The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Internal Rotation in Isopropyl Alcohol
TABLE 111: C-H Stretching Energy Levels, Zero-Point Shifts, Squares of Franck-Condon Factors, and Bending Vibration Frequencies Morse aiscillator, cm- '
--__
n 0 1
2 3 4 5 6 7 8 9 10
effective
0
3052 5987 8805 11505 14088 16553 18901 21132 23245 25242
sq.
zero F-C point factor shift, 0 n cm-' transn
true
0 0 3052 -14 5987 -28 8805 -42 11505 -57 14088 -72 16554 -87 18902 -103 21132 -120 23245 -137 25241 -154
h
up,:, cm1.000 1202 1.000 1186 1.000 1169 1.000 1152 0.999 1135 0.999 1117 0.998 1098 0.997 1079 0.996 1059 0,995 1039 0.994 1018 -+
N
y9p,,
cm
1025 1013 1002 991 979 966 954 941 928 914 900
Includes zero-point shifts.
-
Intensities for the 0 n overtone transition are reduced by the square of the Franck-Condon factor 9. The reduction is less than 1%for n 5 10. For the n n+1 transition the reductions are even smaller. These numerial
-
1457
results are summarized in Table 111. The effective potential reproduces the energy levels of the true Morse oscillator with zero point shifts to within 1 cm-l for n 5 10 and to 10 cm-l for n I20 despite shifts of hundreds of wavenumbers. Likewise intensities are accurately predicted. On the other hand coupling terms that have not been treated quantitatively will lead to a breakdown of the Morse energy level structure for n L 8 since nearly degenerate levels can interact.
References and Notes (1) R. Wallace, Chem. Phys., 11, 189 (1975). (2) R. L. Swofford, M. E. Long, and A. C. Albrecht, J . Chem. fhys., 65, 179 (1976). (3) R. L. Swofford, M. E. Long, M. S. Burberry, and A. C. Albrecht, J . Chem. fhys., 66, 664 (1977). (4) R. L. Swofford, M. S. Burberry, J. A. Morrell, and A. C. Albrecht, J. Chem. fhys., 66, 5245 (1977). (5) R. Bray and M. J. Berry, to be published. (6) E. B. Wilson, J. C. Decius, and P. C. Cross, "Molecular Vibrations", McGraw-Hill, New York, 1955. (7) D. F. Heller and S. Mukamel, J . Chem. fhys., 70, 463 (1979). (8) M. L. Sage and J. Jortner, Chem. Phys. Lett., in press. (9) M. L. Sage, Chem. fhys., 35, 375 (1978). (10) J. C. Duinker and I. M. Mills, Spectrochim. Acta, Part A , 24, 417 (1968). (11) E. J. O'Reilly, J . Chem. fhys., 51, 2206 (1969).
Internal Rotation in Isopropyl Alcohol Studied by Microwave Spectroscopy Eizl Hirotat' Depaflment of Chemistry, Faculty of Science, Kyushu University, Fukuoka 8 12, Japan and Institute for Molecular Science, Okaraki 444, Japan (Received October 10, 1978) Publication costs assisted by the Institute for Molecular Science
The microwave spectrum of isopropyl alcohol was reinvestigated in much more detail than in a previous paper. The trans spectra were analyzed in terms of a rigid-rotor model modified by first-order centrifugal distortion effects. For the gauche form, the spectrq of which were complicated by a tunneling effect between the two equivalent minima, the b-type and C-type transitions in both the symmetric and antisymmetric sublevels were observed in addition to a-type ones which occurred between the symmetric and antisymmetric levels. The observed transition frequencies were analyzed by using an effective 2 X 2 Hamiltonian. The tunneling splitting was determined to be 46798.50 f 0.11 (AQ)MHz. An analysis of the Stark effects gave I(sIpLala)l= 1.114 f 0.015 D, pb = 0.737f 0.025 D, and pLc= 0.8129 f 0.0049 (&to) D. The trans spectra of (CH&CHOD were analyzed similarly to those of the normal species, but a definite assignment could not be made for the gauche form.
Introduction Until 1960 rotational isomerism in molecules was investigated mainly by infrared and Raman spectroscopy, electron diffraction, and dielectric constant measurements? all these methods established the existence of rotameric forms in many molecules and also provided approximate structural parameters of rotamers, including the dihedral angles and their relative stabilities. In 1960 a systematic study of rotational isomerism was started in Professor Wilson's laboratory by using microwave spectroscopy, which was expected to make possible more detailed comparison of molecular properties of different isomers such as structures, dipole moments, quadrupole coupling constants, internal-rotation barriers of methyl groups, torsional frequencies, relative stabilities, and so on. Wilson summarized the results obtained from earlier studies in 0022-3654/79/2083-1457$01 .OO/O
this field in a review articlea3 One interesting feature of microwave investigations is a direct observation of torsional splittings. As is well known, torsional splitting is a very sensitive function of the potential barrier through which tunneling occurs. Therefore, the observed torsional splitting is important in determining the potential function for internal rotation. It should be noted that the rotamer is a static concept; in other words, it only means the presence of a minimum in the potential function. On the other hand, we can derive any information on rotational isomerism from the potential function, and therefore its precise determination is the final goal of experimental approaches t o rotational isomerism. The observation of torsional splittings is possible only when two equivalent rotamers are present. This is the case
