J. Phys. Chem. 1996, 100, 1569-1577
1569
Thermochemistry of Tetrazete and Tetraazatetrahedrane: A High-Level Computational Study Mikhail N. Glukhovtsev*,1a,b and Sergei Laiter1c School of Chemistry, UniVersity of Sydney, Sydney, NSW 2006, Australia, and Laboratory for Molecular Modeling, School of Pharmacy, UniVersity of North Carolina, Chapel Hill, North Carolina 27599 ReceiVed: July 19, 1995; In Final Form: October 5, 1995X
Tetraazatetrahedrane, N4 (2), is 11.3 kJ mol-1 lower in energy than tetrazete (1) at the G2 level, in contrast to its hydrocarbon analogue, tetrahedrane (4), which has 108.9 kJ mol-1 higher energy than that of cyclobutadiene (3). The open-chain Cs structure of tetranitrogen (5) having the triplet ground state is the most stable isomer of N4, and its energy is 62.0 kJ mol-1 lower than that of tetrazete. At the G2 level, the enthalpies of formation, ∆Hf298, of tetraazatetrahedrane, tetrazete, and the open-chain tetranitrogen are 732.5 ( 8.0, 746.5 ( 7.6, and 686.6 ( 7.6 kJ mol-1, respectively. The high thermodynamical instability of tetraazatetrahedrane and tetrazete toward their dissociations into molecular nitrogen may be attributed to the comparative weakness of the single NsN and double NdN bonds, the strengths of which are only 29.0 and 54.2% of the strength of the NtN bond. For the CsC and CdC bonds, the corresponding ratios are 38.0 and 74.8%, respectively, and consequently, cyclobutadiene is stable with respect to dissociation into two acetylene molecules. After correction for the strain energy of the four-membered nitrogen ring, the antiaromatic destabilization of tetrazete is 54.1 kJ mol-1; this is considerably less than the antiaromatic destabilization of cyclobutadiene (170 ( 7 kJ mol-1 at the G2 level). At the G2 level the strain energies of tetraazatetrahedrane, N4, tetrazetine, N4H2, and tetrazetidine, (NH)4, are 205.5, 156.9, and 131.4 kJ mol-1, respectively. Azasubstituted cyclobutadienes have planar structures with bond-length alternation and, with the exception of tetrazete, are lower in energy than the corresponding azasubstituted tetrahedranes. The energy difference decreases with increasing number of the nitrogen atoms, and therefore, tetraazatetrahedrane is eventually more stable than tetrazete. 1,3-Diazete is 42.2 kJ mol-1 lower in energy than 1,2-diazete. The homodesmotic stabilization energies for the azetes show that the azasubstitution results in decreasing destabilization effects in these molecules. However, the more nitrogen atoms in an azete, the greater its tendency to dissociate into triple-bond species, HCtCH, HCtN, or NtN.
1. Introduction Tetrazete (1) and tetraazatetrahedrane (2) are of particular interest as possible high-energy-density materials2-4 like the N6, N8, N10, N12, and N20 molecules.5-10 The isoelectronic and structural relationships of 1 and 2 with cyclobutadiene (3, D2h) and its valence isomer, tetrahedrane (4), which play key roles
in the development of the antiaromaticity and strain theories, respectively, fascinate chemists.3,11-17 Although 3 is 108.9 kJ mol-1 lower in energy than 4 at the G2 level,18 the computational data on the relative stabilities of 1 and 2 indicate a much smaller difference in their energies.2,3 Thus, correspondingly, the prediction of either 1 or 2 as the lower energy valence isomer is controversial and depends strongly upon the level of the calculation used.2,3,19 Earlier estimates of the stability of tetraazatetrahedrane, which were based on the energies of isodesmic bond-separation reactions, showed that the destabilization energy is half that of tetrahedrane.20 These calculaX
Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-1569$12.00/0
tions,20 however, were performed at the HF/3-21G level and ignored the effects of polarization functions (including f functions) and electron correlation although their importance in the description of strained systems has been well established.21 Both unsubstituted parent molecules 1 and 2 as well as their derivatives are still unknown experimentally, albeit some approaches to their syntheses have been suggested.22 Is extreme instability of tetrazete 1 caused by its strong antiaromaticity? How much is the strain energy of tetraazatetrahedrane 2? Thermochemical data for 1 and 2 are important because of their possible role as high-energy-density materials. Since experimental thermochemical data for the tetrazete and tetraazatetrahedrane are unavailable at present, theory offers an attractive alternative for exploring their chemistry. We have carried out high-level ab initio MO calculations on tetrazete and tetraazatetrahedrane at the G2 level of theory. From these results we estimate the enthalpies of formation of these molecules, their relative energies, as well as the antiaromatic destabilization energy of tetrazete. Previous calculations predicted an open-chain structure of N4 (5) to be the lowest energy
isomer,3 similar to the N6 and N8 open-chain structures.4 Therefore, this structure will be considered also. © 1996 American Chemical Society
1570 J. Phys. Chem., Vol. 100, No. 5, 1996
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TABLE 1: Calculated G2 Total Energies (in hartrees) and Relative Energies (in kJ mol-1) of Tetrazete (1), Tetraazatetrahedrane (2), and Open-Chain Structure (5) as Well as of Two Nitrogen Moleculesa Erel (0 K)
G2 (298 K)
∆H (298 K)
0 -11.3 (-9.2)a -98.5 (-62.0)a -753.5 (749.0)a
-218.494 14 -218.498 52 -218.530 23 -218.778 61
0 -11.5 -94.7 (-59.9)a -746.9 (749.8)a
G2 (0 K) tetrazete, 1 tetraazatetrahedrane, 2 open-chain N4 triplet, 5 2NtN
-218.498 24 -218.502 56 -218.535 78b -218.785 22b b
a Calculations of N and N isomers have shown6 that the computed frequencies are sensitive to the level of theory. Therefore, we also calculated 6 8 the relative energies for the N4 isomers using the zero-point vibrational energies (ZPVE) computed at the MP2(full)/6-31G(d) level (the unscaled ZPVE(MP2(full)/6-31G(d)) values are 33.3 (1), 31.5 (2), 54.8 (5), and 13.1 (N2) kJ mol-1; the scaling factor is 0.9646). These relative energies are given in parentheses. Using ZPVE(MP2(full)/6-31G(d)) corrections results in just a 2.1 kJ mol-1 decrease of the energy difference between 1 and 2 compared to the standard G2 values, and this small change in the energies agrees with the conclusion24b that there is no advantage in using MP2 ZPE values in G2 theory. However, the ZPVE(MP2(full)/6-31G(d)) value for the open-chain triplet 5 is considerably larger than the ZPVE(HF/ 6-31G(d)) value (28.2 kJ mol-1, unscaled). As a consequence, using the MP2 ZPVE values leads to a decrease in the energy gap between 5 and 1 by 36.5 kJ mol-1. b The G2 energies, which include the ZPVE(MP2(full)/6-31G(d)) corrections rather than the ZPVE(HF/6-31G(d)) ones, for 1, the triplet 5, and two N2 molecules are -218.501 60 hartrees (-218.497 15 at 298 K), -218.525 22 hartrees (-218.519 98 at 298 K), and -218.786 04 hartrees (-218.782 74 at 298 K), respectively.
