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Structure, methyl internal rotation, centrifugal distortion, and dipole moment of 2-chloropropane
OLJRNAL
OF MOLECULAR
SPECTROSCOPY
IsI,2
17-242 ( 1992)
Structure, Methyl internal Rotation, Centrifugal Distortion, and Dipole Moment of 2-Chloropropane MICHAEL MEYER, JENS-UWE GRABOW,
AND HELMUT DREIZLER
Abteilung Chemische Physik. Institut fir Physikalische Chemie der Universitiit Kiel, Olshausenstr. 40-60, D-2300 Kief, Federal Republic ofGermany AND
HEINZ DIETER RUDOLPH Abteilung fir Physikalische Chemie der Universitiit Urn, Albert-Einstein-Allee 11. D-7900 Ulm, Federal Republic of Germany The microwave spectra of six isotopic species of 2-chloropropane have been investigated by microwave Fourier transform spectoscopy. The quartic and some sextic centrifugal distortion constants of the 35Cland “Cl species are given. The structure has been derived by various methods. The dipole moment was found to be 2.141 D. From excited torsional states the parameters V3 and VIZ’of the torsional potential function were obtained. o 1992Academic PXS. hc. INTRODUCTION
The microwave spectrum of 2-chloropropane, (CH3)$HCl, was assigned by Tobiason and Schwendeman ( 1) for the first time. They prepared several isotopic samples to determine the substitution structure. From the absence of internal rotation splittings in the spectrum a lower limit of 14.43 kJ/mol (3.45 kcal/mol) of the barrier to internal rotation was estimated. Recently Ikeda et al. recalculated the structure from the rotational constants determined by Tobiason and Schwendeman for a comparison with 2-bromopropane and 2-iodopropane (2). Iijima et al. (3) investigated the molecular structure by means of electron diffraction. Durig and Guirgis (4) utilized FIR and Raman spectroscopy to determine the parameters of the torsional potential function. We investigated the spectrum in the torsional ground state with microwave Fourier transform (MWFT) spectroscopy to determine the quartic and some sextic centrifugal distortion constants. The determination of the dipole moment required more accurate hyperfine parameters. The new assignment of the (CH3)2’3CH37C1 and “CH3CH37C1CH3 species and the improved determination of the rotational constants of the other isotopomers enabled us to refine the molecular structure. It was not possible to resolve the torsional fine structure of the ground state transitions even with our high resolution technique. Therefore the parameters I’3 and VI*’ of the torsional potential function were determined from rotational transitions in excited torsional states. The spectroscopic studies were supplemented by ab initio calculations. The details will be published elsewhere (5). 217
0022-2852192 $3.00 Copyright 0
1992 by Academic Press. Inc.
All rights of reproduction in any form resewed.
218
MEYER
ET AL.
EXPERIMENTAL
DETAILS
The sample of 2-chloropropane was obtained from ALDRICH-Chemie, Steinheim. For the measurements waveguide MWFT-spectrometers (6) were used from 5 to 36 GHz. The sample pressure was kept on the order of 1 mTorr (0.13 Pa) and the temperature was in the range of 220 to 250 K. In the case of narrow multiplets caused by nuclear quadrupole hyperfine structure and additional torsional fine structure in the spectra a refinement ( 7) of the measured frequencies was necessary. The spectra of the 13Cspecies were recorded in natural abundance with a molecular beam MWFT spectrometer of the Balle and Flygare type (8,9) in the frequency ranges from 7.5 to 14.5 and 18 to 26 GHz. In order to increase the sensitivity and resolution of the spectrometer the axis of the molecular beam was directed along the resonator axis ( 10). For the determination of the dipole moment the spectrometer was supplemented with Stark plates ( Z1). The beam was prepared from a sample of 2% 2-bromopropane in argon under a backing pressure of 250 Torr (33 kPa). TORSIONAL
GROUND
STATE
The spectrum of 2-chloropropane shows strong a- and weak c-type transitions. The sensitivity of the spectrometers enabled us to detect c-type transitions of this molecule for the first time. The experimental line frequencies were evaluated by a separate nuclear quadrupole hyperfine structure (hfs) and centrifugal distortion analysis. Both analyses were performed in an iterative manner until all quadrupole coupling and centrifugal distortion constants had converged to their final values. The results are given in Tables I to III. For the first-order perturbation treatment of hfs analysis the set of transitions was limited to the completely split lines up to J = 3. The quadrupole coupling constants X+ = xbb + X, and X_ = xbb - X, were fitted to the chlorine hfs splittings relative to the most intense component compiled in Table IV. Since it was not possible to determine the off diagonal element x,, from the spectra the coupling constants in their principal axis system could not be derived. The hypothetical unsplit lines used as input for the centrifugal distortion analysis were then calculated with the quadrupole coupling constants from the hfs analyses. The unsplit lines are given in Table V. We used a Hamiltonian according to Watson’s A-reduction (12) in the representation I’ for the centrifugal distortion analysis. For the species with high natural abundances, ( CH3)zCH35C1 and (CH3)$H3’C1, the quartic and some sextic centrifugal distortion constants could be determined. We fitted the linear combinations (B + C)/2 and A - (Z? + C)/2 and the asymmetry parameter ZQ,since the correlation between the rotational constants is high. The accuracy of the rotational constant A was improved substantially by the inclusion of c-type transitions in the analyses. For the 13Cisotopic species with low natural abundances only A, and A,, could be obtained since the measurements in the molecular beam MWFT spectrometer are limited to low J values. For the determination of the dipole moment of ( CH3hCH 35C1the spacing of the Stark plates was calibrated with OCS using the dipole moment 0.7 15 19 D ( 13). The truncated Stark hamiltonian matrix was set up in the representation I’ to get real matrix elements. The components 1pa I and I ~~1were fitted to the measured frequencies
THE MICROWAVE
SPECTRUM
OF 2CHLOROPROPANE
219
TABLE 1 Centrifugal Distortion Parameters= of Isotopic Species of 2-Chloropropane with High Natural Abundance (CH3)2CH'aCl
(CH3)zCH"Cl
(B+C]/Z
/MHz
3889.2205
(5)b
3800.6093
(4)
A-(B+C)/Z
/MHZ
4178.9640
(2)
4267.0551
(4)
-0.15275058(1
-0.16311718(l)
ba AS
/kHz
1.608
(30)
1.531
AJK
/kHz
(11
2.7015
(44)
2.649
(11
AK
/kHz
2.757
(11)
2.901
(31
6.l
/kHz
0.44842
(29)
0.42265
(61
bK
/kHz
3.3552
(34)
3.3177
(83
OJ
/kHz
1.39
(46)
[1.39]C
4JK
/Hz
-0.01176
(35)
-0.01052
4K
/Hz
0.1188
(89)
[0.1188]
QJK
/Hz
0.01223
(18)
0.01259
(22
(42
Ad
/MHz
8068.1846
(6)
8067.6644
5)
Bd
/MHz
4570.8814
(5)
4452.4044
4)
Cd
/MHz
3207.5597
(5)
3148.8142
4)
ce
/kHz
4
a)
Watson
A-reduction,
b)
single
standard
cl
fixed
parameters
d)
derived
parameters.
e)
standard
deviation
4
representation error
in units
in squared
of the
I=, of the
[QKJ last
- QJ - QK = 0] digit.
brackets.
fit.
of Table VI. This required the consideration of centrifugal distortion up to fourth order in order to avoid systematic errors. The change of the representation from I’ to I’ forced us to convert (14) the centrifugal distortion constants of Table I. This conversion requires only a change of the signs of 6, and hK. The Stark effect analysis was carried out with fixed rotational, centrifugal distortion, and quadrupole coupling constants. The components of the dipole moments 1pa 1 = 2.099 ( 5 ) D and 1p, 1 = 0.423 ( 10) D were determined with a standard deviation of 7 kHz. The total dipole moment is P = 2.141 (5) D.
MEYER
220
ET AL.
TABLE II Nuclear Quadrupole Coupling Constants of Isotopic Species of 2-Chloropropane with High Natural Abundance (C!H3)zC!H35C!l
x+ .a
(CHs)zCH"Cl
/MHz
61.496
(6)
48.510
(6)
X- b /HHz
7.920
(18)
6.188
(15)
-61.496
(6)
-48.510
(6)
X..
/MHz
Xbb
/MHz
34.708
(9)
27.349
(8)
Xcc
/MHz
26.788
(9)
21.161
(8)
Av=
/NH2
10.310
6.600
0
/MHZ
0.007
0.006
a)
x+ =
Xbb
+&c.
b)
X-
xi,,
-&c.
c)
mean
-
experimental
EXCITED
splitting.
TORSIONAL
STATES
The excited torsional states q = 1 and 2 were investigated for the ( CH3)*CH 35C1 species. The lower one has been assigned by Tobiason ( 1). For the assignment of the other one we started searching in the frequency region around the J-J’ = 2-l a-type transitions of the ground state for satellites showing a similar hypertine pattern. Due to the high barrier the torsional fine structure of the low J transitions could not be resolved. The spectroscopic parameters determined from these lines compiled in Tables VII and VIII are given in Table IX. The transitions above J = 7 showed for each hyperfine component the typical triplet pattern of a two-top molecule with a high barrier. An example of the spectra is given in Fig. 1. The internal rotation splittings of the rotational transitions in the state q = 2 are larger than the corresponding splittings for q = 1. They can be well predicted from the parameters of the torsional potential function determined by Durig (4). The procedure for the internal rotation analysis has been given previously (15). We used a semirigid model with a Hamiltonian set up in the principal axis system. The eigenvalues were calculated by a diagonalization of appropriately truncated matrices instead of a Van Vleck perturbation treatment. The computational effort was reduced by the application of group theory and prediagonalizations. For the analysis the measured internal rotation splittings relative to the AA-cornponent in Table X were averaged for the hyperfine structure of each rotational transition separately. On the basis of this treatment a satisfactory fit of the parameters V3 and I’iz’ of the torsional potential function Eq. ( 1) to the averaged splittings in Table XI is possible.
221
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE III Spectroscopic Parameters of Isotopic Species of 2Xhloropropane (CH3)z11CH35C1
with Low Natural Abundance (CH,)z"CH"'Cl
A
/HHZ
8048.468
(35)
8047.896
(32)
B
/HHZ
4553.552
(3)
4434.662
(2)
C
/MHZ
3202.417
(2)
3143.213
(2)
AJ
/kHz
1.36
(13)
1.32
(11)
h,c
/knz
2.66
(53)
2.95
44)
Xaa
/NH2
-61.642
(13)
-48.632
24)
Xtsb /MHz
34.718
(22)
27.305
65)
Xc,
26.924
(22)
21.327
(65)
/NH2
"CH,CH'SCICHx
"CHxCH"ClCHx
A
/MHZ
1812.204
4)
7871.591
(5)
B
/MHZ
4513.134
1)
4394.853
(2)
C
/MHZ
3148.721
1)
3090.717
(2)
A.l
/kHZ
1.28
(7)
1.15
(11)
AJK
/kHz
2.98
(24)
2.98
(35)
X me
/MHz
-61.329
(12)
-48.383
(7)
Xbb
/MHZ
34.642
(17)
27.299
(11)
Xc,
/MHz
26.687
(17)
21.084
(11)
al
see
footnotes
of Table
I.
V(a,, (Yz)= f V,( 1 - cos 3cq) + 5 Vj( 1 - cos 3a*) + Vi2(cos 3a, cos 3~x2- 1) + Vi2’sin 3~yi sin 3cq.
(1)
The results of the analysis are given in Table XII. The remaining parameter Vi, of IQ. ( 1) could not be determined. The moment of inertia Z, and the angles between the symmetry axis i of the top and principal axes of inertia were calculated from the averaged structure discussed below. The angles were kept fixed in a first fit. We noted that it was possible to fit two angles in addition if one is taken from the structure. The result of this second fit listed in Table XII conlirmed our estimations from the structure. It is not possible to determine Z, because this parameter is highly correlated with V, . The reduction of Z, leads to an increase of V,. For example, a fit with the fixed parameter Z, = 3.186 amu A2 derived from the r, structure of Ref. (2) and F = 163.8 GHz and F’ = -1.24 GHz yields V, = 16.61 (12) kJ/mol and Viz’ = -0.837 (21)
222
MEYER ET AL. TABLE IV Hypetine Splittings in the RotationalTransitionsof IsotopicSpeciesof 2-Chloropropane with High NaturalAbundance
(a) J
K-
K+
J' K-'
1
0
1
0
2
2
2
3
3
3
2
0
1
1
0
1
2
2
11 2
2
2
0
0
1
1
1
2
1
1
1
3
0
2
2
1
2
1
2
2
Kc'
0
1
0
1
2
1
0
1
2
0
2
0
0
0
0
0
2
1
2
2F 2F'
5 3 13 7 5 31 5 3 3 13 11 7 5 3 5 3 3 11 7 5 31 5 3 11 13 9 7 5 31 9 7 5 9 7 5 31 7 5 3 11 7 5 5 3 7 5 13
3 3 5 3 5 3 5
5 3
I 5 3 5 5 3 5 3
7 5 3 7 5 3 7 5 3 7 5 3 7 5 3 3 7 5
(CW~)ZCH~~CI ref. /MHz0 spl./HHtb 6/kHz~ 7781.510 15.377 -12.302 15230.740 -0.894 16.427 14.488 -11.249 4.128 -25.716 1.950 16923.933 15.312 -2.885 8.677 9.172
14197.177 15.370 -5.040 6.692 10.581 -11.740
-2 -7 0 -4
-4 -12 -5 -9 -15
LO 10 5
24540.765 16.358 5.134 -11.217 1.869 15.480
3 -2 2 -2 -2
17034.367 -29.857 12637.702 -6.696 14902.841 -21.184 5.358
frequency
of
the
reference
component.
b)
frequency
of
the
reference
component
c)
-4 -10 4 -13 -10 4 -3
22134.596 -0.971 3.073 4.039
a)
given
3 -3
(CH~)ICH"CI ref. /MHz spl./WHz 6/kHz 7603.641 12.134 14909.633 -0.694 12.988 11.505 -8.054 -20.329 1.493 16508.953 12.127 -2.276 6.837 7.238 1.953 -9.123 13901.699 12.132 -3.971 5.294 8.341
between
observed
8 2 9 -11 10 2 -1 3 0 -6 -1 -1
4 -13 4 -8
3.052 21715.903 -0.721 2.462 3.189 24550.688 2.782 3.373 23895.062 12.851 4.008 -8.837 1.358 12.120 2.654 0.400
-7 1 0 -6 3 -2 2 2 6 4 -8 1 4
1 1 -3 0
minus
frequency
component.
difference
6 7
-9.695
and calculated
frequency.
of
the
THE
MICROWAVE
SPECTRUM
223
OF 2-CHLOROPROPANE
TABLE IV-Continued
(bl J
K-
K,
J' K_'
K+'
2F 2F'
5 3 13 7 5 3 7 5 9 7 5 3 7 5 9
3 3 5 3 3 5 3 7 5 3 1 7 5
7
1 5
5 3
3 1
1
1
5 3 9 7 5 7 5
5 3 7 5 3 7 5
(cl J
K-
K,
J' Km'
K,'
2F 2F'
5 3 13 7 5 5 3 11 1
5 3 5 3 11 5 3 13 9 7 5 31 9 1
5 31
3 3 5 3 5 3 5 3 1 5 3 3 3 7 5 3 7 5 3
(CH,)zl'CH'sCl
(CH,)x"CH"Cl
ref./HHz spl./HHz
6/kHz
ref./MHz spl./MHz
d/kHz
0
7580.307 12.157
-1
14867.762 -0.623
-5
21662.641 -0.110 2.494 3.199
-2 14 11
24466.181 2.803 3.194
11 14
23808.312 12.862
3
1159.053 15.410 -12.320
-8
15190.878 -0.880
-3
-11.271
14164.395 15.391 22084.581
-13
-13 0
-0.910
9
3.090
4.048 13.568 -7.311
-3 4 -11
25064.290
3.488 4.021 0.499 12.174 -2.188 -8,154 24456.008 16.319 5.142 1.861 15.521
-7 8 -19 0 1 7 -1 5 14 3
'3CH,C!Hx5C!lCH,
'3CHsCH"ClCH,
ref./MHz spl./HHz
ref./HHz spl./MHz
a/kHz
7664.923
15.336 -12.258 14986.303 -0.940 14.396 -11.234 1.981 13962.868 15.322 -5.031 6.663 10.552 -11.711 12383.991 -6.675 5.339 24788.487 3.451 3.986 0.547 24225.877 16.344 5.151 -11.184
4 8 -2 2 -14 -3 -10 -9 -3 -15 -17 -3 2 6 4 10 -2 -3 8
d/kHz
7487.993 12.099 -9.671 14668.516 -0.666 11.433 -8.838
1 3 -8
13666.951 12.091
-5
5.268 8.326
-3 -5
12265.378 -5.271 4.217 24196.606 2.760 3.165 23579.133 12.842
3 6
0 0 6 6
0
MEYER
224
ET AL.
