J. Phys. Chem. 1987, 91, 823-827
823
Molecular Structure and Conformation of 1,P-Dimethylhydrazine As Determined by Gas Electron Diffraction and Microwave Spectroscopy Kaoru Y amanouchi, Department of Pure and Applied Sciences, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro- ku. Tokyo 153, Japan
Masaaki Sugie, Harutoshi Takeo, Chi Matsumura, National Chemical Laboratory f o r Industry, Yatabe, Tsukuba-gun. Ibaraki 305, Japan
Munetaka Nakata, Toshiko Nakata, and Kozo Kuchitsu* Department of Chemistry, Faculty of Science, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan (Received: July 14, 1986)
Microwave spectra of the inner-outer (IO) and outer-outer (00)conformers of 1,2-dimethylhydrazinewere assigned. The rotational constants (in megahertz) for IO were determined to be A. = 17 308.41 (3), Eo = 4946.70 ( l ) , and Co = 4505.86 (1) and for 00,A. = 27735.26 (3), Bo = 4173.35 (l), and Co = 3937.21 (1). The electron diffraction intensity was measured and analyzed jointly with the above rotational constants and with the optimized geometry and the vibrational force field derived from an SCF calculation with the 4-31G(N*) basis set. The bond lengths (rJ and the bond angles (rr) determined are r(C-H) = 1.115 (4) A, r(N-N) = 1.441 (2) A, r(N-C)(IO) = 1.463 (9) A, r(N-C)(OO) = 1.459 (10) A, LH-C-H = 110.1 (21)", LN,-N,&(IO) = 113.5 (12)O, LN-N-C(OO) = 109.8 (5)O, LC-N-N-C(I0) = 87.8 (7)", and LC-N-N-C(OO) = 165.3 (18)". The listed values are weighted averages of the two conformers unless specified, and the values in parentheses represent estimated limits of error. The abundance ratio of the IO conformer at room temperature is 76% & lo%, from which the enthalpy difference, AH(O0-IO), is estimated to be 0.21 (84) kJ/mol. The total dipole moments derived from the measurement of the Stark effect are 1.66 ( 5 ) and 1.74 (5) D for the IO and 00 conformers, respectively.
I. Introduction Previous reports'-5 have suggested the existence of the three conformers of 1,2-dimethylhydrazine shown in Figure 1, where the inner-outer (IO), outer-outer (00),and inner-inner (11) conformers are discriminated with respect to the relative positions of the methyl groups about the N-N bond. The rotational transitions for the IO and 00 conformers were assigned,6 and the rotational constants derived from microwave spectra (MW) were combined with the gas electron diffraction (ED) intensity to determine the structural parameters and the abundance ratio of the two conformers. The results show that the dominant conformers are IO and 00, and the I1 conformer is negligible at room temperature. The microwave spectra were investigated further in the present study, and the rotational constants for both conformers were refined with the center frequencies of the rotational transitions derived from an analysis of the hyperfine structure^.'.^ An ab initio MO calculation was also carried out with the 4-31G(N*) basis set for both conformers, and their optimized geometries and vibrational force fields were calculated. The optimized geometrical parameters were consistent with those derived from our preliminary analysis: and the ab initio force field was found to reproduce the observed vibrational wavenumbers after slight corrections. With these force fields, the mean amplitudes and shrinkage corrections for all the atom pairs as well as the harmonic cor(1) Aston, J. G.; Jantz, J.; Russel, K. E. J. Am. Chem. Soc. l%l, 73, 1943. (2) Durig, J. R.; Harris, W.C. J. Chem. Phys. 1971,55, 1735. (3) Kimura, K; Osafune, K. Bull. Chem. SOC.Jpn. 1975,48, 2421. (4)Chiu, N. S.; Sellers, H. L.; Schiifer, L.;Kohata, K. J. Am. Chem. SOC. 1979,101, 5883. (5) Kohata, K.; Fukuyama, T.; Kuchitsu, K. Chem. Lett. 1979,257. (6) Nakata, M.; Takeo, H.; Matsumura, C.; Yamanouchi, K.; Kuchitsu, K.; Fukuyama, T. Chem. Phys. Lett. 1981,83,246.
(7) Yamanouchi, K.; Kato, S . ; Morokuma, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Kuchitsu, K. J. Phys. Chem., following article in this issue. (8) Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Kuchitsu, K. J . Mol. Struct. 1985,126, 321.
