J. Phys. Chem. 1990, 94, 1793-1799
1793
some unique (unknown) noncontinuum effect, a safer interpretransitions. Although ion-pairing effects are not treated in an explicit way by existing theories, they are implicit in redox tation is that KIPin CD2CIz is slightly underestimated. If this were true, then even at the very lowest available chromophore asymmetry terms. In that sense, the dependence of EtMCT on concentration (8 X 10” M) significant ion pairing would persist ionic strength is not contrary to dielectric continuum theory. Once (and thereby broaden the absorption envelop). In principle, one ion-pairing effects are removed (by performing experiments at at still lower concould chek this by obtaining values for or near infinite dilution), the optical barrier to electron transfer within B P shows the expected inverse dependence on the optical centrations. Unfortunately, 8 X 10” M appears to be a practical lower limit experimentally in this portion of the near-IR spectrum. dielectric constant. The “correct” dependence on D,, however, is not found experimentally-a conclusion also reached by HenDespite these uncertainties, however, we are inclined to accept drickson and co-workers.s One possible explanation is that dieq 6 as a valid representation of the relation between Ai+/2 and x when a single chromophore is present. electric saturation occurs in low-D, solvents. A more appropriate If the above interpretation of frozen-solvent phenomena is expression then would be E t M C T0: (l/Dop - l/D,(local)). Although the revised expression differs materially from that sugcorrect, it may be enlightening to consider briefly other examples. gested by Marcus-Hush theory, it should be noted that the revision The two that are available in the literature are biferrocene (pz is pyrawas anticipated by Marcus and others in early formulations of monocation and (bpy)zC1Ru11(pz)Ru111Cl(bpy)23+ zine).58 These differ from BfYX- in that almost no change in the theory.’ E t M C Toccurs upon pressure-induced freezing. Furthermore, A ~ I ~ / ~ Experiments in a frozen solvent (CD3CN)5Cappear to be complicated by both ion pairing and dielectric saturation. The changes only slightly, if at all. Both observations would seem to effects apparently can be separated, however, by resort to bandsignal a fundamental change in behavior in comparison to BfYX-. width studies and quasi-empirical correlations between A E t M C T , There is a third observation, however, that may reconcile the results. From studies at millimolar concentrations in liquid solvents KIP,and 0,. Because the effects act in opposite directions, energy (where ion-pairing effects admittedly may exist), the variation compensation exists and EtMcTapproaches (fortuitously) the of EtMCTwith l/Dop - l/Ds is (in both cases) exceedingly value predicted by simple extrapolation from the observed behavior weak.4c*20This implies that xs is very small and further that xi in liquid solvents. will largely determine It follows, then, that both the overall Acknowledgment. This work was supported by the U.S. Detransition energy and the bandwidth will be comparatively inpartment of Energy, Office of Energy Research, Division of sensitive to pressure-induced variations in D, and x,. Chemical Sciences, under Grant DE-FG02-87ER13808. The Conclusions OLIS-modified Cary 14 was acquired with an N S F equipment grant (CHE-8722985) and with funds from an N S F Presidential The present results serve to reinforce and generalize our own Young Investigator Award. R.L.B. acknowledges partial support previous findings16and otherss.6athat ion pairing (and higher order as a Shell Graduate Fellow. ionic association) can influence the energies of intervalence
Molecular Structure and Conformation of Diisopropyl Ketone Studied by Gas Electron Diffraction Combined with Vibrational Spectroscopy and SCF MO Calculationst Hiroshi Takeuchi, Teruhisa Sakurai, Kouichi Takeshita, Kohji Fukushi, and Shigehiro Konaka* Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo 060, Japan (Received: June 6, 1989; In Final Form: September 15, 1989)
The molecular structure and conformation of diisopropyl ketone, MezC(3)HC(2)OC(4)HMez,at 24 ‘C have been investigated by gas electron diffraction with the aid of vibrational spectroscopy and ab initio SCF calculations at the 4-21G level. Three conformers with CI,C,, and C2symmetry exist with the molar fractions of 0.45 (31), 0.31 (12), and 0.24 (22), respectively. The dihedral angles $I(C4CzC3H)and $2(C3C2C4H)of the C , , C,, and C2 conformers (the values are denoted by $z)) are (16’, -62’), ( O O , 180°), and (59’, 59’), respectively, where 4, and $z are defined to be zero when the C-C bond eclipses the C-H bond. The main structural parameters (r and La) of the CI conformer with the limits of error (3a) in parentheses are as follows: r(C=O) = 1.215 (5) A, (r(C-Cf) = 1.535 (2) A, r(C-H) = 1.118 (3) A, LCC(=O)C = 116.6 (17)’, (LCCC) = 110.8 (4)O, and LCCHM, = 111.1 (9)’, where the symbol ( ) denotes average values.
