7211
J. Phys. Chem. 1991, 95, 7211-7216
Structure of the Dimethylamlne-Sulfur Dioxide Complex Jung Jin Oh, Kurt W. Hillig 11, and Robert L. Kuczkowski* Department of Chemistry, University of Michigan, Ann Arbor, Michigan 481 09- I055 (Received: March 18, 1991; In Final Form: May 6, 1991)
The microwave spectrum of the charge-transfer complex between dimethylamine and sulfur dioxide was studied with a pulsed molecular beam Fourier transform microwave spectrometer. The rotational constants (in MHz) of (CH3)2NHS02are A = 4445.495 (3), B = 2063.031 ( l ) , and C = 1752.470 (1). In addition to the normal isotopic form, the rotational spectra of the (CH3)2NH.%02, (CH3)2SNH.S02, (CH3)2NDS02,and two (CH3)2NH.S0'80 isotopic species were assigned. Stark effect measurements gave electric dipole components of pa = 4.025 (I), pc = 1.747 (2),and kmI= 4.388 (1) D. The structure of this complex lacks any symmetry plane. The nitrogen lone pair points toward the S atom, nearly perpendicular to the plane of the sulfur dioxide, and one methyl group staggers the oxygen atoms. The nitrogen-to-sulfur distance of 2.34 (3) A is about 0.08 A longer than in the trimethylamine-S02 complex which correlates with the relative strength of the complexes. From the dipole moment and the nitrogen nuclear quadrupole coupling constants, an upper limit is estimated for electron transfer from the nitrogen to the sulfur atom of 0.25 electron. A6 initio calculationsalso conclude that a methyl group staggers the two oxygens of SO2.
Introduction The properties of both weak and strong charge-transfer (CT) complexes have been studied for more than 50 years.' These complexes have been a testing ground for qualitative and quantitative concepts of donor and acceptor interactions. One of the first models was proposed by Mulliken2 and emphasized the ionization potential of the donor and electron affinity of the acceptor. When ab initio M O techniques were developed, the structures and binding energies of various complexes were calculated and compared with experimental data. It was possible to decompose the binding energies into electrostatic, polarization, charge-transfer, and exchange repulsion terms by using the Morokuma decomposition method which gave considerable insight on the bonding mechanism^.^ The 1:1 complex formed by SO2with ammonia and the methyl amines comprise a particularly interesting chargetransfer series. This group of complexes have binding energies of approximately 10 kcal/mol.' The donor-acceptor interaction is stronger than the usual van der Waals interaction yet weaker than in strong complexes such as TMA-BF3 (TMA = trimethylamine), having binding energies greater than 20 k c a l / m ~ l . ~There have been four ab initio studies of members of this series of c ~ m p l e x e s . ~ - ~ The two more complete investigations'**concluded that the binding energy increases systematically from NH3.S02 to TMA.SO2 (Table I). The calculated structures of the complexes show a systematic change in the N-S distance. (SeeTable I and Figure 1.) In these calculations, only d(N-S), angle j3, and in some cases the amine torsional angle (4) about d(N-S) were varied. The Morokuma energy decomposition (Table I) indicated that the electrostatic interaction is the predominant attractive term; nevertheless, the smaller charge-transfer and polarization terms are the key to the increased stability with successive methyl substitution. (1) (a) Molecular Complexes; Foster, R.. Ed.; Crane, Russak New York, 1073; Vol. I. (b) Intermolecular Complexef;Hobza, P.. Zahradnik, R., Us.; Elsevier: Amsterdam, 1988. (2) (a) Mulliken, R.S. J . Am. Chem. Soc. 1952, 74.81 1. (b) Mulliken, R. S . J . Phys. Chem. 1952,56, 801. (3) Morokuma, K. Arc. Chem. Res. 1977, 10, 294. (4) (a) Christian, S.D.;Grundnes, J. Nature (London) 1967,214, 1 I I I . (b) Grundnes, J.; Christian, S. D. J. Am. Chem. Soc. 1968, 90,2239. (c) Grundnes, J.; Christian, S.D.;Cheam, V.;Farnham, S.B. J . Am. Chem. Soc. 1971, 93, 20. ( 5 ) Bryan, P. S.; Kuczkowrki, R. L. Inorg. Chem. 1972, 1 1 , 553. (6) Lucchese, R. R.; Hakr, K.;Schaefer, 111. H.F. J . Am. Chem. Soc. 1976, 98, 761 I. (7) Douglas, J. E.;Kollman, P. A. 1.Am. Chem. Soc. 1978, 100, 5226. (8) Sakaki, S.; Sata, H.; Imai, Y.;Morokuma, K.;Ohkubo, K. Inorg. Chem. 1985. 24, 4538. (9) Pradeep, T.;Sreekanth. C. S.; Hegde, M. S.;Rao, C. N. R. J . Am. Chem. SOC.1989, I l l , 5058.