0022-3654/87/2091-0823$01.50/0
rections for the rotational constants are reevaluated. The molecular intensity obtained by gas electron diffraction5 was reanalyzed with the refined rotational constants and vibrational corrections in order to derive more accurate geometrical parameters and relative abundances of the two conformers. Some of the optimized geometrical parameters obtained from the above-mentioned MO calculation were used in the analysis as constraints. The utility of the combination of the geometrical parameters derived from an S C F calculation with experimental data for a structural analysis has already been demonstrated for a number of molecules with rotational i s o m e r i ~ m . ~ , ~ - ' ~ 11.
Experimental Section
The sample of 1,2-dimethylhydrazine was obtained by neutralization of its dihydrochloride with sodium hydroxide. The sample was dried by BaO powder and was used after vacuum distillation. The microwave spectra were measured in the region from 8 to 48 G H z by a Stark-modulated spectrometer with a modulation frequency of 100 kHz. The absorption cell was a 3-m X-band waveguide cell. The microwave sources were an HP8672A synthesizer and an HP8690 microwave sweeper phase-locked to the synthesizer. The microwave frequency was swept through an HP-IB system controlled by an HP9835 desk-top computer. In order to avoid adsorption of the sample on the surface of the waveguide cell, the sample was run slowly during the experiment. The waveguide was cooled by dry ice to -60 O C , and the sample pressure was kept at about 15 mTorr. In addition, we remeasured the intensity of electron diffraction (9) Schafer, L. J. Mol. Srrucr. 1983, 100, 51. (10) Pyckhout, W.; Van Nuffel, P.; Van Alsenoy, C.; Van Den Enden, L.; Geise, H. J. J. Mol. Struct. 1983,102, 333. ( I 1) Van Nuffel, P.; Van Den Enden, L.; Van Alsenoy, C.; Geise, H. J. J . Mol. Struct. 1984,116, 99. (12) Pyckhout, W.; Van Alsenoy, C.; Geise, H. J.; Van Der Venken, B.; Pieters, G . J . Mol. Struct. 1986,130, 335. (13) Vanhouteghem, F.; Pyckhout, W.; Van Alsenoy, C.; Van Den Enden, L.;Geise, H . J. J. Mol. Struct. 1986,140, 33.
0 1987 American Chemical Society
824
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
$&M ; M Me
&H H H
H
IO
H
MeMe Me
00
I I
Figure 1. Possible conformers of 1,2-dimethylhydrazine. The innerouter, outer-outer, and inner-inner conformersare denoted as IO, 00, and 11, respectively. The arrows indicate the directions of the calculated dipole moment vectors projected onto the plane perpendicular to the N-N bond (see section 111).
TABLE I: Rotational Constants (MHz) and Centrifugal Distortion Constants (kHz) for the Two Conformers of 1.2-Dimethvlhvdrazine“ A0 BO CO .1J ~
AK
6, 6,
J
K
inner-outer
outer-outer
17308.41 (3) 4946.70 ( 1 ) 4505.86 (1) 75.3 (32) -245.4 (98) 172.1 (65) -34.1 (16) 88.2 (33)
27735.26 (3) 4173.35 (1) 3937.21 (1) 102.2 (14) -307.2 (56) 206.0 (41) -50.5 (7) 103.9 (21)
“The uncertainties represent 2.5 times the standard deviations. photoplates, which had been obtained previ~usly,~ by a new photometry system.I4 The plates used were three sets taken with short and long camera lengths, 107.6 and 243.2 mm, respectively. By drawing a smooth background after correction for the sector shape, we could obtain the molecular intensities with an interval In each set the intensity was consistent in the of As = */lo kl. overlapping region, and hence, these intensity data were joined at s = 12.6 k‘. 111. Analysis of Microwave Spectra