0 1979 American
Chemical Society
1458
The Journal of Physical Chemistry, Vol. 83, No. I I , 1979
for molecules in which both asymmetric tops attached to the internal-rotation axis have a symmetry plane. The first observation of such splittings was reported for 3-fluorop r ~ p e n e .Since ~ then many molecules with asymmetric tops have been shown to exhibit similar splittings. Obviously light tops such as the OH group will show markedly large splittings. In fact, the gauche form of propargyl alcohol, for example, has a splitting of 644 GHz in the ground torsional state.5 However, this molecule exists only in the gauche form. It would be more interesting to investigate a molecule which exists in two nonequivalent rotameric forms, one of which further consists of two equivalent ones. Kondo and Hirota6 investigated isopropyl alcohol as an example of such a molecule and found the trans and gauche forms for the normal species (referred to as the H species). The gauche spectra they observed corresponded to transitions between the symmetric and the antisymmetric states which resulted from splitting of degenerate torsional levels by a tunneling effect through the cis barrier. By analyzing these spectra, they estimated the internal-rotation splitting to be about 46 GHz. Imanov et ala7reported the microwave spectrum of the trans form of isopropyl alcohol. The present work is aimed at making the measurements of Kondo and Hirota6 more complete and detailed. It will also be shown that the original assignments of Imanov et al.; are in error. (Note that these authors have adopted the assignments of ref 6 in a later publication.8)
Experimental Section Microwave spectrometers a t Kyushu University were used in the present work. The cell was normally kept slightly above dry-ice temperature. Stark modulation was utilized not only to observe absorption lines but also to detect double-resonance effects. The only exceptional case was detection of a gauche line, where a pumping klystron was frequency modulated by a 120-kHz square wave. A sample of “normal” isopropyl alcohol which is commercially available was used without further purification. The deuterated species (CH,),CHOD (referred to as the D species) was obtained as follows: a small amount of fresh sodium metal was added to the “normal” isopropyl alcohol to obtain the Na salt after warming the reaction vessel to 70-80 “C. We then pumped off the unreacted alcohol and added deuterium oxide. Before we introduced a sample of the D species to the waveguide cell, we flushed the cell with deuterium oxide. In most cases we did not observe strong lines due to the H species. Rotational Spectra and Analysis 1. “Normal” Species ( t h e H Species). Trans Form. Isopropyl alcohol is a nearly symmetric oblate rotor. The trans form has a symmetry plane which includes the b and c axes. First, b-type Q branch transitions with K,, = 1 2,2 3 , 3 4, and 4 5, each consisting of two series, were observed and assigned. In addition to these both b-type and C-type R branch transitions were observed. The observed transitions are listed in Table I, which is a more complete version of Table I11 of ref 6. The assignment given in Table I was checked by four sets of double-resonance experiments. The pairs chosen were 633 624 (642 6331, 110 000 (220 1101,221 110 (221 212), and 4 2 2 413 (431 422),where the transitions in parentheses are used as pumping transitions. Positive effects were clearly observed in all four cases. The first pair serves to check the assignment of Imanov et al.;; they ascribed two lines a t 23 544.3 and 14 316.4 MHz to 633 624 and 642 633,respectively. We did not observe any double-resonance effects for these two lines. Furthermore,
- - -
-
- - -- -- - -
Eizi Hirota
the 23 544.3-MHz line showed a smaller Stark effect than the 14 316.4-MHz line did. This is contrary to what one expects from the assignment of Imanov et al., because levels with larger K+l have smaller K-type doubling and thus show larger Stark effects. We calculated the frequencies of 423 414, 533 524, 413 404, 523 514, 111 Ooo, and ll0 Ooo, by using the rotational constants of Imanov. No absorption lines were observed a t most of these frequencies; even when some lines were detected, they did not show reasonable Stark effects. Imanov et al. determined the ratio of the dipole-moment components, C L ~ / I . Lby ~ , comparing the intensities of two lines separated by as much as 3140 MHz. It is obvious that such a comparison is hardly of quantitative significance. The observed frequencies listed in Table I were analyzed by taking into consideration five centrifugal distortion constants. The molecular constants which were thus derived are listed in Table 11, and the frequencies calculated by using these constants are compared with the observed frequencies in Table I. A few Q branch lines with K+l = 4 5 show larger discrepancies, which are probably due to incomplete zero basing of the square-wave modulation field. The average deviation is 0.15 MHz. Gauche Form. Because of the symmetry of the molecule we may choose one inertia axis as antisymmetric and the two remaining axes as symmetric with respect to an operation which brings the molecule from one gauche position to another. The antisymmetric