10789
J. Phys. Chem. 1992,96,10789-10792
Ab-Initio Correlated Calculations of SIX Ne Isomers Ray Engelke Los Alamos National Laboratory,' MS P952, Los Alamos, New Mexico 87545 (Received: July 9, 1992; In Final Form: September 29, 1992)
MP2/6-31G*//MP2/6-3 1G* structures, energies, and vibrational frequencies have been calculated for six N6 isomers. These isomers are the nitrogen analogues of the following carbon structures: benzene, Dewar benzene, benzvalene, triprismane, bicyclopropenyl, and a diazide. They are of interest because there are experimentally known metastable isoelectronic CH structures in some cases and because of the predicted extremely high-energy content of the nitrogen forms relative to three N2 molecules. These characteristics make some of the N, structures prime candidates as energetic materials. The nitrogen structures are also of interest from the standpoint of quantum-chemical theory because the character (Le., the number of imaginary vibrational frequencies) of their energy hypersurface stationary points is a strong function of the theoretical model used, e.g., of basis set quality and/or of whether electron correlation is included in the model. Comparisons are made with a variety of ab-initio models to illustrate this point.
I. Introduction We report a uniform set of MP2/6-31G*//MP2/6-31G* calculations (hereafter called MP2/6-3 1G*//) of six stationary points on the N6 energy hypersurface. These stationary point structures are the nitrogen analogues of the carbon-hydrogen forms (1) benzene, (2) Dewar benzene, (3) benzvalene, (4) triprismane, (5) bicyclopropenyl, and (6) a diazide (see Figure 1) and are isoelectronic with the carbon forms. The carbon structures 1-5 are experimentally knownS2 Recently, there have been a significant number of ab-initio calculations on 1-6 and on other pure nitrogen ring structures.+I2 An important motivation for these studies is the possibility that such molecules can be used to store energy. Such metastability is not unusual. For example, ethylene yields ca. 12.5 kcal/mol if it is pyrolyzed to graphite and H2. What is unusual about the nitrogen structures is the omount of energy they are predicted to release upon degradation to N2.The energies are predicted to be in the hundreds of kcal/mol range (i.e., ca. >2 kcal/g). This surpasses the energy storage per unit mass in the b a t performing condensed-phase propellants and explosives presently known. Vibrational frequency calculations indicate that some of these structures may be mistant to decay; Le., very energetic metastable nitrogen molecules may exist that can live for significant periods of time. These molecules are also of interest because various levels of abinitio quantum-chemical theory Mer substantially even in their qualitative predictions concerning them. A change in basis set and/or inclusion of electron correlation in the model can radically alter the predictions (e.g., on whether a particular geometrical form is stable). Comparisonsof the MP2/6-31G*// results with RHF/431G*// and RHF/4-31G// results are used to illustrate this point. The dependence of the energy release obtained from the N6structures upon decay to 3N2molecules is also examined as a function of the quantum-mechanical model used.
