J. Phys. Chem. A 2010, 114, 9289–9299
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Microwave, Raman, and Infrared Spectra; Adjusted r0 Structural Parameters; Conformational Stability; and Vibrational Assignment of Germylcyclohexane† James R. Durig,*,‡ Rachel M. Ward,‡ Andrew R. Conrad,§ Michael J. Tubergen,§ and Gamil A. Guirgis| Department of Chemistry, UniVersity of MissourisKansas City, Kansas City, Missouri 64110, Department of Chemistry, Kent State UniVersity, Kent, Ohio 44242, and Department of Chemistry and Biochemistry, College of Charleston, Charleston, South Carolina 29424 ReceiVed: May 8, 2010; ReVised Manuscript ReceiVed: June 30, 2010
The FT-microwave spectrum of germylcyclohexane, c-C6H11GeH3, has been recorded, and more than 40 transitions for the 70Ge, 72Ge, and 74Ge isotopomers (isotopologues) have been assigned for the chair-equatorial conformer. The heavy atom adjusted r0 structural parameters have been determined [distances, Cγ-Cδ ) 1.533(3) Å, Cγ-Cβ ) 1.532(3) Å, CR-Cβ ) 1.540(3) Å, CR-Ge ) 1.957(3) Å; angles, ∠CγCδCβ ) 111.2(5)°, ∠GeCRCβ ) 111.1(5)°, with the dihedral angle ∠CγCδCβCR ) 55.6(10)°]. Raman and/or infrared spectra of gas, liquid, and solid germylcyclohexane have been recorded. The temperature dependency of the Raman spectrum of the conformer pair 712 (equatorial)/683 (axial) cm-1 gives an enthalpy difference of 453 ( 38 cm-1 (1.30 ( 0.11 kcal/mol) with the chair-equatorial conformer the more stable form. At ambient temperature, the abundance of the axial conformer is 11 ( 1%. Substituent effects on the enthalpy difference and structure of monosubstituted cyclohexanes are discussed for a number of molecules. Introduction There have been several studies of the conformational preferences of monosubstituted cyclohexanes, c-C6H11X, in the last two decades, and many of these molecules (X ) F, Cl, Br, CH3, SiH3) were found to exist as chair-equatorial and chair-axial conformers in the gaseous and liquid states. Extensive results have been reported on the determination of the conformational enthalpy of these compounds by utilizing a variety of techniques, such as NMR, electron diffraction, microwave,1–6 infrared,5–8 and Raman5,9,10 spectroscopies, along with theoretical predictions from molecular mechanics11,12 and ab initio5–10 calculations. For some of these molecules there are very large variations in the values, with several reported results with no estimated experimental uncertainties. Thus, it is difficult to compare enthalpy values for the conformational interchanges of the chair-equatorial to chair-axial forms for most of them, because of the many values reported. As a continuation of our earlier studies of silylcyclohexane,9 where we obtained excellent agreement with the ∆H obtained from Raman data of the liquid with the ab initio MP2 predicted values, we became interested in germylcyclohexane, where the conformational energy difference has been predicted12 to be 420 cm-1 from force field calculations with the chair-equatorial conformer being the more stable form. This value is 105 cm-1 less than the predicted energy difference between the two conformers of silylcyclohexane (525 cm-1), which is in agreement with the experimentally determined enthalpy difference of 520 ( 70 cm-1 for the silane in the liquid state. Thus, we initiated a conformational investigation of germylcyclohexane by utilizing variable-tem† Taken in part from the theses of R.M.W. and A.R.C., which will be submitted in partial fulfillment for a Ph.D. degree. * Corresponding author. Phone: 01 816-235-6038, Fax: 01 816-235-2290. E-mail:
[email protected]. ‡ University of MissourisKansas City. § Kent State University. | College of Charleston.
perature Raman studies along with infrared studies of xenon solutions. Additionally, we were interested in the structural parameters for comparison to those of cyclohexane, which we have obtained13 by adjusting ab initio predicted parameters with microwave-determined rotational constants. To support the vibrational study, we have carried out ab initio calculations at the MP2 level with full electron correlation by the perturbation method14 utilizing a variety of basis sets. We found in the conformational investigation of chlorocyclohexane that the predicted relative stabilities did not vary significantly with the size of the basis set, particularly with the inclusion of diffuse functions. We also carried out density functional theory (DFT) calculations by the B3LYP method with the corresponding basis sets used for the MP2 calculations. We have calculated the optimized geometries, conformational stabilities, harmonic force fields, infrared intensities, and Raman activities. Additionally, we have utilized the ab initio predicted force constants to obtain the centrifugal distortion constants for comparison to the experimental values from the microwave data. The results of these spectroscopic and theoretical studies are reported herein. Experiment and Quantum Chemical Calculation The germylcyclohexane sample was prepared as follows. A Grignard reagent prepared from cyclohexyl bromide in dry diethyl ether was added slowly to ice-cold germanium tetrachloride in dry diethyl ether to yield cyclohexyltrichlorogermane (CHTG). The resulting cyclohexyltrichlorogermane was reduced to germylcyclohexane with LiAlH4 in dry diethyl ether. The compound was purified by a low-temperature, low-pressure fractionation column, and the purity of the sample was verified by comparing the infrared spectrum with the predicted spectrum. Microwave spectra of germylcyclohexane were recorded usinga“minicavity”Fourier-transformmicrowavespectrometer15,16 at Kent State University. The Fabry-Perot resonant cavity is established by two 7.5-in. diameter diamond-tip-finished alu-
10.1021/jp104207v 2010 American Chemical Society Published on Web 08/03/2010
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minum mirrors with a 30.5-cm spherical radius. The Fabry-Perot cavity resides inside a vacuum chamber formed by a six-way cross and a 15-in. long, 8-in. diameter extension tube. One of the cavity mirrors is formed on an 8-in. diameter vacuum flange and mounted on the six-way cross. The second mirror is mounted on 0.75-in. diameter steel rails that pass through ball bearing brackets mounted inside the extension arm; a motorized micrometer is used to position the movable mirror over a 2-in. range of travel. The two cavity mirrors are nominally separated by 30 cm. The vacuum chamber is pumped by a Varian VHS-6 diffusion pump (2400 L s-1) backed by a two-stage Edwards E2M30 rotary pump. The germylcyclohexane sample was entrained in a 70:30 Ne-He carrier gas mixture at 2 atm and 4 K and expanded into the cavity using a reservoir nozzle16 made from a modified Series-9 general valve. The reservoir nozzle is mounted in a recessed region of the mirror flange, external to the vacuum chamber, and the expansion passes through a 0.182-in. diameter hole into the resonant cavity. The center of the expansion is offset from the center of the mirror by 1 in. The sample is irradiated by microwave radiation generated by an Agilent Technologies E8247C PSG CW synthesizer; details of the irradiation and heterodyne detection circuitry can be found in ref 17. Labview software controls the timing of the gas and irradiation pulses, as well as the detection of any free induction decay signal. The software performs signal-averaging and can scan the spectrometer by stepping both the frequency source and the cavity. Microwave circuit elements allow for a spectral range from 10.5 to 26 GHz. The digital frequency resolution, governed by the sampling rate and the length of the free induction decay record, is 2.5 kHz. Rotational transitions are split into Doppler doublets centered at the transition frequency due to the coaxial orientation of the gas expansion to the cavity axis, and the fwhm of each Doppler component is typically 13 kHz. The vacuum system can accommodate pulse repetition rates of up to 15 s-1 while maintaining a pressure below 10-4 Torr, and the instrument can scan 450 MHz in 6 h while averaging 100 shots per scan segment. The frequencies for the measured transitions in the region from 11 000 to 21 000 MHz for three germane isotopomers (isotopologues), 70Ge, 72Ge, and 74Ge (relative abundance