axis is nearly, but not exactly identical with, the a axis, but for the sake of convenience we call it the a axis, and express each rotational level in terms of the conventional rigid-rotor terminology JK.l,K+,.We need further to specify symmetric or antisymmetric in accordance with the substate of the internal rotation to which a rotational level belongs. We thus designate a rotational level, for example, as s 514or as a 413. It is important to note that, because the “a” axis is antisymmetric, the rotational levels in the symmetric state with even K-, and those in the antisymmetric state with odd K-, belong to the same overall symmetry (symmetric), and the remaining levels to the other overall symmetry (antisymmetric). Therefore, s 514, for example, is not a rotational level that belongs purely to the symmetric substate. In fact, we found a few accidental degeneracies, but the designation mentioned above is useful and is utilized throughout the present paper. In a previous paper6 about 20 transitions of a s or of s a were identified. Therefore, in this work we attempted to detect the “b” or “c” type lines which should be either of a a or of s s type. The a 422 a 413 transition was chosen as a first candidate. Because the spectrum was extremely rich, a double-resonance technique was applied by using s 514 a 413 as a pumping transition, which was modulated by a 120-kHz square wave. After long searching, a signal a t 17 173.86 MHz was detected. Once a b-type transition was assigned, it was easy to pick up other transitions. It is, however, to be noted that the so-called Q branch plot could not be applied, because the perturbations due to the internal rotation were large. In addition to this, two lines of nearly equal intensities and with nearly the same Stark effects were often observed a t very close frequencies, and ambiguity arose as to which component was to be assigned to the symmetric or antisymmetric state. We appealed to two methods to establish the assignment; one is the double-resonance experiment, some examples of which are described above, and the other is the sum rule. For example, the a 212 level is accessible from the s 202 level via either s 313 or s 211. Numerous such
-- - - -
-
-
-
-
-
-
-
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Internal Rotation in Isopropyl Alcohol
TABLE I: Rotational Transitions of the Trans Form of "Normal" Isopropyl Alcohol (MHz) transition Vobsd Ava transition uobsd
1 3 254.15 30 232.06 22 294.77 22 784.71 32 063.26 32 108.75
-0.05 0.00 - 0.04 0.11 -0.11 0.11
1 6 530.98 3 3 104.38 33 508.97 32 614.18
0.10 0.06 0.23 - 0.40
9 872.95 9 398.26 8 969.46 8 727.47 8 800.82 9 289.90 10 270.53 11 791.39 1 3 857.71 1 6 413.89
0.27 0.02 0.04 -0.13 0.06 0.07 0.05 0.07 0.05 0.21
11 171.06 11 867.14 12 805.89 1 3 990.30 1 5 416.98 17 074.63 18 943.55 20 996.77 23 202.90 25 530.35
-0.17 -0.01 -0.05 0.00 0.01 0.01 0.03 - 0.01 -0.23 0.13
1 7 318.23 1 7 039.04 1 6 551.75 1 5 058.62 1 5 033.25 1 4 211.26 1 3 558.62 13 237.09 1 3 379.34 1 4 080.52
0.27 0.02 0.01 0.17 0.00 - 0.07 0.00 0.02 - 0-01 - 0.07
17 526.45 17 637.52 17 853.49 18 213.72 1 8 754.54 19 506.41 20 490.85 21 718.94 2 3 190.73 24 894.33
0.05 0.01 - 0.10 - 0.04 0.00 0.06 0.01 -0.15 -0.03 - 0.08
1459
Ava
24 412.56 24 333.44 24 173.25 23 882.65 23 403.57 22 690.76 21 740.22 20 614.68 1 9 444.96
-0.01 0.06 - 0.02 0.03 - 0.01 0.04 0.03
24 430.70 24 402.46 24 375.85 24 367.19 24 404.14 24 521.26 24 758.25 25 155.19 25 748.27
0.20 -0.35 - 0.01 -0.11 -0.03 - 0.08 -0.06 0.03 0.00
- 0.21
0.18
31 412.23b 31 370.02 31 299.17 31 183.94 31 000.33 30 713.71 30 276.67 29 635.01 28 741.97
0.35 0.38 0.36 0.25 0.01 0.04 0.00 0.02 0.07
31 412.23b 31 375.18 31 318.73 31 242.98 31 150.22 31 049.36 30 957.06 30 898.67 30 907.11
-0.79 - 0.09 - 0.37 -0.21 -0.09 -0.01 - 0.02 0.01 -0.01
Calculated by using the molecular constants of Table 11. Not resolved TABLE 11: Observed Rotational Constants and lines are confirmed by double resonance to have common Centrifugal Distortion Constants of the Trans Form levels. of "Normal" Isopropyl Alcohol ( M H z ) ~ By proceeding step by strep we finally assigned the A 8488.99, i 0.026 transitions with J up to 9. Table I11 summarizes the B 8041.91, ?: 0.033 assigned transitions. In the course of this observation we C 4765.21, ~t0.029 noticed a number of accidental degeneracies, some of which Taaaa -0.027, i 0.0088 were already discussed in a previous paper.6 Examples 'bbbb -0.024, 0.0088 mentioned there include those between the K+, = 6 levels Tcccc 0.000, * 0.0089 of the symmetric state and the K+l = 7 levels of the an7 1 = Taabb: .t [ ( A-- B ) / ( A- C)]rCcaa, -0.022, i 0.0091 - 0 . 0 0 , * 0.017 tisymmetric states. Interesting cases are the a J J - ~levels ,~ T 2 = Tbbcc -t [ ( B - C ) / ( A- C)]TCCaa +_
a Errors are stan(darddeviations, and reapp' = reLu0p t 2Tapep.
combinations are available, and the rule was often utilized to detect new transitions. A few low J levels are drawn in Figure 1, where the observed transitions are indicated by solid lines and pairs of transitions connected by bold