II. ACInitio Calculations To orient the reader, we outline the abinitio results on highenergy nitrogen ring compounds reported hitherto. Structure 1 was reportedly observed in a matrix by Vogler et al.;" this stimulated the calculations of 1 reported in refs 3 and 4. Further calculations related to the Vogler claim (but interpreting it as an also see refs 7 and 8. observation of 6) were then publi~hed;~.~ Calculations of 2-5 were reported next.9 Abinitio calculations have also been published for tetrahedral N4and for N8cubane.'*I2 References to earlier calculations on the various nitrogen structures can be found in refs 3-12. Many of the results in refs 3-12 were obtained with self-consistent-field methods (Le., restricted Hartrce-Fock (RHF) calculations). However, structm optimizcd with correlated methods have been reported, along with the associated vibrational frequencies, in some cases (e.g., on 1; scc ref 11). The effect of 0022-3654/92/2096-10789S03.00/0
TABLE I: Character of the Stationary Points vs Model" point
N6 form of benzene (1) Dewar benzene (2) benzvalene (3)
prismane (4) bicyclopropenyl (5) diazide ( 6 )
RHF/C
model RHF/4-
MP2/6-
31G)J
31GiJJ
31GbJJ
stable stable stable stable noneb noneb
stable stable
hill stable
stable stable stable
stable stable
TS
TS stable
TS TS TS
stable stable TS stable stable stable "Entries show the character of the stationary points as determined from the normal vibrations of the structure. bNone means that no stationary point corresponding to this structure could be found within the model. N2
including correlation can be strong. In particular, the predicted energy storage is reduced. To the author's knowledge, there are no reported calculations on 2-5 in which the structural optimizations were done on a correlated energy hypersurface. We report such calculations here and, in addition, characterize the stationary points so found with vibrational analysis on the correlated energy hypersurface. The calculations we report were done with CADPAC4 on a CRAY X-MP computer.14 In these calculations, integrals with magnitude S10-l0 were neglected. The SCF convergencecriteria for an acceptable change in density matrix elements from cycle to cycle were 10" and lo-' for gradient and second-derivative work, respectively. SCF calculations were started by use of the one-electron Hamiltonian. The criterion for having located a stationary point on the energy hypersurface was that the largest component of the (Cartesian coordinate) energy gradient be less than 1.5 X h/bohr. Analytic second derivatives of the energy were used to determine the vibrational frequencies.
III. Results Stable Point Character and Ceometriea Abinitio calculations on 1-6 produce predictions that depend significantly on the level of theory used. This is illustrated by the results in Table I. There, we present the stability predictions of the RHF/4-31G//, RHF/4-31GS//, and MP2/6-31G*// models for the various structures. Structures 1-5 all have classical valence forms,albeit they are, in some cases, highly strained. Except for 1 and 5, the various levels of theory all predict that these structures compond to stable molecules. For 1, the addition of correlation effects alters the conclusion qualitatively. The Dahstructure at the MP2/6-31GS// level is predicted to be a hill with two imaginary frequencies at 216i cm-l; this is in agreement with the results of other workers." 0 1992 American Chemical Society
10790 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Engelke TABLE I 1 MP2/&31G*//Hexmu Isomer Stmhurrl Puuwten’ N, form of
point group
benzene (1) D6h Dewar benzene ( 2 ) C2,
benzvalene ( 3 )
C,
prismane (4)
D3h
bicyclopropenyl (5)
(C2hv C2A
diazide ( 6 )
N2
struc param Rl R1 R2 R3 AI A2 Rl R2 R3 R4 AI A2 A3 Rl R2 RI R2 R3 AI A,
paramb value
electronic state
1.337 ]A* 1.278 1‘41 1.467 1.528 108.3 94.9 1.133 1‘41 2.716 1.393 1.585 101.1 95.3 55.3 1.532 1Al’ 1.500 (1.475, 1.448) (]Ag, ]Al) (1.526, 1.539) (1.239, 1239) (47.9, 47.5) (102.5, 113.4) (1.463, 1.463) (]Ag, ]A,) (1.262, 1.263) (1.155, 1.155) (107.2, 107.3) (171.6, 171.4) 1.130 1zg+
“Not all the structures listed are stable points; see Table I. Lengths are in A and angles in deg.
6
Figure 1. Structures of 1-6.