of 70Ge ) 20.84%, 72Ge ) 27.54%, and 74Ge ) 36.28%), are listed in Table 1 along with their assignments. Also listed are the frequency differences between the measured values and the values obtained from the determined rotational constants and the centrifugal distortion constants (Table 2). The mid-infrared spectrum of gas was obtained from 4000 to 230 cm-1 on a Perkin-Elmer model 2000 Fourier transform spectrometer equipped with a Ge/CsI beamsplitter and a DTGS detector. Atmospheric water vapor was removed from the spectrometer housing by purging with dry nitrogen. The theoretical resolution used to obtain the spectrum of the gas was 0.5 cm-1. Sixty-four interferograms were added and transformed with a boxcar truncation function. The mid-infrared spectra (3500-400 cm-1) of the sample dissolved in liquefied xenon at 10 different temperatures (-55 to -100 °C) were recorded on a Bruker model IFS-66 Fourier transform spectrometer equipped with a globar source, a Ge/ KBr beamsplitter, and a DTGS detector. In all cases, 100 interferograms were collected at a 1.0 cm-1 resolution, averaged, and transformed with a boxcar truncation function. For these studies, a specially designed cryostat cell was used. It consists of a copper cell with a path length of 4 cm with wedged silicon windows sealed to the cell with indium gaskets. The copper
Durig et al. cell was enclosed in an evacuated chamber fitted with KBr windows. The temperature was maintained with boiling liquid nitrogen and monitored by two Pt thermoresistors. The complete cell was connected to a pressure manifold, allowing the filling and evacuation of the system. The Raman spectra (Figure 1) were recorded on a Spex model 1403 spectrophotometer equipped with a Spectra-Physics model 2017 argon ion laser operating on the 514.5 nm line. The laser power used was 0.5 W with a spectral band-pass of 3 cm-1. The spectrum of the liquid was recorded with the sample sealed in a Pyrex glass capillary. The spectrum of the solid and the variable-temperature spectra were obtained with a Harney-Miller Raman cell.18 The measurements of the Raman frequencies are expected to be accurate to (2 cm-1. All of the observed bands in both the Raman spectra of the liquid and solid and the infrared spectra along with their proposed assignments are listed in Table 3. The LCAO-MO-SCF restricted Hartree-Fock calculations were performed with the Gaussian 03 program19 using Gaussiantype basis functions. The energy minima with respect to nuclear coordinates were obtained by the simultaneous relaxation of all geometric parameters using the gradient method of Pulay.20 The various basis sets up to 6-311G(2d,2p) as well as the corresponding ones with diffuse functions were employed with the Møller-Plesset perturbation method14 to the second order [MP2(full)] as well as with the density functional theory by the B3LYP method. The predicted conformational energy differences are listed in Table 4, and the inversion pathway with energy differences calculated at the MP2(full)/6-311+G(d,p) level is shown in Figure 2. Results and Discussion Microwave Spectra. There are two possible conformations of the chair form of germylcyclohexane, i.e., equatorial and axial, but the equatorial form is much more stable and in much greater abundance. Initially, preliminary rotational constants were predicted for the 74Ge isotopomer from ab initio MP2(full)/ 6-311+G(d,p) calculations for the equatorial form which gave a B constant of 875.35 and a C of 761.56 MHz, which differ by only 1.19 and 0.09 MHz, respectively, from the eventually experimentally determined values. The A constant was off by 26.3 MHz, but for an a-type rotor where |µa| was predicted to be 0.930 D, many strong transitions were predicted in the spectral region from 11 000 to 21 000 MHz, which depend primarily on the B and C rotational constants. If one chooses four of the 9r8 transitions with the highest predicted intensities for Ka ) 0, 1, 2, and 3, the observed transitions differed by 10, 7, 4, and 4 MHz, respectively, from the predicted values. With assignments of four transitions, another 36 transitions were assigned for this species, which included six c-type transitions. From the 40 assigned transitions, the rotational constants and five of the centrifugal distortion constants from the asymmetric reduced Hamiltonian were determined (Table 2). The splitting arising from internal rotation of the GeH3 moiety was predicted, and for all of the observed bands it was predicted to be less than 0.00 MHz, and indeed no splitting was observed. For the assignments of the other isotopomers, predictions were made by adjusting the C-C and Ge-C bond lengths to closely reproduce the experimentally determined rotational constants for the first species and shortening the Ge-H bond lengths in accordance with the determined values from the GeH stretching frequencies. These adjusted structural parameters were used to
Conformational Preferences of Germylcyclohexane
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TABLE 1: Rotational Transitional Frequencies (MHz) for Equatorial Germylcyclohexane Isotopomers in the Ground Vibrational States c-C6H1170GeH3
a
c-C6H1172GeH3
transition
νobs
∆νa
νobs
22,0 r 11,0 22,1 r 11,1 32,2 r 21,2 32,1 r 21,1 41,3 r 30,3 42,3 r 31,3 42,2 r 31,2 51,4 r 40,4 61,5 r 50,5 70,7 r 60,6 71,7 r 61,6 71,6 r 61,5 72,6 r 62,5 72,5 r 62,4 73,5 r 63,4 73,4 r 63,3 71,6 r 60,6 80,8 r 70,7 81,8 r 71,7 81,7 r 71,6 82,7 r 72,6 82,6 r 72,5 83,6 r 73,5 83,5 r 73,4 90,9 r 80,8 91,9 r 81,8 91,8 r 81,7 92,8 r 82,7 92,7 r 82,6 93,7 r 83,6 93,6 r 83,5 100,10 r 90,9 101,10 r 91,9 101,9 r 91,8 102,9 r 92,8 102,8 r 92,7 103,8 r 93,7 103,7 r 93,6 110,11 r 100,10 111,11 r 101,10 111,10 r 101,9 112,10 r 102,9 112,9 r 102,8 113,9 r 103,8 113,8 r 103,7 120,12 r 110,11 121,12 r 111,11 121,11 r 111,10 122,11 r 112,10 122,10 r 112,9 123,10 r 113,9 123,9 r 113,8 130,13 r 120,12 131,13 r 121,12
12 956.215 13 072.554 14 864.375 14 521.990 10 517.462 16 715.499 16 047.303 12 506.760 14 575.486 11 526.296 11 245.912 12 076.379 11 679.088 11 857.662 11 729.114 11 736.374 16 732.888 13 116.567 12 838.752 13 781.697 13 336.469 13 596.719 13 410.055 13 424.505 14 691.001 14 427.120 15 477.876 14 989.487 15 347.030 15 092.116 15 118.419 16 252.123 16 011.015 17 163.090 16 637.656 17 105.418 16 774.886 16 819.519 17 803.254 17 590.563 18 835.386
0.001 -0.005 -0.003 0.000 -0.001 0.004 0.004 0.000 0.001 -0.001 0.000 0.000 0.001 -0.001 -0.001 -0.002 -0.001 0.001 0.000 0.001 0.000 0.000 0.001 0.000 -0.001 -0.001 0.001 0.000 0.000 0.000 -0.001 0.001 0.000 0.000 -0.001 0.000 0.001 -0.001 0.000 -0.001 0.000
12 948.446 13 062.474
19 347.876 19 166.006 20 492.770
0.001 0.000 -0.001
20 889.040
0.000
c-C6H1174GeH3 ∆νa 0.000 0.000
νobs
∆νa
12 941.011 13 052.848
-0.004 0.000
14 476.534
0.004
12 409.059 14 451.484 11 412.206 11 134.695 11 948.407 11 558.710 11 729.894 11 606.652 11 613.439
0.003 -0.003 -0.001 0.000 -0.001 -0.001 0.001 0.000 -0.001
12 315.887 14 333.308 11 302.953 11 028.268 11 826.109 11 443.626 11 607.950 11 489.634 11 495.996
-0.002 0.002 -0.001 0.000 0.000 -0.001 -0.001 -0.001 0.000
12 988.225 12 712.179 13 636.374 13 199.372 13 449.141 13 269.927 13 283.437 14 548.743 14 285.342 15 315.648 14 835.852 15 179.506 14 934.314 14 958.921 16 096.070 15 854.167 16 984.501 16 467.688 16 918.061 16 599.437 16 641.207 17 633.335 17 418.766 18 641.068 18 094.447 18 661.003 18 264.781 18 331.760 19 163.883 18 979.356 20 283.444 19 715.748 20 404.243 19 929.736 20 032.063 20 690.709 20 536.234
0.001 0.000 0.000 0.001 0.003 0.002 -0.001 -0.001 0.001 0.001 0.000 0.001 -0.001 0.001 -0.001 0.000 0.001 0.000 -0.002 0.000 -0.002 -0.001 -0.001 -0.001 -0.001 -0.002 -0.001 0.001 0.002 0.000 -0.001 0.001 0.001 0.001 0.001 -0.001 0.000
12 865.284 12 591.043 13 497.459 13 068.284 13 308.309 13 136.030 13 148.696 14 412.447 14 149.639 15 160.527 14 688.936 15 019.644 14 783.535 14 806.603 15 946.553 15 704.029 16 813.670 16 305.130 16 739.250 16 431.792 16 470.972 17 470.548 17 254.305 18 455.113 17 916.447 18 463.545 18 080.321 18 143.186
0.001 0.000 0.000 0.000 -0.001 0.000 0.000 0.000 0.001 0.001 0.001 0.000 0.000 0.000 -0.001 0.001 0.001 0.001 -0.001 0.001 0.000 0.000 0.000 0.000 -0.001 0.001 -0.002 0.001
Calculated from the rotational constants listed in Table 6.