2. Computational Methods Ab initio molecular orbital calculations23 were carried out at the G2 level of theory24 with the use of the GAUSSIAN-92 program.25 This level corresponds effectively to calculations at the QCISD(T)/6-311+G(3df,2p)//MP2(full)/6-31G(d) level with the incorporation of HF/6-31G(d) scaled zero-point energies and so-called higher level corrections. It has been shown24,26 to perform well for calculations of atomization energies, ionization energies, electron affinities, bond energies, proton affinities, acidities, and reaction barriers. The nature of stationary points corresponding to monocyclic and pyramidal structures of the N4-nCnHn (n ) 0-4) valence isomers has been established by calculations of vibrational frequencies at the HF/6-31G(d) and MP2/6-31G(d) levels. To obtain theoretical enthalpies of reactions at 298 K, enthalpy temperature corrections were derived using harmonic frequencies that were calculated at the HF/6-31G(d) level and scaled by 0.8929 according to the G2 scheme24 and using standard statistical thermodynamics formulas.23 All relative energies and reaction energies in this paper correspond to enthalpy changes (∆H) at either 0 or 298 K, as indicated; ∆E and ∆H are, of course, identical at 0 K. The D2h rectangular structure 1 of tetrazete is resulted from the b1g distortion of the N4 square structure of the 1B1g state, which is caused by the second-order Jahn-Teller effect.12-14 Since this distortion leads to an increase in the energy gap between the 1Ag ground state and the lowest excited singlet 1B1g state of the square structure, the rectangular structure 1 is neither biradical nor biradicaloid, in contrast to the N4 D4h structure, which is a biradical. It has been well established for cyclobutadiene, the hydrocarbon analogue of tetrazete, that the equilibrium D2h rectangular structure 3 is a closed-shell singlet amenable to RHF calculations.27 Thus, a single-configuration approach is quite adequate for the D2h rectangular structure (3) of the cyclobutadiene, in contrast to the open-shell (CH)4 square structure.14 Indeed, for a series of isotopically labeled cyclobutadienes, it has been found28 that the frequencies and intensities calculated at the MP2/6-31G(d) level are in excellent agreement with the experimental data. Hence, we conclude that the G2 theory is reliable for calculations of the equilibrium rectangular structures of cyclobutadiene 3 and of its tetraaza analogue, tetrazete 1. Isodesmic29 and homodesmotic30-32 reactions have been widely used to evaluate stabilization energies (SE) and enthalpies of formation (∆Hf) of many molecules,33 and this approach is utilized in the present paper. An energetic criterion for aromaticity and antiaromaticity may be derived based on the energies of homodesmotic reactions.30,32 Theoretical enthalpies of formation were calculated from the G2 enthalpies of
Figure 1. Relative energies (in kJ mol-1) of tetrazete (D2h) and tetraazatetrahedrane (Td) calculated at various computational levels. The basis sets are denoted as A ) 6-31G(d), B ) 6-311G(2df), C ) 6-311+G(3df), and D ) 6-311+G(d).
isodesmic reactions using the experimental enthalpies34 of formation for the corresponding molecules. 3. Results and Discussion Relative Stabilities and Enthalpies of Formation for Tetrazete and Tetraazatetrahedrane. While cyclobutadiene (3) is 108.9 kJ mol-1 more stable than tetrahedrane (4) at the G2 level,18 its aza analogue, tetrazete (1), is 11.3 kJ mol-1 less stable than tetraazatetrahedrane (Table 1). A comparison to the earlier computational data (Figure 1) shows that at the HF/631G(d) level,19 1 is lower in energy than 2, but 1 turns out to be 4.6 kJ mol-1 higher in energy than 2 at the MP4SDTQ/6311+G(d)//MP2/6-31G(d) level.3 The calculations at the CCSD(T)/DZP level yielded a lower energy of 8.4 kJ mol-1 in favor of tetraazatetrahedrane.2 On the other hand, the QCISD(T)(full)/6-311+G(d)//MP2/6-31G(d) calculations indicated that 1 is 13.8 kJ mol-1 lower in energy than 2.3 Inclusion of the f polarization functions has a crucial effect on the energy difference between 1 and 2 and results in a lower energy of 22.9 kJ mol-1 for tetraazatetrahedrane compared to that of tetrazete at the MP4SDTQ/6-311G(2df)//MP2/6-31G(d) level (Figure 1). The open-chain triplet 5 is a minimum with the lowest frequency (au) of 160 cm-1 at the UMP2/6-31G(d) level. Vinylacetylene which is an open-chain isomer of 3, is the most stable isomer of C4H4,35 and likewise, the N4 open-chain structure 5 (but having the triplet ground state, in contrast to the vinylacetylene) is the most stable isomer of N4.3 At the
Tetrazete and Tetraazatetrahedrane
J. Phys. Chem., Vol. 100, No. 5, 1996 1571 TABLE 2: Calculated G2 Total Energies (hartrees) of Molecules Involved in Reactions 1-5 NH3 trans HNdNH H2NsNH2 HNdNNH2, C1 HN(NH2)2, Cs E,E-s-trans N4H2 (6) (NH)4, D2d (7) N4H2, C2 (8)
G2 (0 K)
G2 (298 K)
-56.458 65 -110.480 10 -111.680 45 -165.746 14 -166.920 68 -219.774 67 -220.910 86 -219.752 36
-56.454 84 -110.476 30 -111.676 24 -165.741 74 -166.915 75 -219.769 52 220.906 32 -219.748 17
TABLE 3: G2 Calculated Enthalpies of Reactions 1-5 (in kJ mol-1) reaction
∆H (0 K)
∆H (298 K)
1 2 3 4 5
30.8 233.8 -238.7 -131.3 -156.8
22.1 209.5 -242.3 -135.8 -162.0
TABLE 4: G2 Calculated Enthalpies of Formation of Tetrazete, Tetraazateterahedrane, and the Open-Chain Tetranitrogen (in kJ mol-1) molecule
∆Hf(0 K)
∆Hf(298 K)
tetrazete (1) tetraazatetrahedrane (2) tetranitrogen (5)
752.7 ( 738.0 ( 8.0b 690.7 ( 7.6c
746.5 ( 7.6a 732.5 ( 8.0b 686.6 ( 7.6c
7.6a
a Averaged value calculated from the enthalpies of reaction 1 and of the 1 f 2N2 dissociation (see text). b Averaged value calculated from the enthalpies of reaction 2 and of the 2 f 2N2 dissociation (see text). c Calculated from ∆Hf(1) and the energy difference between 1 and 5. The latter (62.2 kJ mol-1 at 0 K, Table 1) was found using the ZPVE(MP2/6-31G(d)) values.