The case of 5 is more complex. With the RHF/4-31G// model, there does not seem to be a stationary point corresponding to either the C2, or the C, form at all. At the RHF/4-31G*// level, the C, structure is a transition state, whereas the Cu form is predicted to be stable. Including correlation at the MP2/6-31G*// level yields C, and C, structures that are both predicted to be transition states. The diazide 6 is a nonclassical structure. Atoms 3 and 4 are hypervalent;* one would think this would make it a difficult case to calculate. The RHF/C31G// model predicts the Ci structure is a transition state, whereas the C2 form is stable. With RHF/4-31G*// both structures are predicted to be stable. When correlation is included at the MP2/631G*// level both structures are predicted to be transition states. If lower levels of theory (e.g., AM1 or RHF/3-21G//) are used, there seem to be no stationary points at all corresponding to these forms.8 The predictions for 1, 5, and 6 indicate that these molecular geometries depend on subtleties of the energy hypersurface. That is, a change in the level of theory can alter the small energy differences that define the character of the stationary points. This observation argues against these structures being stable molecular forms at ordinary conditions. This is in contrast to the predictions for the structures 2, 3, and 4, which appear to be model independent. The above results constitute a warning that, when calculating structures of this type, one has not reached a level of theory where it is safe to draw even qualitative conclusions about stability until fairly good basis sets are being used and some correlation is included in the model. Another noteworthy point is that it is not safe to do preliminary searches for stationary points Corresponding to molecules of this type with cruder methods, because there may not be corresponding stationary points of any type on the associated
energy hypersurface (e.g., 5 with the RHF/4-31G// model). Next we discuss the quantitative properties of the predicted geometries as given in Table 11. The effect of inclusion of electron correlation on the structures is the point of primary interest. Inclusion of electron correlation usually increaw the predicted length of chemical bonds. This can be understood qualitatively as being due to the electrons more effectively avoiding each other than is possible in a self-consistent-field theory; consequently, the volume between bonded nuclei contains less electronic charge in correlated theories. This causes increased repulsion of the nuclei at a given separation and increased equilibrium bond lengths. RHF geometries for 1-5 (RHF/4-31G// and RHF/4-31G*//) and for 6 (RHF/6-31G*//) have been published in refs 9 and 7, respectively. Comparisons of the bond length values in these references with those of Table I1 bears out the idea that inclusion of correlation energy increases the bond lengths. (Note that we exclude 3 from this discussion because optimization at the MP2/6-3 lG*// level qualitatively altered its geometry.) The N,-N2 piece of the molecule essentially detaches from the remainder of the molecule when MP2/6-31G*// theory is used (i.e,, R2= 2.716 A)). For 1-2 and 4 to 6, the increasein bond lengths in going from RHF/4-31G*// to MP2/6-31G*// is on the average +4.2%, with the maximum (minimum) increase being +6% (+2%). Bond angle changes are not as simple to analyze, because they depend on the method of definition. But, in general, the changes are small, being ca. f 2 % for the same increase of model quality. It is of interest to compare the MP2/6-31G*// bond lengths in 2 and 4 with those computed by the same method for the unstrained structures diimide (N2H3and hydrazine (N2H,,). Note the 2 and 4 are especially interesting because these structures are the ones which are mostly likely to be observed experimentally of those shown in Figure 1. The computed MP2/6-31G*// NN bond lengths in diimide and hydrazine are 1.481 and 1.266 A, respectively. The N-N bonds in 2 are 1.278 A long. This is less than 1% longer than the computed doublebond length in diimide and hints at a kinetic stability similar to diimide. The single bonds in 2 are distinct from each other. The bond between atoms N, and N3 is 1.467 A long. This is actually ca. 1%shorter than the computed single-bond length in N2H4and suggests similar kinetic stability. The N I N zbond in 2 is probably the kinetic weak point on this
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10791
AbInitio Correlated Calculations of Six N6 Isomers
1
TABLE III: Hexrru Isomer Enemieso
N, form of benzene (1) Dewar benzene (2) benzvalene (3) prismane (4) C,, bicyclopropyl (5) C, bicyclopropyl Ci diazide (6) C2 diazide 3N2
absolute E MP2/6-31G*// -321.442 092 -321.388 941 -321.444616 -321.251 688 -321.395 338 -321.388 193 -321.491 916 -327.492059 -321 .184 7 23
relative E MP2/6- RHF/431G*// 31G*// 215 243 24gb 289 213b 303 331b 382 244 286 249 294 184 224c 184 224‘ 0 0
aI
1
(4)
\
1
\
- 400.0
400*0-
2 3so.o-
-
350.0
300.0-
-
900.0
250.0-
- 250.0
0
Y
5 -2
“Absolute energies and energies relative to 3N2 are in hartrees and kcal/mol, respectively. Note that structures, 1, 5, and 6 are not stable points within the MP2/6-31G*// model; see Table I. *The MP2/631G*// zero-point energies for 3N2, N6 Dewar benzene, benzvalene, and prismane are 10.6, 14.0, 11.9, and 13.3 kcal/mol, respectively. These lead to negligible changes in zero-point energy for the reaction N6 isomer 3N2. CRHF/6-31G*// value.
