J. Phys. Chem. 1996, 100, 11297-11304
11297
Quantum Mechanical and Molecular Mechanics (MM3) Studies of Hydrazines Buyong Ma, Jenn-Huei Lii, Kuohsiang Chen, and Norman L. Allinger* Computational Center for Molecular Structure and Design, Department of Chemistry, The UniVersity of Georgia, Athens, Georgia 30602 ReceiVed: March 27, 1996X
The structures, conformational energies, and vibrational frequencies of hydrazines have been studied at 6-31G** MP2 and 6-31G** B3LYP levels. Our theoretical structures generally agree with the available experimental data. However, our theoretical NsN bond length for tetramethylhydrazine is 1.436 Å at the 6-31G** MP2 level, indicating that the experimental NsN distance (1.401 Å) is too short. We confirm that the ab initio NsN bond length strongly depends on the torsional angle even at the correlated levels. The NsN bond lengths are much longer in the syn and anti conformations of 1,1-dimethylhydrazine than that in the gauche conformation. MM3 parameters for hydrazines have been optimized to reproduce experimental or quantum mechanical structures, energies, and vibrational frequencies. The bond lengthening resulting from lone-pair repulsion was accounted for with a torsion-stretch interaction. The heats of formation for hydrazines were calculated via both MP2 and MM3 methods. The optimized MM3 force field was applied to several cyclic hydrazines, and good agreement with experiments was noted. We found that diequatorial dimethylhexahydropyridazine is 0.9 kcal/mol more stable than the axial, equatorial conformer, in agreement with the experimental value of 1.2 kcal/mol.
Introduction The hydrazines have been the subjects of many experimental and theoretical (both quantum and molecular mechanics) studies.1-11 Both experimental and theoretical results agree that the ground states of hydrazine and its methyl derivatives are gauche-like conformations (Figures 1-3), with dihedral angles between the lone pairs of about 90˚. However, the hydrazines with certain kinds of arrangements of substituents may be forced to adopt either syn or anti conformations (Figure 4). The central NsN bond lengths of hydrazines are strongly conformation dependent. The experimental NsN bond length of the parent hydrazine is well-known1 to be 1.449 Å (rg), and the molecule is in a gauche conformation. However, the NsN bond is found to be much longer for a hydrazine in a syn conformation12 (for example, the NsN bond lengths of the sesquibicyclic hydrazines in Figure 4 are about 1.50 Å) or in an anti conformation [for example,13 the NsN bond length is 1.505 Å (rR) for compound 7 in Figure 4]. Therefore, it is important to characterize the central NsN bond lengths. Unfortunately, both theory and experiment have problems in dealing with the NsN bond lengths of hydrazines. For example, the electron diffraction NsN bond length of tetramethylhydrazine9 is reported to be surprisingly short, being only 1.401 Å. Theoretical calculations on hydrazines may be carried out by either quantum mechanical or molecular mechanical methods, with only the latter being practical for large molecules. However, it was recently reported12 that MM2 calculations are inadequate to reliably estimate NsN bond lengths for sesquibicyclic hydrazines. Nelsen et al. pointed out that the errors in the MM2 results came from SCF calculations, from which their MM2 parameters were calibrated.12 However, even though it was shown that the SCF method seriously underestimated NsN bond lengths, few correlated calculations have been reported for substituted hydrazines. In the present work, we studied mono-, di-, tri-, and tetramethylhydrazines with the MP2 and DFT methods. B3LYP functionals were used in the DFT calculations. Core electrons were frozen in the MP2 calculations. Subsequently, X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00920-3 CCC: $12.00
Figure 1. Structures and Newman projections of (a) hydrazine (C2 symmetry); (b) methylhydrazine (inner conformer, no symmetry); (c) methylhydrazine (outer conformer, no symmetry).
we determined a set of optimized MM3 parameters for the hydrazines. Experimental structures and vibrational frequencies are available for hydrazine, methylhydrazine, and the dimethylhydrazines. For other molecules (and structural parameters without experimental information), ab initio results at the 6-31G** DFT (B3LYP) level were used in the parametrization, since calculation of the vibrational frequencies of tetramethyl© 1996 American Chemical Society
11298 J. Phys. Chem., Vol. 100, No. 27, 1996
Ma et al. containing 1-, 2-, and 3-fold components was used to take into account the strong torsion-stretch interactions observed in these molecules. Results and Discussion
Figure 2. Structures and Newman projections of 1,1-dimethylhydrazine: (a) equilibrium structure; (b) anti conformer; (c) syn conformer.
Figure 3. Structures and Newman projections of 1,2-dimethylhydrazine: (a) outer-outer (OO) conformer (C2 symmetry); (b) inner-outer (IO) conformer.