calculate rotational constants for the remaining two isotopomers and their experimental rotational constants are also listed in Table 2. The centrifugal distortion constants were obtained for the asymmetric reduced Hamiltonian for all three of the isotopomers. By using 45, 48, and 40 transitions for the 70Ge, 72Ge, and 74Ge isotopomers, respectively, the values for each of the species were determined. The experimental values are listed in Table 2 along with those obtained from the predicted force constants from the MP2(full)/6-31G(d) calculations. Since the force
constants have small differences between those obtained from the MP2(full)/6-311+G(d,p) calculation compared to those with the smaller basis set, we used those from which the vibrational frequencies were predicted. From the data in Table 2, it can be seen that only the value of 0.61 ( 0.37 kHz for ∆K for the 72 Ge species agrees with the predicted value of 0.645 kHz when the uncertainty is not taken into account. However, taking the uncertainties into account for ∆K, the values all agree, but this constant is poorly determined. However, it should be noted that the centrifugal distortion constants determined for the 72Ge
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TABLE 2: Calculated and Experimental Rotational Constants (MHz) and Centrifugal Distortion Constants (kHz) of Equatorial Germylcyclohexane with Experimental Error in Parentheses 70
rotation and distortion constantsa A B C ∆J ∆JK ∆K δJ δK N (no. of transitions)
72
Ge
74
Ge
Ge
ab initio
exp.
ab initio
exp.
ab initio
exp.
4085.3345 894.7517 776.2088 0.03957 0.10357 0.64185 0.00529 0.14690
4058.8860(20) 895.9125(2) 776.2343(1) 0.04004(49) 0.1058(39) 0.46(39) 0.005438(242) 0.185(40) 45
4085.2789 884.8344 768.7362 0.03892 0.10140 0.64506 0.00516 0.14497
4058.8279(18) 886.0037(1) 768.7868(1) 0.039163(224) 0.1138(34) 0.61(37) 0.004968(168) 0.1459(181) 48
4085.072 875.3525 761.5662 0.03831 0.09931 0.64813 0.00503 0.14311
4058.7744(24) 876.5453(1) 761.6568(1) 0.03780(36) 0.1122(42) 1.09(49) 0.00511(32) 0.1117(279) 40
a Rotation constants from MP2(full)/6-311+G(d,p); distortion constants were calculated from the predicted force constants from MP2(full)/ 6-31G(d).
isotopomer agree very well with the predicted values. For this isotopomer a significantly larger number of J ) 10, 11, 12, and 13 transitions were used to obtain the distortion constants than for the other two isotopomers. Nevertheless, the experimentally determined centrifugal distortion constants are considered to be reasonably well determined. Structural Parameters. We21 have shown that ab initio MP2/ 6-311+G(d,p) calculations predict the adjusted r0 structural parameters for more than 50 carbon-hydrogen distances to better than 0.002 Å compared to the experimentally determined values by comparison of isolated CH stretching frequencies22 to previously determined values from earlier microwave studies. Therefore, all of the carbon-hydrogen distances can be taken from the MP2/6-311+G(d,p)-predicted values for germylcyclohexane. Also a correlation plot of the r0(GeH) values from 1.518 to 1.538 Å versus the GeH stretching frequencies for several molecules gives a linear relation and an equation which gives the distances within (0.002 Å from the frequencies.23 Therefore, from the GeH stretching frequencies the GeHa distance is determined to be 1.533(2) Å and those for the GeHs bonds to be 1.532(2)Å. Thus, only the four heavy atom distances need to be determined. We have found24 that we can obtain good structural parameters by adjusting the structural parameters obtained from the ab initio calculations to fit the rotational constants obtained from the microwave experimental data. In order to reduce the number of independent variables, the structural parameters are separated into sets according to their types. Bond lengths in the same set keep their relative ratio, which could result in only two heavy atom distances for germylcyclohexane. Also, the bond angles and torsional angles in the same set keep their differences in degrees. This assumption is based on the fact that the errors from ab initio calculations are systematic. Therefore, it should be possible to obtain “adjusted r0” structural parameters for chair-equatorial germylcyclohexane by utilizing the nine determined microwave rotational constants from the three isotopomers. The predicted parameters from the MP2(full)/6-311+G(d,p) calculations for both the chair-equatorial and chair-axial conformers are listed in Table 5 with the atomic numbering shown in Figure 3. Only very small adjustments of 0.005 Å or less were needed to be made to the heavy atom distances and no adjustments to the five heavy atom angles to obtain excellent fits to the experimentally determined rotational constants. The C-Ge distance was decreased and the C-C distances increased, as has been found in some recent studies. The fit to the nine rotational constants is given in Table 6, with five of them (three
Figure 1. Comparison of experimental and calculated Raman spectra of germylcyclohexane: (A) liquid, (B) simulated spectrum of mixture of chair-equatorial and chair-axial conformers with ∆H ) 413 cm-1, (C) simulated spectrum of chair-axial, and (D) simulated spectrum of chair-equatorial (E) solid.
A constants and B and C constants of the 72Ge species) agreeing exactly and the other four differing by only 0.01 MHz. Therefore, it is believed that the C-H and Ge-H distances have been determined to an uncertainty of (0.002 Å and the C-C and C-Ge distances to (0.003 Å with angle uncertainties of (0.5°. These determined parameters are probably as accurate as could be determined from rs or rz parameters for the gas phase for this molecule, which has two conformers present at ambient temperature in the vapor state. Vibrational Assignment. In order to obtain a complete description of the molecular motions involved in the fundamental modes of germylcyclohexane, a normal coordinate
ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15 ν16 ν17 ν18 ν19 ν20 ν21
ν22 ν23 ν24
ν25
ν26
ν27 ν28
ν29 ν30 ν31 ν32 ν33 ν34 ν35 ν36 ν37 ν38 ν39 ν40 ν41 ν42
ν43 ν44
ν45
A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′ A′
A′ A′ A′
A′
A′
A′ A′
A′ A′ A′ A′ A′′ A′′ A′′ A′′ A′′ A′′ A′′ A′′ A′′ A′′
A′′ A′′
A′′
vib block. no.