TABLE V Hypothetical Unsplit Frequencies of the Rotational Transitions of Isotopic Species of 2-Chloropropane with (a) High and (b, c) Low Natural Abundance
(a) (CH3)zCH'SCl J
K-
K+
J'
1 2 2 2 3 3 3 3 3 4 4 4 5 5 2 4 6 7 8 9 10 10 11 12 12 13 14 14 13 15 16 17 17 18 19 19 21 22 22 24 25 26 27 27 28 28 29 30 30 32 33 34
0 0
1 2 1 2 1 3 2 3 2 4 2 3 5 5 1 3 4 4 5 6 7 6 7 7 a 8 9 a 8 10 10 10 11 11 12 11 13 13 14 15 16 16 17 16 18 17 18 19 18 20 20 21
0
a)
1 1 2 0 1 1 2 0 2 2 0 1 2 1 2 3 3 3 3 4 4 5 4 5 5 6 5 5 6 7 6 7 7 8 8 9 8 9 9 10 10 11 10 11 11 11 12 12 13 13
difference
1 1 1 2 2 2 2 2 3 3 3 4 4 2 4 6 7 a 9 10 10 11 12 12 13 14 14 13 15 16 17 17 18 19 19 21 22 22 24 25 26 27 27 28 28 29 30 30 32 33 34
K_'
K+’
0 0
0
1 1 2 0 1 1 2 0 2 2 0 1 0 1 2 3 3 3 3 4 4 5 4 5 5 6 5 5 6 7 6 7 7 8 8 9 8 9 9 10 10 11 10 11 11 1': 12 13 13
between
1 0 1 0 2 1 2 1 3 1 2 4 4 2 4 5 5 6 7 8 7 8 8 9 9 10 9 9 11 11 11 12 12 13 12 14 14 15 16 17 17 18 17 19 18 19 20 19 21 21 22 observed
obs.
/HHz
(CH3)zCH"Cl b/kHza 0
7778.435 15229.680 16920.117 14193.536 24536.003 22134.230 25144.417 21105.393 23335.089 28580.335 33381.736 30855.221 34866.441 34470.997 17042.897 13289.565 13307.107 6979.609 12124.850 18543.175 25785.379 10173.930 16438.772 7914.145 23918.681
-2 -3 -10 0 5 10 3 -2 -2 3 -5 2 -5 3 0 -5 1 1 1 -1 -2 0 6 -2
20989.159 5754.107 13645.395
0 -1 -1
17395.373 7761.349 25780.243 13595.037 21422.035 5378.642 16860.637 7023.278 25721.300 20408.425
2 -2 -1 1 -2 0 0 2 -3 0
15369.957 24236.040 6029.264
1 -2 1
11010.254 18446.652
3 0
7545.433 21796.746 9266.172 15977.295
1 0 4 1
and
calculated
obs.
/HHz
b/kHz
7601.211 14908.771 16505.943 13898.823 23891.325 21715.594 24549.435 20681.414 22803.427 32496.172 28076.408
1 -3 -2 -9 0 2 4 3 2 -1 0
34256.509 33819.913
4 -5
12746.213
0
6143.947 10869.480 16896.889 23853.474
5 1 0 2
14357.509
1
21359.127 11291.619
0 1
25836.304 14018.204
0 -1
21534.890
-3
16850.615
-1
19789.436 14582.273 22834.218 10121.231 16918.501
-2 -1 -1 1 0
25983.788
-2
11827.447 19362.139
3 2
9117.410
5
unsplit
frequency.
THE
MICROWAVE
SPECTRUM
225
OF 2-CHLOROPROPANE
TABLE V-Continued
(a) (CH,)zCH"Cl
(CH,)zCH'"Cl J
Km
K,
35 35 36 37 38 38 39 39 40 41 41 42 42 43 43 45 45 46 46 47 48 49 49 50 110 6 2 4 5 8 9 11 12 10 13 14 15 16 18 19 21 21 22 24 25 26 27 28 29 27 30 30 32 33 35
13 14 14 14 14 15 15 14 15 15 16 15 16 17 16 17 16 17 18 18 17 19 18 19
22 21 22 23 24 23 24 25 25 26 25 27 26 26 27 28 29 29 28 29 31 30 31 31
15 2 2 3 3 4 4 5 4 5 5 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 10 11 11 13
0 3 3 6 6 8 8 7 9 10 10 11 12 13 15 14 15 17 17 18 19 19 20 18 20 21 22 23 23
J'
Km'
35 35 36 37 38 38 39 39 40 41 41 42 42 43 43 45 45 46 46 47 48 49 49 50 0 5 2 4 5 8 9 11 12 10 13 14 15 16 18 19 21 21 22 24 25 26 27 28 29 27 30 30 32 33 35
13 14 14 14 14 15 15 14 15 15 16 15 16 17 16 17 16 17 18 18 17 19 18 19 0 2 12 13 2 2 3 3 4 3 4 4 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 9 10 10 12
K,' 23 22 23 24 25 24 25 26 26 27 26 28 27 27 28 29 30 30 29 30 32 31 32 32 0 3
3 6 6 8 8 7 9 10 10 11 12 13 15 14 15 17 17 18 19 19 20 18 20 21 22 23 23
obs./HHz
b/kHZ' 0
25420.118 6186.963 11201.196 18843.069 29315.169 7557.189 13359.363
-4 0 2 -3 2 -3
21968.924 33478.795 9108.780
0 1 1
6013.731 25356.950
-3 4
29007.728
-3 -5 2
7230.503 12790.855 8603.613 32920.249 14939.969 12639.041 34104.949 14908.894 6519.972 15259.103 5784.158 14943.891 6919.403 17221.586 10688.646 12152.136 7802.814 19073.953 13301.986 20562.242 14185.752 5232.818 21732.798 14841.045 5428.351 15299.231 5549.116 15587.369 9673.165
23266.443 23690.549 5607.408 9704.181 5613.823 34192.134
obs./HHz
b/kHZ
15535.791
3
5841.953 10468.202
-1 2
6756.810 27318.718 11901.616
-6 -10 8
30171.971 7736.731
-4 1
13417.241 8781.995 33121.370
-1 1 5
36163.900
1
16692.334 6290.905
3 -11
6703.545 16590.182
1 -1
14561.848
0
22535.099 16567.562
3 -3
20024.852
0
14526.119
-2
-1
2 3 2 1 7 1 0 0 1 -4 -4 2 -3 -1 0 -3 -1 -1 3 2 -2 -1 2 0 0 -1 -1 1 1 2 -12 4
MEYER
226
ET AL.
TABLE V--Continued
(a) (CHX)ZCH'~C~ J
36 37 38 39 40 41 42 42 43 44 44 45 46 47 47 50 50
K-
K+
J'
Km'
I(,’
13 13 14 14 13 14 15 14 15 15 16 15 16 17 16 17 18
24 25 25 26 28 28 28 29 29 30 29 31 31 31 32 34 33
36 37 38 39 40 41 42 42 43 44 44 45 46 4-l 47 50 50
12 12 13 13 12 13 14 13 14 14 15 14 15 16 15 16 17
24 25 25 26 28 28 28 29 29 30 29 31 31 31 32 34 33
obs.
/MHz
(CH,)zCH3'Cl a/kHz*
23983.430 15656.608 34401.410 23897.756
-2 2 3 4
9398.907 23684.802 5406.872 15225.200 9202.665 34260.271 5285.253 14911.853 33951.638 8914.473 8721.703 33510.396
-6 0 1 3 0 -2 12 -9 -10 8 2 5
obs./HHz
L/kHz
6574.442
4
28682.373
0
(b)
J 10 2 2 3 3 3 3 3
K-
0 12 0 12 13 2 2
K+
1 2 3
1 2
J' 0 10 111 2 2 2 2 2
K_'
K+'
0
0 1
0 11 12 2 2
2
0 1
(CHz)z'3CH'SCl
(CH3)z"CH"Cl
obs./NHz
obs./HHz
d/kHz
7755.968
5
15189.813 14160.743 22084.212 25062.714 21050.972 24451.236 23267.699
2 -.6 --5 1 5 --3 3
1577.876 14866.899 13864.241 21662.322 24464.917 20632.178 23804.575 22733.412
d/kHz 6 2 -6 1 -3 1 1 0
(c)
J
10 2 2 110 3 3 3 3
K-
0 12 12 13 2 2
K+
1 2
1 2
J'
0 10 111 0 2 2 2 2
Km'
K+'
0
0 1
0 11 12 2 2
0
0 1
"CH,CH'5C1CH~
'~CHSCH~'C~CHS
obs./HHz
obs./MHz
7661.853 14985.263 13959.239 12385.326 24786.921 20748.119 24221.113 22985.356
a/kHz
4 -1 -4 -1 0 0 -2 2
7485.571 14667.731 13666.951 12266.432 24195.359 20328.521 23575.397 22456.519
b/kHz
5 2 -5 -1 1 0 -3 4
THE
MICROWAVE
SPECTRUM
227
OF 2CHLOROPROPANE
TABLE VI of (CH, ),CH 35CI
Stark Effect Measurements E/VCm-
21.79 36.40
50.96
1
J' K_'K+'
J
K-
1 1
10 01
0
0
0
0
0
0
10
0
0
0
12
1
1
1
K+
1
01
0
0
0
2
12
1
1
1
1 2
01 0
2
0 1
0 0
0 1
108.97
2
0
2
1
0
1
145.30
2
0
2
1
0
1
72.61
217.94
254.27
2
2
0
0
2
2
1
1
0
0
1
1
2F
13 5 5 3 3 3 5 5 31 5 5 7 7 7 5 5 3 3 13 5 5 7 7 7 13 5 5 5 5 31 5 5 7 7 31 5 5 5
2F'
3 3 3 3 3 3 3 3 3 5 5 5 3 3 3 3 3 3 5 5 5 3 3 3 3 3 3 5 5 3 3 3
~HF
obs./MHz
1 1 3 1 3 3 3 1 1 1 3 1 3 5 1 3 1 3 1 1 3 1 3 5 1 1 3 1 3 1 1 3 1 3 1 1 3 3
12632.432 7781.591 7781.576 7766.174 7766.210 12644.559 12637.918 12637.864 14202.406 14182.066 14181.918 14197.297 14197.348 14197.441 7781.666 7781.640 7766.219 7766.286 7793.926 14182.318 14182.018 14197.413 14197.518 14197.697 7794.050 15231.705 15231.562 15231.794 15231.479 15214.270 15231.929 15231.364 15230.622 15230.724 15214.156 15232.307 15231.076 15230.883
6/kHz
-8 0 3 15 11 -1 -4 0 -6 3 -4 3 2 -1 0 2 13 10 13 -4 4 1 0 -5 14 -1 0 2 0 -3 -4 1 5 6 -3 -9 -11 6
kJ/mol. The larger value Z, = 3.222 amu A2 of Table XII is a consequence of the longer CH bond lengths obtained in our structure determination. V, from the internal rotation analyses is in good agreement with the effective barrier I’,@= 16.5 kJ/mol determined by Durig and Guirgis ( 4). STRUCTURE
The structure of 2-chloropropane has been determined from the measured ground state (g.s.) rotational constants by all currently available methods. ro-Derived Methods The g.s. moments of inertia for an isotopomer i in a substitution data set (SDS) of N isotopomers are
228
MEYER ET AL. TABLE VII Hyper!ine Splittings in the Rotational Transitions of (CH3)2CH35C1in Excited Torsional States with Unresolved Torsional Fine Structure= q-2
q-1
J
K-
K+
J’
K-’
K+’
2F
11
2
5 3 13 7 5 31 5 11 7 5 31 5 3 7 5 5 3 9 7 5 9 7 5 5 3
0
2
1
2
1
3
0
3
2
10
a)
see
2P’
footnotes
of
Table
3 3
ref.
/HHZ
SPl.
/WHZ
12622.248 -6.701 5.336 15207.692 -0.893 16.430 14.493 1.951 16897.091 15.381 -2.880 8.684 9.173 14175.707 15.366
5 3 5 5 3 5 3 5 3 5 3 7 5 3 7 5 3 3 3
10.597 22102.181 -0.986 3.084 24500.716 16.365 5.147
ref.
/WHz
spl. /MHz
d/kHz
12606.717 9
17 3 9 -8 2 -6 7 -1 0 9
-2
5.362 15207.896 -0.895 16.434 14.496 1.964 16901.973 15.370 -2.892 8.680 9.163 14176.071 15.380 6.704 10.584
4 -21 -8 -10
24512.500 16.367 5.138
7769.432
15.361
7755.351
14
IVa.
TABLE VIII Hypothetical Unsplit Frequencies of the Rotational Transitions of (CH,),CH ‘?I in Excited Torsional States with Unresolved Torsional Fine Structure
qJ
K-
10
110 2 2 2 3 3 3 3 7 9
a)
K+ 1
0 11 12 0 2 13 2 3 4
see
2
3 1 2 4 6
footnote
J'
K_'
K+'
0 0
0 0 1
0 2 12 2 3 3
2 0
0 0 10 110 111 2 2 2 2 7 9
of
1 5 6
Table
obs. /HHz 1766.364 12623.596 15206.630 16893.271 14172.059 22101.813 24495.947 21073.794 23298.849 6953.159 14966.504
Va.
q-2
1 &/kHz 6 3 -7 -4 5 -5 3 4 1 0 0
obs./HHz
b/kHz
7767.653 12608.057 15206.831 16898.160 14172.421
-11 1 -1 -2 11
24507.735 21073.060
2 -4
229
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE IX Spectroscopic Parameters of ( CH3)?CH 35ClObtained from the Lines with Unresolved Torsional Fine Structure”
A
/MHZ
8060.114
(7)
8042.790
(9)
B
/MHZ
4563.503
(2)
4565.288
(3)
C
/MHZ
3202.861
(2)
3202.381
(3)
*J
/kHz
1.66
(13)
1.29
(17)
*J.
/kHz
2.72
(54)
[2.72]
6.l
/kHz
0.346
(84)
[0.346]
6K
/kHz
5.12
(83)
(5.121
Xae
/MHz
-61.500
(15)
-61.509
(13)
Xt,t,/MHz
34.733
(19)
34.701
(16)
Xc,
26.767
(19)
26.808
(16)
/MHz
a)
see
footnotes
of Table
pO,R= Z!,;(structure)
+ tg)
I.