-
molecule with a computed length ca. 3% longer than that computed for N2H4. For 4 both types of computed single bonds are longer than the computed values for N2H4, being ca. 3% and 1% longer for R , and R2,respectively. The Rl bonds of the cyclopropane rings are the probable kinetic weak point on this structure. Structure 6 is unusual in that it is hypervalent. It can be viewed as the (biradical?) structure resulting from opening the azacyclopropane rings of 5. To give a discussion of 6 similar to that given immediately above for 2 and 4,we need the MP2/6-31G*// value of the N2 bond length, which is 1.130 A. Structure 6 is drawn in Figure 1 with double and triple bonds on the outer atoms. It is drawn in this way because of the computed values of those bond lengths. The computed N1N2bond length ( R , )is 1.463 A; this is ca. 1% shorter than the calculated N-N bond in N2H4. The computed N2N3 bond length (R2)for 6 is 1.262 A; this is ca. 0.3% shorter than the computed value of N-N in diimide. For the N3N4bond length ( R 3 )in 6, one finds 1.155 A, which is only ca.2% longer than the calculated value for N2. Structure 6 is clearly very unusual, and it is not clear that the MP2/631G*// model is complete enough to calculate it accurately. Energies. Table I11 and Figure 2 are the energy results for 1-6. Figure 2 shows the energies of 1-6 (relative to three N2 molecules) as the quality of the quantum-chemical model improves. This figure shows that this relative energy (E) is large for any of the structures (Le., 180 C E < 440 kcalfmol). Note that as the level of theory is increased from RHF/4-31G// to MP2/6-31*//, the relative energies fall. Since, within the MP2/6-31GS// model, only 2,3,and 4 are stable points, we concentrate our attention on them. For structures 2 and 4,the reduction in relative energy as the model is improved is 74 and 109 kcal/mol, respectively. For structure 3,this drop is 134 kcal/mol; structure 3 is a special case, since it is only quasi-bound within the MP2/6-31GS// model. Two of its nitrogen atoms are very stably bonded essentially as an N2 molecule (see the R2 parameter of Table 11). This accounts for 3 being the only structure whose energy trendline in Figure 2 crosses those of the other structures as one increases the level of theory to MP2/6-31G*//. The geometry and vibrational analysis (see below) indicates that 3 is too fragile to be interesting. The MP2/6-31GS// relative energies of 2 and 4 are 289 and 382 kcal/mol, respectively; these values correspond to specific energies
(0)
W
-------
’
200.0
150.0
’
‘
150.0
RHF14-37QN RHFJ4-37Q’fi MP210-3W*11 Figure 2. Energies of structures 1-6 relative to three N2 molecules as
a function of quantum-mechanical model. Sophistication of the model increases to the right. The (?) indicating the RHF/4-31G// value for 5 means that no stationary point could be found within the model.