hydrazine would be too time consuming at the 6-31G** MP2 level. In the MM3 paramerization a torsion-stretch interaction
A. Molecular Structures and Conformational Energies of Hydrazines. Hydrazine has been extensively studied by both experimental and quantum mechanical methods. The experimental structure of hydrazine has been well established1 by Kohata et al. using electron diffraction and microwave methods (Table 1). There are many ab initio calculations for hydrazine.14 The best ab initio results are from the work of DeFrees et al.15 Their NsN bond length for hydrazine (re) was 1.440 Å at the 6-31G* MP3 level. In the present study, our NsN bond length is 1.437 Å at both the 6-31G** MP2 and 6-31G** B3LYP levels (Table 1). It should be noted that the experimental and MM3 bond lengths are rg values, while the ab initio bond lengths are re values. The MM3 difference between rg and re for the hydrazine NsN bond is 0.008 Å. If we apply this correction34 to the ab initio re values, we may see that the ab initio results agree well with experiment [rg (experiment) ) 1.449 Å, rg (MP3) ) 1.448 Å, rg (MP2) ) 1.445 Å, and rg (B3LYP) ) 1.445 Å]. There are two conformers of methylhydrazine, i.e., inner and outer, as indicated in parts b and c of Figure 1. Experimentally, the inner conformer was found to be 0.84 kcal/mol (enthalpy) more stable than the outer.16 Our theoretical calculation agrees with the experiment (Table 2, 0.86 kcal/mol at the MP2 level and 1.05 kcal/mol at the B3LYP level). Ab initio NsN bond lengths also agree with the experimental results (Table 2). The experimental NsN bond length of the inner conformation is longer than that of the outer conformation, in contrast to our quantum mechanical results which show the opposite trend. However, we note that the average values of the experimental NsN and CsN bond distances are consistent with our quantum mechanical results (Table 2). This average value is normally well determined by electron diffraction, whereas the individual values are much less certain. We have studied three conformations of 1,1-dimethylhydrazine, namely, the gauche, anti, and syn (Figure 2). The equilibrium structure of 1,1-dimethylhydrazine is the gauche conformation. The experimental structure from electron diffraction was known (Table 3). Experimental and theoretical results agree well, except for the H-N-H angle, for which the experimental value (116.6°) is about 10° larger than the quantum mechanical value (106°). The experimental H-N-H angle is certainly wrong. Riggs and Radom17 studied 1,1-dimethyhydrazine in the gauche, anti, and syn conformations at the SCF level. They found that the anti conformation was a local minimum, whereas the syn conformation was a transition state. We reached the same conclusion in the present study at the correlated levels. Note that the NsN bond lengths for both the anti and syn conformations (Table 4) are much longer than that in the gauche conformation of 1,1-dimethylhydrazine (Table 3). Previous studies17,18 have noted a similar strong dependence of the NsN bond length on the torsional angle. However, the geometry in the earlier studies17,18 was optimized only at the SCF level. Therefore, our calculations at the 6-31G** MP2 level confirm this interesting behavior of the NsN bond. Mastryukov18 has rationalized the NsN bond length change by a steric mechanism. The steric mechanism may explain the long NsN bond length in the syn conformation. However, it fails to explain the NsN bond length in the anti conformation, where the steric repulsion is small. An electronic explanation may be needed to account for the long NsN bond in the anti conformation.
MM3 Studies of Hydrazines
J. Phys. Chem., Vol. 100, No. 27, 1996 11299
Figure 4. Structures of selected cyclic hydrazines.
TABLE 1: Experimental and Theoretical Structures of Hydrazinea (Figure 1a) geometry N-N N1-H3 N1-H6 N2-N1-H3 N2-N1-H6 H-N-H H3-N1-N2-H5 H3-N1-N2-H4 moment of inertiac A
expb
SCF
1.449(2) 1.021(2) 1.021(2) 106(2) 112(2) 106(2) 91(2)
1.411 0.998 1.001 108.3 112.5 108.5 90.0 -150.0
0.5810
B
3.4818
C
3.4835
dipole moment (D)
1.75
MP2 1.437 1.012 1.016 106.4 111.5 106.8 89.6 -154.3 0.5826 (0.28%) 3.4361 (-1.31%) 3.4427 (-1.17%) 2.30
B3LYP 1.437 1.012 1.016 106.9 111.9 106.9 90.1 -153.2 0.5844 (0.59%) 3.4514 (-0.87%) 3.4556 (-0.80%) 2.14
MM3 1.447 1.023 1.030 107.3 109.6 107.7 90.1 -153.2 0.6022 3.65%)d 3.4898 (0.23%)d 3.4972 (0.39%)d 1.78