(g = a, b, c; i = 1,. . . , N)
The equilibrium moments Zif$ are known functions of the bond distances and angles, but the rovibrational (rovib) contributions cf’ are not known. If the latter are completely neglected, E:) = 0, the system of 3N Eqs. (2) can be linearized and leastsquares (lsq) solved to obtain the ro-structure. Basically, internal coordinates are determined. Since the lsq process is iterated to convergence, Cartesian coordinates in the principal axis system (PAS) of the parent (i = 1)) that satisfy the first and second moment conditions, are also available. All independent internal coordinates must be given initial values, or fixed values if the number 3N for the particular SDS is not large enough for a stable lsq determination of all coordinates. The ro-structure does not depend on the type of quantity fitted (rotational constants B, moments of inertia I, or planar moments P) provided the covariance matrices of the respective quantities are related by the proper transformations (16). This may be expressed symbolically as r. = rB = rI = rp. If isotopic differences are fitted, e.g., AZbfL= Zbfb- Zbtj (i = 2, . . . ) N), it is found, however, that rm # rN (= rhp) and that both structures are different also from the ro-structure. A better approximation for the cg’ than completely neglecting them may be achieved by introducing three isotope-independent constants Q. Lsq fits that have determined the internal coordinates plus three 4 have confirmed that the tg have indeed the order of magnitude expected for rovibrational contributions ( Z7). It can be shown that the rl,e-structure obtained is identical with the rM -structure ( 16) but the three additional Q determined make for a better reproduction of the original ZgL as well as for a better prediction of the rotational constants of new isotopomers.
230
MEYER ET AL.
0
27/2 23/2
13771.7
13768.4 A AE,EA
q
EE
MHz
OAA
FIG. I. Torsional fine and nuclear quadrupole hyperfme structure of the rotational transition JK_-K+ SK_,,. = 1358-I359of (CH,)#ZH ‘%l in the excited torsional state g = 2. Recording conditions: Temperature 200 K, pressure 0.07 Pa, sample interval 20 ns, 1K data points, extended with 3K zeros prior to FFT, 2 X lo6 experiment cycles.
r,-Derived Methods
Kraitchman’s equations ( 18) and subsequent extensions ( 19, 20) are based on the fact that the planar inertial moment tensor of an isotopomer i can be expressed with the aid of the principal planar moments of the parent and the Cartesian coordinates of the atom substituted in the particular isotopomer. Kraitchman’s equations must be separately applied to singly substituted isotopomers (plus the parent) to obtain a partial or complete substitution (TV-)structure. Typke ( 19) has shown how the system of separate equations, including even equations for additional and multiply substituted isotopomers, can be linearized and arranged into a lsq system to obtain an r,-structure from an iterative fit to the planar moments of a sufficiently large SDS of isotopomers. In the limit where the number of equations equals the number of coordinates to be determined, the resulting structure is identical with the results from Kraitchman’s separate equations. Typke’s fitting method shows the characteristic features of a true r,-treatment: (a) for an incomplete SDS unsubstituted atomic positions do not affect the results and (b) in the case of a complete SDS the rs-coordinates do not necessarily satisfy the first and second moment conditions (except by symmetry). However, these conditions can be introduced as constraints into the lsq formalism. If they are, their effect is a more profound change than a mere shift of the origin and the axes. One difference remains: The r&it diverges where Kraitchman’s equations would yield an “imaginary” coordinate. To avoid this complication where it would appear only on formal grounds, the out-of-plane coordinate of a substituted atom known to lie on a molecular symmetry plane is generally preassigned as zero. This means that the principal planar moment component P bf’gof the particular isotopomer i for the
THE
MICROWAVE
SPECTRUM
OF 2-CHLOROPROPANE
231
axis g perpendicular to the symmetry plane is effectively removed from the input data set to the fit. It is worth mentioning that the results of an rs-fit, when the first and second moment constraints are applied, are very nearly identical (including errors and correlations) with the corresponding r1,6-structure (or the identical rM- or rMstructures), provided the Pbfb that are missing from the r, -fit due to substitutions on symmetry planes have also been omitted from the To-derived fits. Berry and Harmony (21) have recently proposed the r&-structure which is an r,derived concept. From a minimum but complete SDS the r,-structure of the molecule is calculated by Kraitchman’s equations and from this the substitution moments of inertia of the parent, I,,(l) . By means of three scaling factors, pg = Z&),l$~, the set of scaled moments, I$; = (2p, - 1) - Ibfb , is generated for all isotopomers i of the SDS. The &structure is then obtained from an r&t to these I$$. The rP,-structure has, in general, shorter bond lengths and is believed to approximate the unknown equilibrium structure better than the r,-structure does. Structure of 2-Chloropropane
The following structure calculations are based on the six isotopomers measured or remeasured recently, Tables I and III, plus five deuterated species measured very much earlier by Tobiason and Schwendeman ( 1) . We have reevaluated the published line frequencies of the deuterated species by asymmetric rotor fits including fourth order centrifugal distortion. We have obtained from the fits A, B, C, and, with greatly reduced significance, also the distortion constant A,, Table XIII. Due to the limited range of transitions available, the remaining distortion constants, AJK, AK, 6~and 6K, were transferred from the parent isotopomer and allowed to be in error by 50%. The resulting errors of A, B, C, and A, are included in the errors given in Table XIII. The experimental errors of the rotational constants of the two groups of isotopomers included in the present investigation, Tables I, III, and XIII, are extremely different. Unfortunately, the high precision of part of the data cannot be fully utilized for the structure determination by present methods, because the systematic (nonrandom) error of the moments of inertia due to the rovib interaction, that remains even after (crude, isotope-independent) rovib contributions have been subtracted, limits the useful accuracy. Costain (22) has derived a popular estimate for the precision of Kraitchman determined r,-coordinates from the observation that the g.s. difference Pt[l - Pbf: does, in general, not vanish for a substitution on a molecular symmetry plane x, y, as does the difference for the corresponding equilibrium quantities. The nonvanishing g.s. difference is usually found in a certain range which has been more closely investigated by van Eijck (23). A rough estimate is 6( pb’.; - Pb!f) N + 0.003 u A2 which obviously still holds after an isotope-independent f(G + 6-v- ez), has been subtracted from both, P$ notation of Eq. (2), G(P!“(structure)
- P!“(structure))
part of the rovib contribution, and Pi!:, which gives, in the N 0.003 u A’.
If it is assumed that the subtraction of this unknown but presumably large part of the rovib contributions removes most of the systematic error correlation between Pii) (structure) and P!_” (structure), and further that the systematic error is of the same
232
MEYER
ET AL.
TABLE Rotational
Transitions
of ( CHS)*CH “Cl in Excited Torsional Torsional
J
K-
K+
J’
K-’
X
K+’
2F
States with Resolved
Fine Structure 2F’
G’
obs. /HHz q-1
7
9
2
3
5
6
2
7
9
6
3
7
17
17
15
15
13
13
11
11
21
21
19
19
17
17
AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA
EE
10
10
11
3
4
4
7
6
7
10
10
11
3
4
4
8
7
8
15
15
23
23
21
21
19
19
17
17
21
21
19
19
25
25
23
23
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE
19515.167 19515.200 19515.230 19513.034 19513.068 19513.098 19513.474 19513.503 19513.536 19515.603 19515.634 19515.666 18488.501 18488.540 18488.579 18485.893 18485.933 18485.974 18486.306 18486.345 18486.384 18488.904 18488.944 18488.983
16375.503 16375.550 16375.596 16372.861 16372.906
obs.
/HHz
q-2 19574.346 19574.388 19574.429 19572.215 19572.256 19572.296 19572.657 19572.695 19572.737 19574.829 19574.870 19574.913 18596.578 18596.627 18596.674 18593.963 18594.012 18594.062 18594.379 18594.430 18594.477 18596.988 18597.035 18597.083 25832.144 25832.205 25832.265 25829.938 25829.997 25830.055 25830.255 25830.316 25830.371 25832.459 25832.518 25832.578 10246.766 10246.805 10246.847 10247.107 10247.154 10247.198 16531.887 16531.944 16532.001 16529.227 16529.285
a) symmetry species of the group C5 x C~V (5)
order of magnitude for g = a, b, c and for any isotopomer i, we conclude that the functions actually evaluated for the structure may be afflicted by a systematic error of the order 6P(‘) g (structure) = 0.003 u A2 or (if factors VT are neglected) 61:)
THE MICROWAVE
SPECTRUM
233
OF 2CHLOROPROPANE
TABLE X-Continued J
12
K-
K+
8
J'
12
K-'
K+'
9
2F
2F'
21
21
19
19
27
27
G EA,AE AA EE EA,AE AA EE EA,AE AA EE
12
13
7
8
12
13
8
9
25
25
23
23
21
21
27
27
25
25
23
23
21
21
29
29
27
27
25
25
23
23
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE
14
14
9
8
14
14
10
9
31
31
7‘I
29
27
27
25
25
31
31
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA El EA,AE AA EE
obs./HHz
obs./HHz
16372.952 16373.206 16373.253 16373.300 16375.847 16375.893 16375.939 23837.981 23838.039 23838.098 23835.444 23835.499 23835.560 23835.748 23835.807 23835.865 23838.282 23838.340 23838.399 7869.049 7869.083 7869.117 7867.063 7867.098 7867.131 7867,308 7867.342 7867.377 7869.278 7869.312 7869.344 13577.255 13577.304 13577.354 13574.847 13574.896 13574.944 13575.114 13575.163 13575.213 13577.516 13577.566 13577.615 20898.235 20898.301 20898.367 20895.663 20895.729 20895.797 20895.931 20895.996 20896.064 20898.497 20898.562 20898.629 5712.761 5712.793
16529.342 16529.576 16529.634 16529.691 16532.231 16532.288 16532.348 24017.314 24017.381 24017.453 24014.767 24014.838 24014.909 24015.074 24015.145 24015.216 24017.612 24017.684 24017.756
13771.056 13771.118 13771.181 13768.624 13768.688 13768.750 13768.895 13768.957 13769.021 13771.321 13771.384 13171.446 21137.949 21138.037 21138.119 21135.356 21135.443 21135.529 21135.631 21135.715 21135.804 21138.216 21138.303 21138.386
MEYER
234
ET AL.
TABLE X-Continued J
15
12
K-
K+
9
8
J'
15
12
K-'
K+'
10
8
2P
2F'
29
29
27
27
25
25
33
33
31
3l-
29
29
21
21
25
25
23
23
G EA,AE AA EE EA,AE
AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA
obs./HHz 5112.825 5111.308 5711.340 5711.370 5712.461 5711.492 5711.524 5112.910 5112.941 5712.970 10545.112 10545.221 10545.274 10543.111 10543.219 10543.271 10543.363 10543.416 10543.460 10545.358 10545.412 10545.462
EE
14
16
10
11
14
16
10
11
31
31
29
29
27
21
25
25
35
35
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE
33
33
31
31
29
29
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE
obs./MHz
10756.065 10756.126 10756.189. 10154.036 10154.095 10754.160 10754.230 10754.292 10754.354 10156.259 10756.320 10756.382 16997.983 16991.938 16997.899 16997.493 16997.449 16991.405
7838.142 7838.111 7838.080 1840.369 7840.340 7840.308 7840.142 7840.108 1840.018 7837.914 7831.883 7837.852 13044.009 13043.949 13043.890
13046.756 13046.702 13046.641 13046.512 13046.448 13046.389 13043.763 13043.708 13043.647
235
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE XI
Averaged Internal Rotation Splittings Relative to the AA Component of the Rotational Transitions of (CH3)&H3%l in Excited Torsional States J'
K_'
K+
9
5
7
2
6
3
6
9
3
7
10
3
7
10
3
8
10
4
6
10
4
7
11
4
7
11
4
8
12
4
8
12
4
9
12
5
7
12
5
8
13
5
8
13
5
9
14
5
9
14
5
10
14
6
8
14
6
9
15
6
9
15
6
10
12
5
8
12
4
8
14
5
10
14
4
10
16
6
11
16
5
11
1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 1 2 2 2 2 1 1 2 2
J
K-
K+
7
2
9
G
EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE
split./kHz
-32 -63 -41 -82 -40 -79 -49 -97 -60 -118 -43 -86 -46 -93 -58 -115 -58 -117 -70 -142 -34 -68 -49 -99 -62 -126 -66 -133 -87 -172 -31 -62 -51 -101 -61 -124 45 86 31 62 58 118
b/kHz
1 3 -2 -5 1 4 0 0 -1 0 -2 -4 2 4 -1 -1 2 4 1 1 1 3 3 6 0 -2 2 4 -6 -9 1 2 1 3 0 -1 2 0 -1 -1 -1 0
(structure) x 0.003 u A2. For 2-chloropropane the ensuing limits of useful accuracy of the rotational constants are then &4 = 0.4 MHz, 6B x 0.15 MHz, and 6C = 0.06 MHz. Most of the gs. rotational constants in the present work were measured with much higher precision, but in view of the contamination by a large systematic error it would be unwise to use the reciprocal squares of the experimental errors as relative weights in a weighted fit, which is the proper procedure if the errors are purely random. This line of reasoning is supported by a preliminary rr,,-fit to the moments of inertia which were assumed equally weighted and uncorrelated. The standard deviation obtained was 0.0046 u A2 which agrees well with the above estimate.
236
MEYER ET AL. TABLE XII Internal Rotation Parameters of 2-Chloropropanea Fit 1 V3
/kJ mol-1
VlZ'
b
Pit 2
16.428 (10)
16.437 (12)
/kJ mol-1
-0.762 (15)
-0.773 (17)
I.
/amu A'
[3.222]
[3.222]
La,i
/"
(63.761
63.98
Lb,i
/o
[34.42]
[34.42]
Lc,i
/a
[69.38]
69.11
F
/GHz
(162.121
162.15 (10)
F'
/GHz
[-1.211
-1.18 (10)
s
112.86
L i,i'cP
1111.21
zi;d /kHz 0
(10)
/kHz
111.2
77
3
3
see footnotes of Table I.
b)
1 cal
(81)
112.94 (10)
77
a)
(81)
(9)
= 4.184 J.
C) angle between internal rotation axes. d)
mean experimental
splitting.