TABLE I: Ab Initio (HF/SCF) Structurrrl Parameters, Bding Energies, and Energy 'Decomposition for AmimSO, Compkxd NHvSO, MA807 DMASO, TMAeSO, AEb/kcalmol-l -1 1.7 -13.9' -14.5' -15.0 2.45 d(N-S)/A 2.63 2.40 2.36 Wegd 85 85 (85) (85) b/degd 60 I20 (0) (0)
Energy Components at d(N-S) = 2.45 A AEe/kcal-mol-' -1 1.3 -13.7 -14.3 -14.8 -33.1 -32.5 -31.8 AEes -33.4 AEPOL -3.4 -4.0 -4.5 4.9 -12.3 -13.3 -14.1 U c T -10.2 35.7 36.0 36.0 AEex 35.7 a Results from ref 7; MA (methylamine), DMA (dimethylamine), TMA (trimethylamine). Calculations were HF/SCF, 4-31G basis set. *The only experimental value is for TMA(g) + S02(g) TMA.S02(g); AE = -9.1 (5) kcal-mol-'. 'H atom staggers the oxygens. dSee Figure 1 for definition. a = ' 0 for all the complexes. Values in parentheses were assumed. e A E = AEes (electrostatic) + AEFL (polarization) + AEm (charge transfer) + AEex (exchange repulsion). See refs 3 and 7 for further discussion.
-
While all four amine.S02 complexes are known, only the structure of the TMA.S02 complex has been investigated by X-ray crystallography.I0 Recently, a structure for this complex in the gas phase was determined" which showed that the N-S distance increased by 0.2 A compared to the case for the crystal. It was also deduced that the TMA and SO2parameters were affected very little in the gas-phase complex (10.01 A in bond distances and 1-2O in bond angles). The binding energy has been determined experimentally only for the TMA-S02 complex (gas, AE = -9.1 ( 5 ) kcal/mol).4 Matrix IR data have been reported for all four amine.S02 complexes,'* and the dipole moment of TMA.S02 (4.95 D) in benzene solvent has also been determined.') A pulsed supersonic nozzle has proven to be an effective tool to detect van der Waals and H-bonded complexes in the gas phase by Fourier transform microwave spectro~copy.'~This method was recently employed to study the TMA.SO, complex." It was attractive to follow up the study of T M A 6 0 2 with another member of the amine.S02 series by this method. This would test the sensitivity of the structural parameters to the small decrease (IO) Van Der Helm, D.; Childs, J. D.; Christian, S. D. Chem. Commun. 1969, 887. ( I 1) Oh,. J.-J.; LaBarge, M. S.; Matos, J.; Kampf, J. W.; Hillig It, K. W.; Kuczkowski, R. L. J . Am. Chem. Soc. 1991, 113, 4732. (12) Saas, C. S.; Ault, B. S.J . Phys. Chem. 1984,88, 432. (13) Moedc, J. A.; Curran, C. J. Am. Chcm. Soc. 1949, 71, 852. (14) Legon, A. C.; Millen, D. J. Chem. Rev. 1986,86,635. See references therein.
