J . Phys. Chem. 1990, 94, 6923-6924
6923
COMMENTS Comments on the Stable Points on the Ne Energy Hypersurface Sir: The last decade has witnessed a continuing interest of theoretical chemists in the stability and observability of the Nq species. Stimulated by the work of Vogler, Wright, and Kunkley' (in 1980) which claimed to have the experimental evidence for the existence of N6in a matrix at low temperature, different groups have carried out a b initio molecular orbital calculations on this interesting m ~ l e c u l e . ~ -The ~ recent synthesis and characterization* of a triple-decker sandwich complex (CSMes)Mo(s6-P6)Mo(c5Mes), in which a cyclic P6 occupies the central bridge position, raises hope for an eventual stabilization of the analogous hexazine ligand 1 by coordination to metal fragments9 As far as free hexazine 1 is concerned, none of the earlier theoretical studies2" were, however, conclusive about its stability with respect to the decay to three N 2 molecules.
In a paper entitled "Is N6 an open-chain molecule?" published in 1983,5 Huber, Ha, and Nguyen ( H H N ) reported that the open-chain form 2 (with a C2symmetry) is more stable than the cyclic 1 by (100 kJ/mol from floating orbital geometry optimization, FOGO, calculations). In an independent work, Ramek6 obtained a similar result from his HF/6-31G calculations. Because of the lack of electron correlation both in the calculations of HHN5 and in those of Ramek? the relative stability between 1 and 2 can be questioned. Nevertheless, the existence of an open-chain form 2 having two azide groups as a local minimum on the N6 potential energy surface merits a serious consideration. Therefore, I was intrigued to read a recent paper by Engelke' on "five stable points on the N, energy hypersurface". Engelke considered five stationary points that all have cyclic structure (analogues to benzene, Dewar benzene, benzvalene, prismane, and bicyclopropenyl of the (CH), isomers) and found that hexazine 1 lies much lower in energy than the other forms. He was apparently not aware of the possibility of an open-chain (N& structure. For instance, Engelke stated "A uniform set of ab initio calculations has been performed on all the valence isomers of N6 ..." (ref 7 , p 5726). In what follows, I intend to point out again, on the basis of refined MO calculations, that the open-chain form 2 is energetically more stable than its cyclic isomer 1. Geometrical parameters of both structures 1 and 2 are optimized at the H F and MP2 levels using the 6-31G(d) basis set. Harmonic vibrational frequencies are computed at the HF/631G(d) level in order to characterize stationary points and to estimate zero-point-vibrational (ZPE) contributions to relative ( I ) Vogler, A.; Wright, R. E.; Kunkley, H. Angew. Cfiem., Inr. Ed. Engl. 1980, 19. 717. ( 2 ) Ha, T. K.;Cimiraglia, R.; Nguyen, M. T. Cfiem. Phys. Lett. 1981.83,
317. ( 3 ) Huber, H. Angew. Cfiem. 1982, 94, 71. (4) Saxe, P.; Schaefer 111, H. F. J. Am. Cfiem. SOC.1983, 105, 1760. (5) Huber. H.; Ha, T. K.; Nguyen, M. T. J. Mol. Srrucr. (THEOCHEM) 1983, l05, 351. (6) Ramek, M. Oesterr. Cfiem. Z . 1983, 84, 254; J . Mol. Struct. ( T H E O C H E M ) 1984, 109, 391. (7) Engelke, R. J . Pfiys. Cfiem. 1989, 93, 5722. (8) Scherrer, 0.J.; Sitzmann, H.; Wolmer-Shauser, G. Angew. Cfiem., Int. E d . Engl. 1985, 24, 351. (9) Moore, D. S.;Robinson, S. D. Ado. Inorg. Cfiem. 1987, 32, 171.