In the attempt to account for the systematic error a little less crudely than by equal weights for all input moments of inertia, we have created a new covariance matrix for the 1::. The original covariance matrix reflects the experimental errors of the moments of all isotopomers of the SDS and the correlations within each isotopomer resulting from the evaluation of the moments from the particular selection of transition frequencies. We have added to all diagonal elements the square of half of the standard deviation of the equally weighted fit, (0.0023 u A2)2. The covariance matrix remains block-diagonal. The ratio of the largest to the smallest error of the moments of inertia, which is roughly 300 for the experimental errors, was thus reduced to 1.5, approximating an almost equally weighted fit with greatly reduced correlations. In effect, this modified covariance matrix is the result of an error model which tries to simulate systematic error by appropriately chosen random errors. We have used this covariance matrix of the moments, properly transformed into that of the rotational constants where required, for all structure calculations in this work. Table XIV shows that the
THE MICROWAVE
SPECTRUM
OF 2CHLOROPROPANE
237
TABLE XIII Re-evaluation of Rotational Constants for Deuterated Isotopomers of 2-Chloropropane CH3CHCICHZD,
(CH,hCClD
A 0
7512.836 (141) MHz 4548.310 (22) MHz
A B
7793.188 (54) MHZ 4470.088 (21) MHz
C
3107.775
C
*J Ll
1.543 (691) 0.099
3201.698 (26) MHz 2.174(1355) kHz 0.076 MHz
(19)
MHz kHz MHz
*J 0
CH&HClCH2D8
CD$DClCH,
A B
A B C
C *J
7876.693 (198) MHz 4370.185 (22) MHz 3079.685 (22) MHz 1.407 (748) kHz
u
0.100
MHz
*1 0
6869.241(374) MHz 4152.573 (27) MHz 2938.541 (69) MHz 1.172 (942) kHz MHz u.115
CH3CHClCH2D, A B C *J (T
7693.578 (165) 4461.681 (22) 3148.847 (21) 0.109 (705) 0.091
MHz MHz MHz kHz MHz
By Asymmetric Rotor Fit from Transitions of Tobiason and Schwendeman (lJ, Centrifugal Parameters AfK, AK, 6,, and 6~ Transferred from Table I with a 50% Allowance of Error.
different fitting methods employed all yield (relative) standard deviations u near unity which indicates that this error model is basically useful. We have applied “Laurie corrections” for a C-H bond length decrease of 0.003 A upon H + D substitution. This can be easily included in the routine for the ro-type methods and somewhat less directly implemented by a preprocessing routine for the r,-type calculations, provided an approximate structure is known. The structures are compared in Tables XIV and XV on the basis of internal and Cartesian coordinates, respectively. The numbering of the atoms is that of Ref. ( 1). For the r,-type methods the internal coordinates and their errors were calculated from the Cartesian coordinates including error propagation by the appropriate transformation of the covariance matrix of the Cartesian coordinates. The ro-structure in column 1 of Tables XIV and XV is listed only for completeness. The rr,,- and r,-structures of columns 2 and 5, respectively, differ significantly only in those bond lengths that involve the central carbon atom C,,,. Inspection shows that this atom appears shifted by 0.0082 A between the two structures, much more than any other atom. The expression introduced by Costain and discussed above gives for the 13Cct, substitution Po,~( 13Cct,) - PO,b(parent) = -0.0072 u A’, which is 2.5 times larger in magnitude than the rough estimate used previously and even 5 times larger than the more specific mean evaluated by van Eijck (23) from a large number of planar “C + 13C substitutions. The rovib contributions obviously change for the
238
MEYER
ET
TABLE Structure of 2-Chloropropane Type of Fit
XIV
in Internal Coordinates
Q,C @)
;a",
AL.
by Six Fitting Methods
rs(+)
rr,c(-) (a
(d)
21
f 0 33
t Equations
33
33
29
29
26
# Variables
IS
18
18
18
18
15
1.905
1.416
1.470
0.712
2.398
relative
e of Fit
2.777
Bond Lengths (A) 1.5202
(14) 1.5196
(24) 1.5210
(19) 1.5212
(20) 1.5231
(21) 1.5176
1.8039
(23) 1.8006
(18) 1.8026
(15) 1.8026
(15) 1.7973
(18) 1.7964
(40)
1.1050
(21) 1.1023
(37) 1.0973
(30) 1.0974
(31) 1.0957
(16) 1.0933
(42)
1.0954
(49) 1.0988
(37) 1.1000
(28) 1.0999
(28) 1.0972
(24) 1.0919
(71)
1.0948
(49) 1.0971
(35) 1.0988
(26) 1.0988
(27) 1.0998
(21) 1.0989
(57)
1.0999
(36) 1.0987
(29) 1.0969
(22) 1.0967
(23) 1.1003
(52) 1.0908
(41)
113.31
(16) 112.88
(29) 112.64
(23) 112.67
(23) 112.62
(26)
112.52
(35)
104.83
(30) 105.02
(27)
(20) 105.07
(21) 105.37
(21)
105.43
(35)
Bond Angles
105.10
(38)
(“)
109.40
( 9) 109.41
(13) 109.21
(11) 109.20
(11) 109.33
(12)
109.28
(15)
111.09
(39) 110.86
(34) 110.67
(25) 110.67
(26) 110.75
(28)
110.73
(55)
109.55
(52) 109.49
(40) 109.24
(30) 109.22
(31) 109.43
(25)
108.71
(56)
109.41
(14) 109.66
(20) 109.92
(16) 109.92
(17) 109.82
(22) 109.87
(25)
Torsional
Angles
(“)
CendCctrCendHol 179.08 (49) 179.18 (33) 179.10 (25) 179.09 (25) 179.17 (14) 178.98 (47) CendCetrCendH~ -59.93 (90) -60.51 (78) -61.12(59) -61.14(60)-60.69 (62) -61.78 (106) CendCctrCendH~
59.43(26) Rovib
59.45 (26) 59.09 (21)
59.08 (22)
(isotope-independent,
Contributions
59.22 (26)
59.04 (29)
ud’)
%
0.0
0.214 (95)
0.199 (90)
n.a.
na.
0.0
s,
0.0
0.139 (88)
0.708 (73)
na.
n.a.
0.0
s.9
0.0
0.437 (91)
0.492 (81)
n.a.
na.
0.0
Types of Fit (to
11 Isotopomers
for (a) through (e)):
(a) ra Fit @)
rr,+ (= rp,E) Fit Fit less four Planar
(cl rI E
(d) ri Fit plus three
Moments
P, for Substitutions
1st and 2nd Moment
Conditions
on the a,c Plane
(for a, c, and ac)
(e) rs Fit (f) r”, Structure:
All
Errors
Laurie
Kraitchman’s Equations (from 8 Species) + Scaling by p (for 11 Species) + ra Fit to Scaled Moments (of 11 Species).
1 o.
Corrections
of -0.003
A
Applied
upon
H +
D Substitution
THE MICROWAVE
SPECTRUM
239
OF 2-CHLOROPROPANE
TABLE XV Structure of 2Chloropropane Type Fit
r,,
in Cartesian Coordinates by Six Fitting Methods r&+)
G (0
(a)
rI,E @)
*I,&-) (c)
# Eqs
33
33
29
29
26
# Var
15
18
18
18
18
1.905
1.416
1.470
rel. B
2.777
(d)
0.712
33 15 2.398
Coordinates a (A) C CFk
0.5201 (22)
0.5173(17)
0.5181(13)
0.5182(14)
0.5121 (12)
0.5154(24)
-1.2293 ( 2) -1.2280 ( 5) -1.2280 ( 4) -1.2279 ( 4) -1.2285 ( 2) -1.2249 (24)
C end
1.1724 ( 8)
1.1720 ( 8)
1.1716 ( 6)
1.1715 ( 7)
1.1693 ( 5)
1.1689 (24)
Hset H,
0.5336 (49) 0.6650 (37)
0.5322 (34) 0.6646 (26)
0.5316 (26) 0.6648 (19)
0.5313 (28) 0.6645 (19)
0.5302 (14) 0.6638 ( 9)
0.5356 (49) 0.6656 (50)
H0
2.2247 (13)
2.2244 (10)
2.2245 ( 7)
2.2243 ( 7)
2.2241 ( 3)
2.2173 (46)
H,
1.1148 (23)
1.1144 (16)
1.1146 (12)
1.1144 (13)
1.1140 ( 6)
1.1132 (35)
C end H,
1.2699 ( 3) 2.1610 (13)
1.2662 (12) 2.1599 ( 9)
1.2661 (12) 2.1596 ( 8)
1.2672 ( 6) 2.1597 ( 4)
1.2619 (28) 2.1505 (45)
Coordinates lb\ (A) 1.2656 (12) 2.1594 ( 8)
HE
1.2918 (25)
1.2899 (19)
1.2891 (16)
1.2895 (15)
1.2898 ( 7)
1.2817 (40)
H,
1.2853 (23)
1.2836 (16)
1.2829 (14)
1.2833 (13)
1.2837 ( 7)
1.2771 (36)
Coordinates c C cti Cl C end
(A)
-0.3948 (16) -0.3973 (37) -0.4020 (30) -0.4020 (31) -0.4037 (16) -0.4003 (37) 0.0454 ( 6) 0.0456 ( 5) 0.0460 ( 4) 0.0460 ( 4) 0.0440 (62) 0.0454 ( 5) 0.1276 (16)
0.1291 (21)
0.1312 (16)
0.1312 (16)
0.1274 (53)
0.1321 (29)
Hsee H,
-1.4998 (17) -1.4995 (12) -1.4993 ( 9) -1.4992 (10) -1.4993 ( 5) -1.4933 (33) -0.2578 (115)-0.2600 (79) -0.2614 (59) -0.2615 (60) -0.2619 (29) -0.2545 (133)
HB
-0.1735 (171)-0.1799
H,
1.2259 (24)
(119)-0.1822
1.2262 (16)
(87) -0.1824 (88) -0.1828 (43) -0.1969 (160)
1.2265 (12)
1.2263 (13)
1.2262 ( 6)
1.2214 (33)
Footnotes see Table XIV.
present 13Cct,substitution too much to be approximated by isotope-independent constants, and the inherently different ri,6- and r,-methods arrive at a larger than usual difference in position. In contrast, the position of the chlorine atom is remarkably stable despite its very small c coordinate which would usually be deemed too small for a safe determination by Kraitchman’s equations. For this substitution the planar moment difference P0,b(37C1)- P,,b(parent) = 0.0007 u A*, which is less than the respective mean value from van Eijck’s statistics (23). The same is true for the difference PO,J D,,) - &,(parent) = 0.0028 u A*. For the rr,c-structures of Table XIV the three rovib constants cg are also given. Although they could be obtained only with little precision from the limited SDS, the accuracy of the structural parameters is not impaired, it is better (rms) than for the ro-structure. The structures listed in columns 3 and 4 of Tables XIV and XV agree very closely, the coordinates as well as the errors, although they have been obtained by basically different methods. As discussed above, the inputs have been made strictly identical
240
MEYER
ET AL.
by removing the planar moments PO,6for the substitutions on the a,c plane also from the input to the r,,,-fit, and the output coordinates have been made physically equivalent PAS coordinates by imposing the three nontrivial first and second moment conditions on the r,-fit. The number of degrees of freedom is the same for both lsq treatments. Of course, the close coincidence of columns 3 and 4 does not necessarily make this common structure preferable from the standpoint of optimum rovib compensation. The error ranges of the structures listed in the four columns 2 to 5 of Tables XIV and XV touch or overlap within less than 2a, even for the C,,, position. From this we conclude that it is possible to determine a molecular structure from the g.s. rotational constants within a few lop3 A and a few 10-l degrees. This structure is consistent within the framework of the rr,,- (or rM-) and r,-methods and their appropriately modified variants. Due to the lsq treatment, the structure can be more balanced for a sufficiently large SDS. The methods also afford a more direct error assessment than the repeated application of Kraitchman’s separate equations to pairs of isotopomers from a minimum SDS. As stated above, Laurie corrections were employed for the deuterated isotopomers. For the four structures of columns 2 to 5, they result almost exclusively in an increase of the corresponding C-H bond lengths of the parent by twice the amount of the correction with negligible influence on the remaining structure and only a minute change of the standard deviation of the respective fit. For columns 2 to 5 of Table XIV, Laurie corrections could have been applied simply by inspection, if they had not already been accounted for in the fitting routines. This is not true for the rostructure of column’ 1. For the rP,-structure of column 6, the basic r,-structure, the substitution moments Ii.‘,/ of the parent, and the three scaling factors pg have been calculated from the minimum SDS of 8 isotopomers by Kraitchman’s equations, retaining also the squares of nonvanishing out-of-plane coordinates for planar substitutions, even if negative (for C,,) . The input data had been properly preprocessed for the H --f D corrections, and the errors were propagated from the modified covariance matrix constructed as described above. The scaling factors with errors and correlations are Pa
0.993833 (2654)
1BOO0
Pb
0.9973 11( 1504)
0.0027
PC
0.995642( 1055)
-0.0006
1.OOOO -0.05 12
1.OOOO.
The moments of inertia of the complete SDS of all available 11 isotopomers were appropriately scaled. The set of the resulting Z$ served as input to an ro-fit with a general (i.e., nondiagonal)weight matrix for which the inverse of the covariance matrix of the Zdi) was used. This covariance matrix is very different from the one created Cl” for the Zo,gwhich was discussed above and used wherever the Zbf; (or the corresponding rotational constants) were required. Since the errors of the Z$ are dominated by those of the scaling factors pg which are common to $1 isotopomers, the correlations p(i) for different i are very high, sepbetween corresponding moment components Zm,g) arately for each g. The highest correlation coefficient found was 0.99996. The covariance matrix is nonetheless positive definite, and the iterative lsq ro-fit converged rapidly. The standard deviation of this fit and also the errors of the structural parameters
241
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE XVI Structure of 2-Chloropropane in Internal Coordinates by Weighted Average of Three Methods” Bond Anales P)
Bond Lengths t&
Cend%
Torsional
An&s
P)
1.521 (4)
cend%rcend
112.7 (5)
Cend%r(&ndHa
1.801 (3)
Cl GtrHsee
105.2 (5)
Cend%rCcndb
179.2 (5) -60.8 (13)
1.097 1.098 1.099 1.098
cendcctrcl CendCct&,c ‘%rCendH, %&&i
109.3 110.0 110.7 109.4
Ccnd%rCendH~
59.2 (5)
%&n&
109.8 (4)
(6) (6) (5) (7)
(2) (4) (6) (6)
For the purpose of comparing the torsional angles with those of (ZJ, the torsional angles with respect to the chlorine atom are cl %&nd%
57.5 (8)
cl %&&
177.4 (10)
c’ Cc&endH~
-62.5
(4)
a The methods are r,,, (column 2 of Table XIV), r, (column 5 of Table XIV), and modified r,,or modified r, (column 3 or 4 of Table XIV). Laurie corrections of -0.003 A were applied upon H + D substitution. Error shown is twice the mean error of the columns cited.
are of the same order of magnitude as for the original ro-fit of column 1. In agreement with the intention of the method, the r&-structure appears contracted, though not uniformly. For lack of comparable information it cannot be further commented upon. We give in Table XVI as the final structure of 2-chloropropane determined in this work the weighted average of columns 2,5, and 3 of Table XIV. It is hence composed from the r,,c-structure, the fitted r,-structure, and the common structure derived from both, and is stated with errors that are twice the mean errors of these columns. The structures included lie all well within this error range. If the bond length increase of the C-H bonds by 0.006 A due to the Laurie corrections of -0.003 A is taken into account, the structure is very similar to the structures reported by Tobiason and Schwendeman ( 1) and by Ikeda et al. (2), though with a lower error margin. The bond angle UC,,,, Cend, H,) is significantly larger, approximately lo, than the corresponding bond angles for the atoms H, and H,, as noted already by the former authors. We find no significant C-H bond length differences. The methyl groups are rigidly rotated, by a significant angle of a little less than lo, such that the H, atoms move out of the plane ( Cend, C,, Cend) and tend to approach the chlorine atom. ACKNOWLEDGMENTS Financial support by the Deutsche Forschungsgemeinschaft, Fonds der Chemie, and the Land SchleswigHolstein is gratefully acknowledged. Dr. W. Stahl assisted us in the Stark effect measurements. The calculations were carried out at the computer centers of the Kiel and Ulm universities. RECEIVED:
August 6, 199 1 REFERENCES
1. F. L. TOBIASON AND R. H. SCHWENDEMAN, J. Chem. Phys. 40, 1014-1021 ( 1964). 2. C. IKEDA, T. INAGUSA, AND M. HAYASHI, J. Mol. Spectrosc. 135, 334-348 ( 1989).
242
MEYER ET AL.