The bond lengths are in angstroms, and the bond angles are in degrees. b Electron diffraction (rg) experiment, ref 1. c In units of 10-39 g‚cm2, ref 1. d Deviation (MM3 - experiment). The deviations should be positive, because the MM3 numbers are on an rg basis, while the experimental values are rz. a
Radom et al.19a have suggested that “back-bonding” between the NsH (or NsC) bonds and the lone pair orbitals, which is maximized at 90°, is responsible for the stable gauche conformation of hydrazine. This mechanism still does not adequately explain the NsN bond length in the anti conformation. Brunck
and Weinhold19b formulated a general explanation for the rotational barriers. They said that the stable gauche conformation of hydrazine is due to the interaction between the lone pair and the trans NsH bond. The barrier at 180° then resulted from the lack of such an interaction. However, it is still hard
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TABLE 2: Experimental and Theoretical Structures of Methylhydrazinea (Figure 1b,c) outer expb (rg) geometry N-N N1-H3 N1-H5 N2-H4 N2-C6 (NN + CN)/2 H3-N1-N2 H4-N2-N1 H5-N1-N2 C6-N2-N1 C6-N2-N1-H3 C6-N2-N1-H5 H7-C6-N2-N1 moment of inertiac A
MP2
1.431 1.032 1.032 1.032 1.466 1.449
109.5
2.1910
B
8.7284
C
9.8521
rel energyd
0.84
inner B3LYP
MM3
expb (rg)
1.433 1.019 1.013 1.018 1.456 1.445 111.1 110.5 107.0 108.8 -83.6 159.8 -177.9
1.431 1.024 1.016 1.022 1.457 1.444 111.8 111.2 107.6 111.0 -83.5 158.7 -179.0
1.443 1.030 1.023 1.032 1.460 1.451 109.9 108.9 108.0 109.5 -80.7 161.6 -179.4
1.433 1.032 1.032 1.032 1.463 1.448
2.1939 (-0.13%) 8.6246 (-1.19%) 9.7502 (-1.03%) 0.86
2.1740 (0.78%) 8.7431 (0.17%) 9.8490 (-0.03%) 1.05
2.2188 (1.27%) 8.8110 (0.95%) 9.9198 (0.69%) 0.66
2.2754
113.5
8.6422 9.8098 0.0
MP2
B3LYP
MM3
1.431 1.014 1.022 1.013 1.456 1.444 106.6 105.8 110.1 113.3 83.3 -31.6 173.3
1.428 1.018 1.026 1.106 1.457 1.443 107.2 106.4 110.8 114.3 84.1 -31.8 173.0
1.438 1.023 1.029 1.024 1.463 1.451 107.3 107.5 109.7 113.8 88.2 -29.2 179.7
2.2740 (-0.06%) 8.6246 (-0.20%) 9.7502 (-61%) 0.0
2.2562 (-0.84%) 8.6857 (0.50%) 9.8252 (0.16%) 0.0
2.3003 (1.10%) 8.7592 (1.35%) 9.9279 (1.20%) 0.0
a
The bond lengths (rg for MM3, re for MP2, B3LYP) are in angstroms, and the bond angles are in degrees. b Electron diffraction experiment, ref 3. c In units of 10-39 g‚cm2, ref 3. The values in parentheses refer to deviation (MM3 - experiment). d Enthalpy, in units of kcal/mol.
TABLE 3: Experimental and Theoretical Structures of 1,1-Dimethylhydrazinea (Figure 2a) geometry N-N N1-H3 N1-H4 N2-C5 N2-C9 N2-N1-H3 N2-N1-H4 N1-N2-C5 N1-N2-C9 H-N-H C-N-C H3-N1-N2-C9 H3-N1-N2-C5 N1-N2-C5-H6 H4-N1-N2-C5 H4-N1-N2-C9 moment of inertiac A B C
expb
MP2
B3LYP
MM3
1.437 1.023 1.023 1.469 1.469 111.2 111.2 108.2 108.2 116.6 111.2
1.432 1.015 1.026 1.456 1.456 106.5 109.3 111.7 107.3 106.4 111.0 -164.2 74.0 179.9 -40.6 81.2
1.431 1.018 1.029 1.457 1.456 107.1 110.0 112.6 108.5 106.5 112.1 -161.9 74.0 181.6 -41.9 82.8
1.436 1.023 1.029 1.463 1.458 107.9 109.9 111.9 108.2 107.9 112.6 -157.5 78.0 181.6 -39.3 85.2
9.2324 9.3940 16.3532
9.3024 9.5134 16.6119
9.3721 9.6340 16.7647
97
potential energy surface of hydrazine. The lone pair repulsion mechanism is also consistent with the strong dependence of the theoretical NsN bond length on the electron correlation effect. The NsN bond lengths at the SCF level are too short because of the improper description of this electron repulsion. Previous theoretical,21 as well as experimental,7 studies of 1,2-dimethylhydrazine indicated that the outer-outer (OO) and inner-outer (IO) conformers are similar in energy (Figure 3 and Table 5), with the IO conformer being slightly lower. The results from the present study agree. The microwave and electron diffraction results7 for 1,2-dimethylhydrazine are available for both rotamers (Table 5). The agreement between theory and experiment is satisfactory. There is no experimental structure or vibrational spectrum available for either ethylhydrazine or trimethylhydrazine. However, Mosquera et al.10,11 studied both of these molecules by the ab initio method at the 4-31G* SCF level. Ethylhydrazine is rich in possible rotamers. For the rotation along the NsN bond, as with methylhydrazine, the possible arrangements are inner and outer conformers.
a
The bond lengths (rg for MM3, re for MP2, B3LYP) are in angstroms, and the bond angles are in degrees. b Electron diffraction (ra) experiment, ref 5. c In units of 10-39 g‚cm2.