which were found t o be higher than the a JJ-3,4levels for J = 4-8, because the former levels were pushed up by the s JJ-1,2 levels. The mixing of the two interacting levels amounts to 30% for J = 8 and 9, but in the case of J = 9 the a 95,4level is lower than s 98,2and thus the normal order is recovered for a 96,4and a 96,4. The assignment of s 61,5 a 51,4and s 62,j a 52,4listed in Table VI11 of ref 6 should therefore be reversed. We could confirm this
-
+
1460
The Journal of Physical Chemistry, Vol. 83, No. 7 1, 1979
Eizi Hirota
TABLE 111: Rotational Transitions of the Gauche Form of "Normal" Isopropyl Alcohol (MHz) sym state transition
-
asym state Aus
obsd
uobsd
AVS
1 3 406.82 30 682.23 22 300.93b 22 942.47 32 146.08°2e26 32 219.43
0.35 0.26 0.27 0.21 0.37 0.40
1 3 409.06= 30 690.92 22 269.65b3e26 22 946.53 32 148.93O,P 32 224.78
0.25 0.33 0.06 0.33 0.24 0.32
1 6 703.44 33 474.48' 33 978.86 32 832.35
0.25 0.25 0.18 0.32
1 6 702.27 33 474.48' 33 983.89 32 825.56
0.21 0.36 0.05 0.07
9 958.00b 9 412.92 9 004.93 8 931.95 9 358.22 10 416.30 1 2 189.3gf 14 646.54f
-0.01 0.04 0.02 0.02 0.02 0.05 0.18 0.40
9 949.47bj4 9 399.43 8 988.40d2e2 8 917.79 9 352.29 10 414.33 12 183.99 1 4 671.29
- 0.22
11 609.64O 12 512.47e4 1 3 738.07p3 1 5 293.91e1 17 182.60 19 416.11
-0.14 -0.23 -0.38 - 0.60 -0.96 - 1.30
11 616.84' 12 523.72 1 3 746.52e16 1 5 283.46 17 119.70 19 225.12 21 555.31 24 055.38
- 0.00
17 623.27 17 201.24e'y 1 6 493.06e2,e1' 1 5 557.20e25 1 4 555.49e23 1 3 704.03 1 3 203.18
0.05 -0.03 -0.11 -0.12 -0.05 0.12 0.55
17 616.17"4 17 173.86d9e3+?1s,g 1 6 447.76e1 1 5 503.00 1 4 507.86 1 3 603.55
17 953.01 18 128.76eZ0 18 446.36e'6~e'8 18 939.86e24 19 604.64h2e22 20 293.455
0.08 -0.12 - 0.20 - 0.37 - 1.31 2.74
17 956.36 18 132.35e" 18 472.79 19 033.59 19 862.34 20 992.60 22 440.96
-0.00 0.05 0.16 0.07 - 0.23
24 924.04 24 818.43e61e15 24 582.84 24 141.4ge9 2 3 432.83e'0 22 468.56e21
0.17 -0.01 - 0.21 -0.30 - 0.40 -0.26
24 926.51e20,h 24 758.47e13je18 24 424.80e24 2 3 827 ,07e22 22 824.3gf
-0.31 0.00 -0.31 - 0.32 0.03
24 24 24 25 25 25
-0.01 - 0.14 - 0.25 -0.27 -0.29 0.05
24 24 24 24 24 25
- 0.01 - 0.10 - 0.09
0.08 -0.27 - 0.41 - 0.50 - 0.39
32 128.47e'2j 32 083.55e7 32 045.23en 32 162.01f 30 521.65e'1
-0.13 -0.05
32 121.74e6>J 32 063.61k 31 996.87eY 31 939.89e10,' 31 939.89e2111
- 0.15 - 0.14
958.80 953.97"~~'~ 971.25e7 046.23" 226.39 564.55e11
32 061.561 32 091.03e13 32 081.85 32 001.88 31 803.61 32 32 32 32 32
064.42j 104.72eL2 129.65 140.12a 143.96
0.19 - 0.04
-0.50 - 0.27 - 0.26
-0.22 -0.13 0.04 0.22 0.37 0.34 0.04 0.14 0.29 0.39 0.32 0.06 - 0.42 - 1.26 - 0.16
-0.30 -0.35 - 0.43 -0.38 - 0.34 -0.13 - 0.06
965.1geI9 911.66e12,e17 870.86e2s 882.49e23 998.80 280.60'
-0.03 -0.06 0.19
-0.18
3.13 - 1.21
0.05 0.00 - 0.51
transition aOoo-s~o,
a101- s o 0 0 a~11-s212
uobsd
33 965.78 59 628.45 24 432.13e26
Aus
0.39 0.35 0.19
transition a 101-~202 a1 ,0-~211 a2 -S3 13
obsd
2 3 921.16 17 835.41 1 4 684,12p
A us
0.19 - 0.00 - 0.02
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Internal Rotation in Isopropyl Alcohol
TABLE 111: (Continued) transition
___* obsd
Avs
20 923.54e13 20 930.84"12 28 256.56"13 28 123.6gei2 23 374.32
1 2 9 432.07 1 3 1 896.99 140 256.85 45 465.89
/
obsd
1 4 776.52e6*j 1 4 773.78e5'i 22 079.97e6re17 2 1 948.40e5,e'8 2 8 260.16e1,e18 30 498.6Ze" 29 413.95e1
0.10 0.82 13.10 0.45 0.18 0.34 0.33 0.23 0.48 - 0.38 - 0.24 -0.09 -0.11 0.08 0.46 0.27 0.30 - 0.14 -0.13 1.11 0.85 0.12 0.13 -0.60 -0.55 0.25 - 0.08 - 1.79 - 1.79 -0.83 -0.79
1 4 582.934 8 312.8'7 1 3 415.18 10 026.05f 11 565.86e15~g 11 531.5leI4 19 210.29'29e15 18 35 3.10e14,e l6 26 715.0'7'' 23 052.82e16 28 385.99 1 1 3 947.14
}
transition
:1 ;:::::
148 226.63 50 094.16 4 3 504.71 36 909.55 56 678.11r 44 014.03 49 589.85 28 844.0ge4 29 184.49 33 947.88e4 2 1 894.92'19 2 1 860.92e20 28 658.5le3reZ0 29 658.7geI9 32 094.31e3
1 4 940.09 1 4 927.1ge7 22 039.17e7,e24 22 420.94e25 27 524.1leZ4 31 734.80e2'
1 8 225.27" 1 5 154.52e9 1 5 107.74e8 22 106.59e81e22 23 010.02e9~e23 26 328.23"" 3 3 337.03e23 8 660.91r 8 656.28' 1 5 303.99 1 5 43l.6gel0 23 944.57e'0 22 235.79 1 1 4 404.38
/
0.08 0.59 0.39 - 0.11 0.30 0.33 0.19 0.42 0.36 0.18 0.33 - 0.02 0.11 0.07
8 206.81 9 129.77 9 146.63 1 5 809.2Oe2I 1 5 491.41e" 20 448.60e" 25 280.60e21,i
1401
Avs
- 0.16
-0.15 -0.16 - 0.02 -0.18 - 0.10 0.01 - 0.67
-0.18 -0.30 -0.52 -0.24 - 0.30 - 1.61 - 0.50 - 0.73 - 0.28 - 0.34
-0.26 -0.14 -0.23 - 0.80
- 0.68 - 0.09
-0.10 0.12 -0.48 0.86 0.86 0.57 0.57 0.7 1 1.21 1.00 0.77 -0.40 0.83
Confirmed by a double-resonance experiment, 202-111{211-202}both for s and a. s and a a Overlapped by other line. Confirmed by a double-resonance experiment, a422-a413{a431-a422}. Confirmed by a 220-110are not resolved. Confirmed by a doublesum rule (four lines), Those shown in1 Figure 1 are not commented. f Tentative assignment. resonance experiment, a4,,-a4,, {s5,,-a4,,]. +0.2 MHz. a9,3-a964and a964-s96,are overlapped with each other, j i-0.5 Reference Overlapped by 3,,-2,, of the trans form. a8,,-a8,, and a964-a9s5are overlapped with each other. MHz. 6. Frequencies of some transitions are remeasured. n 1 , n 2 Assignment given in ref 6 is interchanged. Confirmed by a Confirmed by a double-resonance experiment, a3,,-a2,, double-resonance experiment, 3,,-2,, {221-2,2}both for s and a. i-0.3 MHz. Observed - calculated. {a2,,-s3,,}. c' Confirmed by a double-resonance experiment, a211-a202{a2,,-s3,,}.