3. T. IUIMA, S. SEIU, AND M. KIMURA, Bull. Chem. Sot. Jpn. SO, 2568-2572 ( 1977). 4. J. R. DURIG AND G. A. GUIRGIS, Chem. Phys. 44, 309-314 (1979). 5. M. MEYER, THEOCHEM, in press. 6. M. KRUGER AND H. DREIZLER, Z. Naturforsch. A: Phys. Phys. Chem. Kosmophys. 45,724-726 ( 1990) and citations therein. 7. J. HAEKEL AND H. M~CDER,Z. Naturforsch. A: Phys. Phys. Chem. Kosmophys. 43,203-206 (1988). 8. T. J. BALLE AND W. H. FLYGARE, Rev. Sci. Instrum. 52, 33-45 ( 1981). 9. U. ANDRESEN, H. DREIZLER, J.-U. GRABOW, AND W. STAHL, Rev. Sci. Instrum. 61,3694-3699 ( 1990). 10. J.-U. GRABOWAND W. STAHL, Z. Naturforsch. A: Phys. Phys. Chem. Kosmophys. 45, 1043-1044
(1990). 1 I. N. HEINEKING, W. STAHL, AND C. THOMSEN, J. Mol. Spectrosc. 146,402-408 ( 199 1). 12. J. K. G. Watson, in “Vibrational Spectra and Structure” (J. R. Durig, Ed.), Vol. 6, p. 39, Elsevier,
Amsterdam, 1977. 13. J. M. L. H. REINARTZ AND A. DYMANUS, Chem. Phys. Lett. 24,346-351 ( 1974). 14. V. TYPKE, Z. Naturforsch. A: Phys. Phys. Chem. Kosmophys. 26, 175-177 ( 197 1). 15. M. MEYER AND H. DREIZLER, J. Mol. Spectrosc., 148, 310-323 ( 1991). 16. H. D. RUDOLPH, Struct. Chem., to be published. 17. K. J. EPPLE,Dissertation, Ulm, 1990. 18. J. KRAITCHMAN, Am. J Phys. 21, 17-24 (1953). 19. V. T~PKE, J. Mol. Spectrosc. 69, 173-178 (1978). 20. H. D. RUDOLPH, J. Mol. Spectrosc. 89, 430-439 ( 1981). 21. R. J. BERRY AND M. D. HARMONY, Struct. Chem. 1,49-59 ( 1990) and earlier papers cited therein. 22. J. J. Costain, Trans. Am. Crystallogr. Assoc. 2, 157-164 ( 1966). 23. B. P. van Eijck, J. Mol. Spectrosc. 91,348-362 ( 1982).
OF MOLECULAR
SPECTROSCOPY
IsI,2
17-242 ( 1992)
Structure, Methyl internal Rotation, Centrifugal Distortion, and Dipole Moment of 2-Chloropropane MICHAEL MEYER, JENS-UWE GRABOW,
AND HELMUT DREIZLER
Abteilung Chemische Physik. Institut fir Physikalische Chemie der Universitiit Kiel, Olshausenstr. 40-60, D-2300 Kief, Federal Republic ofGermany AND
HEINZ DIETER RUDOLPH Abteilung fir Physikalische Chemie der Universitiit Urn, Albert-Einstein-Allee 11. D-7900 Ulm, Federal Republic of Germany The microwave spectra of six isotopic species of 2-chloropropane have been investigated by microwave Fourier transform spectoscopy. The quartic and some sextic centrifugal distortion constants of the 35Cland “Cl species are given. The structure has been derived by various methods. The dipole moment was found to be 2.141 D. From excited torsional states the parameters V3 and VIZ’of the torsional potential function were obtained. o 1992Academic PXS. hc. INTRODUCTION
The microwave spectrum of 2-chloropropane, (CH3)$HCl, was assigned by Tobiason and Schwendeman ( 1) for the first time. They prepared several isotopic samples to determine the substitution structure. From the absence of internal rotation splittings in the spectrum a lower limit of 14.43 kJ/mol (3.45 kcal/mol) of the barrier to internal rotation was estimated. Recently Ikeda et al. recalculated the structure from the rotational constants determined by Tobiason and Schwendeman for a comparison with 2-bromopropane and 2-iodopropane (2). Iijima et al. (3) investigated the molecular structure by means of electron diffraction. Durig and Guirgis (4) utilized FIR and Raman spectroscopy to determine the parameters of the torsional potential function. We investigated the spectrum in the torsional ground state with microwave Fourier transform (MWFT) spectroscopy to determine the quartic and some sextic centrifugal distortion constants. The determination of the dipole moment required more accurate hyperfine parameters. The new assignment of the (CH3)2’3CH37C1 and “CH3CH37C1CH3 species and the improved determination of the rotational constants of the other isotopomers enabled us to refine the molecular structure. It was not possible to resolve the torsional fine structure of the ground state transitions even with our high resolution technique. Therefore the parameters I’3 and VI*’ of the torsional potential function were determined from rotational transitions in excited torsional states. The spectroscopic studies were supplemented by ab initio calculations. The details will be published elsewhere (5). 217
0022-2852192 $3.00 Copyright 0
1992 by Academic Press. Inc.
All rights of reproduction in any form resewed.
218
MEYER
ET AL.
EXPERIMENTAL
DETAILS
The sample of 2-chloropropane was obtained from ALDRICH-Chemie, Steinheim. For the measurements waveguide MWFT-spectrometers (6) were used from 5 to 36 GHz. The sample pressure was kept on the order of 1 mTorr (0.13 Pa) and the temperature was in the range of 220 to 250 K. In the case of narrow multiplets caused by nuclear quadrupole hyperfine structure and additional torsional fine structure in the spectra a refinement ( 7) of the measured frequencies was necessary. The spectra of the 13Cspecies were recorded in natural abundance with a molecular beam MWFT spectrometer of the Balle and Flygare type (8,9) in the frequency ranges from 7.5 to 14.5 and 18 to 26 GHz. In order to increase the sensitivity and resolution of the spectrometer the axis of the molecular beam was directed along the resonator axis ( 10). For the determination of the dipole moment the spectrometer was supplemented with Stark plates ( Z1). The beam was prepared from a sample of 2% 2-bromopropane in argon under a backing pressure of 250 Torr (33 kPa). TORSIONAL
GROUND
STATE
The spectrum of 2-chloropropane shows strong a- and weak c-type transitions. The sensitivity of the spectrometers enabled us to detect c-type transitions of this molecule for the first time. The experimental line frequencies were evaluated by a separate nuclear quadrupole hyperfine structure (hfs) and centrifugal distortion analysis. Both analyses were performed in an iterative manner until all quadrupole coupling and centrifugal distortion constants had converged to their final values. The results are given in Tables I to III. For the first-order perturbation treatment of hfs analysis the set of transitions was limited to the completely split lines up to J = 3. The quadrupole coupling constants X+ = xbb + X, and X_ = xbb - X, were fitted to the chlorine hfs splittings relative to the most intense component compiled in Table IV. Since it was not possible to determine the off diagonal element x,, from the spectra the coupling constants in their principal axis system could not be derived. The hypothetical unsplit lines used as input for the centrifugal distortion analysis were then calculated with the quadrupole coupling constants from the hfs analyses. The unsplit lines are given in Table V. We used a Hamiltonian according to Watson’s A-reduction (12) in the representation I’ for the centrifugal distortion analysis. For the species with high natural abundances, ( CH3)zCH35C1 and (CH3)$H3’C1, the quartic and some sextic centrifugal distortion constants could be determined. We fitted the linear combinations (B + C)/2 and A - (Z? + C)/2 and the asymmetry parameter ZQ,since the correlation between the rotational constants is high. The accuracy of the rotational constant A was improved substantially by the inclusion of c-type transitions in the analyses. For the 13Cisotopic species with low natural abundances only A, and A,, could be obtained since the measurements in the molecular beam MWFT spectrometer are limited to low J values. For the determination of the dipole moment of ( CH3hCH 35C1the spacing of the Stark plates was calibrated with OCS using the dipole moment 0.7 15 19 D ( 13). The truncated Stark hamiltonian matrix was set up in the representation I’ to get real matrix elements. The components 1pa I and I ~~1were fitted to the measured frequencies
THE MICROWAVE
SPECTRUM
OF 2CHLOROPROPANE
219
TABLE 1 Centrifugal Distortion Parameters= of Isotopic Species of 2-Chloropropane with High Natural Abundance (CH3)2CH'aCl
(CH3)zCH"Cl
(B+C]/Z
/MHz
3889.2205
(5)b
3800.6093
(4)
A-(B+C)/Z
/MHZ
4178.9640
(2)
4267.0551
(4)
-0.15275058(1
-0.16311718(l)
ba AS
/kHz
1.608
(30)
1.531
AJK
/kHz
(11
2.7015
(44)
2.649
(11
AK
/kHz
2.757
(11)
2.901
(31
6.l
/kHz
0.44842
(29)
0.42265
(61
bK
/kHz
3.3552
(34)
3.3177
(83
OJ
/kHz
1.39
(46)
[1.39]C
4JK
/Hz
-0.01176
(35)
-0.01052
4K
/Hz
0.1188
(89)
[0.1188]
QJK
/Hz
0.01223
(18)
0.01259
(22
(42
Ad
/MHz
8068.1846
(6)
8067.6644
5)
Bd
/MHz
4570.8814
(5)
4452.4044
4)
Cd
/MHz
3207.5597
(5)
3148.8142
4)
ce
/kHz
4
a)
Watson
A-reduction,
b)
single
standard
cl
fixed
parameters
d)
derived
parameters.
e)
standard
deviation
4
representation error
in units
in squared
of the
I=, of the
[QKJ last
- QJ - QK = 0] digit.
brackets.
fit.
of Table VI. This required the consideration of centrifugal distortion up to fourth order in order to avoid systematic errors. The change of the representation from I’ to I’ forced us to convert (14) the centrifugal distortion constants of Table I. This conversion requires only a change of the signs of 6, and hK. The Stark effect analysis was carried out with fixed rotational, centrifugal distortion, and quadrupole coupling constants. The components of the dipole moments 1pa 1 = 2.099 ( 5 ) D and 1p, 1 = 0.423 ( 10) D were determined with a standard deviation of 7 kHz. The total dipole moment is P = 2.141 (5) D.
MEYER
220
ET AL.
TABLE II Nuclear Quadrupole Coupling Constants of Isotopic Species of 2-Chloropropane with High Natural Abundance (C!H3)zC!H35C!l
x+ .a
(CHs)zCH"Cl
/MHz
61.496
(6)
48.510
(6)
X- b /HHz
7.920
(18)
6.188
(15)
-61.496
(6)
-48.510
(6)
X..
/MHz
Xbb
/MHz
34.708
(9)
27.349
(8)
Xcc
/MHz
26.788
(9)
21.161
(8)
Av=
/NH2
10.310
6.600
0
/MHZ
0.007
0.006
a)
x+ =
Xbb
+&c.
b)
X-
xi,,
-&c.
c)
mean
-
experimental
EXCITED
splitting.
TORSIONAL
STATES
The excited torsional states q = 1 and 2 were investigated for the ( CH3)*CH 35C1 species. The lower one has been assigned by Tobiason ( 1). For the assignment of the other one we started searching in the frequency region around the J-J’ = 2-l a-type transitions of the ground state for satellites showing a similar hypertine pattern. Due to the high barrier the torsional fine structure of the low J transitions could not be resolved. The spectroscopic parameters determined from these lines compiled in Tables VII and VIII are given in Table IX. The transitions above J = 7 showed for each hyperfine component the typical triplet pattern of a two-top molecule with a high barrier. An example of the spectra is given in Fig. 1. The internal rotation splittings of the rotational transitions in the state q = 2 are larger than the corresponding splittings for q = 1. They can be well predicted from the parameters of the torsional potential function determined by Durig (4). The procedure for the internal rotation analysis has been given previously (15). We used a semirigid model with a Hamiltonian set up in the principal axis system. The eigenvalues were calculated by a diagonalization of appropriately truncated matrices instead of a Van Vleck perturbation treatment. The computational effort was reduced by the application of group theory and prediagonalizations. For the analysis the measured internal rotation splittings relative to the AA-cornponent in Table X were averaged for the hyperfine structure of each rotational transition separately. On the basis of this treatment a satisfactory fit of the parameters V3 and I’iz’ of the torsional potential function Eq. ( 1) to the averaged splittings in Table XI is possible.
221
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE III Spectroscopic Parameters of Isotopic Species of 2Xhloropropane (CH3)z11CH35C1
with Low Natural Abundance (CH,)z"CH"'Cl
A
/HHZ
8048.468
(35)
8047.896
(32)
B
/HHZ
4553.552
(3)
4434.662
(2)
C
/MHZ
3202.417
(2)
3143.213
(2)
AJ
/kHz
1.36
(13)
1.32
(11)
h,c
/knz
2.66
(53)
2.95
44)
Xaa
/NH2
-61.642
(13)
-48.632
24)
Xtsb /MHz
34.718
(22)
27.305
65)
Xc,
26.924
(22)
21.327
(65)
/NH2
"CH,CH'SCICHx
"CHxCH"ClCHx
A
/MHZ
1812.204
4)
7871.591
(5)
B
/MHZ
4513.134
1)
4394.853
(2)
C
/MHZ
3148.721
1)
3090.717
(2)
A.l
/kHZ
1.28
(7)
1.15
(11)
AJK
/kHz
2.98
(24)
2.98
(35)
X me
/MHz
-61.329
(12)
-48.383
(7)
Xbb
/MHZ
34.642
(17)
27.299
(11)
Xc,
/MHz
26.687
(17)
21.084
(11)
al
see
footnotes
of Table
I.
V(a,, (Yz)= f V,( 1 - cos 3cq) + 5 Vj( 1 - cos 3a*) + Vi2(cos 3a, cos 3~x2- 1) + Vi2’sin 3~yi sin 3cq.
(1)
The results of the analysis are given in Table XII. The remaining parameter Vi, of IQ. ( 1) could not be determined. The moment of inertia Z, and the angles between the symmetry axis i of the top and principal axes of inertia were calculated from the averaged structure discussed below. The angles were kept fixed in a first fit. We noted that it was possible to fit two angles in addition if one is taken from the structure. The result of this second fit listed in Table XII conlirmed our estimations from the structure. It is not possible to determine Z, because this parameter is highly correlated with V, . The reduction of Z, leads to an increase of V,. For example, a fit with the fixed parameter Z, = 3.186 amu A2 derived from the r, structure of Ref. (2) and F = 163.8 GHz and F’ = -1.24 GHz yields V, = 16.61 (12) kJ/mol and Viz’ = -0.837 (21)
222
MEYER ET AL. TABLE IV Hypetine Splittings in the RotationalTransitionsof IsotopicSpeciesof 2-Chloropropane with High NaturalAbundance
(a) J
K-
K+
J' K-'
1
0
1
0
2
2
2
3
3
3
2
0
1
1
0
1
2
2
11 2
2
2
0
0
1
1
1
2
1
1
1
3
0
2
2
1
2
1
2
2
Kc'
0
1
0
1
2
1
0
1
2
0
2
0
0
0
0
0
2
1
2
2F 2F'
5 3 13 7 5 31 5 3 3 13 11 7 5 3 5 3 3 11 7 5 31 5 3 11 13 9 7 5 31 9 7 5 9 7 5 31 7 5 3 11 7 5 5 3 7 5 13
3 3 5 3 5 3 5
5 3
I 5 3 5 5 3 5 3
7 5 3 7 5 3 7 5 3 7 5 3 7 5 3 3 7 5
(CW~)ZCH~~CI ref. /MHz0 spl./HHtb 6/kHz~ 7781.510 15.377 -12.302 15230.740 -0.894 16.427 14.488 -11.249 4.128 -25.716 1.950 16923.933 15.312 -2.885 8.677 9.172
14197.177 15.370 -5.040 6.692 10.581 -11.740
-2 -7 0 -4
-4 -12 -5 -9 -15
LO 10 5
24540.765 16.358 5.134 -11.217 1.869 15.480
3 -2 2 -2 -2
17034.367 -29.857 12637.702 -6.696 14902.841 -21.184 5.358
frequency
of
the
reference
component.
b)
frequency
of
the
reference
component
c)
-4 -10 4 -13 -10 4 -3
22134.596 -0.971 3.073 4.039
a)
given
3 -3
(CH~)ICH"CI ref. /MHz spl./WHz 6/kHz 7603.641 12.134 14909.633 -0.694 12.988 11.505 -8.054 -20.329 1.493 16508.953 12.127 -2.276 6.837 7.238 1.953 -9.123 13901.699 12.132 -3.971 5.294 8.341
between
observed
8 2 9 -11 10 2 -1 3 0 -6 -1 -1
4 -13 4 -8
3.052 21715.903 -0.721 2.462 3.189 24550.688 2.782 3.373 23895.062 12.851 4.008 -8.837 1.358 12.120 2.654 0.400
-7 1 0 -6 3 -2 2 2 6 4 -8 1 4
1 1 -3 0
minus
frequency
component.