0022-3654/91/2095-7211%02.50/0 0 199 1 American Chemical Society
7212 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991
Oh et al.
TABLE 11: Observed Tramition Frequencies for (CH,)2NH.S02 transition F' F Vh' Av6
R"l
21I-
101
1
2 3 2
0 2 2 1
221-111 3 2
2
3 2
2
2 1 2 3 1
2 0
2 2 1 3 1
1
1
220-110 1
202-101
N R'3'
ib)
Figure 1. (a) Definition of parameters used in Table I. (b) Definition of N-S torsional angle (4) which is Oo when the RI-N bond eclipses the C,axis of the SO2(Le., 4 = r(R,NSX) where X is a point on the C2axis of the SO2). For ammonia, R, = R2 = R3 = H; MA, RI = Me, R2 = R, = H; DMA, R, = H, R2 = R, = Me; TMA, R, = R2 = R, = Me. (See also Figures 2 and 3.)
in binding energy predicted by the ab initio calculations and could probe changes in electronic properties through the dipole moment and nitrogen nuclear quadrupole coupling constants. Efforts to detect the NH3.S02 and CH3NH2.S02 complexes have been unsuccessful due to sample handling problems. However, the (CHJ2NH.S02 complex (DMA.S02) was amenable to study, and the results are repoFted here.
Experimental Section Materials. The DMA-S02complex was synthesized by mixing equal amounts of DMA (Aldrich Chemical Co.) and SO2 (Matheson) in a vacuum line. The pale green liquid (ambient vapor pressure -6 Torr) was loaded into a small chamber just upstream from a pulsed gas valve. As the material is hygroscopic, a glovebox was used to transfer the sample. About 1-2 atm of argon was passed through the nozzle chamber which was heated to 50-100 OC to obtain an adequate pressure of nearly completely dissociated DMA-S02. The higher temperatures were necessary toward the end of a sample run (2-4 days of work) since the sample converted to a viscous liquid after use, probably due to reaction with adventitious water in the system. The (CH3)2'sNH sample was obtained by freeing the amine from the DMAaHCI salt (98% lsN, MSD Isotopes) with sodium hydroxide. The free (CH3),I5NH was passed through a barium oxide column to eliminate any water. The (CH3)*NDsample was obtained by dissolving (CH3)2NH into excess D 2 0 and subsequently freeing the (CH3)2NDby adding sodium hydroxide. The SOI8Osample was obtained by first mixing equal amounts of SO2 and S1802(99% 180,Alfa) in a glass bulb where they quickly equilibrated. The spectrum of the % isotopic species was observed in its natural abundance of 4%. Spectrometer. The FTMW spectrometerIs operated in the region 7.0-1 8 GHz and has been described previously."j The operating conditions were the same as those discussed in the TMA.S02 study.11 Line widths (fwhm) for resolved hyperfine components of the normal isotopic species were typically about 20 kHz. Spectra. The 14 assigned transitions of the normal isotopic species were characterized by a and c dipole selection rules and showed hyperfine splittings due to the nitrogen nuclear electric quadrupole moment. The hyperfine splittings were helpful in assigning transitions. The observed transitions and hyperfine (15) B a l k T. J.; Flygare, W.H.Reu. Sei. Insrrum. 1981. 52. 33. (16) (a) Bohn, R.K:; Hillig 11, K. W.;Kuczkowski, R. L. J . Phys. Chem. 1989, 93, 3456. (b) Hillig 11, K. W.; Matos, J.; Scioly, A.; Kuczkowski, R. L. Chem. Phys. & t i . 1987, 133, 359.