-
-
reversed order by observing the Stark effect of the Q the original Hamiltonian onto the ground substates of the branch lines, a JJ-3,3 a JJ-4,4 and a JJ-2,3 a JJ-3,4. gauche form. The two diagonal blocks and the off-diagonal Another examlple of near degeneracy is that between a 96,3 block are given as follows: and s 99,1or s !39,0. This degeneracy makes the assignments (sls) = A,J,2 + B,Jb2 + CsJ,2 + centrifugal terms (1) of the transitions involving these levels uncertain. We could analyze the observed b-type and C - ~ Y P ~ (ala) = A A,J: + B , J ~+~ C,J: + centrifugal terms transitions with J less than 4 separately for the symmetric (2) and the antisymmetric states, by using the rigid-rotor expression modified by the first-order centrifugal distortion and effects. However, the centrifugal distortion constants thus (sla) = - - ~ Q ~- J~~Q , J+, ( ~ / ~ ) R , ~ ( +J ,JJ~~J , )+ obtained, in particular T~ and T ~ were , ~ abnormally large (1/2)Rca(JcJa + JaJJ (3) in magnitude and had different signs for the symmetric and the antisymmetric states. Furthermore, when the where (As,B,, C,) and (A,, B,, C,) denote the effective rotational constants of the symmetric and the antisymtransitions with J values up to 4 were included, this treatment failed. We thus utilized an effective two-dimetric states, respectively, A is the internal-rotation mensional Hamiltonian to analyze the observed spectra splitting, and Qb, Q,, Rab, and R,, are the interaction as a whole. The Hamiltonian was obtained by projecting constants. We assumed the centrifugal distortion con-
+
1462
The Journal of Physical Chemistry, Vol. 83,
TABLE IV: Molecular Constants of the Gauche Form of “Normal” Isopropyl Alcohol ( M H Z ) ~
1
cGnz’ 100
Eizi Hirota
-/p3
I E
No. 11, 1979
__
--
1 1 LI
A, B,
cs
Qb
Q, A
8638.994(15) 8065.126(14) 47 69.54 6(1 0) (-153.0)b (-279.663)b 46798.50(11)
~
A, B, C, Ra, Rca
8641.350(14) 8060.500(14) 47 66.142 ( 11) -58.215(12) 89.5559(92)
a Values in parentheses denote the standard errors applied to the last digits of the constants. The centri. fuga1 distortion constants of the trans form were used both for the s and a states. Fixed.
40t
c
c /
Figure 1. Low Jlevels of the gauche form of “normal” isopropyl alcohol.
stants to be the same for the two substates, and fixed them to the values of the trans form. When A is much larger than the off-diagonal terms, we can derive approximate expressions separately for the rotational spectra of the two substates. It is easy to show that Qb and Q, only modify the B and C constants, respectively, whereas Raband R,, contribute to r1 and r2 as follows: A71
= -4(R,b2 A72
+ [(A
-
B)/(A
= -4[(B - C)/(A
-
-
C)]RcaZ1/A (4)
C)]R,;/A
(5)
where A r l and Arz denote the differences in r1 and r2 of the symmetric and the antisymmetric states, respectively. A preliminary analysis of the transitions with J less than 4, which is mentioned above, gave A r l = -0.603 A 0.023 MHz and AT^ = -1.108 f 0.022 MHz, which, when substituted in the above approximate equations, led to (Rab( = 69.2 MHz and lRcal = 123.4 MHz. The assumed two-dimensional Hamiltonian contains 11 parameters to be determined. However, we found that B, - B, and Qb as well as C, - C, and Q, are well correlated. When Qb and Q, were fixed a t some value, a least-squares analysis rapidly converged. Because Qb and Q, are very sensitive to the internal-rotation potential, we varied them around the values calculated by using a theory of Quade and LinlO and a potential function reported by Inagaki et so as to minimize the sum of deviations between the observed and calculated frequencies. Table IV lists the molecular constants thus obtained, and the frequencies calculated from them are compared with the observed frequencies in Table 111. The average deviation is 0.51 MHz. The two interaction constants, Rab= -58.215 MHz and R, = 89.5559 MHz, may be compared with those (69.2 and 123.4 MHz) derived from an analysis of the low-J lines. 2. Deuterated Species ( t h e D Species). Trans Form. In a previous paper6 we reported eight b-type transitions of the trans form of the D species, (CHJ2CHOD (see Table VI of ref 6). It is, therefore, easy to extend the measurements to other transitions. Table V lists the observed frequencies and Table VI summarizes the molecular constants which were derived. The latter are used to calculate the transition frequencies which are compared with the observed frequencies in Table V. It is interesting to note that the asymmetry parameter of the D species is much smaller than that of the H species. Gauche Form. We first searched the spectra carefully in the frequency region from 8.2 to 20.6 GHz. We observed many strong lines with resolved Stark components, which