Introduction The conformations of diisopropyl ketone (DIK) have been investigated by several authors’-3 with different conclusions. Aroney and co-workers’ measured the molar Kerr constant of DIK in CCl, solution. They assumed the presence of two conformers, one in which both Hi.Pr atoms are anti to the oxygen atom (C, symmetry) and the other in which one Hi-& atom is syn to the oxygen atom and the other is anti to the oxygen atom (C, symmetry). Here, Hi+ denotes the hydrogen atom attached to the tertiary carbon atom. By comparing the observed molar Kerr constant with the calculated ones, they inferred that the two ‘Taken in part from the doctoral thesis presented by H.T. to Faculty of Science, Hokkaido University.
0022-3654/90/2094-1793$02.50/0
conformers exist with the ratio of 1:2. Hirota and co-workers2 measured the infrared spectra of DIK and related ketones in CCI, solution and concluded from the carbonyl stretching frequencies atoms of the predominant conformer of DIK that the two HiAPr are eclipsed with the oxygen atom ( C , symmetry). Suter3 developed a molecular mechanics force field for ketones and aldehydes and calculated the conformational energy of DIK. According to his calculation, the most stable conformer of DIK has C2 symmetry with the dihedral angle,, t#q(C4C2C3H) (=&(1) Aroney, M.; Izsak, D.; Le FEvre, R.J. W. J . Chem. S O ~1961, . 4148. (2) Hirota, M.; Hagiwara, T.; Satonaka, H. Bull. Chem. SOC.Jpn. 1967, 40, 2439. (3) Suter, U. W. J. Am. Chem. SOC.1979, 101, 6481.
0 1990 American Chemical Society
1794 The Journal of Physical Chemisrry, Vol. 94, No. 5 , 1990
Takeuchi et al. TABLE I: Experimental Conditions
V
Q
n
n
cs
Figure 1. Diisopropyl ketone with C, (with atom numbering), C, and C, symmetry.
(C3C2C4H)),of about 30' and its energy is 1.2 kcal/mol lower than that of the next stable conformer with the dihedral angles = 0' and 42 = 180' (C, symmetry). The atom numbering is shown in Figure 1. The results obtained in CC14 solution'q2 contradict each other, and both are inconsistent with the molecular mechanics c a l c ~ l a t i o n . ~ Recently, the molecular structures of diisopropyl ether,5 diisopropylamine,6 and diisopropyl sulfide' have been studied by gas electron diffraction (GED). The most stable conformers of diisopropyl ether and diisopropyl sulfide have C2symmetry with the dihedral angles, +(CXCH) (X = O,S), of 39 (4)O and 57 (8)', respectively. The similar conformer with C2 skeletal symmetry is predominant in the case of diisopropylamine. The observed structures of these molecules reflect the steric repulsion between the isopropyl groups. In the present study, we have determined the molecular structure and conformation of DIK by GED with the help of vibrational spectroscopy and ab initio SCF M O calculations and examined the effect of the nonbonded interactions between the isopropyl groups and the oxygen atom on the molecular geometry and conformation. As is shown later, the conformer with CI symmetry has the largest population. In order to examine whether the difference in the conformational behavior of DIK and the above three compounds is related to the existence of the double bond, the conformation of 2-isopropyl-3-methyl- 1-butene has been investigated by ab initio calculations. Some investigations of the carbonyl stretching band of DIK have been reported in the literature.2.8 The vibrational frequencies of other bands were measured by Karabatsos9 and Katon and Bentley.Io Karabatsos9 recorded the infrared spectra of the normal and isotopically substituted molecules in CS2 solution but did not report the numerical data except for some vibrational frequencies. The infrared spectrum in the region of 700-350 cm-' was reported in ref 10. Thus, vibrational spectroscopic data are limited. We have observed vibrational frequencies in greater detail and performed normal-coordinate analysis. The parameter set for ketones and aldehydes in the MM2 force field" was recently modified by Bowen and co-workers.12 They
camera distance, mm electron wavelength, A uncertainties in the scale factor, % sample pressure, Torr background pressure during exposure, Torr beam current, pA exposure time, s number of plates range of s values, ti-'
244.3 0.062 75
0.08 10-12 3 x 10-5 0.11-0.12 43-52 3 2.6-16.9
109.3 0.062 74 0.06 9-1 1 3 x 10-5 0.14-0.15 160-170 3
9.4-37.1