(CH2)4 twist
CH out-of-plane bend CH2 twist
ring bending ring puckering ring bending ring-Ge in-plane bend (CH2)4 antisymmetric stretch (CH2)4 antisymmetric stretch (CH2)4 symmetric stretch (CH2)4 symmetric stretch GeH3 antisymmetric stretch (CH2)4 deformation (CH2)4 deformation CH2 wag (CH2)4 wag (CH2)4 wag
GeH3 rock ring puckering
GeC stretch
CH2 antisymmetric stretch (CH2)4 antisymmetric stretch (CH2)4 antisymmetric stretch CH2 symmetric stretch (CH2)4 symmetric stretch CH stretch (CH2)4 symmetric stretch GeH3 antisymmetric stretch GeH3 symmetric stretch (CH2)4 deformation (CH2)4 deformation CH2 deformation (CH2)4 wag (CH2)4 wag (CH2)4 twist (CH2)4 twist CH in-plane bend (CH2)4 rock ring stretch (CH2)4 rock GeH3 antisymmetric deformation ring stretch CH2 rock GeH3 symmetric deformation ring stretch
fundamental
1237
1364 1327
410 323 256 121 3139 3126 3083 3070 2088 1547 1540 1430 1426 1402
554 509
753
855
938 884 838
3146 3136 3128 3084 3083 3080 3068 2085 2060 1565 1552 1545 1430 1429 1349 1333 1247 1157 1081 1043 904
1178
1294 1261
402 316 248 121 2944 2932 2892 2880 2088 1451 1445 1358 1353 1330
554 495
727
812
890 840 838
2952 2942 2934 2893 2892 2890 2878 2085 2060 1468 1456 1449 1358 1357 1283 1268 1188 1106 1027 1005 904
ab fixed initio scaledb
4.8
1.0 0.9
0.8 0.8 1.3 0.2 16.1 43.4 17.4 16.4 122.9 2.9 0.3 0.1 0.2 0.3
22.9 1.1
11.3
167.9
0.1 4.7 0.3
61.5 46.4 12.9 24.0 26.7 15.2 6.1 126.0 76.2 0.6 15.2 4.0 0.7 3.1 1.5 0.8 3.5 5.3 0.1 10.3 21.4
IR int
4.0
13.9 2.0
0.9 1.7 2.5 0.0 85.0 12.9 36.1 6.8 84.9 4.4 23.5 3.6 0.1 4.0
5.3 2.1
8.4
9.2
1.3 4.8 0.6
39.3 125.8 119.4 21.8 193.0 17.0 124.7 88.7 172.7 1.7 5.9 15.1 8.7 2.5 14.2 7.1 12.8 10.5 16.8 2.6 20.2
Raman act.
2936 2919 2894 2869 2060 1438 1331
2934 2915 2898 2862 2072 1295 -
385 312 252 2938 2925 2896 2871 2060 1445 1346 1332
548 497
712
801
885 847 820
2938 2938 2925 2896 2889 2851 2060 2060 1486 1463 1438 1346 1346 1267 1184 1101 1028 998 -
1174
1296 1258
384 317 256 2938 2925 2893 2865 2069 1444 1353 1333
558 494
712
802
886 845 825
2938 2938 2925 2893 2886 2853 2062 2056 1470 1463 1438 1353 1345 1268 1258 1184 1100 1032 997 ∼910
Raman Raman solid liquid obs obs
1177 1174 -
1296 1254 -
553 493
713
808
886 847 -
2936 2936 2919 2869 2853 2853 2853 2064 1460 1451 1443 1352 1349 1257 1183 1104 1016 998 903
Xe obs
554 -
715
810
878 834 -
2934 2934 2915 2870 2862 2862 2854 2071 2066 1457 1355 1351 1261 1259 1187 1014 1001 905
IR gas obs
chair-equatorial
TABLE 3: Observed and Calculateda Frequencies (cm-1) for Germylcyclohexane
74 6 97
3 84 4 2 91 13 66 30 77 16 12 100 37 94 49 21 20 33 38 25 12
Ad
26 94 3
97 16 96 98 9 87 34 70 23 84 88 0 63 6 51 79 80 67 62 75 88
Cd
66S27 16S28 16S30, 19S20, 13S31, 12S23 69S29 44S30, 29S31 11S31, 34S26, 24S32 47S32, 24S28, 20S31 73S33, 24S34 64S34, 25S33, 10S36 59S35, 36S36 52S36, 40S35 100S37 88S38, 11S39 88S39, 11S38 43S40, 20S42, 10S48 31S41, 34S45, 15S43 35S42, 21S40, 15S41, 14S44 21S43, 32S47, 27S42 32S44, 21S43, 18S51, 14S45 28S45, 21S41, 17S48
s
s s
20 86 87 4 s s s s s s s s s s
3 95
s
s s
80 14 13 96 s s s s s s s s s s
97 5
42S25, 17S19, 15S24, 100 0 10S18 25S26, 14S32, 11S18 0 100
59S22, 13S16 38S23, 14S20, 13S22 84S24
49S1, 39S2, 11S3 34S2, 44S1, 11S3 66S3, 23S2 68S4, 19S5, 11S7 37S5, 26S7, 24S4 66S6, 23S7, 10S5 29S7, 32S6, 30S8 92S8 92S9 65S10, 34S12 79S11, 16S12 49S12, 29S10, 19S11 65S13, 13S15 76S14, 11S16 56S15, 17S16 46S16, 21S15, 11S17 37S17, 33S18 20S18, 24S17, 12S23 39S19, 26S13, 21S24 32S20, 23S28, 16S17 86S21
PEDc
1195
1360 1332
453 384 246 120 3144 3125 3094 3066 2076 1556 1547 1431 1427 1388
556 516
713
852
925 885 840
3150 3138 3125 3094 3083 3082 3064 2091 2058 1570 1560 1546 1435 1424 1346 1330 1257 1132 1085 1052 906
1136
1293 1267
441 378 243 120 2950 2931 2903 2876 2076 1460 1451 1358 1354 1317
556 496
689*
809
880 842 840
2955 2943 2932 2902 2892 2891 2874 2091 2058 1473 1463 1468 1363 1352 1281 1266 1197 1081 1032 1014 906
ab fixed initio scaledb
1.1
7.3 0.4
2.5 0.7 0.8 0.1 15.1 36.5 19.2 20.1 120.0 6.7 2.3 0.0 0.1 0.3
3.7 11.7
22.3
67.0
0.8 20.0 100.3
67.6 38.9 18.1 10.7 22.0 34.1 26.5 105.5 89.4 2.4 12.8 3.4 0.6 5.8 3.4 1.5 2.6 4.1 0.5 2.2 14.4
IR int
3.5
0.9 16.2
1.4 0.5 1.0 0.2 67.6 16.3 44.7 14.4 80.8 4.3 24.5 2.7 0.5 0.2
9.3 3.0
4.8
12.8
2.8 0.9 8.8
33.0 109.1 114.4 127.8 164.5 51.6 117.0 56.9 185.5 5.3 1.2 21.2 2.5 1.7 6.8 22.5 8.4 2.1 10.7 3.0 19.5
Raman act. PEDc
83
98 10 89
56 69 92 0 70 25 39 22 98 60 4 98 60 91 82 99 74 99 72 0 2
Ad
12S42 14S44
11S36
17S27 22S28
16S30
27S45, 32S47, 17S50
36S43, 29S46 47S44, 18S47
40S29, 27S28, 41S30, 41S29 40S31, 26S32, 36S32, 33S31, 70S33, 30S34 60S34, 28S33, 55S35, 42S36 47S36, 45S35 100S37 80S38, 18S39 80S39, 19S38 51S40, 13S46, 52S41, 14S43, 69S42, 13S40
s
s s
40 27 88 99 s s s s s s s s s s
10S26, 22S28, 11S30, 29 10S31 42S27, 19S20 69 40S28, 11S26 52
27S25, 45S24, 14S19
69S22 39S23, 17S21, 12S20 48S24, 28S25, 11S19
49S1, 30S2, 20S3 60S2, 18S1, 10S3 60S3, 29S1, 11S7 51S4, 43S7 75S5, 14S6 68S6, 17S5 37S7, 38S4, 19S6 91S8 91S9 77S10, 18S12 89S11, 10S12 71S12, 22S10 53S13, 13S14, 11S16 63S14, 12S13, 11S15 23S15, 35S16 43S16, 27S15 33S17, 29S18, 11S23 35S18, 18S17, 13S23 35S19, 26S13, 21S25 30S20, 22S26, 11S32 70S21
chair-axial
s
s s
60 73 12 1 s s s s s s s s s s
31 48
71
17
2 90 11
44 31 8 100 30 75 61 78 2 40 96 2 40 9 18 1 26 1 28 100 98
Cd
Conformational Preferences of Germylcyclohexane J. Phys. Chem. A, Vol. 114, No. 34, 2010 9293
14S56 17S55
ν51 ν52 ν53 ν54 ν55 ν56 ν57 A′′ A′′ A′′ A′′ A′′ A′′ A′′
Durig et al. a All ab initio frequencies, infrared intensities (km/mol), Raman activities (Å4/u), depolarization ratios, and percentage potential energy distributions are calculated at the MP2(full)/6-31G(d) level. b Scaled frequencies with scaling factors of 0.88 for CH stretches and deformations, 1.0 for germyl motions, and 0.90 for all other modes; observed axial fundamentals are marked with an asterisk. c Symmetry coordinates with potential energy distributions contribution less than 10% are omitted. d Values refer to percentage A- and C-type infrared band contour composition; entries with a dash are symmetry-forbidden.