indicated the lines to be Q branch transitions. Furthermore some of them seemed to form at least three series. Some of the observed lines showed Stark effects which deviated from second order. To assign these Q-branch lines we first assumed that the “a” axis is antisymmetric as in the case of the normal species, but we could not reproduce the observed frequencies. The b-type a JJ-l,l a Jj-z,z transitions were expected to appear close to an observed Q-type series, but we observed no series that were to be assigned to the s JJ-l,l s JJ-2,2 transitions. Furthermore, the frequencies of the observed series increase much more rapidly with J than are expected for b-type Q branch lines. The antisymmetric axis may be assigned to the “b” axis. This possibility is supported by a “rigid-rotor’’ calculation; at the cis conformation the symmetry plane may include the a and c axes, and, if so, the b axis is likely to be antisymmetric also around the gauche positions. In any case the choice of the a and b axes is critically dependent on the structural parameters chosen. If the “b” axis is really antisymmetric, the three observed series may be assigned to a J J , ~s J J - ~ , s~ J, J , ~ a Jj-1,2, and a J j - 1 ~ s J j - 2 ~ . A trial calculation was carried out by using A,, B,,A,, B,, and A as adjustable parameters. It was however very difficult to draw a definite conclusion, because the fitting was also dependent on other constants which could not be adjusted simultaneously with the above five constants. Stark Effect and Dipole Moment. In a previous paper6 the Stark effects were measured for the trans form of the “normal” species to determine the dipole moment. The gauche form will show Stark effects which are complicated by the presence of the symmetric and antisymmetric substates with a separation of A. These two states will be coupled by the “a” component of the dipole moment. Furthermore, both the “b” and “c” components are not necessarily identical for the two substates. However, in the present analysis the two components were assumed to take the same value for the two states; nothing was observed to invalidate this assumption. Table VI1 summarizes the observed Stark effects and the dipole moment components obtained therefrom, of the gauche form of the “normal” species. If ( sIN,la) is simply interpreted as the a component, the total dipole moment of the gauche form is 1.564 f 0.026 D, which may be compared with the trans value of 1.58 f 0.03 D.‘ Energy Difference of the Two Rotamers. The intensities of the trans and the gauche lines of the “normal” species were compared a t T = 22 f 2 “C to determine the energy difference of the two rotamers. Two pairs of the lines were chosen, 321 312[trans, 9398.26 MHz and (antisymmetric) gauche, 9399.43 MHz] and 431 422[trans, 8969.46 MHz and (antisymmetric) gauche, 8988.40 MHz]. The ratios I[t]/I[(a)g] obtained are 1.54 f 0.20 and 1.58 f 0.41, respectively. The average of the two values, 1.55 f 0.20, when corrected for the differences in the dipole moment and the
-
-
-
-
-
-
-
Internal Rotation in Isopropyl Alcohol
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
1463
TABLE V: Rotational Transitions of the Trans Form of Deuterated Isopropyl Alcohol (MHz)
-
transition
Vobsd
A vu
1 2 779.896 28 977.67 21 952.61 22 141.13 31 407.19 31 414.69
0.113 -0.05 -0.09 0.03 0.05 -0.02
1 6 017.08 32 214.98 31 852.83
0.04 0.00 -0.02
9 719.38 9 481.52 9 201.76 8 910.89 8 644.00 8 439.70 8 333.69 8 358.27 8 540.82 8 903.81 9 466.06b 1 0 241.33 11 237.26 1 2 452.75 1 3 875.69 1 5 483.42C,d 17 242.32C,d 1 9 114.14C1d 1 0 254.34 1 0 530.87 1 0 901.22 11 367.59 11 931.27 1 2 592.99 1 3 352.58 14 208.13 1 5 158.77 1 6 198.38 17 321.96 18 523.05 1 9 793.97
0.30 0.05 -0.05
1 6 606.68 1 6 554.31 16 453.61 1 6 286.60 1 6 038.88 1 5 704.00 1 5 287.17 1 4 806.07 1 4 290.49 13 778.98 1 3 315.06 1 2 943.4 5 1 2 705.94 1 2 639.09 1 2 772.74 13 130.44 1 3 729.22 1 4 578.88 1 5 681.09 17 027.62 18 598.56 16 643.21 1 6 662.82 1 6 701.97 1 6 769.98 1 6 876.43 1 7 031.49 1 7 245.27 17 527.28 17 886.34 18 329.85
0.05
-0.26 -0.08 0.00 0.01 0.04 -0.07 -0.03 -0.04 -0.06 -0.02 -0.05 0.29 0.09 0.09 -0.06 0.02 -0.01 0.01 0.03 0.03 0.02 0.03 0.11 0.11 -0.01 0.04 0.23 0.10 0.10 0.06 0.06 0.07 0.04 0.09 0.02 -0.01 0.00 -0.05 -0.04 -0.06 -0.03 -0.11 -0.15 -0.09 -0.11 -0.19 --0.13 -0.20 0.02 0.10 -0.05 -0.03 -0.02 -0.01 0.02 -0.02 -0.02 -0.03
transition
Vobsd
18 863.92
--
A VU
1 9 492.34 20 217.93
0.09 -0.11 -0.18
23 280.03C1e 23 268.09 23 246.53 23 209.12 23 148.04 23 052.84 22 910.54 22 706.18 22 424.80 22 053.30 20 371.73 1 9 667.41 1 8 942.99 18 244.65 17 620.61 17 120.08 1 6 788.13 1 6 663.36 1 6 776.63 17 150.83 17 800.84 18 732.96 1 9 943.37
0.42 0.11 0.13 0.02 -0.04 -0.04 - 0.02 -0.13 -0.13 -0.10 0.12 0.1 1 -0.29 -0.02 -0.01 -0.02 -0.04 -0.03 -0.00 0.03 0.07 0.18 0.06
23 280.63C1e 23 273.19 23 261.84 23 247.35 23 231.12 23 215.94 23 206.22 23 207.90 23 228.52
-0.29 0.01 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.01
29 933.9BCle 29 926.03Cpe 29 914.1BCve 29 896.20 29 870.35 29 834.20 29 784.16 29 715.53 29 622.49 29 497.13 29 329.63 29 108.28 28 819.24C,d 20 509.32f
0.27 0.09 0.28 0.17 0.02 0.03 0.06 -0.00 0.02 0.01 -0.05 0.02 -0.01 1.05
29 933.98C,e 29 926.03C2e 29 914.1BCle 29 897.84 29 875.18 29 845.45 29 808.28 29 763.19 29 710.96 29 653.34 29 592.29 29 532.53 29 479.12 29 439.06C,d 29 420.42C3d 29 432.50C,d 29 485.68C2d
0.23 -0.08 -0.36 -0.11 -0.10 -0.16 -0.03 -0.07 -0.09 0.15 -0.07 -0.02 -0.06 -0.03 -0.02
--
-0.01
0.29
a Observed -- calculated. Calculated frequencies are obtained by using the constants of Table VI. The weight is 1.0 unless otherwise noted. Weight is 0.2. This line may be overlapped by other line. Weight is 0.5. These lines were not completely modulated. e The K-type doublings were not resolved. Weight i s 0.2.