of 3.4 and 4.6 kcal/g. Such energies of metastability are remarkably high. Current high-performance explosives typically have energies of metastability of ca. 1.5 kcalfg. As noted in a footnote of Table 111, the MP2/6-31G*// zero-point energy corrections to the metastability energies of 2, 3,and 4 are negligible, being ca. 3 kcalfmol. There is a final point to be made concerning the relative energies. Such energies have been previously published for lower levels of theory (see Table 111 of ref 9). Comparing the MP2/ 6-31G*// values of Table 111 with the MP2/4-3 lG*//RHF/43 1G* values of ref 9 shows agreement between the two models within a few kcal/mol, except for 3. As already noted, benzvalene (3) is a special case since going to the MP2/6-31G*// level qualitatively changed the predicted stable geometry. We conclude that, if the geometrical structure of molecules such as 1-5 is well defined by the lower levels of theory, the effect of correlation on the relative energies can be satisfactorily included by calculating it at the RHF geometry. A similar result has been found for N8 cubane (see refs 10 and 11). This is important for larger molecules of the type being treated because geometry optimizations on correlated energy hypersurfaces can be computationally expensive. Vibrations. MP2/6-3 lG*// energy second derivatives were obtained in order to characterize the stationary points. These quantities can also yield vibrational normal modes and frequencies in the harmonic approximation. We will only discuss the vibrations of 2,3, and 4,since only these structures are predicted to be stable within the MP2/631G*// model (see Table I). Results for the other structures are available from the author. The vibrational frequencies and symmetries are given in Table IV. Both 2 and 4 appear to be quite well defined by the MP2/6-3 lG*// energy hypersurface; they have lowest energy vibrations of ca. 450 cm-I. In contrast, the lowest energy vibration of 3 is only 67 cm-I; this normal mode consists of a torsion of the Nl-N2 and the N3-N4-N,-N, “molecules”relative to each other (see Figure 1). This low-frequency mode and the anomalously large value of R2 for 3 indicate that this molecule is not chemically bound and so is uninteresting in this sense. Structures 2 and 4 appear to be realizable molecules. A question concerning them is whether their normal modes indicate
TABLE I V MP2/&31C*// Stable H e x ” Isomer Vibrational Frequencies (cm-’) N6 form Of Dewar benzene (2) benzvalene (3) prismane (4)
1
429 a2 61 a2 490 e”
2 431 b, 117 a, 490 e”
3 452 b2 126 bl 550
a,’’
4 462 a, 142 b2 695 e’
5 101 a2 201 b2 695 e’
6 712 a, 336 a2 819 e’
1 868 b2 694 bl 819 e’
8 936 a, 163 a, 891 e”
9 911 a2 985 ai 891 e”
10 1059 b2 1309 a1 826 a,‘
11 1349 bl 1456 b2 931 a;
12 1406 a1 2153 81
1133 a,’
10792 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 routes to dissociation via a reaction N6 isomer 3N2. Interestingly, the highest energy normal modes for both structum point to such reactions. For onehalf cycle, the 4al mode (at 1406 cm-I) of 2 consists of a shortening of the N,-N2, N3=N4, and NFN, bonds, while the R2distances increase. Three N2 molecules would be formed by large distensions of this mode. Similarly, for 4, the 2a', mode (at 1133 cm-I) consists of a motion (during one-half the cycle) in which the N1-Nz, N3-N4, and N5-Ns bonds shorten as the Rzdistances increase; carried to the extreme, this motion would lead to three N2 molecules. This reaction of 4 is a highly symmetry-forbidden [4 4 + 41 concerted reaction and, consequently, should have a large activation barrier.ls Vibrational frequencies obtained at the RHF/4-31G// and RHF/4-31 *G// levels of theory are known for structures 2 and 4;see ref 9. Comparison of the frequencies obtained at these lower levels of theory with the values of Table IV shows that the inclusion of correlation decreases the calculated frequencies significantly. A 20% drop in frequency is not unusual in going from RHF/431G*// to MP2/6-31G*// values. This indicates that the standard factor used to calibrate ab-initio RHF frequencies for hydrocarbon-based molecules (i,e,, a ca. 10% reduction) cannot be used with confidence to "correct" RHF frequencies for cyclic nitrogen molecules. A comparison of Table I1 of ref 9 with Table IV of this paper shows that the RHF/4-31G// frequencies for 2 and 4 lie closer to the MP2/6-31G*// frequencies than the RHF/4-31G*// ones. That is, for pure nitrogen ring structures, the RHF/4-31G// model predicts frequencies in better agreement with MP2/631G*// than does RHF/4-31G*//; this has been commented on before; see refs 9 and 10. +