to understand why the NsN bond length in the anti conformation is as long as that in the syn conformation. Experimental evidence suggests a simple lone pair interaction mechanism. Nelsen and Buschek20 studied the photoelectron spectra of hydrazines. They found that the lone pair interaction was strongest in the anti conformation and smallest in the gauche conformation. The key point here is that the lone pair electrons are not localized as in the classic picture. According to Nelsen and Buschek,20 using sp3 hybridized Slater atomic orbitals on nitrogen, a nearly cos θ relationship is observed for the overlap of both n+ and n-, resulting in nearly equal overlap at θ ) 0 and 180° and nearly zero overlap at 90°. Therefore, the lone pair interaction is operating even in the anti conformation, and it explains the dependence of energy and NsN bond distance on the torsional angle. More recently, Smits et al.19c developed an energy decomposition scheme that indicates that the lone pair repulsion is primarily responsible for the shape of the
For the rotation along the CsN bond, the expected conformations are
The combinations of the above conformations lead to six conformers of ethylhydrazine, namely, IG, IG′, IT, OG, OG′, and OT, with the IT conformer being the equilibrium structure. We studied the above six conformers at the 6-31G** B3LYP
MM3 Studies of Hydrazines
J. Phys. Chem., Vol. 100, No. 27, 1996 11301
TABLE 4: Experimental and Theoretical Structures of 1,2-Dimethylhydrazinea (Figure 3) anti geometry N-N N1-H3 N2-C5 N2-N1-H3 N1-N2-C9 H-N-H C-N-C H3-N1-N2-C9 H3-N1-N2-C5 N1-N2-C5-H6 rel energy
syn
MP2
B3LYP
MM3
MP2
B3LYP
MM3
1.474 1.020 1.458 103.7 105.6 102.8 109.3 -68.6 175.7 176.2 2.32
1.477 1.023 1.460 104.0 106.4 102.9 110.3 -67.5 174.9 177.1 2.93
1.469 1.022 1.464 105.7 106.7 99.8 108.6 -69.4 174.6 176.1 1.83
1.469 1.021 1.453 107.0 109.3 103.3 110.6 115.7 -5.5 -177.4 13.05
1.471 1.024 1.452 107.2 110.2 103.3 112.0 117.2 -6.9 -176.7 8.68
1.471 1.027 1.466 107.9 110.7 99.6 109.3 114.1 -7.2 -178.6 7.18
a The bond lengths (r for MM3, r for others) are in angstroms, and the bond angles are in degrees. The relative energy is in kcal/mol and based g e on the gauche conformation.
TABLE 5: Experimental and Theoretical Structures of 1,2-Dimethylhydrazinea (Figure 3) outer-outer (OO) b
MP2
exp geometry N-N N1-H9 N2-H7 N2-C3 N1-C8 H7-N2-N1 H9-N1-N2 C3-N2-N1 C8-N1-N2 C8-N1-N2-H7 C8-N1-N2-C3 moment of inertiac A
1.441 1.030 1.030 1.459 1.459 109.8 109.8 165.3 3.0001
B
20.0424
C
21.2497
rel enthalpyd
0.05 (20)
B3LYP
inner-outer (IO) b
MM3
exp
MP2 1.430 1.022 1.014 1.458 1.458 105.9 109.4 113.2 109.8 -152.1 88.3
1.427 1.025 1.016 1.460 1.460 106.6 110.2 114.2 111.1 -150.1 87.9
1.434 1.030 1.024 1.460 1.464 107.4 109.3 114.6 110.6 -151.1 87.2
4.8335 (0.18%) 16.7618 (-0.94%) 18.3896 (-0.94%) 0.0
4.8071 (-0.37%) 17.0386 (0.70%) 18.6886 (0.67%) 0.0
4.8831 (1.21%) 17.0991 (1.06%) 18.7997 (1.27%) 0.0
1.429 1.022 1.022 1.456 1.456 110.0 110.0 109.2 109.2 -75.4 165.2
1.426 1.025 1.025 1.456 1.456 110.7 110.7 110.4 110.4 -74.6 164.0
1.443 1.031 1.031 1.460 1.460 108.9 108.9 109.9 109.9 -71.8 169.6
1.441
30.0912 (0.30%) 19.8966 (-0.73%) 21.0839 (-0.78%) 0.25
2.9960 (-0.14%) 20.1408 (0.49%) 21.2905 (0.19%) 0.14
3.0289 (0.96%) 20.3464 (1.52%) 21.5638 (1.48%) 0.56
4.8248
1.463 1.463
87.8
16.9200 18.5649 0.0
B3LYP
MM3
a The bond lengths (r for MM3, r for MP2, B3LYP) are in angstroms, and the bond angles are in degrees. b Electron diffraction (r ) experiment, g e g ref 7. c In units of 10-39 g‚cm2, ref 7. The values in the parentheses refer to deviation (MM3 - experiment). d In units of kcal/mol.
TABLE 6: Relative Energies and CCNN Torsional Angle of the Rotamers of Ethylhydrazine rel energy (kcal/mol)
a
CCNN torsion (deg)
conformationa
MP2
B3LYP
MM3
MP2
B3LYP
MM3
IT IG IG′ OT OG OG′
0 1.09 0.06 2.72 1.01
0 0.98 0.24 3.26 1.42 1.31
0 0.40 0.61 1.73 1.06 1.20
-174.2 61.0 -73.1 -170.6 60.4
-173.9 61.6 -74.3 -170.4 62.0 -71.7
-174.8 76.0 -66.5 -166.0 73.5 -66.6
See text for the Newman projections.