1464
The Journal of Physical Chemistry, Vol. 83,No. 11, 1979
TABLE VI: Observed Rotational Constants and Centrifugal Distortion Constants of the Trans Form of Deuterated Isopropyl Alcohol (MHz)’”
-_ A l3 C
aaaa Tbbbb 7 cccc
= Taabb: f [(A - B ) / ( A- c)]Tccaa, 72 = Tbbcc f [ ( B - C ) / ( A- c)]Tccaa T1
a
8099.065 i 0.019 7918.010 t 0.024 4680.729 ?- 0.022 -0.0342 + 0.0064 -0.0309 i 0.0064 -0.0097 i- 0.0065 - 0.0390 i 0.0068 -0.028 i 0.013
See footnote to Table 11.
TABLE VII: Stark Effect and Dipole Moment of the Gauche Form of “Normal” Isopropyl Alcohol
--__
A v / e 2 [ l 0 - j MHz ( V / ~ r n ) - ~ ]
transition
M
obsd
obsd - calcd
1.0770 1.0640 0.9043 0.8410 1.2642 - 5.5586 1.7258 2.3719 1.1759 0.8769 6.8830 - 6.6061 - 6.1686 0.2694 7.7659 8.0669
-0.0017 -0.0028 0.0242 0.0097 0.0033 0.1896 0.0064 -0.0261 0.0158 -0.0015 0.4891 0.0930 0.4998 -0.0104 0.1749 0.0140
1.11, ? 0.015 D 0.73, i 0.025 D 0.812, i 0.0049 D 1.56, ?- 0.026 D
rotational constants, leads to the energy difference L E = Eltrans] - E[(a)gauche] of 490 f 190 cal/mol, or 175 h 70 cm-*. One more factor should be taken into account: because both the trans and the gauche forms are near oblate rotors, the line strength depends critically on the asymmetry parameters. In fact, the line strengths of 321 312and 431 422are 1.944 and 3.007 for the trans form and 2.065 and 3.203 for the antisymmetric gauche form, where the rigid-rotor assumption is used. When these differences are taken into account, the energy difference decreases to 450 f 210 cal/mol, or 158 f 72 cm-l. The present value of AI3 is thus much larger than that reported by Inagaki et al.,” 8.7 cm-l.
-
-
Discussion Because the isopropyl alcohol molecule has a “symmetry plane”, we may take the “molecule-fixed” coordinates to be x, y, and z such that x is antisymmetric, and y and z are symmetric, with respect to the symmetry plane. One of the internal rotors, the OH group, is so light that x is very close to the a axis, at least for the “normal” species. In fact, we could understand the gauche spectra of the H species by assuming that the a axis is antisymmetric and the b and c axes symmetric; in other words, the K-l = even levels of the symmetric substate and the K-l = odd levels of the antisymmetric substate belong to the totally symmetric species and other levels to the antisymmetric species. However, for the D species, the asymmetry parameter of the molecule is much smaller, so that even exchange of the a and b axes may occur when we change the internal-rotation angle, as noted above. In addition to this, rotational level structure is subjected to local perturbation, because the internal-rotation splitting is of
Eizi Hirota
the order of 2000-3000 MHz. These facts probably explain why the gauche spectra of the D species have not been assigned. Nevertheless the three series of Q branches, which were observed, may provide a clue to the assignments to be made in future. Inagaki et al.ll observed two bands in the infrared region for both the H and D species, which they assigned to the u = 1 0 torsional transitions of the trans and gauche forms. By adding the torsional splitting which we determined for the gauche H species, they evaluated the first three terms in a Fourier expansion of the potential function. The energy difference between the trans and gauche forms, which they obtained, is, however, not in agreement with our value from relative intensity measurements, as mentioned above. It will therefore be worth repeating the calculation of the potential function, when we determine the torsional splitting for the gauche D species. It is of some interest to explain the observed dipolemoment components in terms of two bond moments, p(H-0) and p(C-O), which have the following signs, H+-Oand C+-O-, respectively. When we take a coordinate system x’, y‘, and z’such that z’is on the C-0 bond with the direction of C 0 and y’, perpendicular to x’, is included in the plane bisecting the CCC angle with its positive end on the same side as the two CH3 groups, the three components are given by
-
m
m
&(a) =
C F p cos na
=
n=O
(8)
where a denotes the internal rotation angle (taken to be zero a t the trans position) and pLI and pll are the components of the dipole moment perpendicular and parallel to the C-0 bond, respectively: p 1 = p(H-0) sin 6’ (9) 1111 =
h(H-0)
COS
6’
+ p(C-0)
(10)
with 0 denoting the COH angle. We then estimated the “ a ” , “b”, and “c” components by rotating the y’and z‘axes about the x’axis (an angle of 20.87’ between z’and “b” was used commonly for trans and gauche) and by taking the matrix elements of cos a and sin a, where the eigenfunctions of Inagaki et al.ll were used. The expressions thus obtained for the dipole-moment components are as follows: p.,(sla) = 0 . 8 3 3 ~ ~ (11) / L ~ ( s )= 0.135pL
O.934pll
(12)
pb(a) = 0 . 1 5 6 ~-~0.933pll
(13)
-
+ + 0.360pll
p C ( s )= 0 . 3 5 3 ~ 1 0.356p.11
(14)
p*,(a)= 0.405p,
(15)
for the gauche form and pb
= -0.288111 - 0.9461111
p, =
+
-0.842~1 0.323pll
(16)
(17)
for the trans form. Comparisons of eq 12 and 13 and of eq 14 and 15 show that the b and c components are nearly equal for the symmetric and antisymmetric states, in
The Journal of Physical Chemistry, Vol. 83,
Molecular Structure of Hexaborane(l0)
agreement with the experimental results. Therefore the two expressions were averaged to obtain p b = O.145/~1- O.934bll (18) pee, =
0.379pL
+ O.358pll
(19)
It is reasonable to choose the following signs for the observed components: pa = +1.114, & = -0.737, pC = +OH3 D for the gauche form and & = -1.40, pc = -0.73 D for the trans form. A least-squares fitting gave pl = 1.315 D and plI = 0.979 D for the gauche, whereas p L = 1.285 D and pll = 1.089 D were obtained for the trans. These values may be compared with p L = 1.44 D and plI = 0.885 D of methanol.12 Equations 6-8 will be of some use to calculate the intensities of the torsional bands in the far-infrared region.