Figure 2. Geometries of the N4 rectangular (1) and tetrahedral (2) singlets and open-chain triplet (5) optimized at the MP2(full)/6-31G(d) level. The bond lengths and bond angles in 5 optimized at the CISD(fc)/6-31G(d) level are shown in parentheses.
G2 level, we have found 5 to be 98.5 and 87.2 kJ mol-1 lower in energy than 1 and 2, respectively (Table 1). By use of the ZPVE(MP2/6-31G(d)) values rather than the ZPVE values calculated at the HF/6-31G(d) according to the standard G2 theory, these corrected relative energies are 62.0 and 52.8 kJ mol-1, respectively. Since the UMP2 level is not reliable for calculations of an open-chain structure of the N4•+ radical cation,36 we also optimized the open-chain triplet 5 at the CISD/ 6-31G(d) level. The structure 5 did not “dissociate” during this optimization, and the geometry obtained was similar to that found at the UMP2 level (Figure 2). The structures 1, 2, and 5 are minima at both the HF/6-31G(d) and the MP2(full)/6-31G(d) levels. The NN bond length in tetraazatetrahedrane (1.478 Å) is 0.040 Å longer than that found in hydrazine (C2 gauche form). The NN bond length in 2 calculated at the MP2/6-31G(d) level is close to the value of 1.471 Å obtained from the recent CASSCF/DZP calculations,37 whereas the optimization of 2 at the CCSD/DZP level led to a 0.020 Å shorter NN bond length.38 The NN bond lengths in tetrazete 1 show considerable alternation; the shorter bond length is 1.287 Å and the longer one is 1.542 Å (Figure 2). The NdN bond in 1 is slightly longer than the NdN bond length in trans diazene (1.266 Å).39 The elongation of the N-N bond in 1 compared to the N-N bond in hydrazine is notable and can be considered a geometrical manifestation of the antiaromaticity of tetrazete, which results in significant bond length alternation.13,14 The two terminal NN bonds in the open-chain structure
5 are similar (1.168 Å) to the NtN bond in N2 (1.130 Å), whereas the central NN bond in 5 is elongated by 0.027 Å with respect to the NN bond length in hydrazine. The ability of G2 theory to calculate enthalpies of formation directly from atomization energies is known to be diminished for molecules containing multiple bonds.40-42 For example, the enthalpy of formation from the G2 calculation41 for benzene, obtained from atomization energies, deviates by 16.2 kJ mol-1 from the experimental value.34 Calculations of enthalpies of formation for molecules containing multiple-bonds, such as benzene, 1,3-butadiene, and the tropylium cation, show that using isodesmic and homodesmotic reactions leads to considerable improvement of the results obtained at the G2 level.41b,42 Thus, the benzene ∆Hf298 value found from the calculated enthalpy of the isodesmic bond-separation reaction is 82.5 kJ mol-1 (298 K),42 which is very close to the experimental ∆Hf298 value34 of 82.9 ( 0.3 kJ mol-1. Following the apparent success of this procedure, we have applied the same approach to tetrazete and tetraazatetrahedrane. Accordingly, we used the isodesmic reactions 1 and 2 in order to calculate ∆Hf values for tetrazete and tetraazatetrahedrane (Tables 2-4). The calculated G2 energies for reactions 1 and 2 are given in Table 3.
tetrazete + 4NH3 f 2H2NsNH2 + 2 trans HNdNH (1) tetraazatetrahedrane + 8NH4 f 6H2NsNH2
(2)
We have considered only stable molecular conformations in our estimates of (de)stabilization energies, and therefore, the trans configuration of diazene, which is 21.1 kJ mol-1 (at 298 K) more stable than the cis isomer at the G2 level (the experimental energy difference is 20 kJ mol-1 at 298 K),34 was employed in eq 1.
1572 J. Phys. Chem., Vol. 100, No. 5, 1996
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TABLE 5: G2 Calculated Bond Dissociation Enthalpies, D0 (kJ mol-1)a X)N bond
G2 D0 (0 K)
exptl D0 (0 K)
X ) CH RNb
G2 D0 exptl D0 (0 K) (0 K)
RCb
H2XsXH2 269.0 273.8 ( 3.4c 0.290 369.5 366.4c 0.380 trans-HXdXH 513.8 510.7 ( 1.2d 0.542 729.7 719.3c,e 0.748 XtX 936.4 941.6c 1.0 946.7 961.8 1.0 a Calculated from the G2 energies given in refs 24a and 39. b Ratios of XsX or XdX bond enthalpy to XtX bond enthalpy. Ratios of the NsN to NdN bond enthalpies as well as of the CsC to CdC bond enthalpies are 0.536 and 0.509, respectively. c Calculated from the experimental data given in ref 34. d Taken from ref 43. e Recent experimental estimates of the CdC and CtC bond strengths in ethylene and acetylene give the values of 715.5 ( 5.0 and 957.3 ( 2.9 kJ mol-1, respectively.47
From the enthalpy of reaction of eq 1 (Table 3) and the experimental ∆Hf values of ammonia, hydrazine,34 and diazene43 we obtain a ∆Hf298 value for tetrazete of 746.1 ( 7.6 kJ mol-1 at 298 K (Table 4). The enthalpy of dissociation of 1 into molecular nitrogen yields ∆Hf298(1) ) 746.9 kJ mol-1. On the basis of an average of the above two values, we estimate a ∆Hf298 value for tetrazete of 746.5 ( 7.6 kJ mol-1. Applying the same procedure to estimate the ∆Hf value for 2 leads to a calculated G2 ∆Hf298 value of 729.5 ( 8.0 kJ mol-1 (based on the enthalpy of reaction 2 and the experimental ∆Hf values of ammonia and hydrazine34). Alternatively, estimating this value from the calculated G2 enthalpy of dissociation of 2 into molecular nitrogen (Table 1) leads to a ∆Hf298(2) value of 735.4 kJ mol-1. The averaged ∆Hf298(2) value of the two above estimates is 732.5 ( 8.0 kJ mol-1 (Table 4). The energy of reaction 2 was recently used as an estimate for the stabilization energy of tetraazatetrahedrane at the HF/ 3-21G level, which was found20 to be -342.3 kJ mol-1, i.e., 2 is significantly destabilized. This value substantially differs from our G2 result (+233.8 kJ mol-1 at 0 K), indicating the absence of any destabilization of 2 if the bond-separation isodesmic reaction 2 is employed to evaluate its stabilization energy. In contrast to 2, G2 calculations18 of the stabilization energy of its parent hydrocarbon, 4, show a considerable destabilization of 419.6 kJ mol-1. Why are neither tetraazatetrahedrane nor its derivatives known experimentally, whereas a few substituted tetrahedranes44,45 are rather stable? One of the factors that affect the stability of 2 is the weakness of the single NsN bond6 compared to the NtN bond strength (Table 5). The NsN bond enthalpy in hydrazine consists of only 29% of the NtN bond enthalpy in the dinitrogen molecule, whereas this ratio rises to 38% for the CsC and CtC bond strengths in ethane and acetylene, respectively (Table 5). If the energy of the NsN bond in 2 is roughly approximated with the NsN bond enthalpy in hydrazine, the sum of the six NsN bond energies in 2 is 259 kJ mol-1 less than the energy of the two NtN bonds of N2. Although the G2 calculations indicate tetrahedrane to be 79.9 kJ mol-1 less stable with respect to its dissociation into two acetylene molecules,18 its N4 analogue is considerably unstable with respect to its dissociation into two N2 molecules. A remarkable feature of nitrogen chemistry is the relatively small number of compounds containing only single N-N bonds.46 Therefore, the high thermodynamical instability relative to dissociation into two triple-bonded dinitrogen molecules is a particular feature of 2. However, 2 should be stable kinetically since the barrier of its dissociation into two N2 molecule was calculated37,38 to be within the range 255-264 kJ mol-1. It is noteworthy that the ratio of the NsN and NdN bond strengths (0.536) is close to that of the CsC and CdC bonds (0.509) (Table 5).