and 6-31G** MP2 levels. The relative energies and CCNN torsional angles of the six rotamers are shown in Table 6. There are two stable conformers of trimethylhydrazine, i.e., inner and outer, according to the positions of the hydrogen atoms in the Newman projections. The inner conformer is more stable than the outer by 2 kcal/mol at the 6-31G** MP2 level (supporting information Table 1), primarily due to the fact that the methyl groups are less sterically demanding in the inner conformation. The structure of tetramethylhydrazine has been obtained from an electron diffraction experiment (Table 7). It was found that the equilibrium structure has the gauche conformation. The reported experimental NsN bond distance is surprisingly short, being only 1.401 Å. However, the average value of NsN and
CsN bond lengths agrees with the theoretical calculation. The short experimental distance is presumably in error, due to the difficulty of determining it in the presence of the much stronger diffraction from the four CsN distances. As mentioned ealier, the lone pair repulsion affects the NsN bond lengths of hydrazine. Methyl substitution will decrease the electron densities on the nitrogen atoms22 (electronegativity effect23). Therefore, the NsN bond lengths should generally decrease with the increasing methyl substitutions. On the other hand, the presence of an additional methyl group leads to increasing steric repulsion. It might be expected from the balance of these effects that the NsN bond length would go through a minimum at the point where two or three methyls
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TABLE 7: Experimental and Theoretical Structures of Tetramethylhydrazinea geometry N-N N-C N-C NN + CN av N-N-C1 N-N-C C-N-C C-N-N-Cc C-N-N-Cd moment of inertiae A B C
expb
MP2
1.401 1.463 1.463 1.451 113.5 113.5 110.8
1.436 1.460 1.454 1.453 114.8 109.2 111.5 -43.8 82.2
1.432 1.462 1.455 1.453 115.6 110.4 112.6 -46.8 82.5
1.423 1.461 1.458 1.452 115.9 110.6 113.8 -50.8 80.7
17.7007 30.5015 31.8188
17.9511 30.9496 32.3102
18.1605 30.8309 32.7263
B3LYP
MM3
a The bond lengths (r for MM3, r for MP2, B3LYP) are in g e angstroms, and the bond angles are in degrees. Since the molecule has C2 symmetry, only the symmetry unique geometry parameters are reported. b Electron diffraction (ra) experiment, ref 9. c Angle between the two inner methyl groups. d Angle between an inner and an outer methyl group. e In units of 10-39 g‚cm2.
were present and then increase, analogous to what happens with the fluorinated ethanes.23 Indeed, this is what is found (Table 8). A difficult computational problem with hydrazines has been to get the relative energies of diequatorial and equatorial, axial dimethylhexahydropyridazine (structures 10 and 11, Figure 4) correct. Experimental data indicated26 that the ee conformation is more stable than the ae conformation by ∆E ) 0.8 kcal/mol, and the axial, axial conformer (structure 12, Figure 4) was not observed. Note that there are no adjustable parameters to fit here. The MM3 calculations were simply carried out. As may be seen in Table 11, the results indicate that the ee conformer is more stable than the ae conformer by ∆E ) 1.0 kcal/mol, while the aa conformer is 2.7 kcal/mol higher in energy than the ee. It should be noted that ab initio calculations at 6-31G** MP2 and 6-31G* BLYP levels failed to get the relative energies even qualitatively correct (the ee conformer was found to be less stable than the ae by 1.43, 1.47, and 0.24 kcal/mol at the 6-31G** SCF, 6-31G** MP2, and 6-31G* BLYP levels, respectively, and the aa conformer was more stable than either, except for the BLYP calculation).31 Recently, Nelsen and Chen32 measured the relative amounts of exo and endo tert-butyl invertomers (conformers 13 and 14, Figure 4). They found that the exo tert-butyl conformers (13) were preferred for R ) iPr, Et, and Me groups. Our MM3 calculations agree with the experiments for R ) Et and Me groups. For the isopropyl group, MM3 indicated the exo conformer is of lower enthalpy. However, entropy made the endo conformer (R ) iPr, conformer 14, Figure 4) more stable (∆G). A difficulty with MM3 comes from the fact that the lowest vibrational frequency of the endo conformer (R ) iPr, conformer 14, Figure 4) is only 40 cm-1, and it is difficult to calculate an accurate entropy for a molecule with such a flat potential surface. However, our MM3 calculations agree with the experiments32 in that the 13:14 ratio is in the order of iPr . Et > Me. B. Heats of Formation of Hydrazines. Presently, there are only three hydrazines for which experimental heats of formation (H°f) in the gas phase are known24 (methylhydrazine, 1,1-dimethylhydrazine, and 1,2-dimethylhydrazine, see Table 8). Experimentally, 1,2-dimethylhydrazine is 2.0 kcal/mol less stable than 1,1-dimethylhydrazine (Table 8), whereas our ab initio calculations (including vibrational corrections) indicate that the gap is 3.1 kcal/mol. The available data are not sufficient for parametrization of the MM3 calculation in the usual
way.27,29,33 We have reported the evaluation of heats of formation by ab initio homodesmotic methods.25,26
2CH3-NH-NH2 f CH3-NH-NH-CH3 + N2H4 (1) 2CH3-NH-NH2 f (CH3)2-N-NH2 + N2H4
(2)
3CH3-NH-NH2 f (CH3)2-N-NH-CH3 + 2N2H4
(3)
4CH3-NH-NH2 f (CH3)2-N-N-(CH3)2 + 3N2H4
(4)