211-1
212-1
1
2 1
10
2 1
2 0
II
2 2 1 3 1
1 2 1
2 0
312-202 2 4 3
1 3 2
2 4
1
3
3 4
2 3
3 4
2 3
3 4 2
2 3
3 4 2
2 3
4 4
4 3 4 2 3
303-202 313-21 2 312-211 322-221 1
321-220 1
423-322 5
3 3 422-321 4 5
3
3 4 2
10634.514 10633.211 10633.920 10634.460 10634.955 15 399.465 15 399.301 15 399.909 15117.323 15 117.166 15 1 17.738 7 602.514 7 601.48 1 7 601.651 7 602.519 7 602.585 7 604.234 7 941.490 7 940.630 7 941.160 7 941.465 7 941.698 1942.795 1320.395 7 319.533 7 320.036 7 320.420 7 320.605 7321.677 14925.435 14 925.082 14 925.401 14925.661 I 1 334.149 1 1 333.975 1 1334.186 10963.479 10963.262 IO 963.574 11 893.437 11 893.220 11 893.530 I 1446.336 1 1445.475 11 446.582 11 447.198 11 558.428 1 1 557.563 11 558.675 11 559.291 15 239.426 15 239.08 1 15 239.08 1 15 239.55 1 15 239.673 15 239.673 15510.144 15 509.795 15 5 10.271 15 5 10.394
0 2 -3 -1
-2 -2 -1 1
2 0 0 -1
-2 3 2 -2 -1
0 2 0 -2 -1 0 -1 0
0 1 -1
1
0 -1
0 I -1
2 -2 2 -2 2 2 -2 2 0 1 -1 0 1
2 -1
-2 0 -1 -1 0
I 1 -1 0 -1 1
"Observed frequency ( u ~ in) MHz. The first frequency listed for each transition is vo, the center frequency in the absence of hyperfine splitting. b A =~ uh - ualC (in kHz). The calculated frequency was obtained using A, B, C,0,. xgg, etc. in Table Ill to calculate uo and the hyperfine components.
components are listed in Table 11 for the normal isotopic species. The splittings were fit to determine the nitrogen quadrupole coupling constants and the unsplit transition frequencies. The unsplit frequencies were fit by using a Watson S-reduced Hamiltonian (Prepresentation) to obtain the rotational and centrifugal distortion constants." The derived spectroscopic constants are summarized in Table Ill. A similar procedure was used to assign (17) Watson, J.
K. G. J . Chem. Phys. 1967,16, 1935.
The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 7213
Dimethylamine-Sulfur Dioxide Complex
TABLE Ilk Spectroscopic Constants for the Isotopic Species of (CH3)zNH.S0z normal no. of lines’ AIMHz BIMHz CIMHz Dj/kHz DJK/
kHz
DK/kHZ dl/kHZ dJkHz Av,,b/ kHz x,/MHz Xb6lMHZ
14 (47) 4445.495 (3) 2063.031 ( I ) 1752.470 ( I ) 2.06 (2) -1.38 (8) 1.076 (57) -0.43 (3) -0.22 ( I ) 1.6 -3.448 (2) 1.671 (2)
3%
I5N
(CH>)2ND.S02
!SO(1)’
8 (23) 443 1.668 ( I ) 2043.841 ( I ) 1738.935 ( I ) 2.02 ( I ) -1.36 ( I ) 1.076d -0.42 ( I )
17 4435.625 (2) 2048.742 ( I ) 1742.915 ( I ) 2.02 ( 1 ) -1.24 (3) 1.076d -0.42 ( I ) -0.21 ( I ) 1.9
12 (35) 4360.221 (6) 2033.921 (2) 1738.003 (2) 1.99 (3) -1.21 (15) 1 .076d -0.30 (6) -0.19 ( I ) 3.8 -3.480 (3) 1.699 (7)
8 (231 4357.180 (4) 2024.313 (2) 1712.107 (2) 2.00 (5) -1.15 (IO) 1 .076d -0.45 (6) -0.21 ( I ) 1.8 -3.371 (2) 1.601 (6)
-0.19 ( I ) 0.1 -3.458 (4) 1.691 (9)
‘Number in parentheses is the number of measured quadrupole components. bAv = vob to the value for the normal isotope.