Acknowledgment. The author thanks Dr. Jon T. Hougen for critiical reading of the manuscript. The cal-
No. l l , 1979 1465
culations in the present work were carried out at the Computer Centers of Kyushu University and of Nagoya University.
References and Notes Address correspondence to the author at the Institute for Molecular Science, Okazaki 444, Japan. S. Mizushima, "Structure of Molecules and Internal Rotation", Academic Press, New York, 1954. E. B. Wilson, Jr., Cbem. SOC. Rev., 1, 293 (1972). E. Hirota, J . Cbem. Phys., 42, 2071 (1965); P. Meakin, D. 0. Harris, and E. Hirota, J. Cbem. fbys., 51, 3775 (1969). E. Hirota, J . Mol. Spectrosc., 26, 335 (1968). S.Kondo and E. Hirota, J . Mol. Spectrosc., 34, 97 (1970). L. M. Imanov, A. A. Abdurakhmanov, and M. N. Elchiev, Opt. Spectrosc., 28, 136 (1970). A. A. Abdurakhmanov, M. N. Elchiev, and L. M. Imanov, J . Struct. Cbem., 15, 37 (1974). , Table 11. For definitions of T , and T ~see C. R. Quade and C. C. Lin, J . Cbem. Phys., 38, 540 (1963). F. Inagaki, I.Harada, and T. Shimanouchi, J . Mol. Specfrosc., 46, 381 (1973). E. V. Ivash and D. M. Dennison, J . Chem. Pbys., 21, 1804 (1953).
Gas Phase !Skeletal Molecular Structure of Hexaborane( I O ) Determined by Microwave Spect roscopy ID. Schwoch,t B. Don, A. B. Burg, and I?. A. Beaudet*+ iDepartment of Chemistry, University of Southern California, Los Angeles, California 90007 (Received September 18, 1978)
The microwave spectra of six boron-substituted species of B6H10 have been determined. From this data the gas phase skeletal molecular structure was determined, with the following bond lengths (A): B2-B3, 1.818 f 0.004; B3-B4, 1.710 f 0.006; B4-B5, 1.654 f 0.003; BI-B,, 1.774 f 0.013; B1-B3, 1.762 f 0.004; Bl-B4, 1.783 f 0.011. The dipole moment has been determined to be pa = 1.68 f 0.02 D, M~ = 1.85 f 0.04 D, ptot= 2.50 f 0.04 D. Anomalous line splittings have been observed in some species, but have not yet been explained.
Introduction The electron deficient boron hydrides and carboranes have been of continuing interest in inorganic chemistry. The geometry of most of these compounds has been inferred from NMR, and the accurate skeletal structures of many have been determined by low temperature X-ray diffracti0n.l The gas phase structures of only BzH: and B5Hg3-5have been determined. Recently our interest has been focussed on the nature of the bridge hydrogen bonds and hydrogen tautomerism in boron hydrides and carboranes. This interest originated from the confirmation of a four-centered hydrogen bond in CB5H: and the rapid tautomerism of the hydrogen over the four possible sites. Large amplitude motions have also been suggested to explain discrepancies in the pure rotational spectrum of B5H9.5 Hexaborane is another long standing case where the C5"symmetry of the room temperature NMR spectrum can only be explained by rapid bridge hydrogen tauitomerization. As a first step in studying the hydrogen locations and motion in B&10 we have determined its gas phase skeletal structure. In the solid state, it was found that the boron atoms in B6H10 are arranged as an approximate pentagonal pyramid' (cf. Figure 1). A terminal hydrogen is attached to each boron atjom. The remaining four hydrogens assume bridging positions in four of the five existing basal sites. Detailed boron and proton NMR studies show a change Department of Physical Chemistry, University of Ulm, Ulm, West Germany.
0022-3654/79/2083-1465$01 .OO/O
from CbUto C, symmetry on cooling to -147 0C.879 This phenomenon has been explained as a fast flipping of the four bridging hydrogens between the five possible basal sites. The terminal hydrogens do not scramble with the bridge hydrogens as has been shown by selective deuteration.loa Because of the different measurement time scales, any large amplitude motion of the bridge hydrogens observed in the NMR study should be frozen out in the microwave spectrum.
Experimental Section The first sample of hexaborane was kindly provided by S. G. Shore and used without further purification. The synthesis of 'OB6Hlo began with 96% loB enriched CaFBF, (from the Electronics Division, Eagle-Picher Industries, Miami, Okla.); the BF3 was delivered to the vacuum line by flame heating in a Vycor tube, and converted to l0BzH6by action of LiAlH, in ether. This diborane was partially converted to 10B5H11by means of a vertical concentric-cylindrical hot-cold reactor with the internal cold finger at -78 "C and the outside at 150-180 "C. The resulting 10B5Hll,containing about 5% pentaborane(9), was converted to the desired 10B&tloby (CH&O cata1ysis.lob From 1.246 mmol of actual 'OB5H11,with 0.366 mmol of 1°B2H6and 1.000 mmol of (CH3)20,and warming from -78 to -20 "C in 2 h, the yield of 'OB6Hlo was 0.278 mmol, representing 27% of the actual pentaborane(ll), all of which was destroyed. The yield of 1°B2H6was approximately 1 mmol, representing 32% of the pentaborane(l1). The yield of BsH12and B9H15 together was 0 1979 American Chemical Society