CH3-NH-NH2 + CH3-CH3 f CH3-CH2-N-NH2 + CH4 (5) CH3-NH-NH2 + (CH3)2-CH2 f (CH3)2-CH-N-NH2 + CH4 (6) CH3-NH-NH2 + (CH3)3-CH f (CH3)3-C-N-NH2 + CH4 (7) On the basis of homodesmotic reactions 1-7, the H°f values for hydrazine, trimethylhydrazine, tetramethylhydrazine, ethylhydrazine, isopropylhydrazine, and tert-butylhydrazine are readily evaluated as follows:25
∆H°f(target molecules) )
∑H°f(reactants) - nH°f(byproducts) + ∆H° (enthalpy changes for the homodesmotic reactions)
The H°f values obtained this way at the 6-31G** MP2 level are given in Table 8. C. MM3 Parametrization for Hydrazines. We have optimized MM3 parameters29,33 for hydrazines. As mentioned earlier, the torsion-stretch interaction is very strong for hydrazines. To account for the lone pair replusion and the resulting severe bond length change, we introduced a torsionstretch interaction containing three terms:
ETS ) 11.995∆l[Kts1(1 + cos ω) + Kts2(1 - cos 2ω) + Kts3(1 + cos 3ω)](1/2) The optimized MM3 parameters for hydrazines are listed in Table 9. The MM3 structures of several hydrazines are reported in Tables 1-5. All experimental and MM3 bond lengths are rg unless otherwise stated. Our MM3 structure (Table 1) for hydrazine itself reproduced the experimental data adequately. For methylhydrazine (Table 2), the MM3 NsN bond lengths are 0.013 and 0.006 Å longer than the electron diffraction distances for the outer and inner conformers, respectively. However, the corresponding average N-N and C-N distances from MM3 are only 0.002 and 0.003 Å longer than the experimental values, so agreement with experiment may claimed. With three torsion-stretch interaction constants, MM3 reproduced the experimental (gauche conformation) and quantum mechanical (anti and syn conformations) structures of 1,1dimethylhydrazine (Tables 3 and 4). MM3 results for 1,2-dimethylhydrazine (Table 5), ethylhydrazine (Table 6), trimethylhydrazine (supporting information Table 1), and tetramethylhydrazine (Table 7) also agree with the available experimental or quantum mechanical data. We have mentioned that the experimental NsN bond length of tetramethylhydrazine is too short. Our MM3 NsN bond length (1.425 Å) falls between the experimental and ab initio bond lengths. To test our MM3 parameters, we have carried out MM3 calculations on seven cyclic hydrazines (Table 10 and Figure
MM3 Studies of Hydrazines
J. Phys. Chem., Vol. 100, No. 27, 1996 11303
TABLE 8: N-N Bond Lengths, Energetics, and the Heats of Formation of Hydrazines hydrazine
methylhydrazine
1,1-dimethylhydrazine
1,2-dimethylhydrazine
exp MP2 B3LYP
1.449 1.437 1.437
1.431 1.431 1.428
1.439 1.432 1.431
MP2 B3LYP
111.53609 111.86866
150.71290 151.18298
189.89171 190.49626
B3LYP
33.46
51.28
68.65
24.3 4.7
22.6 22.6b 22.7
20.1 20.1b 19.9
exp MP2a MM3c
trimethylhydrazine
tetramethylhydrazine
ethylhydrazine
isopropylhydrazine
tert-butylhydrazine
N-N Bond Lengths (Å) 1.441 1.430 1.432 1.427 1.428
1.401 1.436 1.432
1.432 1.429
1.434 1.430
1.430 1.426
Total Energy (Negative, au) 189.88762 229.06679 190.49388 229.80718
268.24170 269.11551
189.89801 190.50254
229.08393 229.82038
268.27132 269.13843
69.12
86.70
104.39
14.9 14.9
6.8 6.8
-2.4 -2.4
Zero-Point Vibrational Energy (kcal/mol) 68.91 86.27 103.49 Heats of Formation (kcal/mol) 22.0 22.0b 18.1 16.7 21.9 19.1 17.1
a The zero-point vibrational energies (unscaled) at the 6-31G** B3LYP level were used. b Taken from experimental value as reference. c The MM3 heat parameters for hydrazines are N-N ) 29.9078, C-N ) 13.9362, N-H ) -1.178 (fixed), C-N-C ) -11.8846, Me-N ) 3.9004, Ipr-N ) -5.0700, tert-butyl-N ) -12.0900.
TABLE 9: Optimized MM3 Parameters for Hydrazines A. Torsional Parameters atom type
V1
V2
V3
23-150-150-23 1-150-150-23 5-1-150-150 5-1-150-23 5-1-150-1 1-150-150-1 1-1-150-150 1-1-150-23 5-1-1-150
0.30 -0.50 0.00 -2.00 -3.60 -0.30 2.00 -7.00 0.00
-3.50 -2.00 0.00 -4.00 1.00 -2.10 -1.79 1.82 0.00
0.35 0.50 0.80 1.40 1.00 1.50 2.38 3.13 0.37
B. Bending Parameters atom type
Kb
θ0 (type I)
θ0 (type II)
23-150-150 23-150-23 1-150-150 1-150-23 5-1-150 1-150-1 1-1-150
0.87 0.65 0.80 0.70 0.85 1.10 0.78
104.58 102.90 102.47 102.55 109.08 (type III) 106.98 109.14 (type III)
105.85 103.66 109.38
C. Stretching Parameters atom type
Ks
I0
bond moment
150-150 23-150 1-150
3.00 6.36 3.80
1.5490 1.0214 1.4429
0.00 1.28 1.00
D. Torsion-Stretching Parameters (Type 1) atom type
V1
V2
V3
150-150 1-150
-0.05 0.00
-2.70 0.0
-0.15 0.05
E. Bohlmann Effect atom type
V1
V2
V3
150
0.000
0.004
0.004
TABLE 10: N-N Bond Lengthsa of Several Cyclic Hydrazines (Figure 4) compd
X-rayc
1 2 3 4 5 6 7 8 9
1.500 1.514 1.511 1.497 1.492 1.505b 1.420f 1.415f
MM2d
AM1
1.403 1.416 1.410 1.412 1.418 1.409
1.442 1.425 1.423 1.414 1.409 1.406
6-31G* SCFe
MM3
1.473 1.462 1.467 1.461 1.456 (1.490, MP2)
1.474 1.479 1.474 1.472 1.482 1.479 1.480 1.390 1.390
a The bond lengths are in angstroms. MM3 results are from the present work; other data are from ref 12. b Reference 13. c Since X-rays locate the center of electron density for nitrogen, instead of the nuclear position, X-ray N-N bond lengths are about 0.2-0.4 Å longer than rg bond lengths for the same molecule. d MM2 lacks the torsion-stretch interaction; hence, the bond lengths for the gauche conformation (or for any other similar conformation) can be well fit, but if the gauche is fit, the syn and anti are found to be too short. The torsion-stretch interaction in MM3 allows a better overall fit to all of the conformation. e Correlation will cause the N-N bond in hydrazine to lengthen, so SCF values may be assumed to be too short, in general. f Reference 30.