(CH3)2NH.34S02,(CH3)iND.S02, (CH3)2’SNH.S02,and two different (CH3)2NH.S01 0 species labeled as (1) and ( 2 ) according to the atom numbering shown in Figure 4. The observed hyperfine components, unsplit frequencies, and quadrupole coupling constants for the isotopic species are listed in Tables SI-S5 as supplementary material (see final paragraph regarding availability of supplementary material). The spectroscopic constants are given in Table 111. The deuterium hyperfine splitting could not be resolved in (CHJ2ND-S02. There was no evidence for methyl group internal rotation or inversion splittings in these transitions, although such effects are prominent in the spectrum of free DMA. By use of an internal rotation program based on the method of HerschbachI8 and the direction cosines calculated from the structure (see below), the observed V3 methyl barrier of 3.22 (2) k ~ a l / m o lin~ free ~ dimethylamine splits the transitions of the complex less than 1 kHz. It is estimated that a barrier of about 2.3 kcal/mol (or lower) is needed to produce resolvable splittings (210 kHz).” The large increases in the moments of inertia from free DMA are a factor contributing to the quenched internal rotation splittings. Dipole Moment. The second-order Stark effects ( A v / E 2 )for 9 M components from three transitions of the (CH3)2’5NH.S02 species were determined. The ISN species was chosen since it is free of nitrogen hyperfine splittings. The calibration2’ and measurement procedure have been described previously.”V1” A least-squares fit of Au/E2 using the calculated second-order coefficients gave pa = 4.030 ( 4 ) ,pc = 1.752 ( 4 ) ,and kohl= 4.395 ( 4 ) D with the p t component equal to -0,019 D2. Since the value of pb2 was small and negative, we concluded that pb = 0.01 (1) D. With pb fixed at zero, the dipole components pa = 4.025 ( I ) , pe = 1.747 ( 2 ) , and p,otal= 4.388 ( I ) D were obtained. The experimental values of Au/E2 are listed in Table S6. The agreement between the experimental and calculated values of Au/E2 was good; the rms deviation was 0.71%.
Results and Discussion Structure. The gas-phase structural information is contained in the moments of inertia, I, = x,mi(b: + cp), etc., or the related planar second moments, Pbb = (I, I, - 1b)/2 = Cimib? and similarly for Pa, and Pcc.22 Planar second moments are useful for determining whether a molecule has a plane of symmetry. On the basis of an ab initio report,’ which had assumed that DMAaSO, has C, symmetry with the H atom of the amine staggering the two oxygens (cf. Table I), we initially expected an (ICsymmetry plane. Therefore, u and c dipole selection rules were anticipated and Pbb was expected to be -99 amu.A2, i.e., close to the sum calculated from the structures of free DMA23dand
+
(18) (a) Herschbach, D. R. J . Chem. Phys. 1959,31,91. (b) Hirota, E. J . Chem. Phys. 1966, 45, 1984. (c) Stelman, D. J . Chem. Phys. 1964.41, 2111. (19) Wollrab, J. E.; Laurie, V. W. J . Chem. Phys. 1971, 54, 532. (20) Since the two methyl group are not equivalent, each methyl group was treated separately and top-top coupling was ignored. (21) Patel, D.; Margolese, D.; Dyke,T. R. J . Chem. Phys. 1979, 70,2740. (22) I,, * h/(8*2A) etc. where the conversion factor h/(8n2)= 505 379.05 amu.A2.MHz was used.