s s s s s s s s s s s s s s 21.3 0.0 32.6 1.4 0.4 0.1 0.1 869 791 574 432 293 181 85 s s s s s s s 875 785 541 426 877 548 428 876 774 543 437 888 777 549 1.5 0.6 6.1 0.2 0.0 0.0 0.0 879 778 558 439 244 169 136 926 819 558 446 247 169 136
4.8 0.3 31.9 0.0 0.0 0.2 0.0
903 ν50 A′′
GeH3 antisymmetric deformation (CH2)4 rock (CH2)4 rock GeH3 rock ring twisting ring twisting ring-Ge out-of-plane bend GeH3 torsion
903
27.7
18.1
905
903
911 910 919 916 0.6 1.3 961 ν49 A′′
ring stretch
913
1025 1028 1039 1040 2.6 1.2 1041 1096 ν48 A′′
ring stretch
48S51, 29S49 82S52, 11S48 86S53 82S54 90S55 87S56 97S57
s s s s s s s
915 833 575 441 297 181 85
5.2 877 s s
905
1.9 s s
978
928
17S50 12S48
66S51, 82S52, 74S53 78S54 66S55, 73S56, 93S57 13.7 0.8 4.9 0.7 0.1 0.0 0.0
s s 39S50, 29S51, 20S45
s s
3.3
s s 0.8 s s
1088
1032
7.8
70S49
s s 0.0 s s 1126 ν47 A′′
(CH2)4 twist
1069
0.5
2.0
1082
1079
1072
1072
28S47, 16S44, 12S42, 12S41, 10S48 38S48, 26S47, 15S40, 11S43 28S49, 30S51, 12S46, 10S44 93S50
s 1.7 1100 A′′
1159 ν46
block.
ring stretch
vib no.
fundamental
0.2
-
1101
-
60S46, 24S49
s
1143
1084
0.7
1.4
s s
36S46, 21S41, 16S43, 11S44 33S47, 21S45, 13S41, 10S40 53S48, 15S42, 11S43 0.0 1107 1167
Raman act. IR int fixed scaledb ab initio Cd Ad Xe obs ab initio
fixed scaledb
IR int
Raman act.
IR gas obs
Raman liquid obs
Raman solid obs
PEDc
chair-axial chair-equatorial TABLE 3 Continued
0.1
Cd Ad
J. Phys. Chem. A, Vol. 114, No. 34, 2010
PEDc
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TABLE 4: Calculated Energies (hartree) and Energy Differences (cm-1) for the Chair-Equatorial and Chair-Axial Conformations of Germylcyclohexane method/basis set
equatoriala
axialb
MP2/6-31G(d) MP2/6-31+G(d) MP2/6-311G(d,p) MP2/6-311+G(d,p) MP2/6-311G(2d,2p) MP2/6-311+G(2d,2p) averagec B3LYP/6-31G(d) B3LYP/6-31+G(d) B3LYP/6-311G(d,p) B3LYP/6-311+G(d,p) B3LYP/6-311G(2d,2p) B3LYP/6-311+G(2d,2p) averagec
0.535 9578 0.580 5472 3.259 1643 3.263 3464 3.351 4642 3.354 1747
318 772 396 444 422 389 413 ( 22 263 898 628 628 622 619 627 ( 5
3.055 5936 3.093 5875 5.146 1289 5.147 0313 5.154 7372 5.155 5645
a The energy of the equatorial conformer is given as -(E + 2309)H. b The energy for the axial conformer is relative to the equatorial form. c Arithmetic mean of the four highest basis set predictions with standard deviation error.
analysis has been carried out. The force field in Cartesian coordinates was obtained with the Gaussian 03 program at the MP2(Full) level with the 6-31G(d) basis set. The internal coordinates used to calculate the G and B matrices are shown in Table 5 with the atomic numbering shown in Figure 3. By using the B matrix,25 the force field in Cartesian coordinates was converted to a force field in internal coordinates. Subsequently, scaling factors of 0.88 for CH stretches and distortions, 1.0 for germyl motions, and 0.9 for all other modes were applied, along with the geometric average of scaling factors for interaction force constants, to obtain the fixed scaled force field and resultant wavenumbers. The same set of symmetry coordinates as those previously used for the corresponding silane9 was used to determine the corresponding potential energy distributions (PEDs). A comparison between the observed and calculated wavenumbers, along with the calculated infrared intensities, Raman activities, and potential energy distributions for equatorial and axial germylcyclohexane are listed in Table 3. The simulated Raman spectrum is plotted with the scaled ab initio frequencies and Raman scattering activities calculated at the MP2(full)/6-31G(d) level. The Raman scattering cross sections, ∂σj/∂Ω, which are proportional to the Raman intensities, can be calculated from the scattering activities and the predicted frequencies for each normal mode.26–29 In order to obtain the polarized Raman cross sections, the polarizabilities are incorporated into Sj by multiplying Sj with (1 - Fj)/(1 + Fj), where Fj is the depolarization ratio of the jth normal mode. The Raman scattering cross sections and the predicted scaled frequencies were utilized, together with a Lorentzian line-shape function, to obtain the simulated spectra. The predicted spectra and the experimental Raman spectrum of the polycrystalline solid are shown in Figure 1. The predicted spectrum of the chair-equatorial form is in excellent agreement with the observed spectrum. For the assignment of the fundamentals of germylcyclohexane, considerable reliance was placed on the MP2(full)/6-31G(d) predictionswiththreescalingfactorsof0.88forthecarbon-hydrogen stretches and deformations, 1.0 for the motions involving germanium, and 0.90 for the other bends and stretches. Additionally, the band contours in the infrared spectrum of the gas and the ab initio predicted infrared and Raman band intensities as well as the Raman depolarization data were of
Conformational Preferences of Germylcyclohexane
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9295
Figure 3. Structure of chair-equatorial germylcyclohexane with atomic numbering.
Figure 2. Calculated potential function of germylcyclohexane at the MP2(full)/6-311+G(d,p) level during inversion from the chair-equatorial conformer to the chair-axial conformer.
considerable value. Finally, comparisons were made to the recently reported vibrational assignment for cyclohexane30 and silylcyclohexane,9 particularly for the heavy atom modes.