TABLE 11: Relative Thermodynamic Values of Several Cyclic Hydrazines (Figure 4) from MM3 Calculations compd
steric energy (kcal/mol)
enthalpy (kcal/mol)
entropy (cal/k‚mol)
free energy (kcal/mol)
10a 11a 12a 13 (iPr)b 14 (iPr)b 13 (Et)b 14 (Et)b 13 (Me)b 14 (Me)b
0 0.8 2.7 0 1.0 0 1.1 0 1.2
0 0.9 2.8 0 0.7 0 0.9 0 1.2
0 1.3 0.4 0 2.7 0 1.4 0 1.3
0 0.5 2.7 0 -0.1 (0.1)c 0 0.5 (1.1)c 0 0.8 (1.5)c
a Relative to conformation 10, Figure 4. b Relative to conformation 13, Figure 4. cExperimental value at °C: Me, Et 25, iPr -27.
F. Electronegativity bond
end atom
attached atom
parameter
150-150
150
1
-0.005
4) for which both MM2 and AM1 are reported to fail to adequately describe the NsN bond lengths.12 As we may see from Table 10, the MM3 results for these compounds are satisfactory. Molecular mechanics has been quite successful in the calculation of heats of formation.27,33 In the present work, we obtained the MM3 heat parameters for hydrazines by fitting the experimental H°f data available for methylhydrazine, 1,1-
dimethylhydrazine, and 1,2-dimethylhydrazine. As may be seen in Table 8, our MM3 heats of formation also agree well with those evaluated by the ab initio method at the 6-31G** MP2 level. D. Vibrational Spectra for Hydrazines. Our MM3 vibrational frequencies (supporting information Table 2) for hydrazine itself reproduced the experimental data adequately, with RMS deviation between our MM3 values and experiment being 30 cm-1. Durig et al. reported experimental gas phase IR spectra of methylhydrazine.4 Both the quantum mechanical and the
11304 J. Phys. Chem., Vol. 100, No. 27, 1996 MM3 results generally agree with their assignments. However, as pointed by Murase et al.,3 the experimental assignment of one NsNsH bending mode is questionable (supporting information Table 3). If we do not include the vibrational frequency for this NsNsH bending mode, the RMS deviations between our MM3 frequencies and the experimental values are 34 cm-1 for outer methylhydrazine and 26 cm-1 for inner methylhydrazine (supporting information Table 3). The MM3 vibrational frequencies of the three conformations of 1,1-dimethylhydrazine also agree reasonably well with the experimental or quantum mechanical results (supporting information Tables 4 and 5). Quantum mechanical and MM3 calculations both indicated that the anti conformation is a local minimum and that the syn conformation is a transition state. Conclusions The structures, conformational energies, and vibrational frequencies of hydrazines have been studied at 6-31G** MP2 and 6-31G** B3LYP levels.28 Our theoretical structures generally agree with the experimental data. However, our theoretical NsN bond length for tetramethylhydrazine is 1.436 Å at the 6-31G** MP2 level, indicating that experimental NsN distance (1.401 Å) is too short. We confirm that the ab initio NsN bond length strongly depends on the torsional angle, even at the correlated levels. The NsN bond lengths are much longer for the anti and syn conformations of 1,1-dimethylhydrazine than for the gauche conformation. A MM3 force field for hydrazine was developed from the experimental and theoretical data. The lone pair repulsion and the resulting severe bond length changes were accounted for by a torsion-stretch interaction. Molecular mechanical (MM3)29 parameters of hydrazine have been optimized to reproduce experimental or quantum mechanical structures, energies, and vibrational frequencies. The heats of formation for hydrazines were calculated via both MP2 and MM3 methods. The overall MM3 results are as expected for MM3, quite good for structures, heats of formation, and conformational energies and adequate for vibrational spectra. Acknowledgment. This research was supported by NSF Grant CHE-9222655. We are grateful to Professor S. F. Nelsen for providing unpublished information and for helpful discussion. Supporting Information Available: Supporting information available: Six Tables containing the structures and vibrational frequencies of hydrazines (9 pages). Ordering information is given on any current masthead page. References and Notes (1) Kohata, K.; Fukuyama, T.; Kuchitsu, K. J. Phys. Chem. 1982, 86, 602. (2) Schmitz, B. K.; Euler, W. B. J. Mol. Struct. 1992, 257, 227. (3) Murase, N.; Yamanouchi, K.; Egawa, T.; Kuchitsu, K. J. Mol. Struct. 1991, 242, 409.