“O(2)’ 8 (28) 43’08.580 (12) 2036.350 (5) 1730.625 (8) 2.06 (15) -1.40 (31) 1.076d -0.38 (18) -0.24 (4) 5.5 -3.484 (3) 1.708 (5)
- vWlc. cSee Figures 1 and 4 for atom labeling. dFixed
S02?3a While the predicted selection rules were found, the values of Pbb for the normal, 34S, and ISN isotopic species of 78.548, 78.697,and 78.610 a m d 2 , respectively, were clearly inconsistent with the initially assumed structure. Indeed, the observed second moments for these isotopes agreed very well with a rotation of the dimethylamine by 120° about the N-S bond. Based on spectral predictions for this new structural model, two nonequivalent l8O isotopic species were assigned as well as the species with deuterium substituted at the nitrogen. Given these isotopic data, it was clear that the structure of the complex had no symmetry plane and that the hydrogen replaces one of the outsf-plane methyl groups of the TMA.S02 complex.” The determination of the structure of a complex with no symmetry elements is not trivial. One simplification is to assume that no changes occur in the internal parameters23of DMA and SO2 upon complexation. This is apparently a viable assumption, Le., one not likely to affect the derived structural parameters very greatly, based on an examination of its validity in the related TMA.S02 complex.24 The structure of the complex can then be defined by six parameters which include a distance (R) between two points located in DMA and SO2,a dihedral angle, and four tilt and torsional angles locating the DMA and SO2 relative to R and each other. These six parameters (described more fully in the Appendix) were fit to the 18 moments of inertia by using a least-squares procedure. However, the structure can be more conveniently described as in Figure 1 by the distance d(N-S) between N and S , a tilt angle 0 of the SO2 plane relative to d(N-S), a tilt angle (Y of the pseudo-C3 axis of DMA relative to d(N-S), and a torsional angle (4) describing the relative orientation of DMA and SO2. This is useful since the bonds around DMA have essentially C3symmetry (Le. ( C N C (HNC), and this pseudo-C3 axis points nearly along the N-S bond vector. Moreover, one methyl group nearly exactly staggers the oxygens in SO2. The values obtained for these parameters from the least-squares fit analysis are given in Table IV as the LSF parameters. A more complete description of the derived structure in terms of the more generalized set of six internal parameters mentioned above and described more fully in the Appendix is given in Table S7, along with the values for AI, = Ixulc - Ixob.The quality of the fit given by AI,, is about 0.04 amu.A2, which is quite acceptable. The principal axis coordinates obtained for the heavy atoms and the amine hydrogen are given in Table V under the column LSF.
-
(23) (a) SO2: Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendeman, R. H.; Ramsay, D. A.; Lovas, F. J.; Lafferty, W. J.: Maki. A. G. J . Phys. Ref.Duta 1979,8, 619. (b) NH,: Helminger, P.; De Lucia, F.; Gordy, W. J . Mol. Spectrosc. 1971, 39,94. (c) MA: Kreglewski, M. J . Mol. Spectrosc. 1989. 133, IO. (d) DMA: Wollrab, J. E.; Laurie, V. W. J . Chem. Phys. 1968, 48, 5058. (e) TMA: Wollrab, J. E.; Laurie, V. W. J . Chem. Phys. 1969, 51, 1580. (24) The question of structural changes in TMA-S02was explored in the study of TMA.SO,.ll It was concluded that the neglect of vibrational averaging effects obscured the detection of any unambiguous structural changes, which were less than -0.01 A in bond distances and 1-2O in bond angles. in any case. Also, according to earlier work,’ substitution of the experimental values for the bond angles with tetrahedral values in DMA affects the binding energies by less than 0.1 kcal/mol.