applied the MM2 force field with the new parameter set to cyclohexane-l,4-dione and decaline- 1,4-dione and reported that the calculated results are more reasonable than the results given by the original parameter set. In the present study, we compare the observed conformation of DIK with the conformation given by the MM2 calculations. Experimental Section
The sample obtained from Tokyo Chemical Industry Co., Ltd., had a purity of more than 99% and was used after distillation in vacuum. The diffraction patterns were recorded at room temperature (about 24 'C) with an accelerating voltage of about 38 kV and camera distances of 109.3 and 244.3 mm, in an electron diffraction apparatus equipped with an r3-sector.13 The wavelength of incident electrons was determined from the diffraction patterns of carbon disulfide (ra(C-S) = 1.5570 ,&)I4 taken in the same sequence of exposures. The other experimental conditions and information on the photographic plates used for data analysis are listed in Table I. Optical densities were measured at an interval of mm by microphotometry and converted to total inten~ities.'~They were divided by the theoretical background. Elastic and inelastic scattering factors were taken from ref 16 and 17, respectively. Leveled intensities were averaged at each camera distance. The details of the data reduction are given in ref 15. The Raman spectrum in the liquid phase was measured with a Jasco Model R300S laser Raman spectrophotometer using the 632.8-nm line of a He-Ne laser. The infrared spectrum in the gas phase was measured on a Digilab Model FTS-14A Fourier transform spectrometer fitted with a cell with KBr windows. The far-infrared spectrum of the liquid was measured by using a far-infrared interferometer installed at beam-line 6A of UVSOR at the Institute for Molecular Science. The observed vibrational frequencies are consistent with those reported in the literature9J0 and are listed in Table 11, columns 1 and 2.
Ab Initio Calculations Diisopropyl Ketone. Ab initio S C F M O calculations have been performed with the 4-21G basis set18and Pulay's program TEXAS,^^ since the empirical values of the differences, rg - re, are available for this basis set.*O In order to search for stable conformers, the total energies for several conformations were calculated varying the values of &(C4C2C3H)and 42(C3CzC4H)4 at the interval of 20'. The conformers around 4I = 42 = 180' were excluded in the calculations since they are considered to be unstable because of the strong CH3-CH, interactions between the isopropyl groups. The resulting potential energy surface shows three energy minima = 60' (C2 symmetry), dI = 0" and 42 = 180' (C, at r#q = I#J~
(4) Dihedral angles, $, and &, were defined to be zero when the C-C bond is eclipsed with the C-H bond and to be positive when the C-H bond rotates clockwise looking along the direction of the (O==)C-C axis. For the conformer with C, symmetry, $, is equal to $z. (5) Takeuchi, H.; Fujii, M.; Konaka, S.; Kimura, M. J. Phys. Chem. 1987, 91 ., in15 .- .- . (6) Takeuchi, H.; Konaka, S.; Kimura, M. J . Mol. Srrucr. 1986, 146, 361. (7) Kondo, H.: Takeuchi, H.; Konaka, S.; Kimura, M. NiDDOn .. Kaaaku Kaishi 1986, 1458. (8) (a) Fusion, N.: Josien, M. L.; Shelton, E. M. J . Am. Chem. SOC.1954, 76,2526. (b) Michel. G.; Duvckaerts, G.SDectrochim. Acta 1958. 10. 259. (c) Massat, A.; Dubois, E. J.-Mol. Srruct.'1980, 65, 87. (9) Karabatsos, G. J. J . Org. Chem. 1960, 25, 315. (10) Katon, J. E.; Bentley, F. F. Specrrochim. Acto 1963, 19, 639. (1 1) (a) Allinger, N . L.J . Am. Chem. SOC.1977,99, 8127. (b) Allinger, N . L.; Yuh, Y. H. QCPE 1980, 12, 395. (c) Jaime, C.; Osawa, E. Tetrahedron 1983, 39, 2769. ~
(12) Bowen, J. P.; Pathiaseril, A.; Profeta, S., Jr.; Allinger, N . L.J . Org. Chem. 1987, 52, 5126. (13) Murata, Y.; Kuchitsu, K.; Kimura, M. Jpn. J . Appl. Phys. 1970, 9, 591. (14) Tsuboyama, A.; Murayama, A.; Konaka, S.; Kimura, M. J . Mol. Strucr. 1984, 118, 351. (15) Konaka, S.; Kimura, M. Bull. Chem. SOC.Jpn. 1970,43, 1693. (16) Kimura, M.; Konaka, S.; Ogasawara. M. J . Chem. Phys. 1967, 46, 2599. (17) Tavard, C.; Nicolas, D.; Rouault, M. J . Chim. Phys. 1967,154, 540. (18) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J . E. J . Am. Chem. SOC. 1979. 101. 2550. (19) d l a y , P. Theor. Chim. Acta 1979, 50, 299. (20) (a) Schafer, L.; Van Alsenoy, C.; Scarsdale, J. N . J . Mol. Srruct. (Theochem.) 1982, 86, 349. (b) Schafer, L. J . Mol. Srruct. 1983, 100, 51.