Assignment of Rotational Transitions. Rotational transitions for the two conformers were observed in the microwave spectra. Each of the conformers has low-frequency modes of the skeletal torsion, and the rotational transitions of their excited vibrational states were nearly as intense as those of the ground state. Therefore, the microwave spectra of this molecule were congested in the whole region measured. The initial assignment of the transitions was based on the assumed geometrical structures. Some series of the b- and C-type Q-branch transitions for the IO conformer were first assigned and then the R branch transitions were assigned by a double-resonance technique applied to the 3 12-202and 202-212transitiom6 Subsequently the transitions assignable to the C-type Q-branches of the 00 conformer were found in the remaining spectral lines. The rotational constants and the centrifugal distortion constants for both conformers were obtained as shown in Table I by a least-squares analysis. The fitting was made on the 58 transitions of the a, b, and c types and the 25 transitions of the c type for the IO and 00 conformers, respectively. The assigned transitions and the residuals for the IO and 00 conformers are summarized in Tables I1 and 111, respectively. The unperturbed center frequencies used in the above fitting were determined by calculation of the hyperfine structures using the nuclear quadrupole coupling constants obtained in previous rep o r t ~ No . ~ ~rotational ~ transition assignable to the I1 conformer was observed in the spectra in spite of careful search. Dipole Moments and Nuclear Quadrupole Coupling Constants. The dipole moments for both conformers were determined by measuring the second-order Stark effect for several low-J transitions. The effective length between the electrodes of the waveguide cell was calibrated by using the J = 1-2 transition of OCS.15 The 212-202and 1 lo-O)oo transitions for the 00 conformer and the 11l-lol, 21,-202, 212--11,,and l,o-Ooo transitions for the IO conformer were used. The dipole moments determined are listed in Table I\’. (14) Kohata, K.; Fukuyama, T.; Kuchitsu, K. J . Phys. Chem. 1984, 86, 602. (15) Muenter, J. S. J . G e m . Phys. 1986, 48, 4544.
Yamanouchi et al. TABLE 11: Transition Frequencies (MHz) for the Inner-Outer Conformer of 1,2-Dimethylbydrazine (Ground Vibrational State) transition obsd obsd - calcd 38416.75 0.05 220-2 12 40 141.30 0.05 41 494.37 0.04 38 405.17 0.02 39073.40 -0.07 13 954.07 -0.01 35 738.65 -0.01 39 968.48 -0.01 14 926.34 -0.06 -0.07 34 894.45 16 203.40 -0.02 34 016.67 0.07 -0.02 17 822.05 0.04 33 173.32 -0.06 19820.61 0.04 32437.47 -0.01 31 882.13 31 576.52 0.01 28 398.01 0.00 31 582.81 0.01 32 155.31 0.01 31 955.28 0.02 36 337.00 0.01 0.02 32 740.50 -0.01 33978.21 35 701.75 -0.03 0.06 22 254.88 12361.76 -0.04 37 083.76 0.00 32 147.87 0.04 0.08 11933.11 36 43 1.09 0.03 -0.07 42 265.01 1 1 311.67 -0.01 -0.08 35 565.82 10523.84 0.03 34 493.16 -0.04 0.01 9 603.63 33219.90 0.00 8592.13 0.05 31 755.33 -0.03 30 1 12.00 -0.04 28 306.14 -0.02 21 814.24 -0.09 19345.59 0.04 18 464.67 0.03 0.08 18 893.48 0.03 39 622.70 0.04 36 508.1 1 -0.05 46 712.18 -0.04 15056.53 -0.04 32 105.44 -0.01 40 112.41 33 522.00 0.00 47 717.99 0.05 36 920.81 0.00 43 984.99 0.01 28 185.16 -0.01
The dipole moments for both conformers are found to be about 1.7 D. The direction of the dipole moment relative to the mol-