This consideration of the NsN, NdN, and NtN bond enthalpies leads to the conclusion that Nn isomers containing a larger number of multiple NN bonds should be more stable than isomers with a prevailing number of single NN bonds unless other factors contribute considerably (e.g., antiaromatic destabilization of tetrazete). Indeed, open-chain N4 and N6 structures with multiple NN bonding are the most stable N4 and N6 isomers, respectively.3,4 Pentazole, N5H, should be stabilized because of its aromaticity, and phenylpentazole is stable enough to be studied by X-ray diffraction.48 In contrast, the Nn molecules with high-energy content should have polyhedral structures maximizing the number of the single N-N bonds. From the relative energies of the N4 isomers 1, 2, and 5, the ∆Hf298 value for the open-chain triplet 5 can be estimated to be 686.6 ( 7.6 kJ mol-1 (Table 4). This C2h structure 5 is the most stable isomer of N4 although even this N4 isomer is 687.0 kJ mol-1 unstable relative to dissociation into two N2 molecules (Table 1). Antiaromatic Destabilization of Tetrazete. As mentioned above, there is an obvious contribution to the relative instability of tetrazete, namely, antiaromatic destabilization.13,14 We now estimate this contribution at the G2 level. Antiaromatic destabilization is a manifestation of cyclic electron delocalization.14 Therefore, estimation of the energy of this delocalization is the aim of various schemes for the evaluation of the aromaticity or antiaromaticity effects. An isodesmic bondseparation reaction like reaction 1 gives an estimation of the net stabilization (or destabilization) of a molecule rather than the effects of aromatic stabilization or antiaromatic destabilization.14 Furthermore, if a molecule has a positive stabilization energy obtained from an isodesmic bond-separation reaction, it does not necessarily imply that this molecule is stable. Its instability may result from the strain energy, from the existence of lower energy isomers separated by low barrier heights, and from other factors, the balance of which determines whether the species can be considered stable under the given experimental conditions. Tetrazete is an illustrative example. It possesses a positive stabilization energy of 30.8 kJ mol-1 calculated from the isodesmic bond-separation reaction 1, but this molecule is highly unstable and still unknown experimentally. The scheme of homodesmotic reactions provides the possibility of evaluating antiaromatic stabilization (destabilization).30 Thus, the calculation of the antiaromatic destabilization energy of tetrazete comes to the evaluation of the enthalpy of reaction 3. After that a correction for the N4 four-membered ring strain should be introduced.
tetrazete + 2(trans HNdNH) f 2(E,E-s-trans HNdNsNdNH (6)) (3) The E,E-s-trans configuration and E,Z-s-trans configuration of N4H2 are the most stable among various N4H2 configurations.49 The C2h configuration (6)50 is marginally more stable (by 0.1 kJ mol-1 at the G2 level) than the Cs E,Z-s-trans configuration of N4H2. Therefore, the C2h configuration was used in eq 3. The strain energy of 1 can be estimated from the strain energies of the (NH)4 cycle (tetrazetidine, 7) and of the N4H2 cycle (tetrazetine, 8). To calculate the strain energies of these molecules,50 we have used the homodesmotic reactions 4 and 5, respectively.51 Thus, we have followed the scheme of strain energy estimation31 in which the H2NNHNH2 and HNdNNH2 open-chain molecules are considered to be strain-free acyclic reference molecules. In fact, the evaluation of strain energies using the homodesmotic reactions 4 and 5 can be considered
Tetrazete and Tetraazatetrahedrane
J. Phys. Chem., Vol. 100, No. 5, 1996 1573
TABLE 6: Calculated G2 Antiaromatic Destabilization Energies of Tetrazete and Cyclobutadienea tetrazete (1) cyclobutadiene (3)b total stabilization energy ring strain correction antiaromatic destabilization energy
-242.3 188.2c 54.1
-310.2 140.6 ( 7.0 170 ( 7
a At 298 K, in kJ mol-1. b The data for cyclobutadiene were taken from ref 18. c Estimated from the enthalpies of reactions 4 and 5 (see Table 3).
Strain Energy of Tetraazatetrahedrane. To estimate the strain energy of tetraazatetrahedrane, we used the homodesmotic reaction (eq 6) following the general approach developed by George et al.31
N4 (2) + 6H2N-NH2 f 4N(NH2)3
The enthalpy of the reaction 6 calculated using G2 theory is -205.5 kJ mol-1. Therefore, the strain energy of 2 is 205.5 kJ mol-1 or 49.1 kJ mol-1 per one three-membered N3 ring in 2. In eq 6, hydrazine and triaminoammonia are used as ring-strainfree molecules. In other words, eq 6 can be considered (particularly, if it is rewritten as eq 6a) an evaluation of the strain energy of 2 using the increment system in which N(NH2)3 and H2NNH2 serve as the increments for the sp3-type nitrogen connected to another sp3-type nitrogen and for the amino group, respectively.52
N4 (2) f 4N(NH2)3 - 6H2N-NH2 increments.52
as using an additive scheme based on We used the lowest energy structures of H2NNHNH2 and HNdNNH2,50 which have Cs and C1 symmetries, respectively.26g The most stable configuration of (NH)4 is a D2d structure 7.46a,50,51 For the N4H2 cycle, we have found a C2 structure 8.50 The enthalpies of reactions 4 and 5, which are -135.8 and -162.0 kJ mol-1 (at 298 K), respectively, allow us to estimate the strain increase, due to the introduction of a single NdN double bond into the tetrazete ring, to be 26.2 kJ mol-1. Therefore, the strain energy of tetrazete (with two double bonds) is estimated to be 188.2 kJ mol-1 at the G2 level (Table 6).