Molecular Structure and Conformation of Diisopropyl Ketone
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1795
TABLE 11: Observed and Calculated Frequencies (cm-') and Potential Energy Distribution (%) for Diisopropyl Ketone
obsd" Raman (liquid) 2970 s 2935 s 2910 vs 2870 vs 2755 vw 2714 vw 1712 w 1464 m 1449 m
IR (vapor) 2979 vs 2945 s 2910 s 2887 s 1730 vs I480 sh 1470 s 1394 m 1389 m 1384 m 1370 m
1326 vw 1280 vw
1174 w 1129 vw 1115 m 1085 vw 1070 vw 964 w 895 vs 860 w 740 s 716 m 609 vw 568 vw 525 vw 471 s 395 vw 330 290 240 206
w
1298 vw 1264 vw 1207 sh 1188 sh 1183 w 1178 sh 1127 w 1080 m 1027 s 986 w 960 sh 930 vw 860 vw -800 vw 740 vw 610 w 565d 553d 525d 488d 468d 39Id 332d
m sh w 45e
calcdb
PEDc
C1
C2
C,
2965-2963 (8)
2965-2963 (8)
2965-2963 (8)
ua(CH3) 98-99
2912, 2908 2883 (4)
2909, 2908 2883 (4)
2913, 2909 2883 (4)
u(CH~.R)97, 98 US(CH3) 99
1736 1481 1474-1473 (3) 1461-1453 (4) 1390 1388 1380 (2) 1366 1340-1328 (3)
1742 1486 1479-1476 (3) 1465-1459 (4) 1395 1391 1386, 1385 1370 1346-1333 (3)
1713
u(C=O) 64 6a(CH3) 54 6,(CH3) 58-63 6,(CH3) 77-84 6SCH3) 58 6ACH3) 73 6,(CH3) 96, 94 6,(CH3) 25 G(CHi.p,) 46-47
1272 1208
1278 1203 1185 1174 1150
1180 1 I62 1 I46 1114 1090
1024, I010 982 976
903 859
899 863
1387, 1386 1381, 1378 1355 1335-1325 (3) 1291 1205 1192 1172 1157
1113 1092
1019, 1010 980 973
1476-1470 (4) 1459-1451 (4)
1111 1054 1014, I010 98 1 973 906 886
734 612 559
C,
~ ( C H , . ~ ,25 ) r(CH3) 43 r(CH,) 43 r(CH3) 36; v(CC) 34 r(CH3) 43 r(CH3) 48; C~(CH,.~,) 30 r(CH3) 58 r(CH3) 54, 49; u(CC) 32, 36 r(CH3) 74; 6(CHi.p,) 31 r(CH3) 69; 6(CHi.p,) 27 u(CC) 66 u(CC) 79 u((O=)CC) 46
713 623
708 608 576
S(CCC) 40; w(C0) 27 6(CCC) 39
524 499, 489 483 408 337 292, 285 252-238 (4) 200 179 34, 30
403 373
398 371
297, 277 247-239 (4) 195 184 36, 29
312, 274 242-236 (4) 181, 176 36, 28
6(CCC) 36 S(CCC) 79 S(CCC) 77 6(CCC) 70, 64 t(CH3) 72-99 6(CCC) 46 [(CO) 40; 6(CCC) 39 t((O=)CC) 97,99
"Abbreviations used: vs, very strong; s, strong; m, medium; w, weak; vw, very weak; sh, shoulder. bValues in parentheses are the numbers of bands calculated in this range. CPotential energy distributions (PED)of the only C, conformer are listed. Contributions less than 25% were omitted. Symbols: u, stretching; 6, bending; r, rocking; a, asymmetric; s, symmetric; t, torsion; o,in-plane bending; [, out-of-plane bending. dThe liquid-phase frequencies taken from ref 10. 'The liquid-phase frequency.
symmetry) and +1 = 20" and 42 = -60" (C, symmetry). The geometries of the C2and C, conformers were optimized until the residual Cartesian forces were below 0.001 au. The optimization procedure for the Cl conformer was terminated when the largest residual Cartesian force was 0.0013 au, since many more iterations were needed for achieving the same level of the optimization as made for the C, and C,conformers. The geometries and energies of these conformers are listed in Table 111. The most stable conformer has the CI symmetry, and the C, and C, conformers are less stable than the C1conformer by 0.09 and 1.17 kcal/mol, respectively. From these energy differences, the populations of the CI, C,,and C, conformers at 24 "C were calculated to be 66%, 29%, and 5%, respectively, by assuming the Boltzmann distribution. 2-lsopropyl-3-methyl-1-butene. Calculations were performed by using the 3-21G basis set.2' The calculation procedure is (21) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J . Am. Chem. SOC.1980,
102, 939.