ecule-fixed axes cannot be determined from the Stark effect for only one isotopic species. As shown in Table IV, however, the absolute values of the dipole moment components estimated from an ab initio calculation with the 4-31G(N*) basis set correspond well with the experimental values, the calculated values being overestimated by about 10%. Therefore, the directions of the calculated dipole moments are believed to be correct. With the dipole components derived from the measurement of the Stark effect, the direction of the dipole moment vector of the IO conformer can be determined as shown in Figure 1. Arrows in Figure 1 indicate that the projection of the dipole moment vector for each conformer is nearly parallel to the bisector of the dihedral angle between the two “lone pairs” of the nitrogen atoms: this implies
Molecular Structure of 1,2-Dimethylhydrazine
The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
TABLE 111: Transition Frequencies (MHz) for the Outer-Outer Conformer of 1.2-Dimethvlhvdrazine (Ground Vibrational State) obsd
obsd - calcd
39 778.18 28 754.37 24 870.59 36636.53 37 492.40 43 688.96 43 838.43 35 462.42 35680.15 31 908.20 40 254.51 23 328.00 22980.31 22 523.03 21 961.26 20 552.52 23 104.04 30 422.94 37 584.39 44578.11 33 971.31 43 031.81 36009.21 42 127.02 42 309.03
-0.07 0.04 0.00 -0.01 0.05 0.03 -0.05 0.01 -0.01 0.00 0.05 0.03 -0.04 0.00 -0.06 -0.03 0.03 0.00 0.01 0.00 -0.05 0.04 -0.05 0.03 0.00
transition
TABLE VI: Mean Amplitudes and Shrinkage Corrections ( r , - r:) for the 10 and 00 Conformers of 1,2-Dimethylhydrazine (lo4 A). atom pair
obsdb 0.63 (5) 0.61 (5) 1.41 (5) 1.66 (5) 1.74 (5)
cco
C(b
PC PtOt
outer-outerd
WC
calcdc 0.926 0.802 1.294 1.782 1.986
=
1 D (debye) 3.3356 X C m. bAbsolute values obtained by the Stark effect measurement. The directions of the total dipole moments for both conformers are shown in Figure l (see text). CEvaluated at the experimental rz structure with the DZP basis set (see ref 7 and 8). ”For the 00 conformer, pc is equal to +to, because of its C2 symmetry. TABLE V Observed and Calculated Nuclear Quadrupole Coupling Constants (MHz) for 1,2-Dimethylhydrazine inner-outer
obsd“ 2.92 (30) 1.35 (32) 2.38 (33) -4.69 (35) 2.84 (30) 0.32 (43)
Xaal Xbbl x002 XbbZ
outer-outer
Xaa Xbb
calcdb 3.43 1.25 2.57 -5.16 3.04 0.17
“Taken from ref 7. The uncertainties represent standard deviations. bEvaluated at the experimental rz structure with the DZP basis set (see ref 7 and 8).
lii
ra - r:
atom pair
li,
ra - r 2
721 731 788 788 787 791 807 801 487 495 499 1009 996 1042 1037 1052 1060 1051 1060
Inner-Outer 136 128 187 181 184 186 177 175 8 15 14 46 37 44 42 90 79 77 77
Conformer HII-NI H21-N2 C2-NI Cl-N2 H2-Cl H21-NI HZI-NI HI3-N2 HII-N, H,3-C2 H21-CI C2-CI Hi42 H22-NI HIZ-N, H23-CI HII-C2 H12-C2 H22-Cl
1033 1037 674 679 1577 1748 1741 1707 1662 2091 2135 1207 1057 1003 1004 2406 2303 1522 1550
88 81 -1 3 -7 -4 1 -22 -36 -34 -10 -74 -77 -42 -16 47 44 -1 14 -9 8 -6 -8
Outer-Outer Conformerb HII-NI 1041 114 CZ-NI 687 151 H23-Nl 1637 158 H2-Cl 1589 142 H21-Nl 1657 33 H22-Nl 1005 25 CI-C2 716 30 H23-CI 1745 43 H21-CI 1589 67 H22-CI 1209 83
76 2 -2 1 -33 -13 46 -12 -39 -24 10
746 782 789 809 477 492 997 1046 1054 1070
TABLE I V Observed and Calculated Dipole Moments (D) for 1,2-Dimethylhydrazinea inner-outer
825
“Calculated at 298 K. See Figure 2 for the numbering of atoms. The values for H-H pairs are not listed. bExcept for the N-N and C-C pairs, each one of the two equivalent atom pairs is listed. TABLE VII: Geometrical end Conformational Parameters for 1,2-Dimethylhydrazine Structural Parameters bond length, A r(C-H)a/ r(N-WaV r(N-C)(IO),,b r(N-C)(OO) r(N-N)sv