The assignment of the fundamentals associated with the heavy atoms is of the most interest, since there is significant interaction of some of the germyl modes with the ring modes. There is a reasonable correlation of the frequencies for these modes in the Raman spectrum of cyclohexane13 with the germyl-substituted molecule, which makes it possible to assign the symmetric ring stretches at 1028, 885, and 801 cm-1 and the corresponding antisymmetric motions at 1101, 1040 (IR) and 916 (IR) cm-1, where the 1040 cm-1 infrared band shifts in the solid so it could
TABLE 5: Structural Parameters and Rotational Constants for Chair-Equatorial and Chair-Axial Conformations of Germylcyclohexane MP2(full)/6-311+G(d,p) structural parametersb r(C1C10,11) r(C10C16, C11C17) r(C4C16,17) r(C4Ge6) r(C1H2) r(C1H3) r(C10H12, C11H13) r(C10H14, C11H15) r(C16H18, C17H19) r(C16H20, C17H21) r(C4H5) r(Ge6H7) r(Ge6H8,9) ∠C10C1C11 ∠C1C10C16, ∠C1C11C17 ∠C4C16C10, ∠C4C17C11 ∠C16C4C17 ∠Ge6C4C16,17 ∠C10,11C1H2 ∠C10,11C1H3 ∠H2C1H3 ∠C1C10H12, ∠C1C11H13 ∠C1C10H14, ∠C1C11H15 ∠C16C10H12, ∠C17C11H13 ∠C16C10H14, ∠C17C11H15 ∠H12C10H14, ∠H13C11H15 ∠C4C16H18, ∠C4C17H19 ∠C4C16H20, ∠C4C17H21 ∠C10C16H18, ∠C11C17H19 ∠C10C16H20, ∠C11C17H21 ∠H18C16H20, ∠H19C17H21 ∠C16,17C4H5 ∠Ge6C4H5 ∠C4Ge6H7 ∠C4Ge6H8,9 ∠H8Ge6H9 ∠H7Ge6H8,9 τC1C10C16C4, τC1C11C17C4 A B C a
internal coordinates R 1, R 2 R3, R4 R 5, R 6 R7 r1 r2 r4, r5 r6, r7 r8, r9 r10, r11 r12 r13 r14, r15 φ1 φ2 , φ3 φ4 , φ5 φ6 θ 1, θ 2 R1 , R 2 β 1, β 2 γ ε 1, ε 2 δ 1, δ 2 η 1, η 2 κ 1, κ 2 χ 1, χ 2 µ 1, µ 2 ν 1, ν 2 π1 , π 2 σ 1, σ 2 F1 , F2 ω1 , ω 2 ζ ο1 ο 2, ο 3 ψ1 ψ2 , ψ 3 τ
chair-equatorial
chair-axial
adjusted r0 chair-equatorial
predicted r0 chair-axiala
1.529 1.531 1.535 1.962 1.099 1.096 1.098 1.096 1.100 1.097 1.100 1.526 1.525 110.9 111.0 111.4 110.5 111.3 109.1 110.4 106.9 109.2 110.4 109.0 110.1 107.0 109.1 110.5 108.8 110.0 106.8 108.3 106.8 109.1 110.7 109.0 108.6 56.1 4085.1 875.4 761.6
1.530 1.531 1.536 1.970 1.099 1.096 1.097 1.096 1.100 1.097 1.099 1.523 1.525 111.3 111.0 112.1 110.3 113.0 109.0 110.3 106.9 109.2 110.1 109.9 109.8 106.7 108.5 110.7 108.4 110.4 106.6 108.4 103.4 113.6 109.0 109.0 108.1 55.5 3022.7 1114.0 1017.1
1.533(3) 1.532(3) 1.540(3) 1.957(3) 1.099(3) 1.096(3) 1.098(3) 1.096(3) 1.100(3) 1.097(3) 1.101(3) 1.533(3) 1.532(3) 111.1(5) 111.2(5) 111.3(5) 110.7(5) 111.1(5) 109.0(5) 110.4(5) 106.9(5) 109.2(5) 110.4(5) 108.8(5) 110.0(5) 107.0(5) 109.1(5) 110.5(5) 108.6(5) 110.3(5) 106.8(5) 108.3(5) 107.0(5) 109.1(5) 110.7(5) 109.0(5) 108.6(5) 55.6(10) 4058.8 886.0 768.8
1.534(3) 1.532(3) 1.541(3) 1.965(3) 1.099(3) 1.096(3) 1.097(3) 1.096(3) 1.100(3) 1.097(3) 1.100(3) 1.530(3) 1.532(3) 111.5(5) 111.2(5) 112.0(5) 110.5(5) 112.8(5) 108.9(5) 110.3(5) 106.9(5) 109.2(5) 110.1(5) 109.7(5) 109.7(5) 106.7(5) 108.5(5) 110.7(5) 108.2(5) 110.7(5) 106.6(5) 108.4(5) 103.6(5) 113.6(5) 109.0(5) 109.0(5) 108.1(5) 54.8(10) 3012.0 1123.7 1023.7
Predicted r0 values based upon equatorial values. b r values are in Å, angles are in deg, and rotational constants are in MHz.
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Durig et al.
TABLE 6: Comparison of Rotational Constants (MHz) Obtained from Modified Ab Initio MP2(full)/6-311+G(d,p) Predictions from Microwave Spectra and the Adjusted Structural Parameters for Equatorial Germylcyclohexane isotopomer 70
C6H11 GeH3 C6H1172GeH3 C6H1174GeH3
rotational MP2(full)/ adjusted constant 6-311+G(d,p) microwave r0 A B C A B C A B C
4085.33 894.75 776.21 4085.28 884.83 768.74 4085.07 875.35 761.57
4058.89 895.91 776.23 4058.83 886.00 768.79 4058.77 876.54 761.66
4058.89 895.92 776.24 4058.83 886.00 768.79 4058.77 876.54 761.65
|∆| 0.00 0.01 0.01 0.00 0.00 0.00 0.00 0.01 0.01
not be resolved from the relatively strong Raman line at 1028 cm-1. The skeletal bends, which are in the lower frequency region, are then assigned for the A′ modes at 497, 385, 312, and 252 cm-1 and those for the A′′ modes at 428 cm-1 and predicted at 244 cm-1, which was not observed, since the predicted intensity for this mode is zero for both the infrared and Raman spectra. A comparison of the frequencies of those modes of cyclohexane with those for the germyl-substituted cyclohexane is given in Table 7. For the fundamentals for the GeH3 moiety, nine normal modes were assigned. The three GeH stretches are well-known to be around 2060 cm-1 with the three deformations around 900 cm-1 and the two rocks ∼550 cm-1 based on the values for these motions in several YGeH3 molecules.31 The torsion is expected below 150 cm-1 with predicted intensities near zero in both the infrared and Raman spectrum. The other three heavy atom modes are the Ge-C stretch and two ring-GeH3 bends, which were assigned at 712, 169, and 121 cm-1, which are near the expected values for the similar modes in cyclohexane and are predicted rather well from ab initio MP2(full)/6-31G(d) calculations with a scaling factor of 0.90. The assignments for these vibrations are listed in Table 3 along with the ab initio predicted values of the frequencies. Conformational Stability. We have calculated the conformational energy difference by ab initio second-order perturbation with full electron correlation with a variety of basis sets, and the average value from the four largest basis sets is 413 ( 22 cm-1 (Table 4), which compares very well with the previously reported value of 420 cm-1 from force constant calculations.12 We also predicted the value by density functional theory
Figure 4. Region of predicted Raman spectrum used for ∆H determination: (A) simulated spectrum of mixture of chair-equatorial and chair-axial conformers with ∆H ) 413 cm-1, (B) simulated spectrum of chair-equatorial, and (C) simulated spectrum of chair-axial.
calculations by the B3LYP method, and there is little variation with the basis size, but the average value is significantly larger at 627 ( 5 cm-1 (Table 4). With only two experimentally observable conformers, we investigated the conformer pair by variable-temperature Raman effect beginning at 30 °C and raised the temperature in seven increments to 75 °C. The temperature was increased because the sample solidified in the capillary below -11 °C and crystallized below -37 °C. The 683 cm-1 band of the axial conformer is clearly predicted in the Raman spectrum (Figure 4), easily recognized in the experimental spectrum, and disappears from the polycrystalline solid, while the 712 cm-1 band was clearly predicted as equatorial and persisted in the spectrum of the solid. The data set obtained from this conformer pair’s intensity ratio (Table 8) was fit to the Van’t Hoff equation, -ln K ) ∆H/RT - ∆S/R, where the intensity ratio of the more stable conformer to the less stable one is used for K and it is assumed
TABLE 7: Observed Skeletal Modes (cm-1) for Cyclohexane, Methylcyclohexane, and Germylcyclohexane cyclohexane sym block.
vib no.
observeda
approximate description
A1u Eu
ν9 ν11
1066 862
C-C stretch C-C stretch + CH2 bend
A1g Eg
ν5 ν23
800 798
C-C stretch C-C stretch
A2u Eg
ν16 ν24
522 425
C-C stretch + CH2 bend C-C-C skeletal bend
A1g Eu
ν6 ν12
387 241
C-C-C skeletal bend C-C-C skeletal bend
a
chair-equatorial methylcyclohexane
chair-equatorial germylcyclohexane
sym. block.
vib no.