almost similar to that for DIK except for the optimization level. The optimization of the geometries was terminated at the level of about 0.002 au. The results indicated that two stable conformers with + I = 4, = 30" (C, symmetry) and +1 = 0" and 42 = 180" (C, symmetry) exist with the populations of 47% and 53% (total energies are -3 10.52047 and -3 10.520 58 hartrees), respectively. The detailed information about the geometries of the two conformers is not presented, since it is not important in the present study. Molecular Mechanics Calculations
We have carried out the MM2I1 calculations by using the new parameter set for ketones.', The MM2 calculations show that two conformers are major constituents: one has CI symmetry with dI = 10" and 4, = -53O and 65% population, and the other has Czsymmetry with + I = 4, = 63" and 26% population. This result is similar to the result of the 4-21G calculations. Other possible conformers are as follows: two C1conformers with +1 = 8' and +z = 179" (6%) and + I = 141' and = -44" (3%), and one C,
+*
1796 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
Takeuchi et al.
TABLE 111: Structures and Energies Obtained by the 4-21G Calculations'
parameter r(C=O) r(c2-c3) r(c2-c4) r(C3-CJ
CI
parameter r(C3--C6) r(C4-C7) r(C4-Ca) r(C-H)
C, 1.550 1.536 1.547 I .082b
C, 1.549 1.549 1.537 1 .082b
C, 1.545 1.545 1.545 1 .082b
119.4 119.7 120.9 109.0 109.0 1 1 1.1
Lc2c4c8
LC7,8C4H LCCHM,'
111.6 109.8 110.9 109.6b 108.7b 1 10.5b
110.4 110.1 110.1 108.6b 108.6b 110.5b
111.1 110.1 111.1 109.4 109.0 110Sb
178.2 -59.0 59.4 -59.0 178.2
119.9 -1 19.9
@(C$X4H) @J(C~C~CSH)" @J(C2C3C6H)d 6(C2C4C7H)d @J(C2C4CsWd
-61.6 -2.2 4.1 0.1 0.3
59.4 -0.6 0.2 0.2 -0.6
-3.3 3.3 -3.1 3.1
0.09
1.17
1.216 1.53 1 1.528 1.540
C, 1.216 1.531 1.531 1.537
1.217 1.530 1.525 1.545
Lc2c4c7
118.5 120.1 121.5 110.0 108.4 110.3
118.6 120.7 120.7 110.4 111.5 111.5
6(c4c2c3c5) @(c4c2c3c6) @J(C4CK3H) @(C3C2C4C7) '#'(c3c2c4c8)
136.7 -103.3 16.0 179.7 55.9
AEC
0.0
Lc3c2c4 L0,c2c3 L01c2c4
Lc2c3c5 LC2C3C6
C,
0.0 62.1 -62.1
Lc5c3c6
LC7C4C8 LC5,6C3H
180.0
'Bond lengths in angstroms and angles in degrees. bAverage value. CHMcdenotes the hydrogen atom in methyl groups. dAverage value of the kilocalories per mole. Total energies of the C,, C2, and C, deviation of the dihedral angles, C2CCH, from the staggered form (&60° or 180'). conformers are -347.350 IO, -347.349 95, and -347.348 23 hartrees, respectively. TABLE IV: Valence Force Field for Diisopropyl Ketone
force constanta stretch K(C=O) K ( (O=)C-C) K(C-C) K(C-H,.P,) K(C-HML bend H(CC(=O)C) H(0CC) H((O=)CCC) H(CCC) H((O=)CCH,.p,) H(CC Hi-Pr1 H(CCHMe) H(HCH) H(C=O, out of plane) torsion H,( (O=)C-C) HAC-C)
valueb
force constanto
atoms common to interacting coordinates C C C
9.168 3.736 4.019 4.606 4.705
c-c c-c c-c c-c c-c
1.820 1.220 1.021 1.095 0.718 0.648 0.687 0.503 0.21 5 0.026 0.100
valueb
}
0.192c 0.030
1 }
0.255' 0.289 0.395'
C C C
1
c-c c-c c-c C-H C-H
j :;tc ) 0.025c
( H)C-C(H)"
I
c-c c-c c-c
0.018C
O.08Ic 0.161
'Hi.Pr and H M c denote a hydrogen atom attached to the tertiary carbon atom and a hydrogen atom in methyl groups, respectively. units of millidyne per angstrom (stretch constants), millidyne per radian (stretch-bend interaction constants), and millidyneeangstrom per square radian (bend and torsion constants). 'These values are refined as groups. "Trans bond.