Ma et al. (4) Durig, J. R.; Harris, W. C.; Wertz, D. W. J. Chem. Phys. 1969, 50, 1449. (5) Structure Data of Polyatomic Molecules; Kuchitsu, K., Ed.; Springer-Verlag: Berlin, 1992; p 207. (6) Durig, J. R.; Harris, W. C. J. Chem. Phys. 1969, 51, 4457. (7) Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Nakata, M.; Nakata, T.; Kuchitsu, K. J. Phys. Chem. 1987, 91, 823. (8) Durig, J. R.; Harris, W. C. J. Chem. Phys. 1971, 55, 1735. (9) Naumov, V. A.; Litvionv, O. A. J. Mol. Struct. 1983, 99, 303. (10) Mosquera, R. A.; Va¨zquez, S.; Rios, M. A.; Van Alsenoy, C. J. Mol. Struct. 1990, 206, 49. (11) Mosquera, R. A.; Va¨zquez, S.; Rios, M. A.; Van Alsenoy, C. J. Mol. Struct. 1990, 206, 49. (12) Nelsen, S. F.; Wang, Y.; Powell, D. R.; Hayashi, R. K. J. Am. Chem. Soc. 1993, 115, 5246. (13) Nelsen, S. F.; Hollinsed, W. C.; Kessel, C. R.; Calabrese, J. C. J. Am. Chem. Soc. 1978, 100, 7876. (14) Schmitz, B. K.; Eular, W. B. J. Mol. Struct. 1992, 257, 227, and refrences cited therein. (15) DeFrees, D. J.; Raghavacharic, K.; Schlegel, H. B.; Pople, J. A. J. Am. Chem. Soc. 1982, 104, 5576. (16) Murase, N.; Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Hamada, Y.; Tsuboi, M.; Kuchitsu, K. J. Mol. Struct. 1988, 194, 301. (17) Riggs, N. V.; Radom, L. Aust. J. Chem. 1987, 40, 1783. (18) Mastryukov, V. S.; Boggs, J. E.; Samdal, S. J. Mol. Struct. 1993, 288, 225. (19) (a) Radom, L.; Hehre, W. J.; Pople, J. A. J. Am. Chem. Soc. 1972, 94, 2371. (b) Brunck, T. K.; Weinhold, F. J. Am. Chem. Soc. 1979, 101, 1700. (c) Smits, G. F.; Krol, M. C.; Altona, C. Mol. Phys. 1988, 63, 921. (20) Nelsen, S. F.; Buschek, J. M. J. Am. Chem. Soc. 1973, 95, 2011. (21) Yamanouchi, K.; Kato, S.; Morokuma, K.; Sugie, M.; Takeo, H.; Mastsumura, C.; Kuchitsu, K. J. Phys. Chem. 1987, 91, 828. (22) Nelsen, S. F.; Buschek, J. M. J. Am. Chem. Soc. 1974, 96, 2392. (23) Allinger, N. L.; Imam, M. R.; Frierson, M. R.; Yuh, Y. H.; Schaefer, L. In Mathematics and Computational Concepts in Chemistry; Trinajstic, N. E., Ed.; Ellis Horwood: London, 1986; p 8. (24) Thermochemical Data of Organic Compounds; Pedley, J. B., Naylor, R. D., Kirby, S. P., Eds.; Chapman and Hall: London, 1986; p 163. (25) Ma, B.; Sulzbach, H. M.; Xie, Y.; Schaefer, H. F. J. Am. Chem. Soc. 1993, 116, 3529. (26) Schweig, A.; Thon, N.; Nelson, S. F.; Grezzo, L. A. J. Am. Chem. Soc. 1980, 102, 1438. (27) Allinger, N. L.; Schmitz, L. R.; Motoc, I.; Bender, C.; Labanowski, J. K. J. Am. Chem. Soc. 1992, 114, 2885. (28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, revision F.2; Gaussian Inc., Pittsburgh, PA, 1993. For DFT see: Labanowski, J. W.; Andzelm, J. Pittsburgh, PA, 1993. (29) Allinger, N. L.; Yuh, Y. H.; Lii, J-H. Molecular mechanics. The MM3 force field for hydrocarbons I, II, and III. J. Am. Chem. Soc. 1989, 111, 8551-8582. The MM3 program is available to all users from Tripos Associates, 1699 S. Hanley Road, St. Louis, MO 63144, and to academic users only from the Quantum Chemistry Program Exchange, University of Indiana, Bloomington, IN 47405. (30) Nelsen, S. F.; Chen, L-J.; Powell, D. R.; Neugebauer, F. A. J. Am. Chem. Soc. 1995, 117, 11434. (31) Nelsen, S. F.; Tran, H. Q. Personal communication of unpublished calculations. (32) Nelsen, S. F.; Chen, L-J. J. Org Chem. 1995, 60, 3263. (33) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982. (34) Ma, B.; Lii, J-H.; Schaefer, H. F.; Allinger, N. L. J. Phys. Chem. 1996, 100, 8763-8769.
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