difference
6 7
-9.695
and calculated
frequency.
of
the
THE
MICROWAVE
SPECTRUM
223
OF 2-CHLOROPROPANE
TABLE IV-Continued
(bl J
K-
K,
J' K_'
K+'
2F 2F'
5 3 13 7 5 3 7 5 9 7 5 3 7 5 9
3 3 5 3 3 5 3 7 5 3 1 7 5
7
1 5
5 3
3 1
1
1
5 3 9 7 5 7 5
5 3 7 5 3 7 5
(cl J
K-
K,
J' Km'
K,'
2F 2F'
5 3 13 7 5 5 3 11 1
5 3 5 3 11 5 3 13 9 7 5 31 9 1
5 31
3 3 5 3 5 3 5 3 1 5 3 3 3 7 5 3 7 5 3
(CH,)zl'CH'sCl
(CH,)x"CH"Cl
ref./HHz spl./HHz
6/kHz
ref./MHz spl./MHz
d/kHz
0
7580.307 12.157
-1
14867.762 -0.623
-5
21662.641 -0.110 2.494 3.199
-2 14 11
24466.181 2.803 3.194
11 14
23808.312 12.862
3
1159.053 15.410 -12.320
-8
15190.878 -0.880
-3
-11.271
14164.395 15.391 22084.581
-13
-13 0
-0.910
9
3.090
4.048 13.568 -7.311
-3 4 -11
25064.290
3.488 4.021 0.499 12.174 -2.188 -8,154 24456.008 16.319 5.142 1.861 15.521
-7 8 -19 0 1 7 -1 5 14 3
'3CH,C!Hx5C!lCH,
'3CHsCH"ClCH,
ref./MHz spl./HHz
ref./HHz spl./MHz
a/kHz
7664.923
15.336 -12.258 14986.303 -0.940 14.396 -11.234 1.981 13962.868 15.322 -5.031 6.663 10.552 -11.711 12383.991 -6.675 5.339 24788.487 3.451 3.986 0.547 24225.877 16.344 5.151 -11.184
4 8 -2 2 -14 -3 -10 -9 -3 -15 -17 -3 2 6 4 10 -2 -3 8
d/kHz
7487.993 12.099 -9.671 14668.516 -0.666 11.433 -8.838
1 3 -8
13666.951 12.091
-5
5.268 8.326
-3 -5
12265.378 -5.271 4.217 24196.606 2.760 3.165 23579.133 12.842
3 6
0 0 6 6
0
MEYER
224
ET AL.
TABLE V Hypothetical Unsplit Frequencies of the Rotational Transitions of Isotopic Species of 2-Chloropropane with (a) High and (b, c) Low Natural Abundance
(a) (CH3)zCH'SCl J
K-
K+
J'
1 2 2 2 3 3 3 3 3 4 4 4 5 5 2 4 6 7 8 9 10 10 11 12 12 13 14 14 13 15 16 17 17 18 19 19 21 22 22 24 25 26 27 27 28 28 29 30 30 32 33 34
0 0
1 2 1 2 1 3 2 3 2 4 2 3 5 5 1 3 4 4 5 6 7 6 7 7 a 8 9 a 8 10 10 10 11 11 12 11 13 13 14 15 16 16 17 16 18 17 18 19 18 20 20 21
0
a)
1 1 2 0 1 1 2 0 2 2 0 1 2 1 2 3 3 3 3 4 4 5 4 5 5 6 5 5 6 7 6 7 7 8 8 9 8 9 9 10 10 11 10 11 11 11 12 12 13 13
difference
1 1 1 2 2 2 2 2 3 3 3 4 4 2 4 6 7 a 9 10 10 11 12 12 13 14 14 13 15 16 17 17 18 19 19 21 22 22 24 25 26 27 27 28 28 29 30 30 32 33 34
K_'
K+’
0 0
0
1 1 2 0 1 1 2 0 2 2 0 1 0 1 2 3 3 3 3 4 4 5 4 5 5 6 5 5 6 7 6 7 7 8 8 9 8 9 9 10 10 11 10 11 11 1': 12 13 13
between
1 0 1 0 2 1 2 1 3 1 2 4 4 2 4 5 5 6 7 8 7 8 8 9 9 10 9 9 11 11 11 12 12 13 12 14 14 15 16 17 17 18 17 19 18 19 20 19 21 21 22 observed
obs.
/HHz
(CH3)zCH"Cl b/kHza 0
7778.435 15229.680 16920.117 14193.536 24536.003 22134.230 25144.417 21105.393 23335.089 28580.335 33381.736 30855.221 34866.441 34470.997 17042.897 13289.565 13307.107 6979.609 12124.850 18543.175 25785.379 10173.930 16438.772 7914.145 23918.681
-2 -3 -10 0 5 10 3 -2 -2 3 -5 2 -5 3 0 -5 1 1 1 -1 -2 0 6 -2
20989.159 5754.107 13645.395
0 -1 -1
17395.373 7761.349 25780.243 13595.037 21422.035 5378.642 16860.637 7023.278 25721.300 20408.425
2 -2 -1 1 -2 0 0 2 -3 0
15369.957 24236.040 6029.264
1 -2 1
11010.254 18446.652
3 0
7545.433 21796.746 9266.172 15977.295
1 0 4 1
and
calculated
obs.
/HHz
b/kHz
7601.211 14908.771 16505.943 13898.823 23891.325 21715.594 24549.435 20681.414 22803.427 32496.172 28076.408
1 -3 -2 -9 0 2 4 3 2 -1 0
34256.509 33819.913
4 -5
12746.213
0
6143.947 10869.480 16896.889 23853.474
5 1 0 2
14357.509
1
21359.127 11291.619
0 1
25836.304 14018.204
0 -1
21534.890
-3
16850.615
-1
19789.436 14582.273 22834.218 10121.231 16918.501
-2 -1 -1 1 0
25983.788
-2
11827.447 19362.139
3 2
9117.410
5
unsplit
frequency.
THE
MICROWAVE
SPECTRUM
225
OF 2-CHLOROPROPANE
TABLE V-Continued
(a) (CH,)zCH"Cl
(CH,)zCH'"Cl J
Km
K,
35 35 36 37 38 38 39 39 40 41 41 42 42 43 43 45 45 46 46 47 48 49 49 50 110 6 2 4 5 8 9 11 12 10 13 14 15 16 18 19 21 21 22 24 25 26 27 28 29 27 30 30 32 33 35
13 14 14 14 14 15 15 14 15 15 16 15 16 17 16 17 16 17 18 18 17 19 18 19
22 21 22 23 24 23 24 25 25 26 25 27 26 26 27 28 29 29 28 29 31 30 31 31
15 2 2 3 3 4 4 5 4 5 5 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 10 11 11 13
0 3 3 6 6 8 8 7 9 10 10 11 12 13 15 14 15 17 17 18 19 19 20 18 20 21 22 23 23
J'
Km'
35 35 36 37 38 38 39 39 40 41 41 42 42 43 43 45 45 46 46 47 48 49 49 50 0 5 2 4 5 8 9 11 12 10 13 14 15 16 18 19 21 21 22 24 25 26 27 28 29 27 30 30 32 33 35
13 14 14 14 14 15 15 14 15 15 16 15 16 17 16 17 16 17 18 18 17 19 18 19 0 2 12 13 2 2 3 3 4 3 4 4 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 9 10 10 12
K,' 23 22 23 24 25 24 25 26 26 27 26 28 27 27 28 29 30 30 29 30 32 31 32 32 0 3
3 6 6 8 8 7 9 10 10 11 12 13 15 14 15 17 17 18 19 19 20 18 20 21 22 23 23
obs./HHz
b/kHZ' 0
25420.118 6186.963 11201.196 18843.069 29315.169 7557.189 13359.363
-4 0 2 -3 2 -3
21968.924 33478.795 9108.780
0 1 1
6013.731 25356.950
-3 4
29007.728
-3 -5 2
7230.503 12790.855 8603.613 32920.249 14939.969 12639.041 34104.949 14908.894 6519.972 15259.103 5784.158 14943.891 6919.403 17221.586 10688.646 12152.136 7802.814 19073.953 13301.986 20562.242 14185.752 5232.818 21732.798 14841.045 5428.351 15299.231 5549.116 15587.369 9673.165
23266.443 23690.549 5607.408 9704.181 5613.823 34192.134
obs./HHz
b/kHZ
15535.791
3
5841.953 10468.202
-1 2
6756.810 27318.718 11901.616
-6 -10 8
30171.971 7736.731
-4 1
13417.241 8781.995 33121.370
-1 1 5
36163.900
1
16692.334 6290.905
3 -11
6703.545 16590.182
1 -1
14561.848
0
22535.099 16567.562
3 -3
20024.852
0
14526.119
-2
-1
2 3 2 1 7 1 0 0 1 -4 -4 2 -3 -1 0 -3 -1 -1 3 2 -2 -1 2 0 0 -1 -1 1 1 2 -12 4
MEYER
226
ET AL.
TABLE V--Continued
(a) (CHX)ZCH'~C~ J
36 37 38 39 40 41 42 42 43 44 44 45 46 47 47 50 50
K-
K+
J'
Km'
I(,’
13 13 14 14 13 14 15 14 15 15 16 15 16 17 16 17 18
24 25 25 26 28 28 28 29 29 30 29 31 31 31 32 34 33
36 37 38 39 40 41 42 42 43 44 44 45 46 4-l 47 50 50
12 12 13 13 12 13 14 13 14 14 15 14 15 16 15 16 17
24 25 25 26 28 28 28 29 29 30 29 31 31 31 32 34 33
obs.
/MHz
(CH,)zCH3'Cl a/kHz*
23983.430 15656.608 34401.410 23897.756
-2 2 3 4
9398.907 23684.802 5406.872 15225.200 9202.665 34260.271 5285.253 14911.853 33951.638 8914.473 8721.703 33510.396
-6 0 1 3 0 -2 12 -9 -10 8 2 5
obs./HHz
L/kHz
6574.442
4
28682.373
0
(b)
J 10 2 2 3 3 3 3 3
K-
0 12 0 12 13 2 2
K+
1 2 3
1 2
J' 0 10 111 2 2 2 2 2
K_'
K+'
0
0 1
0 11 12 2 2
2
0 1
(CHz)z'3CH'SCl
(CH3)z"CH"Cl
obs./NHz
obs./HHz
d/kHz
7755.968
5
15189.813 14160.743 22084.212 25062.714 21050.972 24451.236 23267.699
2 -.6 --5 1 5 --3 3
1577.876 14866.899 13864.241 21662.322 24464.917 20632.178 23804.575 22733.412
d/kHz 6 2 -6 1 -3 1 1 0
(c)
J
10 2 2 110 3 3 3 3
K-
0 12 12 13 2 2
K+
1 2
1 2
J'
0 10 111 0 2 2 2 2
Km'
K+'
0
0 1
0 11 12 2 2
0
0 1
"CH,CH'5C1CH~
'~CHSCH~'C~CHS
obs./HHz
obs./MHz
7661.853 14985.263 13959.239 12385.326 24786.921 20748.119 24221.113 22985.356
a/kHz
4 -1 -4 -1 0 0 -2 2
7485.571 14667.731 13666.951 12266.432 24195.359 20328.521 23575.397 22456.519
b/kHz
5 2 -5 -1 1 0 -3 4
THE
MICROWAVE
SPECTRUM
227
OF 2CHLOROPROPANE
TABLE VI of (CH, ),CH 35CI
Stark Effect Measurements E/VCm-
21.79 36.40
50.96
1
J' K_'K+'
J
K-
1 1
10 01
0
0
0
0
0
0
10
0
0
0
12
1
1
1
K+
1
01
0
0
0
2
12
1
1
1
1 2
01 0
2
0 1
0 0
0 1
108.97
2
0
2
1
0
1
145.30
2
0
2
1
0
1
72.61
217.94
254.27
2
2
0
0
2
2
1
1
0
0
1
1
2F
13 5 5 3 3 3 5 5 31 5 5 7 7 7 5 5 3 3 13 5 5 7 7 7 13 5 5 5 5 31 5 5 7 7 31 5 5 5
2F'
3 3 3 3 3 3 3 3 3 5 5 5 3 3 3 3 3 3 5 5 5 3 3 3 3 3 3 5 5 3 3 3
~HF
obs./MHz
1 1 3 1 3 3 3 1 1 1 3 1 3 5 1 3 1 3 1 1 3 1 3 5 1 1 3 1 3 1 1 3 1 3 1 1 3 3
12632.432 7781.591 7781.576 7766.174 7766.210 12644.559 12637.918 12637.864 14202.406 14182.066 14181.918 14197.297 14197.348 14197.441 7781.666 7781.640 7766.219 7766.286 7793.926 14182.318 14182.018 14197.413 14197.518 14197.697 7794.050 15231.705 15231.562 15231.794 15231.479 15214.270 15231.929 15231.364 15230.622 15230.724 15214.156 15232.307 15231.076 15230.883
6/kHz
-8 0 3 15 11 -1 -4 0 -6 3 -4 3 2 -1 0 2 13 10 13 -4 4 1 0 -5 14 -1 0 2 0 -3 -4 1 5 6 -3 -9 -11 6
kJ/mol. The larger value Z, = 3.222 amu A2 of Table XII is a consequence of the longer CH bond lengths obtained in our structure determination. V, from the internal rotation analyses is in good agreement with the effective barrier I’,@= 16.5 kJ/mol determined by Durig and Guirgis ( 4). STRUCTURE
The structure of 2-chloropropane has been determined from the measured ground state (g.s.) rotational constants by all currently available methods. ro-Derived Methods The g.s. moments of inertia for an isotopomer i in a substitution data set (SDS) of N isotopomers are
228
MEYER ET AL. TABLE VII Hyper!ine Splittings in the Rotational Transitions of (CH3)2CH35C1in Excited Torsional States with Unresolved Torsional Fine Structure= q-2
q-1
J
K-
K+
J’
K-’
K+’
2F
11
2
5 3 13 7 5 31 5 11 7 5 31 5 3 7 5 5 3 9 7 5 9 7 5 5 3
0
2
1
2
1
3
0
3
2
10
a)
see
2P’
footnotes
of
Table
3 3
ref.
/HHZ
SPl.
/WHZ
12622.248 -6.701 5.336 15207.692 -0.893 16.430 14.493 1.951 16897.091 15.381 -2.880 8.684 9.173 14175.707 15.366
5 3 5 5 3 5 3 5 3 5 3 7 5 3 7 5 3 3 3
10.597 22102.181 -0.986 3.084 24500.716 16.365 5.147
ref.
/WHz
spl. /MHz
d/kHz
12606.717 9
17 3 9 -8 2 -6 7 -1 0 9
-2
5.362 15207.896 -0.895 16.434 14.496 1.964 16901.973 15.370 -2.892 8.680 9.163 14176.071 15.380 6.704 10.584
4 -21 -8 -10
24512.500 16.367 5.138
7769.432
15.361
7755.351
14
IVa.
TABLE VIII Hypothetical Unsplit Frequencies of the Rotational Transitions of (CH,),CH ‘?I in Excited Torsional States with Unresolved Torsional Fine Structure
qJ
K-
10
110 2 2 2 3 3 3 3 7 9
a)
K+ 1
0 11 12 0 2 13 2 3 4
see
2
3 1 2 4 6
footnote
J'
K_'
K+'
0 0
0 0 1
0 2 12 2 3 3
2 0
0 0 10 110 111 2 2 2 2 7 9
of
1 5 6
Table
obs. /HHz 1766.364 12623.596 15206.630 16893.271 14172.059 22101.813 24495.947 21073.794 23298.849 6953.159 14966.504
Va.
q-2
1 &/kHz 6 3 -7 -4 5 -5 3 4 1 0 0
obs./HHz
b/kHz
7767.653 12608.057 15206.831 16898.160 14172.421
-11 1 -1 -2 11
24507.735 21073.060
2 -4
229
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE IX Spectroscopic Parameters of ( CH3)?CH 35ClObtained from the Lines with Unresolved Torsional Fine Structure”
A
/MHZ
8060.114
(7)
8042.790
(9)
B
/MHZ
4563.503
(2)
4565.288
(3)
C
/MHZ
3202.861
(2)
3202.381
(3)
*J
/kHz
1.66
(13)
1.29
(17)
*J.