Raman obsb
approximate description
sym block.
vib no.
Raman obs
approximate description
A′′ A′ A′′ A′ A′′ A′ A′ A′′ A′ A′ A′′ A′
ν47 ν22 ν50 ν25 ν52 ν27 ν28 ν54 ν30 ν31 ν57 ν32
1107 1033 971 851 869 770 547 440 403 330 224 179
ring stretch ring stretch ring stretch ring stretch ring stretch ring stretch ring pucker ring twist ring bend ring pucker ring twist ring bend
A′ A′ A′′ A′ A′′ A′ A′ A′′ A′ A′ A′′ A′
ν46 ν19 ν48 ν22 ν49 ν25 ν28 ν54 ν29 ν30 ν55 ν31
1101 1028 1028 885 910 801 497 428 385 312 〈244〉c 252
ring stretch ring stretch ring stretch ring stretch ring stretch ring stretch ring pucker ring twist ring bend ring pucker ring twist ring bend
A1g and Eg values are Raman-active and reported in ref 13. A2u and Eu values are IR-active and reported in ref 30. A1u is inactive and predicted in ref 30. b Reference 10. c Scaled predicted frequency from ab initio calculation; not observed.
Conformational Preferences of Germylcyclohexane
J. Phys. Chem. A, Vol. 114, No. 34, 2010 9297
TABLE 8: Temperature and Intensity Ratio from the Temperature Study of Germylcyclohexane T (°C)
1000/T (K)
I683/712
30 35 40 45 50 70 75 ∆H (cm-1)
3.2987 3.2452 3.1934 3.1432 3.0945 2.9142 2.8723
0.1111 0.1132 0.1203 0.1226 0.1260 0.1376 0.1504 453 ( 38
that ∆H is not a function of temperature in the experimental temperature range. By using a least-squares fit, the ∆H value, which corresponds to the slope of the Van’t Hoff plot (Figure 5), was determined, with a conformational enthalpy difference of 435 cm-1 with a statistical uncertainty (2σ) of 38 cm-1. The relative spread in the values is normally what is obtained by this technique because of the interference from combination and overtone bands as well as the baseline correction and band deconvolution processes. Additionally, there is some difficulty in obtaining the intensities of relatively weak bands, which appear as shoulders on much stronger bands. Clearly, the overall uncertainties in the obtained ∆H values can not be described statistically by 2σ alone, since the systematic errors described above cannot be ignored. Thus, the realistic uncertainty may be as much as 10%, though it is beyond doubt that the ∆H value is relatively large and only a relatively small amount of the second form exists in the fluid phases at ambient temperature. Discussion The determined structural parameters for the germyl moiety are consistent with those obtained for several other organogermanes.31 For example, for methylgermane the experimental GeH distance23 is 1.528 Å, while the MP2(full)/6-311+G(d,p) predicted value is 1.522 Å, which is about the same difference found in the current study of cyclohexylgermane. At this level of calculation the ab initio predicted distance is usually too short by 0.003-0.007 Å compared to the value obtained from the GeH stretching frequencies. The heavy atom distances for the cyclohexane ring show a slight change (Table 9) for the CRCβ distance, but the remaining parameters are, in general, quite consistent over the substitution from the methyl group to the germyl group. Also, the GeC distance is in good agreement with this parameter in several other organogermanes.31 Therefore,
Figure 5. Van’t Hoff plot of -ln(K) as a function of 1/T.
we believe the estimated listed uncertainties are realistic values and it would be difficult to improve upon the relative values with rs or rz determinations with additional microwave or electron diffraction studies. In Table 9 the structural parameters for chloro- and bromocyclohexane are listed and there is a significant reduction in the CRCβ distance with the attachment of these electronegative elements. This is in marked contrast to the elongation obtained from the substitution of the CN group5 to cyclohexane, where the CRCβ distance was determined to be 1.544(3) Å. Thus, the change in this bond distance follows the trend expected by the nature of the added group. The predicted fundamental frequencies for the MP2(full)/631G(d) calculations with only two scaling factors for the force constants are in excellent agreement with the experimentally determined values with an average error of 10.4 cm-1 (0.7% error) for the A′ modes. One-half of this error is due to the predicted values for the carbon-hydrogen stretching frequencies with the error for the remaining fundamentals of 5 cm-1. Similarly excellent predictions are obtained for the A′′ modes, which indicates that this relatively small basis set with the MP2 calculations is quite adequate for predicting the fundamentals to aid in making the assignments for the substituted cyclohexane molecules. The mixing is quite extensive for many of the vibrations below 1200 cm-1 with ν18, ν26, and ν28 for the A′ modes having maximum values of 25% or less for the symmetry coordinate indicated as the approximate description of the motion. The ν28
TABLE 9: Heavy Atom r0 Structural Parameters of Cyclohexane and Some Monosubstituted Chair-Equatorial Cyclohexanes structural parametersf
cyclohexanea
methylcyclohexaneb
silylcyclohexanec
germylcyclohexane
chlorocyclohexaned
bromocyclohexanee
r(CδCγ) r(CγCβ) r(CRCβ) r(CRX) ∠CγCδCγ ∠CδCγCβ ∠CRCβCγ ∠CβCRCβ ∠XCRCβ τCδCγCβCR A B C ∆H (calculated) ∆H (observed)
1.536(3) 1.536(3) 1.536(3) 111.1(2) 111.1(2) 111.1(2) 111.1(2) 55.7(2) 4305.90 4305.90 2463.30
1.535(3) 1.535(3) 1.536(3) 1.532(3) 110.8 (5) 111.0(5) 111.9(5) 110.0(5) 111.4(5) 55.7(10) 4201.8 2195.7 1593.6 644(34) 712(71)g
1.534(3) 1.530(3) 1.544(3) 1.880(3) 111.0(5) 111.1(5) 111.5(5) 110.3(5) 111.6(5) 56.0(10) 4074.7 1366.6 1105.7 525(10) 520(70)g/414(19)h
1.533(3) 1.532(3) 1.540(3) 1.957(3) 111.1(5) 111.2(5) 111.3(5) 110.7(5) 111.1(5) 55.6(10) 4058.83 886.00 768.79 413(22) 453(38)g
1.532(3) 1.536(3) 1.524(3) 1.802(5) 110.6(5) 111.3(5) 109.7(5) 112.6(5) 110.1(5) 56.3(10) 4293.2 1397.6 1127.1 161(18) 132(13)h
1.532(3) 1.539(3) 1.524(3) 1.966(5) 110.9(5) 111.3(5) 109.4(5) 112.5(5) 109.6(5) 55.9(10) 4280.9 894.8 775.9 168(22) 239(24)h
a
Reference 13. b Reference 10. c References 6, 9. d Reference 7. e Reference 8. f r values are in Å, angles are in deg, and rotational constants are in MHz. g Raman variable temperature study of the liquid. h Infrared variable temperature study of xenon solution.