conformer with = 42 = 163' (0%). According to the MM2 calculations with the original parameter set, the most stable conformer has C2symmetry (dl = d2 = 61') and 65% population, and the conformer with 41 = 26O and 42 = -63O is the next stable with 24%population. Thus, the two calculations give quite different conformational compositions. Vibrational Data Analysis
The methyl stretching and deformation modes and the C-Hi-R stretching and bending modes were assigned by following the assignments for diisopropyl ether22and diisopropylamine.6 The carbonyl stretching vibration is located at 1730 cm-1.2,8The bands at 240 and 45 cm-' were considered to be due to the methyl and isopropyl torsional modes, respectively. The other vibrational modes were assigned by carrying out normal-coordinate analyses. The valence force constants were initially transferred from those (22) Snyder, R.G : Zerbi, G. Spectrochim. Acta, Part A 1967, 23A, 391
for acetone,23diethyl ketone,24and hydrocarbon^.^^ Some force constants with small values were ignored and some force constants were assumed to be the same in order to simplify the force field. The resulting force field consists of 27 independent force constants. The geometry of the C1conformer determined by GED was used in the normal-coordinate analysis. Most of the observed bands could be assigned to fundamental modes of this conformer by using the normal values of the force constants, but there remained some bands that could not. They are considered as combination bands, overtones, or bands attributable to other conformers. Therefore, they were excluded in the initial normal-coordinate analysis, and the force constants except that of the isopropyl torsion were modified until the calculated frequencies reproduced well the (23) Cossee, P.; Schachtschneider, J. H. J . Chem. Phys. 1966, 44, 97. (24) Buric, Z.; Krueger, P. J. Spectrochim. Acra, Part A 1974,30A, 2069. ( 2 5 ) Snyder, R. G.; Schachtschneider, J. H. Spectrochim.Acta 1965,2/, 169.
Molecular Structure and Conformation of Diisopropyl Ketone
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1797
TABLE V: Calculated Mean Amplitudes (4) and Experimental Interatomic Distances (rv)for Diisopropyl ketone (A)''
atom pairb 0-C C2-C3 C2-C4 C3-C5
c3-c6 C& C4-Cs C-H O.-C3 O..*C4 O--Cs O***C6 0
4
7
O*..C, C2"*C5 Cy-C6 C2***C7 C2***Cg C3***C4 C3.**C7 CyCg C4*.*Cs
c4"'c6
C5.*-C6 CS***C7 Cj-*Cg C6"'c7 C6**-CB CyCB
c,
CI
G
I,
r,!
I,
r.c 1J
I,
0.040 0.052 0.052 0.052 0.053 0.052 0.052 0.079 0.061 0.061 0.178 0.214 0.108 0.161 0.077 0.078 0.076 0.076 0.067 0.078 0.230 0.165 0.237 0.074 0.186 0.247 0.245 0.445 0.073
1.214 1.532 1.529 1.531 1.541 1.527 1.538 1.112 2.393 2.408 2.874 3.072 2.780 3.470 2.504 2.486 2.507 2.532 2.595 3.875 3.067 3.726 3.444 2.537 4.832 4.444 4.638 3.389 2.542
0.040 0.052 0.052 0.053 0.052 0.052 0.053 0.079 0.061 0.061 0.167 0.108 0.108 0.167 0.076 0.076 0.076 0.076 0.067 0.078 0.235 0.235 0.078 0.073 0.239 0.542 0.104 0.239 0.073
1.214 1.532 1.532 1.540 1.528 1.528 1.540 1.112 2.402 2.402 3.450 2.768 2.768 3.450 2.536 2.508 2.508 2.536 2.598 3.876 3.095 3.095 3.876 2.531 4.406 3.589 4.950 4.406 2.531
0.040 0.052 0.052 0.053 0.053 0.053 0.053 0.079 0.061 0.061 0.170 0.170 0.204 0.204 0.076 0.076 0.077 0.077 0.067 0.204 0.204 0.243 0.243 0.073 0.304 0.419 0.419 0.304 0.073
ri;
1.215 1.526 1.531 1.536 1.536 1.536 1.536 1.112 2.400 2.389 3.410 3.410 2.952 2.952 2.519 2.519 2.486 2.486 2.604 3.594 3.594 3.125 3.125 2.559 4.402 3.685 3.685 4.402 2.559
"Only the mean amplitudes for relatively important atom pairs are listed. *See Figure 1 for atom numbering. CTher, distances obtained from the structural parameter values in Table VII.