rB 1.115 (4) 1.030 1.463 (9) 1.459 (10) 1.441 (2)
rz
1.092 (4)c 1.012d 1.460 (9) 1.455 (10) 1.439 (2)
bond angle, deg LH-C-Ha, LNo-N,-C LN,-N,-C LN-N-C(O0) LC-N-N-C(I0) LC-N-N-C(O0)
rr 110.1 (21) 113.5 (12) 110.4* 109.8 (5) 87.8 (7) 165.3 (18)
Mean Amplitudes (angstroms) ll(N-C)av l3(C*.*N),, R/ %
0.0551 (46) 0.0702 (86)
/2(N.**C)au /4(C**C)(OO)
0.0982 (50) 0.1219 (220)
Conformational Parameters 76 ( I O ) AH,g kJ/mol
0.21 (84)
“Subscript “av” means weighted average of inequivalent bond lengths. IO and 00 represent the inner-outer and outer-outer conformers, respectively. ‘Numbers in parentheses represent estimated limits of error. dThe difference between r(C-H)av and r(N-H)&”was fixed at the ab initio (4-31G(N1)) value in the analysis. eThe difference between LN,-N,-C and LN,-No-C was fixed at the 4-31G(N*) value. /The relative abundance of the inner-outer conformer at room temperature. Enthalpy difference, AH(I0-00). f
10 Hll&H13b@%
00 N
H1
H2 Hi HI2
H22
H1Z
Figure 2. Numbering of the atoms in the two stable conformers of 1.2-dimethylhydrazine. The H I , , HI,, and H I , atoms of the 00 conformer are equivalent to the H,,, H22, and H23 atoms, respectively. t h a t t h e lone pairs have a d o m i n a n t contribution t o t h e dipole moment. The nuclear quadrupole coupling constants were determined,’.*
a s shown in T a b l e V, from a n analysis of t h e hyperfine splittings in t h e llo-Ooo and 321-313transitions for t h e IO conformer and those in the 41,-322 and 2,,-1,, transitions for t h e 00 conformer. A comparison is m a d e in T a b l e V with t h e values calculated with t h e DZP basis set using the rz s t r u c t u r e determined in t h e next section. T h e discrepancies between t h e theoretical a n d experimental values a r e only about 5% when t h e DZP basis set is used.
IV. Analysis of Electron Diffraction Intensities
Vibrational Corrections. T h e molecular intensity obtained from
826 The Journal of Physical Chemistry, Vol. 91, No. 4, 1987
Yamanouchi et ai.
TABLE VIII: Correlation Matrix" (X100) for 1,Z-Dimethylbydrazine k,
k2
ki 100
40 100
k2
H ri
R -28 -9
ri 41 13
100
-23 100
r2
r3
r4
-26
13 8 -41 3 -87 100
21 6 -43 22 -93 84
-18
39 -19
100
r2
73
100
r4
81
8, 83
0, 10 -11 -27 4
82
83
84
85
1,
25 7 -52
20
-7 -4
50
49
74
-3 -3 3 -3 58 -43
65 100
89
-65
62 100
-12 -44 100
-61
26 -86
8
-25 20 -31 -4 35 25
61 -27 100
84
11
-7 69 -54 -76 -23 -56 98 -30
100
03
I,
85 -18 18 -30 14 13 -6
15 -5 14 -7 100
12 I:,
12
13
I4
-25 -7 53 -26 82 -81 -87 -77 -88 22 -28 36 -14 100
2 23 19 -12 44 -37 -53
-5
14
6 44 -10
20 -20 -23
-48
-20
-68 21 -52 29 20 57 100
-29 0 -16 5 1
30 16 100
" k , and k2 are indices of resolution for the long- and short-distance data, 0.891 (10) and 1.018 (16), respectively, R is the relative abundance for the inner-outer conformer, r l = r(C-H)av, rz = r(N-C)(IO)av, r3 = r(N-C)(OO),,, r4 = r(N-N)av, O1 = IH-C-Ha,, 8, = LN,-K>-C, 0, = IN-NC(OO), 0, = K-N-N-C(IO), B5 = LC-N-N-C(OO), I , = [(N-C),", l2 = /(C...H),,, I , = I(C.-.N),,, and I4 = I(C..C)(OO).
I
I-
IO
20
.
-
-,-
C-N
.-I
30
Stii')
Figure 3. Typical molecular intensities for 1,2-dimethylhydrazine.Ob-
1.0
2.0
3.0
4.0
r(A)
served values are shown as open circles, and the solid curve represents the best-fit theoretical intensity. The lower solid curve represents the residuals.