(NH)4 (7) + 4H2NsNH2 f 4H2NsNHsNH2
(4)
(6)
(6a)
Hence, eq 6 yields the conventional ring strain energy of 2 as the difference between the energy of the corresponding hypothetical reference strain-free cyclic structure and the energy of 2 itself. Earlier we calculated18 using G2 theory the conventional strain energy of 4 to be 571 ( 4 kJ mol-1. Thus, we conclude that the strain energy of 2 is about a one-third as much as the strain energy of its hydrocarbon analogue, 4. Azasubstituted Cyclobutadienes and Tetrahedranes. To reveal trends in the relative stability of the C4-nH4-nNn (n ) 0-4) planar and pyramidal valence isomers and the effect of azasubstitution on the antiaromaticity of azasubstituted cyclobutadienes, we have carried out calculations of azetes and azatetrahedranes, 9-16, and their total energies are listed in Table 7.
N4H2 (8) + HNdNH + 3H2NsNH2 f 2H2NsNdNH + 2H2NsNHsNH2 (5) If we now subtract the tetrazete strain energy (188.2 kJ mol-1 at 298 K) from the total destabilization energy of tetrazete of 242.3 kJ mol-1 at 298 K (derived from the enthalpy of reaction 3), we obtain an estimate for the antiaromatic destabilization energy of tetrazete, which is 54.1 kJ mol-1 at 298 K (Table 6). This is significantly less than the antiaromatic destabilization of cyclobutadiene, which was found to be 170 kJ mol-1 at the G2 level.18 In light of this value, why has not tetrazete been isolated, in contrast to cyclobutadiene?14,44 In fact, the total thermodynamical stability of a molecule is determined by a balance of various effects of which aromatic stabilization or antiaromatic destabilization are not necessarily the major components. In contrast to tetrazete with its extreme instability of 753.5 kJ mol-1 toward dissociation into two N2 molecules (Table 1), cyclobutadiene is 21.9 kJ mol-1 lower in energy (at the G2 level)18 than two acetylene molecules. Bunker and Peyerimhoff, in an earlier study on the comparative stability of cyclobutadiene and tetrazete,54 placed emphasis on the stabilization effect of the CsH bonds in cyclobutadiene. Another factor that may be amenable for the instability of tetrazete is the relative weakness of the NdN bond. Indeed, the ratio of the NdN and NtN bond enthalpies is 0.542 whereas the ratio of the CdC and CtC bond enthalpies is 0.748, with the NtN and CtC bond strengths being close to each other (Table 5). If we estimate the NsN and NdN bond strengths in tetrazete using the NsN and NdN bond enthalpies in hydrazine and trans diazene, respectively, the sum of these two NsN and two NdN bond energies is 307.2 kJ mol-1 less than the two NtN bond energies in N2 (Table 5).
Although tetrazete is still unknown experimentally, and the detection and/or synthesis of its stabilized derivatives remains a challenge for the chemistry of reactive molecules, a lot of effort55-57 has been directed to the solution of “the azacyclobutadiene problem”.54a This has resulted in the syntheses of kinetically stabilized azetes, e.g., tri-tert-butylazete (17),15 and
in X-ray, 1H NMR, and 13C NMR spectrometry and photoelec-
1574 J. Phys. Chem., Vol. 100, No. 5, 1996
Glukhovtsev and Laiter
TABLE 7: Total Energies of Cyclobutadiene (3), Tetrahedrane (4), Azasubstituted Cyclobutadienes (1, 9, 11, 12-15), and Azasubstituted Tetrahedranes (2, 10, 13, 16) Calculated at the MP4SDTQ/6-311+G(d,p)// MP2(full)/6-31G(d,p) Level as Well as Zero-Point Vibrational Energies (ZPVE) Calculated at the HF/6-31G(d) Level molecule
ZPVEa
total energyb
(CH)4, D2h (3) (CH)4, Td (4) C3H3N, Cs (9) C3H3N, C3V (10) C2H2N2, C2h (11) C2H2N2, C2V (13) C2H2N2, C2V (14) C2H2N2, C2V (12) CHN3, Cs (15) CHN3, C3V (16) N4, D2h (1) N4, Td (2)
174.4 170.2 143.2 140.5 111.4 111.3 110.2 108.7 78.3 75.6 45.8 41.5
-154.293 46 -154.246 55 -170.326 37 -170.288 46 -186.362 78 -186.346 67 -186.326 23 -186.318 18 -202.352 54 -202.337 31 -218.341 61 -218.343 41
TABLE 8: Energy Differences Between Planar and Pyramidal (Tetrahedral) Structures of C4-nNnH4-n (n ) 0-4) Valence Isomersa,b molecule
∆E
(CH)4, 4 - 3 C3H3N, 10 - 9 C2H2N2, 12 - 11 CHN3, 16 - 15 N4, 2 - 1
119.4c 97.1 114.7 37.6 -8.5d
a In kJ mol-1. b Calculated at the MP4SDTQ/6-311+G(d,p)//MP2(full)/ 6-31G(d,p) level including ZPVE(HF/6-31G(d)) scaled with 0.8929. c 108.9 kJ mol-1 using G2 theory.18 d G2 calculations give -11.3 kJ mol -1 (Table 1).
a In kJ mol-1; ZPVE values calculated at the HF/6-31G(d) level were used for consistency with the G2 calculations of (CH)4 and N4 molecules. b In hartrees.
tron spectroscopic studies of their structures15,16 and reactivities.55 Our calculations show that the azetes have planar structures with a well-pronounced bond-length alternation,58 which are minima both at the HF/6-31G(d) and MP2/6-31G(d,p) levels. This agrees with the experimental findings for 17 and 18, which showed planar distorted rectangular structures of the four-membered rings.15 The CdC (1.337 Å) and CsC (1.537 Å) bond lengths in azete 9 calculated at the MP2/6-31G(d,p) level are close to those (1.35 and 1.59 Å, respectively)15b found by the X-ray study of 18. A similar agreement is observed for the calculated CdN (1.296 Å) and CsN (1.567 Å) bond lengths in 9 and the X-ray values of 1.28 and 1.58 Å, respectively.15b The CdC and CsC bond lengths in 9 are slightly shortened when compared to the corresponding bond lengths in cyclobutadiene (1.344 and 1.564 Å at the MP2/631G(d,p) level).58 As should be expected from considering the stabilization of a 4 π-electron four-membered ring (a half-filled π-system) via heterosubstitution,59 1,3-triazete 11 is more stable than 1,2diazetes 13 and 14 (Table 7), in agreement with the earlier calculations.12,13,17,19,60 Furthermore, the enthalpy of the homodesmotic reaction 7 (∆H ) -235.3 kJ mol-1 at MP4SDTQ/ 6-311+G(d,p)//MP2/6-31G(d,p) + ZPVE(HF/6-31G(d))) shows that 1,3-diazete is stabilized relative to cyclobutadiene and tetrazete.