observed ones. The band assigned to the isopropyl torsion in the spectrum of the liquid was broad, and the frequency is expected to differ considerably from that in the vapor phase.26 Since the mean amplitudes and shrinkage corrections of nonbonded atom pairs are sensitive to this force constant, the value of the force constant was estimated by the analysis of GED data as described in the next section. Vibrational frequencies of the C2 and C, conformers were calculated by employing the force constants determined for the C1 conformer. The calculated frequencies and the final force constants are listed in Tables I1 and IV, respectively. The agreement between the observed and calculated frequencies shows that most of the observed bands are assigned to the vibrational modes of the C,conformer and that some bands are due to the C, and/or C2conformers. The mean amplitudes and shrinkage corrections calculated from the force constants were used in the data analysis of GED. The normal-coordinate analysis and the diffraction data analysis were repeated until the calculated frequencies, the calculated mean amplitudes, and the determined geometry were little different from those obtained in the preceding step. Analysis of Electron Diffraction Data The following assumptions in data analysis were made because it is difficult !b determine the coordinates of hydrogen atoms precisely by GED: (1) all C-H bond lengths are equal; (2) four methyl groups have the same local geometry with C3"symmetry and have no tilt; (3) each methyl group takes staggered conforbond; and (4) LC5C3Hand mation against the (O=)C-C LC,C,H are equal to LC,C,H and LC8C4H,respectively. In addition, the equilibrium geometry of the OC2C3C4group was assumed to be planar. Thus, r(C=O), r(C2-C3), r(C2-C4), r(c3-C~)~r(C3-C6), r(C4-C7), r(C4-c~)~r(C-H), LC3C2C4,
I
I
I
I
LOC2C3, Lc2c3C5, Lc2c3c6, Lc2c4c7, LC2C4C8, LC5C3C67 LC7C4C8, LC5,6C3H, LC,,~C~H,LCCH, and q52 were selected
as independent structural parameters. Assumptions about differences in some of these parameters are described later. The mean amplitudes of the C-H and C-C bonds and the 1,3 0-C and 1,3 C-C atom pairs were refined in groups. The other mean amplitudes and all the shrinkage corrections were fixed at the values calculated from the force constants since they could not be refined. The differences between the mean amplitudes refined as groups were taken from the calculated values. For example, the differences between I(C2--C5)and I(C3-C4)was fixed at 0.010 A for the C, conformer (see Table V). The determination of the force constants except the force constant for the isopropyl torsion has been discussed in the previous section. The force constant of the isopropyl torsion was estimated in the following manner. The mean amplitudes and shrinkage corrections were calculated from various values of the torsional force constant. We repeated the data analysis until the minimum value of the R factor27was obtained. Then, we determined the torsional force constant to be 0.026 mdyn A rad-2. Table V gives the calculated mean amplitudes for relatively important atom pairs. The asymmetry parameters, K, for bonded atom pairs were estimated in a diatomic approximation,28K = (a/6)I4, by assuming the Morse parameter a to be 2 A-1, while those for nonbonded atom pairs were assumed to be zero. The preliminary data analysis of GED showed that at least two conformers exist with considerable abundance. Therefore, it is quite difficult to investigate the conformation of DIK by GED alone. Thus, the conformational analysis was carried out by assuming the presence of the C,, C2, and C, conformers, which are suggested to be stable by the 4-21G calculations. The radial distribution curves obtained for the three conformers by using the structural parameter values listed in Table VI1 are shown in Figure 2. The agreement between the observed and calculated radial distribution curves shows that the C, conformer is predominant. The number of the independent structural parameters required to define the geometry of the C, conformer is 21 whereas 12 and 15 independent structural parameters are necessary for the C2 and C, conformers, respectively. Since it is impossible to determine all of them by GED, additional constraints were introduced to reduce the number of adjustable parameters. That is, the dif-
{EW ( h s M ( ~ ) , ) ~ / ~ , W , ( s M ( s ) P "where ) ~ l l 'AsM(s), ~, = sMis a diagonal element of the weight matrix. (28) (a) Kuchitsu, K. Bull. Chem. Soc. Jpn. 1967,40,498. (b) Kuchitsu, K.; Bartell, L. S . J . Chem. Phys. 1961, 35, 1945. (27) R =
( 2 6 ) For example, in diisopropyl sulfide, the frequencies of the isopropyl torsion were measured at 83 and 74 cm-' in the liquid and gas phases, respectively. Crowder, G. A.; Scott, D. W. J. Mol. Spectrosc. 1965, 16, 122.
I
3 4 rlH 5 6 Figure 2. Experimental radial distribution curves (0)and the theoretical ones (-) for the C,, C,,and C, conformers. The residuals are shown on the same scale.
(s),Obsd S M ( S ) , ~and I~
Takeuchi et al.