0022-3654/90/2094-6923$02.50/ 0
TABLE I: Optimized Geometries for 1 and 2" form (D6h)
2 (Ci)
Darameter
HF/6-31G(d)b
MP2/6-31G(d)
r(N-N) r(N-N,) rW,-NJ r(N2-N3) LNNlN2 LN I N 2 N 3
1.285 1.430 1.236 1.101 107.3 174.8
1.337 1.463 1.262 1.155 107.2 171.6
'Bond lengths are given in angstroms and bond angles in degrees. bThe zero-point energies are not much different: 17.5 and 17.0 kcal/ mol for 1 and 2, respectively. Vibrational wavenumbers of 1 have been discussed in ref 7. The wavenumbers of 2 are as follows: 2489 (a8, 0); 2390 (bu, 2021); 1419 (ag, 0); 1307 (bu, 443); 1048 (ag, 0); 709 (bu, 52); 680 (ag, 0); 630 (bg, 0); 588 (au, 34); 318 (ag, 0); 184 (bu, 1.6); and 34 (a", 2.5). Values are in cm-I. In parentheses are the normal modes and IR intensities in km/mol. The 6-31G(d) basis is identical with the conventional 6-31G* basis.
TABLE 11: Relative Energies between Ns Isomers" relative energyd total energyC levelb basis set 2 2-1 2-(3N2) -17.0 HF 6-31G(d) -326.457 11 219.1 -327.471 30 -30.8 MP2 184.8 6-31G(d) -17.3 MP3 193.5 -327.429 85 6-31G(d) -27.5 182.7 -327.527 86 M P4 6-31G(d) -18.4 -326.53036 HF 220.9 6-311G(d) -35.1 188.3 MP2 -327.59023 6-31 lG(d) HF -15.5 221.3 -326.54464 6-311G(2d) -31.9 -327.658 64 MP2 185.7 6-31 lG(2d) -21.8 HF 216.2 -326.543 43 6-311G(df) -35.3 -327.695 42 MP2 179.0 6-31 lG(df) Employing MP2/6-31G(d)-optimized geometries. Frozen cores in MPn calculations. In hartrees; energies of other structures are omitted for simplicity. kcal/mol with respect to 2.
energies. The latter are determined from single-point MdlerPlesset perturbation theory calculations (MPn)'O with different basis sets using MP2/6-3 1G(d)-optimized geometries. In previous s t u d i e ~employing ~,~ lower level calculations (FOGO, HF/3-21G, and HF/6-31G), a gauche structure with a C2 symmetry has been calculated to be lower in energy than the trans form 2 (C, symmetry). In this work, attempt to locate such a C2 structure at both the H F and MP2 levels with the 6-31G(d) basis set has not been successful. The trans form 2 is characterized as a minimum having all real wavenumbers (Table I). As usual, the correlation effect on the bond distances is significant. All the bond lengths under consideration are lengthened in going from the H F level to the MP2 (Table I ) . Recent studies" suggested that, for the molecules of this type, the true ro distances may lie inbetween the H F and MP2 values. Of particular interest is the relative energy between both open-chain and cyclic forms. As seen in Table 11, the diazide structure 2 is calculated to lie lower in energy than the hexaaza form 1 at all levels of theory considered. In addition, correlation energy tends to enlarge the energy diference in favor of the open form. Assuming a simple additivity relationship between the effects of basis set and correlation, a value of about 28 f 3 kcal/mol can be estimated for the enthalpy difference (at 0 K) between both isomers (at an approximate MP4/6-31 lG(2df) (IO) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A,; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Gaussian-82; Carnegie-Mellon University: Pittsburgh, PA, 1983. ( 1 1) (a) Nguyen, M. T.; Riggs, N. V.; Radom, L.; Winnewisser, W.; Winnewisser, B. P.; Birk, M. Cfiem. Pfiys. 1988, 122, 305. (b) Nguyen, M. T. Cfiem. Pfiys. Left. 1989, 157, 430.
D 1990 American Chemical Society
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~~~~
~
~~~
~
~~
~~
~~~~
( 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 dissociates dissociates RHF/3-2 1G becomes C2. stable RHF/6-31G RHF/6-31G* 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