The C2V structure of 1,2-diazete 13 containing the two NdC bonds is 53.7 kJ mol-1 lower in energy than the C2V structure 14 having the NdN and CdC bonds (Table 7). Both 1,2-diazete 13 and triazete 15 feature rather long NsN bond lengths.58,61 The C2V structure of azete, the D2h structure of 1,3-diazete, and the C2V structure of triazete are not minima on the potential energy surface of the closed-shell singlet state, and they are not considered here. The CdN bond lengths in 11 is 0.016 Å shorter than those in 13.58 The all azasubstituted tetrahedranes (10, 12, 15, and 16) are minima (both at the HF/6-31G(d) and MP2/6-31G(d,p) levels) and possess, except tetraazatetrahedrane, higher energies than their planar valence isomers (Table 8). However, this energy difference diminishes as the number of the nitrogen atoms in the ring increases (Figure 3). The isodesmic bond-separation
Figure 3. Energy differences (in kJ mol-1) between planar structures of azasubstituted cyclobutadienes and pyramidal structures of the azasubstituted tetrahedranes calculated at the MP4/6-311+G(d,p)//MP2(full)/6-31G(d,p) + ZPVE(HF/6-31G(d)) level. The relative energies are listed in Table 8.
energies for the azatetrahedranes show that the larger number of nitrogen atoms, the smaller the destabilization of the azatetrahedranes.63 The effect of azasubstitution on the bondseparation energies eventually results in a positive bondseparation energy (233.8 kJ mol-1 at the G2 level; Table 3) for 2. The shortening of the CN bond lengths, which are 1.498 Å in 10, 1.469 Å in 12, and 1.423 Å in 16, signals the increase of the CN bond strength upon subsequent azasubstitution.58 This agrees with an increase in the CN bond orders in these molecules.64 The CC bond lengths also display a shortening (1.443 Å in 10 and 1.399 Å in 12). The NN bond length in 2 (1.478 Å) is 0.049 and 0.066 Å shorter than the NN bond lengths in triazatetrahedrane 14 and diazatetrahedrane 12, respectively (at the MP2/6-31G(d,p) level).58 Homodesmotic stabilization energies (HSE) derived from the energies of reactions 3 and 8-11 (all the open-chain molecules have s-trans configurations)65 give evidence for the decreasing destabilization of the azetes with azasubstitution (Table 9).
(CH)4 (3) + 2H2CdCH2 f 2(s-trans H2CdCHsCHdCH2) (8) C3H3N (9) + H2CdCH2 + H2CdNH f H2CdCHsNdCH2 + H2CdCHsNdCH2 (9) C2H2N2 (11) + 2H2CdNH f H2CdNsCHdNH
(10)
CHN3 (15) + H2CdNH + HNdNH f HNdNsNdCH2 + HNdNsCHdNH (11) This agrees with the earlier calculations19,60,66 of the HSE as well as the calculations of the Hess-Shaad resonance energies
Tetrazete and Tetraazatetrahedrane
J. Phys. Chem., Vol. 100, No. 5, 1996 1575
TABLE 9: Homodesmotic Stabilization Energies of Cyclobutadiene and Its Azasubstituted Derivatives Calculated at the MP4SDTQ/6-311+G(d,p)//MP2(full)/ 6-31G(d,p) Levela molecule
reaction
∆E
cyclobutadiene azete 1,3-diazete triazete tetrazete
8 9 10 11 3
-325.1b -304.2 -270.7 -241.8 -254.4c
a In kJ mol-1; total energies of the molecules involved in reactions 3 and 8-16 are listed in Table S1 given as supporting information. b -306.8 kJ mol-1 using G2 theory.18 c Calculations using G2 theory yield -238.7 kJ mol-1 (Table 3).
Figure 4. Comparison of the dissociation energies (in kJ mol-1) for cyclobutadiene and azasubstituted cyclobutadienes (reactions 12-16) calculated at the MP4/6-311+G(d,p)//MP2(full)/6-31G(d,p) + ZPVE(HF/6-31G(d)) level.
(HSRE)67 and topological resonance energies (TRE),68 indicating the less antiaromatic character of azete 9, 1,3-diazete 11, and triazete 15 when compared to cyclobutadiene 3.69 However, while cyclobutadiene is stable with respect to dissociation into two acetylene molecules,18 the azasubstitution leads to instability of the azetes with respect to dissociation into triple-bond species, HCtCH, HCtN, and/or NtN (eqs 12-16; reaction enthalpies (the ∆H values are given in kJ mol-1) were calculated at the MP4/6-311+G(d,p)//MP2/6-31G(d,p) + ZPVE(HF/6-31G(d)) level). The enthalpies of reactions 12-16 manifest the considerable effect of the number of nitrogen atoms on the instability of the azasubstituted cyclobutadienes (Figure 4), and this instability apparently hampers the experimental study of azasubstituted cyclobutadienes.