Figure 4. Experimental (open circles) and theoretical radial distribution curves for 1,2-dimethyIhydrazine. A damping factor, exp(-0.0023s2), was used. The lower solid line represents the residuals.
electron diffraction5 was analyzed after correction for the vibrational effects, which required the force field. Durig and Harris2 reported the assignments of the absorption bands, but the differences between the vibrational frequencies for the conformers have never been investigated. The I O and 00 conformers have C , and C, symmetries, respectively. Therefore, almost all the normal modes are infrared active, and their infrared spectra are complicated. In such a case an a b initio M O calculation, even at the Hartree-Fock level, provides a useful vibrational force field, as demonstrated by a series of reports by Hamada et aI.'"'* Therefore, an ab initio calculation of the vibrational force field was made for both conformers using the optimized geometry for the 4-31G(N*) basis set.Ig The calculated vibrational wavenumbers are in good correspondence with observed values,2 except that the calculated values are overestimated by 5-1 5%. The off-diagonal elements of the calculated F, matrix were and the diagonal elements were varied by multiplied by 0.8 a trial-and-error method so that the observed wavenumbers were reproduced. The force field thus obtained agreed with the observed wavenumbers, after a slight change in the assignment, to within 5% for both conformers. The mean amplitudes and the correction for the shrinkage effects for atom pairsz0were also calculated, as summarized in Table VI. Most of the mean amplitudes were fixed to these values in the least-squares analysis of the diffraction intensity, but a part of the amplitudes was varied as independent parameters, as de-
scribed in the next section. The vibrational corrections for the rotational constants,20 B,-Bo, were also evaluated with the same force field. Structural Parameters and Relative Abundances of the Conformers. The geometrical parameters for both conformers were determined by a joint analysis of the molecular intensity and the rotational constants. The following geometrical parameters and mean amplitudes were fixed to the corresponding theoretical values obtained by the 4-3 lG(N*) calculation mentioned above, because the optimized geometrical parameters agreed well with the results of our preliminary analysis6 of the electron diffraction intensity: (1) the differences between the C-H and N-H bond lengths, (2) the conformational difference between the N-N bond lengths, (3) the difference between the two inequivalent C-N bond lengths for the IO conformer, (4) the differences between the N-C-H angles, (5) the difference between the skeletal bond angles, LN,-N,-C and LN,-N,-C, for the IO conformer, ( 6 ) the N-N-H angles, (7) all the differences between the mean amplitudes, l(C-H) and l(N-H), (8) all the differences between l(C-N) and l(N-N), (9) all the differences between I(C-.H) and I(N-.H). and (10) all the differences between I(C-.N). Thus four bond distances, three bond angles, two dihedral angles, the relative abundance of the IO conformer, and four mean amplitudes were refined as independent parameters in the least-squares analysis; the results are listed in Table VII. The correlation matrix for the obtained parameters is shown in Table VIII. Typical observed molecular intensity and radial distribution curves are shown in Figures 3 and 4, respectively, with residuals. The rotational constants calculated by the obtained rz structure are compared with the observed constants in Table IX.
(16) Hamada, Y.; Tanaka, N.; Sugawara, Y.;Hirakawa, A. Y . ;Tsuboi,
M.; Kato, S.; Morokuma, K. J . Mol. Spectrosc. 1982, 96, 313. (17) Tanaka, N.; Hamada, Y.; Sugawara, Y.; Tsuboi, M.; Kato, S.; Mo-
rokuma, K. J. Moi. Spectrosc. 1983, 99, 245. (18) Yamanouchi, K.; Matsuzawa, T.; Kuchitsu, K.; Hamada, Y.; Tsuboi, M. J . Mol. Srrucr. 1985, 126, 305. (19) Yamanouchi, K.; Hamada, Y.; Kuchitsu, K., unpublished results. (20) Kuchitsu, K.; Cyvin, S. J. In Molecular Structure and Vibrations; Cyvin, S. J., Ed.; Elsevier: Amsterdam, 1972; Chapter 12.