/kHz
2.72
(54)
[2.72]
6.l
/kHz
0.346
(84)
[0.346]
6K
/kHz
5.12
(83)
(5.121
Xae
/MHz
-61.500
(15)
-61.509
(13)
Xt,t,/MHz
34.733
(19)
34.701
(16)
Xc,
26.767
(19)
26.808
(16)
/MHz
a)
see
footnotes
of Table
pO,R= Z!,;(structure)
+ tg)
I.
(g = a, b, c; i = 1,. . . , N)
The equilibrium moments Zif$ are known functions of the bond distances and angles, but the rovibrational (rovib) contributions cf’ are not known. If the latter are completely neglected, E:) = 0, the system of 3N Eqs. (2) can be linearized and leastsquares (lsq) solved to obtain the ro-structure. Basically, internal coordinates are determined. Since the lsq process is iterated to convergence, Cartesian coordinates in the principal axis system (PAS) of the parent (i = 1)) that satisfy the first and second moment conditions, are also available. All independent internal coordinates must be given initial values, or fixed values if the number 3N for the particular SDS is not large enough for a stable lsq determination of all coordinates. The ro-structure does not depend on the type of quantity fitted (rotational constants B, moments of inertia I, or planar moments P) provided the covariance matrices of the respective quantities are related by the proper transformations (16). This may be expressed symbolically as r. = rB = rI = rp. If isotopic differences are fitted, e.g., AZbfL= Zbfb- Zbtj (i = 2, . . . ) N), it is found, however, that rm # rN (= rhp) and that both structures are different also from the ro-structure. A better approximation for the cg’ than completely neglecting them may be achieved by introducing three isotope-independent constants Q. Lsq fits that have determined the internal coordinates plus three 4 have confirmed that the tg have indeed the order of magnitude expected for rovibrational contributions ( Z7). It can be shown that the rl,e-structure obtained is identical with the rM -structure ( 16) but the three additional Q determined make for a better reproduction of the original ZgL as well as for a better prediction of the rotational constants of new isotopomers.
230
MEYER ET AL.
0
27/2 23/2
13771.7
13768.4 A AE,EA
q
EE
MHz
OAA
FIG. I. Torsional fine and nuclear quadrupole hyperfme structure of the rotational transition JK_-K+ SK_,,. = 1358-I359of (CH,)#ZH ‘%l in the excited torsional state g = 2. Recording conditions: Temperature 200 K, pressure 0.07 Pa, sample interval 20 ns, 1K data points, extended with 3K zeros prior to FFT, 2 X lo6 experiment cycles.
r,-Derived Methods
Kraitchman’s equations ( 18) and subsequent extensions ( 19, 20) are based on the fact that the planar inertial moment tensor of an isotopomer i can be expressed with the aid of the principal planar moments of the parent and the Cartesian coordinates of the atom substituted in the particular isotopomer. Kraitchman’s equations must be separately applied to singly substituted isotopomers (plus the parent) to obtain a partial or complete substitution (TV-)structure. Typke ( 19) has shown how the system of separate equations, including even equations for additional and multiply substituted isotopomers, can be linearized and arranged into a lsq system to obtain an r,-structure from an iterative fit to the planar moments of a sufficiently large SDS of isotopomers. In the limit where the number of equations equals the number of coordinates to be determined, the resulting structure is identical with the results from Kraitchman’s separate equations. Typke’s fitting method shows the characteristic features of a true r,-treatment: (a) for an incomplete SDS unsubstituted atomic positions do not affect the results and (b) in the case of a complete SDS the rs-coordinates do not necessarily satisfy the first and second moment conditions (except by symmetry). However, these conditions can be introduced as constraints into the lsq formalism. If they are, their effect is a more profound change than a mere shift of the origin and the axes. One difference remains: The r&it diverges where Kraitchman’s equations would yield an “imaginary” coordinate. To avoid this complication where it would appear only on formal grounds, the out-of-plane coordinate of a substituted atom known to lie on a molecular symmetry plane is generally preassigned as zero. This means that the principal planar moment component P bf’gof the particular isotopomer i for the
THE
MICROWAVE
SPECTRUM
OF 2-CHLOROPROPANE
231
axis g perpendicular to the symmetry plane is effectively removed from the input data set to the fit. It is worth mentioning that the results of an rs-fit, when the first and second moment constraints are applied, are very nearly identical (including errors and correlations) with the corresponding r1,6-structure (or the identical rM- or rMstructures), provided the Pbfb that are missing from the r, -fit due to substitutions on symmetry planes have also been omitted from the To-derived fits. Berry and Harmony (21) have recently proposed the r&-structure which is an r,derived concept. From a minimum but complete SDS the r,-structure of the molecule is calculated by Kraitchman’s equations and from this the substitution moments of inertia of the parent, I,,(l) . By means of three scaling factors, pg = Z&),l$~, the set of scaled moments, I$; = (2p, - 1) - Ibfb , is generated for all isotopomers i of the SDS. The &structure is then obtained from an r&t to these I$$. The rP,-structure has, in general, shorter bond lengths and is believed to approximate the unknown equilibrium structure better than the r,-structure does. Structure of 2-Chloropropane
The following structure calculations are based on the six isotopomers measured or remeasured recently, Tables I and III, plus five deuterated species measured very much earlier by Tobiason and Schwendeman ( 1) . We have reevaluated the published line frequencies of the deuterated species by asymmetric rotor fits including fourth order centrifugal distortion. We have obtained from the fits A, B, C, and, with greatly reduced significance, also the distortion constant A,, Table XIII. Due to the limited range of transitions available, the remaining distortion constants, AJK, AK, 6~and 6K, were transferred from the parent isotopomer and allowed to be in error by 50%. The resulting errors of A, B, C, and A, are included in the errors given in Table XIII. The experimental errors of the rotational constants of the two groups of isotopomers included in the present investigation, Tables I, III, and XIII, are extremely different. Unfortunately, the high precision of part of the data cannot be fully utilized for the structure determination by present methods, because the systematic (nonrandom) error of the moments of inertia due to the rovib interaction, that remains even after (crude, isotope-independent) rovib contributions have been subtracted, limits the useful accuracy. Costain (22) has derived a popular estimate for the precision of Kraitchman determined r,-coordinates from the observation that the g.s. difference Pt[l - Pbf: does, in general, not vanish for a substitution on a molecular symmetry plane x, y, as does the difference for the corresponding equilibrium quantities. The nonvanishing g.s. difference is usually found in a certain range which has been more closely investigated by van Eijck (23). A rough estimate is 6( pb’.; - Pb!f) N + 0.003 u A2 which obviously still holds after an isotope-independent f(G + 6-v- ez), has been subtracted from both, P$ notation of Eq. (2), G(P!“(structure)
- P!“(structure))
part of the rovib contribution, and Pi!:, which gives, in the N 0.003 u A’.
If it is assumed that the subtraction of this unknown but presumably large part of the rovib contributions removes most of the systematic error correlation between Pii) (structure) and P!_” (structure), and further that the systematic error is of the same
232
MEYER
ET AL.
TABLE Rotational
Transitions
of ( CHS)*CH “Cl in Excited Torsional Torsional
J
K-
K+
J’
K-’
X
K+’
2F
States with Resolved
Fine Structure 2F’
G’
obs. /HHz q-1
7
9
2
3
5
6
2
7
9
6
3
7
17
17
15
15
13
13
11
11
21
21
19
19
17
17
AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA
EE
10
10
11
3
4
4
7
6
7
10
10
11
3
4
4
8
7
8
15
15
23
23
21
21
19
19
17
17
21
21
19
19
25
25
23
23
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE
19515.167 19515.200 19515.230 19513.034 19513.068 19513.098 19513.474 19513.503 19513.536 19515.603 19515.634 19515.666 18488.501 18488.540 18488.579 18485.893 18485.933 18485.974 18486.306 18486.345 18486.384 18488.904 18488.944 18488.983
16375.503 16375.550 16375.596 16372.861 16372.906
obs.
/HHz
q-2 19574.346 19574.388 19574.429 19572.215 19572.256 19572.296 19572.657 19572.695 19572.737 19574.829 19574.870 19574.913 18596.578 18596.627 18596.674 18593.963 18594.012 18594.062 18594.379 18594.430 18594.477 18596.988 18597.035 18597.083 25832.144 25832.205 25832.265 25829.938 25829.997 25830.055 25830.255 25830.316 25830.371 25832.459 25832.518 25832.578 10246.766 10246.805 10246.847 10247.107 10247.154 10247.198 16531.887 16531.944 16532.001 16529.227 16529.285
a) symmetry species of the group C5 x C~V (5)
order of magnitude for g = a, b, c and for any isotopomer i, we conclude that the functions actually evaluated for the structure may be afflicted by a systematic error of the order 6P(‘) g (structure) = 0.003 u A2 or (if factors VT are neglected) 61:)
THE MICROWAVE
SPECTRUM
233
OF 2CHLOROPROPANE
TABLE X-Continued J
12
K-
K+
8
J'
12
K-'
K+'
9
2F
2F'
21
21
19
19
27
27
G EA,AE AA EE EA,AE AA EE EA,AE AA EE
12
13
7
8
12
13
8
9
25
25
23
23
21
21
27
27
25
25
23
23
21
21
29
29
27
27
25
25
23
23
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE
14
14
9
8
14
14
10
9
31
31
7‘I
29
27
27
25
25
31
31
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA El EA,AE AA EE
obs./HHz
obs./HHz
16372.952 16373.206 16373.253 16373.300 16375.847 16375.893 16375.939 23837.981 23838.039 23838.098 23835.444 23835.499 23835.560 23835.748 23835.807 23835.865 23838.282 23838.340 23838.399 7869.049 7869.083 7869.117 7867.063 7867.098 7867.131 7867,308 7867.342 7867.377 7869.278 7869.312 7869.344 13577.255 13577.304 13577.354 13574.847 13574.896 13574.944 13575.114 13575.163 13575.213 13577.516 13577.566 13577.615 20898.235 20898.301 20898.367 20895.663 20895.729 20895.797 20895.931 20895.996 20896.064 20898.497 20898.562 20898.629 5712.761 5712.793
16529.342 16529.576 16529.634 16529.691 16532.231 16532.288 16532.348 24017.314 24017.381 24017.453 24014.767 24014.838 24014.909 24015.074 24015.145 24015.216 24017.612 24017.684 24017.756
13771.056 13771.118 13771.181 13768.624 13768.688 13768.750 13768.895 13768.957 13769.021 13771.321 13771.384 13171.446 21137.949 21138.037 21138.119 21135.356 21135.443 21135.529 21135.631 21135.715 21135.804 21138.216 21138.303 21138.386
MEYER
234
ET AL.
TABLE X-Continued J
15
12
K-
K+
9
8
J'
15
12
K-'
K+'
10
8
2P
2F'
29
29
27
27
25
25
33
33
31
3l-
29
29
21
21
25
25
23
23
G EA,AE AA EE EA,AE
AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA
obs./HHz 5112.825 5111.308 5711.340 5711.370 5712.461 5711.492 5711.524 5112.910 5112.941 5712.970 10545.112 10545.221 10545.274 10543.111 10543.219 10543.271 10543.363 10543.416 10543.460 10545.358 10545.412 10545.462
EE
14
16
10
11
14
16
10
11
31
31
29
29
27
21
25
25
35
35
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE AA EE
33
33
31
31
29
29
EA,AE AA EE EA,AE AA EE EA,AE AA EE EA,AE
obs./MHz
10756.065 10756.126 10756.189. 10154.036 10154.095 10754.160 10754.230 10754.292 10754.354 10156.259 10756.320 10756.382 16997.983 16991.938 16997.899 16997.493 16997.449 16991.405
7838.142 7838.111 7838.080 1840.369 7840.340 7840.308 7840.142 7840.108 1840.018 7837.914 7831.883 7837.852 13044.009 13043.949 13043.890
13046.756 13046.702 13046.641 13046.512 13046.448 13046.389 13043.763 13043.708 13043.647
235
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE XI
Averaged Internal Rotation Splittings Relative to the AA Component of the Rotational Transitions of (CH3)&H3%l in Excited Torsional States J'
K_'
K+
9
5
7
2
6
3
6
9
3
7
10
3
7
10
3
8
10
4
6
10
4
7
11
4
7
11
4
8
12
4
8
12
4
9
12
5
7
12
5
8
13
5
8
13
5
9
14
5
9
14
5
10
14
6
8
14
6
9
15
6
9
15
6
10
12
5
8
12
4
8
14
5
10
14
4
10
16
6
11
16
5
11
1 1 2 2 1 1 2 2 2 2 2 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 1 2 2 2 2 1 1 2 2
J
K-
K+
7
2
9
G
EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE EE EA,AE
split./kHz
-32 -63 -41 -82 -40 -79 -49 -97 -60 -118 -43 -86 -46 -93 -58 -115 -58 -117 -70 -142 -34 -68 -49 -99 -62 -126 -66 -133 -87 -172 -31 -62 -51 -101 -61 -124 45 86 31 62 58 118
b/kHz
1 3 -2 -5 1 4 0 0 -1 0 -2 -4 2 4 -1 -1 2 4 1 1 1 3 3 6 0 -2 2 4 -6 -9 1 2 1 3 0 -1 2 0 -1 -1 -1 0
(structure) x 0.003 u A2. For 2-chloropropane the ensuing limits of useful accuracy of the rotational constants are then &4 = 0.4 MHz, 6B x 0.15 MHz, and 6C = 0.06 MHz. Most of the gs. rotational constants in the present work were measured with much higher precision, but in view of the contamination by a large systematic error it would be unwise to use the reciprocal squares of the experimental errors as relative weights in a weighted fit, which is the proper procedure if the errors are purely random. This line of reasoning is supported by a preliminary rr,,-fit to the moments of inertia which were assumed equally weighted and uncorrelated. The standard deviation obtained was 0.0046 u A2 which agrees well with the above estimate.
236
MEYER ET AL. TABLE XII Internal Rotation Parameters of 2-Chloropropanea Fit 1 V3
/kJ mol-1
VlZ'
b
Pit 2
16.428 (10)
16.437 (12)
/kJ mol-1
-0.762 (15)
-0.773 (17)
I.
/amu A'
[3.222]
[3.222]
La,i
/"
(63.761
63.98
Lb,i
/o
[34.42]
[34.42]
Lc,i
/a
[69.38]
69.11
F
/GHz
(162.121
162.15 (10)
F'
/GHz
[-1.211
-1.18 (10)
s
112.86
L i,i'cP
1111.21
zi;d /kHz 0
(10)
/kHz
111.2
77
3
3
see footnotes of Table I.
b)
1 cal
(81)
112.94 (10)
77
a)
(81)
(9)
= 4.184 J.
C) angle between internal rotation axes. d)
mean experimental
splitting.