7214 The Journal of Physical Chemistry, Vol. 95, No. 19, 1991 TABLE I V Structural Parameters (& deg) for (CHJ2NH.SOZ
LSFa d(N-S) d(S-01) 4s-02)
d(N-H) d(N-C) Rcmd cle
d
L(oI-s-02) L( N-S-01 ) L( N-S-02)
H-N-S-Ol)h H-N-S-02) T(C~-N-S-OI) ~(c2-N-S-02) T ( CJ-N-S-01) T ( CJ-N-S-02) T( T(
2.360 (5) 1.43Ic 1.43Ic 1.019c 1.467' 2.758 (2) 0.8 (5) 80.4 (7) 125.0 ( I ) 1 19.3c 94.0 (4) 95.6 (4) -174.9 (2) 65.2 (2) 65.0 (2) -55.0 (2) -55.3 (2) -175.3 (2)
KP 2.335 (30) 1.440 (20) 1.452 (20) 1.000 (20) 1.499's
TABLE VI: Comparison of the Structural Panmeters, Stretching Force Constants (k,),Vibrational Frequencies (o,), and Binding Energies (e) for Several Similar SO2 Complexes
TMA.SO2" d(N-S)/A a/deg Bldeg
3.4 (30)g 78.7 (30)g 115.8 (20) 93.7 (20) 96.7 (20) -177.2 (30) 66.2 (30) 64.6 (30)g -52.0 (30)g -56.0 (30)g -172.5 (30)g
TABLE V Heavy Atom Coordinates (A) for (CH&NH-SO, a b C KP LSFb Kr LSF Kr LSF S -1.033 -1.054 0.278 0.262 0.326 -0.297 0.925 0.920 0, -0.895 -0.910 1.001 1.002 02 -1.515 -1.520 -1.075 -1.090 -0.219 -0.243 N 1.239 1.238 -0.253 -0.287 -0.441 -0.426 H' 1.350 1.367 -0.739 -0.769 -1.307 -1.314 C2 1.558 -1.148 0.717 CJ 1.973 0.981 -0.380
" Coordinate from Kraitchman (Kr) substitution method. See Figure 4 for atom numbering. Sign chosen to be consistent with LSF. bCoordinates from least-squares fit of all isotope data holding DMA and SO2 geometries fixed at values for free DMAZMand S02.23a Hydrogen bonded to nitrogen. In addition to the least-squares method, the Kraitchman coordinates were calculated.2s and are shown in Table V under Kr. The structural parameters from this method are also listed in Table IV. The agreement between the LSF and Kr parameters is good although small discrepancies are apparent. The differences between d(N-S) and d ( S - 0 ) are close in magnitude and even in sign to those obtained from a similar analysis of TMA.S02." It was pointed out in that case that it is unclear whether the small changes in the SO2parameters upon complexation suggested by the Kr data are bonafide, since in both the LSF and Kr analyses the effects of vibrational averaging on the moments of inertia were neglected. Nevertheless, for consistency with the TMA.S02 analysis, we recommend the Kr values for d(N-S), a,and 0 as preferred since some cancellation of vibrational effects should occur with this method. The uncertainties assigned in Table IV are sufficient to encompass the values from the LSF calculation. Reference 1 1 should be consulted for a further discussion of the meaning of the structural parameters. A comparison of the pertinent structural parameters for DMA.S02 and TMA-S02are given in Table VI along with data
2.26 1
79 0.32gd w,/cm-' 134.5 @/kcal.mo1-' 4.90 ((ARc,,,2))1/2h/A 0.064
k,/mdyn.A
"Using least-squares fit coordinates from Table V. See Figure 4 for atom numbering. Numbers in parentheses are one standard deviation of the fit. The six structural parameters defined in the Appendix which were determined by the least-squares fit were R(XI-X2) = 3.002 (2) A, ~(S-xl-Xz) = 73.4 (7)O, L(N-X,-X,) = 6.1 ( S ) ' , T(OI-S-XI-X~) = -91.0 ( 2 ) O , r(H-N-X,-X,) 125.0 (I)', T(N-X~-XI-S) ' 0 (fixed at optimum value). Kraitchman (Kr)coordinates from Table V. This structure is preferred by the authors (see text), and numbers in parentheses are overall estimated uncertainties. Not fitted. Values from free DMA and SO2. dDistance between centers of mass of DMA and SO2. cSee Figure 1 for definition. /This is N C 2 ; the value for N C 3 was 1.438 A. EThe least-squares fit coordinates for the carbon atoms were used. hThe torsional angles and atom numbering are consistent with the conformation in Figure 4, and the signs of the dihedral angles are defined in ref 39.
( 2 5 ) Kraitchman, J. Am. J . Phys. 1953, 21, 17.
Oh et al.
DMA.SO2'
HCN.SO2'
2.34 3 79 0.21 I C 116.3 3.72 0.074
2.98 23 71 0.026 46.5 0.65 0.138
@ReferenceI I . All three structures are gas-phase determinations. bThis work.