V. Discussion
Geometrical Parameters. In the present study, the geometrical parameters are refined and determined precisely by use of the rotational constants obtained by microwave spectroscopy. For example, the dihedral angle of the 00 conformer, which was
Molecular Structure of 1,2-Dimethylhydrazine TABLE IX: Comparison of the Rotational Constants (cm-') for 1,2-Dimethylhydrazine obsd" calcdb inner-outer A, 0.57832 0.5783 ( I O ) Bz 0.164 91 0.1649 (2) cz 0.15030 0.1503 (2) outer-outer A, 0.93006 0.9301 (10) Bz 0.139 22 0.1392 (2) cz 0.131 31 0.1313 (2) ~~
"Transformed from the observed rotational constants (Ao, Bo,and Co) with harmonic corrections (ref 20) by use of the corrected ab initio force field (see section IV). bCalculated from the geometrical parameters determined in the present study (Table VII). The uncertainties are estimated from those in the structural parameters.
reported to be 150.9 (328)O by Chiu et al.,4 is now determined to be 165.3 (18)' in the present analysis. The bond length r&N-N) is compared with that estimated from the ab initio calculation in Table X, where the calculated and observed N-N bond lengths in hydrazine are also compared. The theoretical r,(N-N) values estimated with the 4-31G(N*) basis set for hydrazine derivatives are shorter than the r,(N-N) bond lengths by about 0.035 A. However, the corresponding differences in the C-N bond lengths are about 0.01 A. For both conformers the N-C-H angles (-114') for the methyl hydrogen atom which is trans to the direction of the lone pair of the nitrogen atom is calculated to be larger, by about 4 O , than those for the other hydrogen atoms ( w 1 loo) in the same methyl A similar tilt of the methyl group was found in the results calculated by the 4-31G basis set.4 This tilt predicted in the present ab initio calculation is similar to that of the methyl groups in dimethylamine observed by Wollrab and Laurie21 and by McKean.22 Enthalpy Difference f o r the Two Conformers. The relative abundance of the two conformers in the gas phase, listed in Table VII, leads to the enthalpy difference between the conformers, AH(O0-IO), by use of the vibrational and rotational entropy differences and the statistical weight of 2 for the IO conformer, the vibrational contribution being based on the observed wave(21) Wollrab, .I. E.; Laurie, V. W. J . Chem. Phys. 1968, 48, 5058 (22) McKean, D. C. J . Chem. Phys. 1984, 79, 2095.
The Journal of Physical Chemistry, Vol. 91, No. 4, I987
821
TABLE X Comparison of Experimental (rp)and Theoretical ( r e ) Bond Lengths for 1,2-Dimethylhydrazine and Hydrazine (A) 1,2-dimethylhydrazine hydrazine rpo r,b r. - re r; r,b r. - re r(N-H) 1.030 1.004 0.026 1.021 (3) 1.001 0.020 r(N-N) 1.441 (2) 1.405 0.036 1.449 (2) 1.413 0.036 1.453 0.010 r(N-C)(IO) 1.463 (9) r(N-C)(OO) 1.459 (10) 1.450 0.009 "Determined in the present study. boptimized bond lengths by the 4-31G(N*) basis set (ref 7 ) . cDetermined by Kohata et al. (ref 14).
TABLE XI: Observed and Calculated Enthalpy Differences, AH(O0-IO). for 1.2-Dimethvlhvdrazine (kJ/mol) ab initio obsd 0.21 (84)O
0.16b
0.llC
-0.42d
ODerived in the present study. bEvaluated at the r Astructure determined in the present analysis with the D Z P basis set (ref 7 ) . CEvaluated at the re structure by the 4-31G(N*) basis set (ref 7). dEvaluated at the re structure by the 4-31G basis set (ref 4).
numbers.* The AH value is calculated to be 0.21 (84) kJ/mol, and, hence, the enthalpy difference is essentially equal to zero. This value is consistent with the calculated values using various basis set^,^.^.^ as listed in Table XI. The abundance of the I1 conformer is estimated to be less than 1% according to an estimate using the 4-31G basis set4 This explains why no evidence for the existence of the I1 conformer was found in the microwave and infrared spectra. Acknowledgment. We are grateful to Professor L. Schafer, University of Arkansas, Drs. T. Fukuyama and K. Kohata, National Institute for Environmental Studies, Professor K. Kimura, Institute for Molecular Science, and Dr. Toru Nakagawa, Fujitsu Ltd., for their helpful advice. Registry No. 1,2-Dimethylhydrazine, 540-73-8.
Supplementary Material Available: Table of experimental data of the total intensity for 1,2-dimethylhydrazine obtained by gas electron diffraction (2 pages). Ordering information is given on any current masthead page.