(CH)4 (3) f 2HCtCH ∆H ) 8.1,
(12)
∆H ) 21.9 (G2 theory) C3H3N (9) f HCtCH + HCtN ∆H ) -127.7 (13) C2H2N2 (11) f 2HCtN ∆H ) -253.9
(14)
CHN3 (15) f NtN + HCtN ∆H ) -525.5 (15) N4 (1) f 2NtN ∆H ) -799.6,
(16)
∆H ) -753.5 (G2 theory) 4. Conclusions 1. Tetraazatetrahedrane, N4 (2), is 11.3 kJ mol-1 lower in energy than tetrazete (1) at the G2 level, in contrast to its hydrocarbon analogue, tetrahedrane (4), which has 108.9 kJ mol-1 higher energy than that of cyclobutadiene (3). The open-
chain Cs triplet structure of tetranitrogen (5) is the most stable isomer of N4, and its energy is 62.0 kJ mol-1 lower than the energy of tetrazete. 2. At the G2 level, enthalpies of formation, ∆Hf298, of tetraazatetrahedrane, tetrazete, and open-chain tetranitrogen are 732.5 ( 8.0, 746.5 ( 7.6, and 686.6 ( 7.6 kJ mol-1, respectively. The high thermodynamical instability of tetraazatetrahedrane and tetrazete with respect to dissociation into molecular nitrogen may be attributed to the comparative weakness of the single NsN and double NdN bonds, the strengths of which are only 29.0 and 54.2% of the strength of the NtN bond. For the CsC and CdC bonds, the corresponding ratios are 38.0 and 74.8%, respectively, and consequently, cyclobutadiene is stable relative to dissociation into two acetylene molecules. 3. After correction for the strain energy of the four-membered nitrogen ring, the antiaromatic destabilization of tetrazete is 54.1 kJ mol-1, which is considerably less than the antiaromatic destabilization of cyclobutadiene (170 ( 7 kJ mol-1). 4. At the G2 level the strain energies of tetraazatetrahedrane, N4, tetrazetine, N4H2, and tetrazetidine, (NH)4, are 205.5, 156.9, and 131.4 kJ mol-1, respectively. 5. Azasubstituted cyclobutadienes have planar structures with bond-length alternation. These are lower in energy than the corresponding azasubstituted tetrahedranes, albeit the energy difference decreases with increasing number of nitrogen atoms, and therefore, tetraazatetrahedrane (N4) is eventually more stable than tetrazete. 1,3-Diazete has a lower energy than 1,2-diazete. The homodesmotic stabilization energies for the azetes show that azasubstitution results in decreasing the destabilization effects in these molecules. The more nitrogen atoms in an azete, however, the greater its tendency to dissociate into the triplebond species, such as HCtCH, HCtN, or NtN. Acknowledgment. We thank the Laboratory for Molecular Modeling, School of Pharmacy, University of North Carolina for computer time as well as Dr. I. Bytheway and a reviewer for helpful comments. Supporting Information Available: Geometries of HNd NNH2, HN(NH2)3, E,E-s-trans N4H2 (6), (NH)4 (7), and N4H2 (8) optimized at the MP2(full)/6-31G(d) level (Figure S1), geometries of the azasubstituted cyclobutadienes and tetrahedranes as well as of the cyclobutadiene (3) and tetrahedrane (4) optimized at the MP2(full)/6-31G(d,p) level (Figure S2), and the total energies of the molecules involved in reactions 3 and 8-16 calculated at the MP4SDTQ/6-311+G(d,p)//MP2(full)/6-31G(d,p) level (Table S1) (10 pages). Ordering information is given on any current masthead page. References and Notes (1) (a) School of Chemistry, University of Sydney. (b) Current address: Department of Chemistry, Wayne State University, Detroit, Michigan 48202. (c) School of Pharmacy, University of North Carolina. (2) Lauderdale,W. J.; Stanton, J. F.; Bartlett, R. J. J. Phys. Chem. 1992, 96, 1173. (3) Glukhovtsev, M. N.; Schleyer, P. v. R. Int. J. Quantum Chem. 1993, 46, 119. (4) Glukhovtsev, M. N.; Schleyer, P. v. R. Chem. Phys. Lett. 1992, 198, 547. (5) Engelke, R.; Stine, J. R. J. Phys. Chem. 1990, 94, 5689. (6) Engelke, R. J. Am. Chem. Soc. 1993, 115, 2961. (7) Leininger, M. L.; Sherrill, C. D.; Schaefer, H. F. J. Phys. Chem. 1995, 99, 2324. (8) Alkota, I.; Elguero, J.; Rozas, I.; Balaban, A. T. J. Mol. Struct.: THEOCHEM. 1991, 228, 47. (9) Bliznyuk, A. A.; Shen, M.; Schaefer, H. F. Chem. Phys. Lett. 1992, 198, 249. (10) Michels, H. H.; Montgomery, J. A.; Christe, K. O.; Dixon, D. A. J. Phys. Chem. 1995, 99, 187.
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Glukhovtsev and Laiter (34) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data, Suppl. 1 1988, 17. (35) Hess, B. A.; Allen, W. D.; Michalska, D.; Schaad, L. J.; Schaefer, H. F. J. Am. Chem. Soc. 1987, 109, 1615. (36) (a) Kemister, G.; Peel, J. B. Org. Mass Spectrom. 1993, 28, 311. (b) Carmichael, I. J. Phys. Chem. 1994, 98, 5044. (37) Dunn, K. M.; Morokuma, K. J. Chem. Phys. 1995, 102, 4904. (38) Lee, T. J.; Rice, J. E. J. Chem. Phys. 1991, 94, 1215. (39) Pople, J. A.; Curtiss, L. A. J. Chem. Phys. 1991, 95, 4385. (40) Martin, J. M. L. J. Chem. Phys. 1992, 97, 5012. (41) (a) Nicolaides, A.; Radom, L. J. Phys. Chem. 1994, 98, 3092. (b) Nicolaides, A.; Radom, L. J. Am. Chem. Soc. 1994, 116, 9769. (42) Glukhovtsev, M. N.; Laiter, S. Theor. Chim. Acta, in press. (43) Biehl, H.; Stuhl, F. J. Chem. Phys. 1994, 100, 141. (44) Maier, G. Angew. Chem., Int. Ed. Engl. 1988, 27, 309. (45) Maier, G.; Born, D.; Bauer, I.; Wolf, R.; Boese, R.; Cremer, D. Chem. Ber. 1994, 127, 173. (46) (a) Ritter, G.; Ha¨felinger, G.; Lu¨ddecke, E.; Rau, H. J. Am. Chem. Soc. 1989, 111, 4627. (b) Magers, D. H.; Salter, E. A.; Bartlett, R. J.; Salter, C.; Hess, B. A.; Schaad, L. J. J. Am. Chem. Soc. 1988, 110, 3435. (c) Workentin, M. S.; Wagner, B. D.; Negri, F.; Zgierski, M. Z.; Lusztyk, J.; Siebrand, W.; Wayner, D. D. M. J. Phys. Chem. 1995, 99, 94. (47) Ervin, K. M.; Gronert, S.; Barlow, S. E.; Giles, M. K.; Harrison, A. G.; Bierbaum, V. M.; DePuy, C. H.; Lineberger, W. C.; Ellison, G. B. J. Am. Chem. Soc. 1990, 112, 5750. (48) Wallis, J. D.; Dunitz, J. D. J. Chem. Soc., Chem. Commun. 