1798 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
TABLE VII: Observed Structures and Mean Amplitudes of Diisopropyl Ketone (Bond Lengths and Mean Amplitudes in Angstroms and Angles in Degrees)"
TABLE VI: Relation among Structural Parameters"
parameter
CI
C,
C,
rl
rl
r2 r2 - 0.003 r2 - 0.001 r2 0.009 r2- 0.005 r2 0.006
r2 r2
+ +
r3
+
rl 0.001 r2 - 0.006 r2 - 0.001 r2 + 0.004 r2 + 0.004 r2 0.004 r2 + 0.004
r2 + 0.008 r2 - 0.004 r2 - 0.004
+
r2 + 0.008 r3
r3
+
+
0,
+ 1.7 O2 + 0.9 03 0, + 1.1
0 , 0.1 179.95 - 0,/2.0 179.95 - 0,/2.0 0, 1.5 02 0.4 0, 0.4 02 1.5 0 , + 0.1 0 , 0.1 o3 - 1.1 O3 - 1.1
84
04
04
$l(C4C2C3H) $ z ( C ~ C Z C ~ H7)2
73
Ob
73
180b
0, 179.3 - 0,/2.0 180.7 - 0,/2.0 02
02 02 02
-
1.6
+ 0.3
o2 - 0.2
0.9 180.15 - 8,/2.0 178.95 - e,/2.0 o2 1.1 o2 1.1 8, - 1.0 o2 - 1.0 O2 1.3 0, 0.3 83 - 0.65 O3 -- 0.25
+ + + + +
+ + + +
"Adjustable parameters in the least-squares calculation are r , , r2, r3, O , , 02, 0,. 04, r , , r2, and r3. bThese values are determined by symmetry consideration. I
0.1: -0.1-
-- "n- - I
1
I
I
I
I
I
1
1
V. I
AsM(s) 1
I
I
I
ferences among similar structural parameters were fixed at the values based on the 4-21G calculations as shown in Table VI. For the (O=)C-C and C-C bond lengths, we used the differences in the rBstructure converted from the re(4-21G) structure with the empirical corrections.20 Consequently, 1 0 structural parameters, r l - r3, O1 - 04, and T ] - 7 3 , were required to define the , geometries of the C,, C2,and C, conformers. Here T ] . T ~ and T~ represent I$] and 42of the C1conformer and I$] (=42)of the C, conformer, respectively. The values of T , , 72rT ~ and , O3 could not be determined, and therefore they were fixed at the values obtained by the 4-2 1G calculations. Other structural parameters and the conformational composition were refined by the leastsquares calculations on the molecular scattering intensities. The molar fractions of the CI, C,, and C, conformers were determined to be 45 (31)%, 31 (12)%, and 2 4 (22)%, respectively. The observed values of the structural parameters and mean amplitudes are listed in Table VI1 together with the limits of error. The observed mean amplitudes are in good agreement with the calculated ones. The limits of error were estimated from random errors, and the systematic errors due to the uncertainties accompanied with scale factors. Random errors were taken to be 3 times the standard deviations in the least-squares calculation. The systematic errors due to the uncertainties accompanied with the 4-2 1 G constraints were not included in the limits of error because
1.534 (2) 1.531 (2) 1.533 (2) 1.543 (2) 1.529 (2) 1.540 (2) 1.118 (3)
1.534 (2) 1.534 (2) 1.542 (2) 1.530 (2) 1.530 (2) 1.542 (2) 1.118 (3)
1,529 (2) 1.533 (2) 1.538 (2) 1.538 (2) 1.538 (2) 1.538 (2) 1 118 (3)
116.6 (17) 121.0 (8) 122.4 (8) 110.6 (4) 109.0 (4) 110.9 (4) 112.3 (4) 110.4 (4) 1 1 1.5 (4) 109.0* 110.lb 111.1 (9) 1 6b -62b
116.7 (17) 121.7 (8) 121.7 (8) 112.1 (4) 11 1.0 (4) 11 1.0 (4) 112.1 (4) 110.7 (4) 110.7 (4) 107.9b 107.9b 111.1 (9) 5 96 5 96
117.5 (17) 121.9 (8) 120.7 (8) 111.7 (4) 111.7 (4) 109.6 (4) 109.6 (4) 1 1 1.9 (4) 110.9 (4) 108.4b
0.053 0.079 0.057 0.069
0.053 0.079 0.057 0.069
(2) (5) (8) (9)
108.8b I 1 I I (9) Ob
I 80b
(2) (5) (8) (9)
0.053 0.079 0.057 0.069
(2) (5) (8) (9)
"The result obtained for the conformational composition of 45 (31)% Cl + 3 1 (l2)% C, + 24 (22)% C,. Values in parentheses are the limits of error attached to the last digit of the parameter values. The uncertainties accompanied with the 4-21G constraints were not taken into account to estimate the limits of error. The indices of resolution for the long and short camera distances are 1.02 (2) and 0.90 (4), respectively. bFixed at the calculated value.