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vibration is rather unique with the PED of more than 10 modes with contributions of 3-7%, but the ring bending motion assignment has been selected on the basis of a similar vibrational assignment for many monosubstituted cyclohexane molecules. Thus, a few of the descriptions of the fundamentals are for “bookkeeping” rather than giving the most significant molecular motion. The enthalpy determination was attempted from the xenon solution, but a suitable pair of bands could not be found. Decomposition occurred when the sample was placed in the xenon due to the very small amount of water that is difficult to remove from xenon. We then relied on the Raman spectrum of the liquid, where the simulated spectrum indicated that two of the fundamentals for the chair axial form should give distinct bands in the 500 cm-1 region (Figure 4). However, this spectral region is much more complex than predicted, so the only fundamental for the axial form was observed at 683 cm-1, which was then coupled with the equatorial band at 712 cm-1 from which the enthalpy difference was obtained. The experimentally obtained enthalpy difference value of 453 ( 38 cm-1 compares well with the value of 413 ( 22 cm-1 obtained by averaging the results of the four largest basis set calculations using the MP2(full) method. However, as we have seen in other enthalpy difference calculations,6,10 the B3LYP method produces results that are significantly higher than the experimental value, regardless of basis set, with an average from the four highest basis sets of 627 ( 5 cm-1 (Table 4). The smallest basis sets [6-31G(d) and 6-31+G(d)] gave results that were very different from the higher level calculations and were omitted from the average. The small number of calculated orbitals, particularly in the case of a period 3 atom, likely contributes to this irregularity, which has been seen to a lesser extent in the study of silylcyclohexane6 and was nonexistent in the study of methylcyclohexane.10 As Oulette has postulated11,12 and as we have found,6,10 for group 4 monosubstituted cyclohexanes for which the electronegativity of the substituent group is not the dominating factor conformational preference is determined primarily by nonbonded repulsive interactions of axial hydrogens and the “over the plane” hydrogen of the substituent group. The smaller methyl group has the shortest ring-substituent bond length of the series to the ring carbon and a larger CCH bond angle than both the silane and the germane (107.2 versus 103.2 and 103.4, respectively), placing the axial methyl hydrogen closer to the axial ring hydrogens than is found for the silane and germane in the axial conformation, due to the longer Si-C and Ge-C bond lengths and smaller SiCH and GeCH bond angles. These repulsive H-H nonbonded interactions would explain the MP2(full) calculated ∆H for methylcyclohexane that is 119 and 231 cm-1 larger than the analogous calculated ∆H for silylcyclohexane and germylcyclohexane, respectively (Table 9). The predicted ∆H for silylcyclohexane is 112 cm-1 larger than that predicted for the germylcyclohexane, indicating a consistent trend within the group. Experimentally, however, the ∆H values for the three compounds using the same experimental methods9,10 are found to be 712(71), 520(70), and 453(38), for methyl-, silyland germylcyclohexane, respectively, which is not such an orderly progression. This may partly be due to the fact that the predicted values from ab initio are for gas-phase materials, while the experimental values were obtained from liquid-phase samples and therefore have intermolecular interactions influencing molecular behavior. Additionally, the methyl- and silylcyclohexane studies were performed at low temperatures, and packing effects influence conformational preferences as the
Durig et al. freezing point is approached. The difference between gas-phase and liquid-phase experimental determination can be seen6,9 in the 100 cm-1 difference in the determined ∆H by the Raman study of the liquid and the infrared study of the xenon solution for silylcyclohexane. Conclusions We have determined the adjusted r0 structural parameters for the more stable chair-equatorial conformer of germylcyclohexane by combining the predicted parameters from ab initio calculations with rotational constants obtained from the observed FT-microwave spectra for three isotopomers of germanium and have predicted the parameters for the chair-axial form. We have also recorded and assigned the Raman and infrared spectra of this molecule. Temperature-dependent Raman spectroscopy was used to determine the conformational enthalpy difference between the two stable forms of germylcyclohexane, and the result is in good agreement with the energy difference predicted by MP2(full) calculations, whereas B3LYP calculations gave an energy difference much greater than the experimental value. Acknowledgment. J.R.D. acknowledges the University of MissourisKansas City, for a Faculty Research Grant for partial financial support of this research. References and Notes (1) Caminati, W.; Scappini, F.; Damiani, D. Microwave Spectrum of Axial Cyclohexyl Chloride and Conformational Equilibrium in Cyclohexyl Chloride. J. Mol. Spectrosc. 1984, 108, 287–298. (2) Pierce, L.; Beecher, J. F. Microwave Spectrum of Cyclohexyl Fluoride. Structure and Dipole Moment of the Axial Isomer, and the AxialEquatorial Ratio. J. Am. Chem. Soc. 1966, 88, 5406–5410. (3) Caminati, W.; Damiani, D.; Scappini, F. High-Resolution Microwave Spectrum of Cyclohexyl Bromide. J. Mol. Spectrosc. 1984, 104, 183–193. (4) Scharpen, L. H. Axial-Equatorial Energy Difference in Cyclohexyl Fluoride from Rotational Transition Intensity Measurements. J. Am. Chem. Soc. 1972, 94, 3737–3739. (5) Durig, J. R.; Ward, R. M.; Conrad, A. R.; Tubergen, M. J.; Nelson, K. G.; Groner, P.; Gounev, T. K. Microwave, Raman, and Infrared Spectra, r0 Structural Parameters, Conformational Stability, and Vibrational Assignment of Cyanocyclohexane. J. Mol. Struct. 2010, 967, 99–111. (6) Durig, J. R.; Ward, R. M.; Conrad, A. R.; Tubergen, M. J.; Guirgis, G. A.; Gounev, T. K. Microwave Spectra, r0 Structural Parameters, and Conformational Stability from Xenon Solutions of Silylcyclohexane. J. Mol. Struct. 2009, 922, 19–29. (7) Durig, J. R.; El Defrawy, A. M.; Ward, R. M.; Guirgis, G. A.; Gounev, T. K. Conformational Stability of Chlorocyclohexane from Temperature-Dependent FT-IR Spectra of Xenon Solutions, r0 Structural Parameters, and Vibrational Assignment. Struct. Chem. 2008, 19, 579–594. (8) Durig, J. R.; El Defrawy, A. M.; Ward, R. M.; Guirgis, G. A.; Gounev, T. K. Conformational Stability of Bromocyclohexane from Temperature Dependent FT-IR Spectra of Xenon Solutions, r0 Structural Parameters and Vibrational Assignment. J. Mol. Struct. 2009, 918, 26–38. (9) Zheng, C.; Subramaniam, S.; Kalasinsky, V. F.; Durig, J. R. Raman and Infrared Studies Supported by Ab Initio Calculations for the Determination of Conformational Stability, Silyl Rotational Barrier and Structural Parameters of Cyclohexyl Silane. J. Mol. Struct. 2006, 785, 143–159. (10) Durig, J. R.; Ward, R. M.; Guirgis, G. A.; Gounev, T. K. Conformational Stability from Raman Spectra, r0 Structural Parameters, and Vibrational Assignment of Methylcyclohexane. J. Raman Spectrosc. 2009, 40, 1919–1930. (11) Ouellette, R. J.; Baron, D.; Stolfo, J.; Rosenblum, A.; Weber, P. Conformational AnalysissXV: Force Field Calculations and NMR Determination of Conformational Equilibria of Organosilicon Compounds. Tetrahedron 1972, 28, 2163–2181. (12) Ouellette, R. J. Conformational Analysis. XVIII. Force Field Calculations of Conformational Equilibriums of Group IV Organometallic Compounds. J. Am. Chem. Soc. 1972, 94, 7674–7679. (13) Durig, J. R.; Zheng, C.; El Defrawy, A. M.; Ward, R. M.; Ravindranath, K.; Rajeswara Rao, N.; Gounev, T. K. On the Relative Intensities of the Raman Active Fundamentals, r0 Structural Parameters, and Pathway of Chair-Boat Interconversion of Cyclohexane and Cyclohexane-d12. J. Raman Spectrosc. 2009, 40, 197–204. (14) Moller, C.; Plesset, M. S. Note on an Approximation Treatment for Many-Electron Systems. Phys. ReV. 1934, 46, 618–622.
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