1983, 16, 910. (49) Glukhovtsev, M. N.; Schleyer P. v. R. To be published. (50) Geometries of HNdNNH2, HN(NH2)3, E,E-s-trans N4H2 (6), (NH)4 (7), and N4H2 (8), optimized at the MP2(full)/6-31G(d) level, are available as supporting information (Figure S1). (51) Zhao, M.; Gimarc, B. M. J. Phys. Chem. 1994, 98, 7497. (52) G2 increments for calculating strain-free energies of NnHm species are as follows (in hartrees): -55.240 050 for the H2Ns unit (from H2NNH2); -55.840 225 for the HNd unit (from trans HNdNH); -54.665 825 for the sNd unit (from HNdNsNH2); -54.240 220 for the sNHs unit (from HN(NH2)2; -54.645 205 for the >Ns unit (from N(NH2)3; the G2 energy of triaminoammonia is -222.165 88 hartrees26g). The G2 strainfree energies of (NH)4 D2d 7, N4H2 C2 8, and N4 Td 2 are -220.960 88, -219.812 09, and -218.580 82 hartrees, respectively. These give the same strain energies as the ones found using reactions 4-6 (see text). The increment system developed by Schleyer et al. using density functional calculations opens the possibility of estimating strain energies of large polynitrogen molecules.53 (53) Glukhovtsev, M. N.; Jiao, H.; Schleyer, P. v. R. J. Am. Chem. Soc., submitted. (54) Buenker, R. J.; Peyerimhoff, S. D. J. Chem. Phys. 1968, 48, 354. (55) (a) Regitz, M. In Abstracts, The Second Heron Island Conference on Unusual Molecules and Reactive Intermediates, Queensland, Australia, 1994; p 46. (b) Vogelbacher, U. J.; Ledermann, M.; Schach, T.; Michels, G.; Hees, U.; Regitz, M. Angew. Chem., Int. Ed. Engl. 1988, 27, 272. (56) (a) Maier, G.; Scha¨fer, U. Tetrahedron Lett. 1977, 1053. (b) Maier, G.; Scha¨fer, U. Liebigs Ann. Chem. 1980, 798. (b) Maier, G.; Fleischer, F. Liebigs Ann. Chem. 1995, 169. (c) Maier, G.; Fleischer, F.; Kalinowski, H.-O. Liebigs Ann. Chem. 1995, 173. (57) (a) Adger, B. M.; Keating, M.; Rees, C. W.; Storr, R. J. Chem. Soc., Chem. Commun. 1973, 19. (b) Seybold, G.; Jersak, M.; Gomper, R. Angew. Chem., Int. Ed. Engl. 1973, 12, 847. (58) Geometries of the azasubstituted cyclobutadienes and tetrahedranes as well as of the parents cyclobutadiene (3) and tetrahedrane (4) optimized at the MP2(full)/6-31G(d,p) level are available as supporting information (Figure S2). Geometrical parameters of 1,2-diazete 13 optimized at the Becke3LYP/6-31G(d,p) level are also shown in Figure S2. (59) (a) Burdett, J. K.; Lee, S.; McLarnan, T. J. J. Am. Chem. Soc. 1985, 107, 3083. (b) Burdett, J. K.; Canadell, E.; Hugnbanks, T. J. Am. Chem. Soc. 1986, 108, 3971. (60) Simkin, B. Ya.; Glukhovtsev, M. N. Khim. Geterotsikl. Soedin. 1989, 1587. (61) Although the MP2/6-31G(d,p) geometries of 9, 11, and 15 are close to those found by CASSCF(4,4)/DZP calculations,17 the CASSCF(4,4) calculations (active full π-space) yield a much shorter N-N bond length in 13 (1.520 Å). Our calculations of 13 using density functional theory (Becke3LYP/6-31G(d,p); Etot ) -186.756 71 hartrees)62 give a longer N-N bond length (1.650 Å)58 than that found with the CASSCF(4,4) calculations.17 The structure 13 is a well-defined minimum at the MP2/6-31G(d,p) and Becke3LYP/6-31G(d,p) levels (the lowest frequencies (a2) are 454 and 503 cm-1, respectively). Therefore, although 13 is definitely a minimum, its geometry should still be refined by further calculations at a higher level of theory. (62) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Stevens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (63) The isodesmic bond-separation energies of tetrahedrane and azatetrahedranes, which are -529.3 kJ mol-1 for 4, -396.8 kJ mol-1 for 10, -240.0 kJ mol-1 for 12, -54.8 kJ mol-1 for 16, and +152.5 kJ mol-1 for
Tetrazete and Tetraazatetrahedrane 2 at the MP4SDTQ/6-311+G(d,p)//MP2/6-31G(d,p) level, are rather sensitive to the used computational level, which should give an adequate description of these strain molecules. The aforementioned values can serve only as an indicator of the qualitative trends in stability. The G2 values for 4 and 2 are larger (-419.6 and +233.8 kJ mol-1, respectively) than the MP4SDTQ/6-311+G(d,p) results. The HF/3-21G calculations20 yield energies that are too negative (-631.8 kJ mol-1 for 4, -583.2 kJ mol-1 for 10, -518.0 kJ mol-1 for 12, -436.0 kJ mol-1 for 16, and -342.3 kJ mol-1 for 2). (64) Seminario, J. M.; Politzer, P. Chem. Phys. Lett. 1989, 159, 27. (65) These are the most stable configurations. See, for example, the following. (a) Bock, C. W.; George, P.; Trachtman, M. J. Comput. Chem. 1984, 5, 395. (b) Bachrach, S. M.; Liu, M. J. Am. Chem. Soc. 1991, 113, 7929. (c) Wiberg, K. B.; Rablen, P. R.; Marquez, M. J. Am. Chem. Soc. 1992, 114, 8654.
J. Phys. Chem., Vol. 100, No. 5, 1996 1577 (66) (a) Haddon, R. C. Pure Appl. Chem. 1982, 52, 1129. (b) Glukhovtsev, M. N.; Simkin, B. Ya.; Minkin, V. I. Zh. Org. Khim. 1983, 19, 1353. (67) Hess, B. A.; Schaad, L. J.; Holyoke, C. W. Tetrahedron 1975, 31, 295. (68) (a) Gutman, I.; Milun, M.; Trinajstic, N. J. Am. Chem. Soc. 1977, 99, 1692. (b) Singh, S.; Mishra, R. K.; Mishra, B. K. Indian J. Chem. 1988, 27A, 653. (69) HSRE(3) ) -1.072; HSRE(9) ) -0.640; HSRE (11) ) -0.453 (in β units);67 TRE(3) ) -0.3065; TRE(9) ) -0.1936; TRE(11) ) -0.1356; TRE(15) ) -0.1833 (in β units).68 For details of the application of HSRE and TRE to estimate the aromaticity and antiaromaticity effects in heterocyclic chemistry, see, for example, recent reviews (refs 13 and 14).
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