+
IV. Discussion New results have been presented for structures 2-6,and our calculations support the best reported calculations on 1." The new feature of the present calculations is that all the geometry optimizations are carried out on a correlated (MP2) energy hypersurface with a (6-31G*) split-valence + polarization function basis set. The stationary points, so obtained, are characterized by a vibrational analysis at the same level of theory (Le., MP2/6-3 lG*//). An interesting feature of the current work is that three of the structures (1,5, and 6) that are predicted to be stable with models as good as RHF/4-31G*// are predicted not to be stable when correlation at the MP2 level is included, this was previously hown to be true for 1,Il A fourth structure's geometry (3) changes radically when correlation is included; this structure becomes quasi-bound and is not interesting for this reason. Thus,inclusion
Engelke of correlation at the MP2 level qualitatively alters the character of four of the six structures studied. It is clearly not safe to draw conclusions about the stability of such unusual molecules from calculations done on an RHF energy hypersurface, even when high-quality basis sets are used. The two remaining structures (2and 4)are found to be stable points on the MP2/6-31G1// hypersurface. In fact, the lowest-energy normal modes of these structures have quite high energies (ca. 450 cm-I). This indicates that the geometries of these structures are fairly rigidly defined by the MP2/6-3lG*// energy hypersurface. Furthermore, unless there are very rapid changes in the hypersurface energy derivatives as a function of normal mode distension, the calculated frequencies point to nontrivial barriers to autodissociation of the two structures. Thus, 2 and 4 may be experimentally realizable. If either 2 or 4 could by synthesized, they would be significantly more powerful energetic materials than any now known. Structure 4 would seem to be the more likely candidate for synthesis because its unimolecular dissociation to 3N2is a symmetry-forbidden [4 + 4 + 41 reaction;I5 such reactions have significant activation barriers. Finally, note that since a nitrogen atom and the CH group are isoelectronic, there are isoelectronic mixed carbon-hydrogennitrogen forms of structures 2 and 4. While these molecules would not be as energetic as the pure nitrogen forms, it is likely they would be kinetically more stable (see ref 12) and, therefore, probably more easily synthesized.
References and Notes (1) This work was supported by the US.Department of Energy. (2) (a) Kobayashi, Y.; Kumasaki, I. Top. Curr. Chem. 1984,123, 103. (b) Scott, L. T.; Maitland Jr., J. Chem. Rev. 1972, 72, 182. ( 3 ) Ha, T. K.; Cimiraglia, R.; Nguyen, M. T. Chem. Phys. Lett. 1981,83, 317. (4) Saxe, P.; Schaefer 111, H. E. J . Am. Chem. Soc. 1983, 105, 1760. ( 5 ) Huber, H.; Ha, T. K.; Nguyen, M. T. J . Mol. Srrucr. (THEOCHEM) 1983, 105, 351. (6) Ramek, M. J. J. Mol. Strucr. (THEOCHEM) 1984, 109, 391. (7) Nguyen, M. T. J . Phys. Chem. 1990, 94, 6923. ( 8 ) Engelke, R. J . Phys. Chem. 1990, 94, 6924. (9) Engelke, R. J . Phys. Chem. 1989, 93, 5722. (10) Engelke, R.; Stine, J. R. J . Phys. Chem. 1990, 94, 5689. (1 1) Lauderdale, W. J.; Stanton, J. F.; Bartlett, R. J. J. Phys. Chem. 1992, 96, 1173. (12) Engelke, R. J . Org. Chem. 1992, 57,4841. (13) Vogler, A.; Wright, R. E.; Kunkley, H. Angew Chem., Int. Ed. Engl. 1980, 19, 717. (14) Amos, R. D.; Rice, J. E. CADPAC, The Cambridge Analytic Derivative Package, Issue 4.0; Cambridge, 1987. (15) Woodward, R. B.; Hoffman, R. The Conservation of Orbital Symmetry; Academic: New York, 1970.