In the attempt to account for the systematic error a little less crudely than by equal weights for all input moments of inertia, we have created a new covariance matrix for the 1::. The original covariance matrix reflects the experimental errors of the moments of all isotopomers of the SDS and the correlations within each isotopomer resulting from the evaluation of the moments from the particular selection of transition frequencies. We have added to all diagonal elements the square of half of the standard deviation of the equally weighted fit, (0.0023 u A2)2. The covariance matrix remains block-diagonal. The ratio of the largest to the smallest error of the moments of inertia, which is roughly 300 for the experimental errors, was thus reduced to 1.5, approximating an almost equally weighted fit with greatly reduced correlations. In effect, this modified covariance matrix is the result of an error model which tries to simulate systematic error by appropriately chosen random errors. We have used this covariance matrix of the moments, properly transformed into that of the rotational constants where required, for all structure calculations in this work. Table XIV shows that the
THE MICROWAVE
SPECTRUM
OF 2CHLOROPROPANE
237
TABLE XIII Re-evaluation of Rotational Constants for Deuterated Isotopomers of 2-Chloropropane CH3CHCICHZD,
(CH,hCClD
A 0
7512.836 (141) MHz 4548.310 (22) MHz
A B
7793.188 (54) MHZ 4470.088 (21) MHz
C
3107.775
C
*J Ll
1.543 (691) 0.099
3201.698 (26) MHz 2.174(1355) kHz 0.076 MHz
(19)
MHz kHz MHz
*J 0
CH&HClCH2D8
CD$DClCH,
A B
A B C
C *J
7876.693 (198) MHz 4370.185 (22) MHz 3079.685 (22) MHz 1.407 (748) kHz
u
0.100
MHz
*1 0
6869.241(374) MHz 4152.573 (27) MHz 2938.541 (69) MHz 1.172 (942) kHz MHz u.115
CH3CHClCH2D, A B C *J (T
7693.578 (165) 4461.681 (22) 3148.847 (21) 0.109 (705) 0.091
MHz MHz MHz kHz MHz
By Asymmetric Rotor Fit from Transitions of Tobiason and Schwendeman (lJ, Centrifugal Parameters AfK, AK, 6,, and 6~ Transferred from Table I with a 50% Allowance of Error.
different fitting methods employed all yield (relative) standard deviations u near unity which indicates that this error model is basically useful. We have applied “Laurie corrections” for a C-H bond length decrease of 0.003 A upon H + D substitution. This can be easily included in the routine for the ro-type methods and somewhat less directly implemented by a preprocessing routine for the r,-type calculations, provided an approximate structure is known. The structures are compared in Tables XIV and XV on the basis of internal and Cartesian coordinates, respectively. The numbering of the atoms is that of Ref. ( 1). For the r,-type methods the internal coordinates and their errors were calculated from the Cartesian coordinates including error propagation by the appropriate transformation of the covariance matrix of the Cartesian coordinates. The ro-structure in column 1 of Tables XIV and XV is listed only for completeness. The rr,,- and r,-structures of columns 2 and 5, respectively, differ significantly only in those bond lengths that involve the central carbon atom C,,,. Inspection shows that this atom appears shifted by 0.0082 A between the two structures, much more than any other atom. The expression introduced by Costain and discussed above gives for the 13Cct, substitution Po,~( 13Cct,) - PO,b(parent) = -0.0072 u A’, which is 2.5 times larger in magnitude than the rough estimate used previously and even 5 times larger than the more specific mean evaluated by van Eijck (23) from a large number of planar “C + 13C substitutions. The rovib contributions obviously change for the
238
MEYER
ET
TABLE Structure of 2-Chloropropane Type of Fit
XIV
in Internal Coordinates
Q,C @)
;a",
AL.
by Six Fitting Methods
rs(+)
rr,c(-) (a
(d)
21
f 0 33
t Equations
33
33
29
29
26
# Variables
IS
18
18
18
18
15
1.905
1.416
1.470
0.712
2.398
relative
e of Fit
2.777
Bond Lengths (A) 1.5202
(14) 1.5196
(24) 1.5210
(19) 1.5212
(20) 1.5231
(21) 1.5176
1.8039
(23) 1.8006
(18) 1.8026
(15) 1.8026
(15) 1.7973
(18) 1.7964
(40)
1.1050
(21) 1.1023
(37) 1.0973
(30) 1.0974
(31) 1.0957
(16) 1.0933
(42)
1.0954
(49) 1.0988
(37) 1.1000
(28) 1.0999
(28) 1.0972
(24) 1.0919
(71)
1.0948
(49) 1.0971
(35) 1.0988
(26) 1.0988
(27) 1.0998
(21) 1.0989
(57)
1.0999
(36) 1.0987
(29) 1.0969
(22) 1.0967
(23) 1.1003
(52) 1.0908
(41)
113.31
(16) 112.88
(29) 112.64
(23) 112.67
(23) 112.62
(26)
112.52
(35)
104.83
(30) 105.02
(27)
(20) 105.07
(21) 105.37
(21)
105.43
(35)
Bond Angles
105.10
(38)
(“)
109.40
( 9) 109.41
(13) 109.21
(11) 109.20
(11) 109.33
(12)
109.28
(15)
111.09
(39) 110.86
(34) 110.67
(25) 110.67
(26) 110.75
(28)
110.73
(55)
109.55
(52) 109.49
(40) 109.24
(30) 109.22
(31) 109.43
(25)
108.71
(56)
109.41
(14) 109.66
(20) 109.92
(16) 109.92
(17) 109.82
(22) 109.87
(25)
Torsional
Angles
(“)
CendCctrCendHol 179.08 (49) 179.18 (33) 179.10 (25) 179.09 (25) 179.17 (14) 178.98 (47) CendCetrCendH~ -59.93 (90) -60.51 (78) -61.12(59) -61.14(60)-60.69 (62) -61.78 (106) CendCctrCendH~
59.43(26) Rovib
59.45 (26) 59.09 (21)
59.08 (22)
(isotope-independent,
Contributions
59.22 (26)
59.04 (29)
ud’)
%
0.0
0.214 (95)
0.199 (90)
n.a.
na.
0.0
s,
0.0
0.139 (88)
0.708 (73)
na.
n.a.
0.0
s.9
0.0
0.437 (91)
0.492 (81)
n.a.
na.
0.0
Types of Fit (to
11 Isotopomers
for (a) through (e)):
(a) ra Fit @)
rr,+ (= rp,E) Fit Fit less four Planar
(cl rI E
(d) ri Fit plus three
Moments
P, for Substitutions
1st and 2nd Moment
Conditions
on the a,c Plane
(for a, c, and ac)
(e) rs Fit (f) r”, Structure:
All
Errors
Laurie
Kraitchman’s Equations (from 8 Species) + Scaling by p (for 11 Species) + ra Fit to Scaled Moments (of 11 Species).
1 o.
Corrections
of -0.003
A
Applied
upon
H +
D Substitution
THE MICROWAVE
SPECTRUM
239
OF 2-CHLOROPROPANE
TABLE XV Structure of 2Chloropropane Type Fit
r,,
in Cartesian Coordinates by Six Fitting Methods r&+)
G (0
(a)
rI,E @)
*I,&-) (c)
# Eqs
33
33
29
29
26
# Var
15
18
18
18
18
1.905
1.416
1.470
rel. B
2.777
(d)
0.712
33 15 2.398
Coordinates a (A) C CFk
0.5201 (22)
0.5173(17)
0.5181(13)
0.5182(14)
0.5121 (12)
0.5154(24)
-1.2293 ( 2) -1.2280 ( 5) -1.2280 ( 4) -1.2279 ( 4) -1.2285 ( 2) -1.2249 (24)
C end
1.1724 ( 8)
1.1720 ( 8)
1.1716 ( 6)
1.1715 ( 7)
1.1693 ( 5)
1.1689 (24)
Hset H,
0.5336 (49) 0.6650 (37)
0.5322 (34) 0.6646 (26)
0.5316 (26) 0.6648 (19)
0.5313 (28) 0.6645 (19)
0.5302 (14) 0.6638 ( 9)
0.5356 (49) 0.6656 (50)
H0
2.2247 (13)
2.2244 (10)
2.2245 ( 7)
2.2243 ( 7)
2.2241 ( 3)
2.2173 (46)
H,
1.1148 (23)
1.1144 (16)
1.1146 (12)
1.1144 (13)
1.1140 ( 6)
1.1132 (35)
C end H,
1.2699 ( 3) 2.1610 (13)
1.2662 (12) 2.1599 ( 9)
1.2661 (12) 2.1596 ( 8)
1.2672 ( 6) 2.1597 ( 4)
1.2619 (28) 2.1505 (45)
Coordinates lb\ (A) 1.2656 (12) 2.1594 ( 8)
HE
1.2918 (25)
1.2899 (19)
1.2891 (16)
1.2895 (15)
1.2898 ( 7)
1.2817 (40)
H,
1.2853 (23)
1.2836 (16)
1.2829 (14)
1.2833 (13)
1.2837 ( 7)
1.2771 (36)
Coordinates c C cti Cl C end
(A)
-0.3948 (16) -0.3973 (37) -0.4020 (30) -0.4020 (31) -0.4037 (16) -0.4003 (37) 0.0454 ( 6) 0.0456 ( 5) 0.0460 ( 4) 0.0460 ( 4) 0.0440 (62) 0.0454 ( 5) 0.1276 (16)
0.1291 (21)
0.1312 (16)
0.1312 (16)
0.1274 (53)
0.1321 (29)
Hsee H,
-1.4998 (17) -1.4995 (12) -1.4993 ( 9) -1.4992 (10) -1.4993 ( 5) -1.4933 (33) -0.2578 (115)-0.2600 (79) -0.2614 (59) -0.2615 (60) -0.2619 (29) -0.2545 (133)
HB
-0.1735 (171)-0.1799
H,
1.2259 (24)
(119)-0.1822
1.2262 (16)
(87) -0.1824 (88) -0.1828 (43) -0.1969 (160)
1.2265 (12)
1.2263 (13)
1.2262 ( 6)
1.2214 (33)
Footnotes see Table XIV.
present 13Cct,substitution too much to be approximated by isotope-independent constants, and the inherently different ri,6- and r,-methods arrive at a larger than usual difference in position. In contrast, the position of the chlorine atom is remarkably stable despite its very small c coordinate which would usually be deemed too small for a safe determination by Kraitchman’s equations. For this substitution the planar moment difference P0,b(37C1)- P,,b(parent) = 0.0007 u A*, which is less than the respective mean value from van Eijck’s statistics (23). The same is true for the difference PO,J D,,) - &,(parent) = 0.0028 u A*. For the rr,c-structures of Table XIV the three rovib constants cg are also given. Although they could be obtained only with little precision from the limited SDS, the accuracy of the structural parameters is not impaired, it is better (rms) than for the ro-structure. The structures listed in columns 3 and 4 of Tables XIV and XV agree very closely, the coordinates as well as the errors, although they have been obtained by basically different methods. As discussed above, the inputs have been made strictly identical
240
MEYER
ET AL.
by removing the planar moments PO,6for the substitutions on the a,c plane also from the input to the r,,,-fit, and the output coordinates have been made physically equivalent PAS coordinates by imposing the three nontrivial first and second moment conditions on the r,-fit. The number of degrees of freedom is the same for both lsq treatments. Of course, the close coincidence of columns 3 and 4 does not necessarily make this common structure preferable from the standpoint of optimum rovib compensation. The error ranges of the structures listed in the four columns 2 to 5 of Tables XIV and XV touch or overlap within less than 2a, even for the C,,, position. From this we conclude that it is possible to determine a molecular structure from the g.s. rotational constants within a few lop3 A and a few 10-l degrees. This structure is consistent within the framework of the rr,,- (or rM-) and r,-methods and their appropriately modified variants. Due to the lsq treatment, the structure can be more balanced for a sufficiently large SDS. The methods also afford a more direct error assessment than the repeated application of Kraitchman’s separate equations to pairs of isotopomers from a minimum SDS. As stated above, Laurie corrections were employed for the deuterated isotopomers. For the four structures of columns 2 to 5, they result almost exclusively in an increase of the corresponding C-H bond lengths of the parent by twice the amount of the correction with negligible influence on the remaining structure and only a minute change of the standard deviation of the respective fit. For columns 2 to 5 of Table XIV, Laurie corrections could have been applied simply by inspection, if they had not already been accounted for in the fitting routines. This is not true for the rostructure of column’ 1. For the rP,-structure of column 6, the basic r,-structure, the substitution moments Ii.‘,/ of the parent, and the three scaling factors pg have been calculated from the minimum SDS of 8 isotopomers by Kraitchman’s equations, retaining also the squares of nonvanishing out-of-plane coordinates for planar substitutions, even if negative (for C,,) . The input data had been properly preprocessed for the H --f D corrections, and the errors were propagated from the modified covariance matrix constructed as described above. The scaling factors with errors and correlations are Pa
0.993833 (2654)
1BOO0
Pb
0.9973 11( 1504)
0.0027
PC
0.995642( 1055)
-0.0006
1.OOOO -0.05 12
1.OOOO.
The moments of inertia of the complete SDS of all available 11 isotopomers were appropriately scaled. The set of the resulting Z$ served as input to an ro-fit with a general (i.e., nondiagonal)weight matrix for which the inverse of the covariance matrix of the Zdi) was used. This covariance matrix is very different from the one created Cl” for the Zo,gwhich was discussed above and used wherever the Zbf; (or the corresponding rotational constants) were required. Since the errors of the Z$ are dominated by those of the scaling factors pg which are common to $1 isotopomers, the correlations p(i) for different i are very high, sepbetween corresponding moment components Zm,g) arately for each g. The highest correlation coefficient found was 0.99996. The covariance matrix is nonetheless positive definite, and the iterative lsq ro-fit converged rapidly. The standard deviation of this fit and also the errors of the structural parameters
241
THE MICROWAVE SPECTRUM OF 2-CHLOROPROPANE TABLE XVI Structure of 2-Chloropropane in Internal Coordinates by Weighted Average of Three Methods” Bond Anales P)
Bond Lengths t&
Cend%
Torsional
An&s
P)
1.521 (4)
cend%rcend
112.7 (5)
Cend%r(&ndHa
1.801 (3)
Cl GtrHsee
105.2 (5)
Cend%rCcndb
179.2 (5) -60.8 (13)
1.097 1.098 1.099 1.098
cendcctrcl CendCct&,c ‘%rCendH, %&&i
109.3 110.0 110.7 109.4
Ccnd%rCendH~
59.2 (5)
%&n&
109.8 (4)
(6) (6) (5) (7)
(2) (4) (6) (6)
For the purpose of comparing the torsional angles with those of (ZJ, the torsional angles with respect to the chlorine atom are cl %&nd%
57.5 (8)
cl %&&
177.4 (10)
c’ Cc&endH~
-62.5
(4)
a The methods are r,,, (column 2 of Table XIV), r, (column 5 of Table XIV), and modified r,,or modified r, (column 3 or 4 of Table XIV). Laurie corrections of -0.003 A were applied upon H + D substitution. Error shown is twice the mean error of the columns cited.
are of the same order of magnitude as for the original ro-fit of column 1. In agreement with the intention of the method, the r&-structure appears contracted, though not uniformly. For lack of comparable information it cannot be further commented upon. We give in Table XVI as the final structure of 2-chloropropane determined in this work the weighted average of columns 2,5, and 3 of Table XIV. It is hence composed from the r,,c-structure, the fitted r,-structure, and the common structure derived from both, and is stated with errors that are twice the mean errors of these columns. The structures included lie all well within this error range. If the bond length increase of the C-H bonds by 0.006 A due to the Laurie corrections of -0.003 A is taken into account, the structure is very similar to the structures reported by Tobiason and Schwendeman ( 1) and by Ikeda et al. (2), though with a lower error margin. The bond angle UC,,,, Cend, H,) is significantly larger, approximately lo, than the corresponding bond angles for the atoms H, and H,, as noted already by the former authors. We find no significant C-H bond length differences. The methyl groups are rigidly rotated, by a significant angle of a little less than lo, such that the H, atoms move out of the plane ( Cend, C,, Cend) and tend to approach the chlorine atom. ACKNOWLEDGMENTS Financial support by the Deutsche Forschungsgemeinschaft, Fonds der Chemie, and the Land SchleswigHolstein is gratefully acknowledged. Dr. W. Stahl assisted us in the Stark effect measurements. The calculations were carried out at the computer centers of the Kiel and Ulm universities. RECEIVED:
August 6, 199 1 REFERENCES
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242
MEYER ET AL.
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