 4 3 e (N,), and +0.17e (N3)for 2’s various centers. In contrast, the charges carried by individual centers of the five structures studied in ref 1 all lie in the range -0.15e to +0.08e, when calculated at the RHF/4-31G* level. Thus, 2 should be much more subject to nucleophilic and electrophilic attack than the cyclic N6 structures. A last point is that, in contrast to Nguyen’s observation, I was able to find a C, stationary point at the RHF/6-31G* level of theory for which the RHF/6-31G* harmonic frequencies are all real. There are significant differences between the geometries of the C, RHF/6-31G and RHF/6-31G* structures, e.g., up to 0.04 8, in bond lengths and 2O in angles. The RHF/6-31G* Ci and C, structures are geometrically quite similar-aside from the difference in their point groups. The difference in the nuclear repulsion energy between them is 0.0441 hartree (27.7 kcal/mol). However, the difference in their total energies is only 0.0001 hartree (0.05 kcal/mol), Le., negligible. Acknowledgment. This work was supported by the United States Department of Energy. Los Alamos National Laboratory, MS P952 Los Alamos, New Mexico 87545 Received: February 20, I990
Ray Engelke
