Anal. Chem. 1995, 67,4322-4329
Stereochemical Analysis of Methyl-Substituted Cyclohexanes Using 2 1 Resonance-Enhanced Multiphoton lonization Spectroscopy
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Dale R. Nesselmdt, Alan R. Potts, and Tomas Baer* Department of Chemisty, University of North Carolina, Chapel Hill, North Carolina 27599-3290
2 + 1 resonance-enhanced multiphoton ionization spectroscopy has been used to perform stereochemical analysis on methyl-substituted cyclohexanes. Structures with axial methyl substituents exhibit lower energy 3s u transition origins than those with only equatorial methyl groups. Energy differences between transition origins for stereoisomers of the same constitutional isomer are typicallygreater than 700 cm-', which are easily resolved for samples cooled in a supersonic expansion. Three additive shift parameters have been derived and used to predict transition origins to within an average error of f58 cm-' for 14 different methylcyclohexanes. In addition, an interesting correlation between the ground-statesteric properties of the molecule and the 3s u transition origins has been discovered.
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Since saturated six-membered rings are commonly found as structural components in biologically interesting systems, we have evaluated 2 1 resonance-enhanced multiphoton ionization (REMPI) spectroscopy as a tool for stereochemical analysis of methyl-substituted cyclohexanes. Our hope is that these results can then be applied to larger molecules. In general, the room temperature one-photon absorption spectra of alkanes have received less attention than compounds containing x or lone pair electrons because their transitions are broader and tend to lack vibrational structure.'-? The HOMOS of methylcyclohexanes contain o-bonding electrons which can be excited to the corresponding u* orbital or promoted to a Rydberg orbital. Unlike their linear counterparts, rigid cycloalkanes exhibit some vibrationally resolved Rydberg transitions for low values of the principle quantum n ~ m b e r . ~Therefore, .~ the Rydberg states for these molecules are more likely to contain structural information about the position and orientation of substituents than the valence states. The lowest and most accessible Rydberg states are those for the quantum number n = 3. The term values (the energies below the ionization potential) for the 3p and 3d Rydberg states of cycloalkanes are about 18 000 and 13 000 cm-l, respectively, regardless of ring size.6 The term value for the 3s Rydberg state vanes from 22 000 to 35 000 cm-', depending upon the number
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(1) Robin, M. B. Higher Excited States of Polyatomic Molecules: Academic Press: New York 1974; Vol. 1, Chapter 3. (2) Basch, H.; Robin, M. B.; Kuebler, N. A. 1. Chem. Phys. 1969,51, 52-66. (3) Raymonda, J. W.; Simpson. W. T. J. Chem. Phys. 1967,47, 430-448. (4) Lombos, B. A.; Sauvageau, P.; Sandorfy, C. J. Mol. Spectrosc. 1967,24, 253-269. (5) Robin, M. B.; Kuebler, N. A. J. Chem. Phys. 1978,69, 806-810. (6) Raymonda, J. W. J. Chem. Phys. 1972,56, 3912-3920.
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Analytical Chemistry, Vol. 67, No. 23, December 1, 1995
of ring carbons.' In cyclohexane with its IP of 79 526 cm-l,* the 3s, 3p, and 3d states thus lie near 56 800,61500, and 66 500 cm-l, respectively. At least three other groups have utilized 2 1REMPI to ionize cyclohexane by pumping its 3s u t r a n ~ i t i o n . ~ ,In ~ , '2~ 1 REMPI, two UV photons are simultaneously absorbed by the molecule to promote an electron to a real excited state. Once in the excited state, absorption of a third photon ionizes the molecule if the intermediate electronic state lies at an energy greater than two-thirds of the ionization potential. All of the n = 3 Rydberg states for the methylcyclohexanes satisfy this criterion and so can be analyzed by 2 1 REMPI. The simultaneous two-photon transition is rate limiting under the laser powers normally used for these experiments.l1>l2As a result, signal will only be observed when the energy of two photons is in resonance with a real state of the molecule. Therefore, by monitoring the electron (or ion) signal as a function of wavelength, an absorption spectrum of the intermediate state can be obtained. Various researchers have employed 2 1 REMPI and other multiphoton ionization schemes to differentiate isomers on the basis of their intermediate Rydberg or valence-state ~ p e c t r a . l ~ - * ~ This sensitivity to structural variations is made possible by highresolution laser spectroscopy coupled with the use of molecular beams. For most molecules, many rotational and vibrational states are populated at ambient temperatures, leading to spectral congestion so that the subtle differences between the absorption spectra for different stereoisomers become obscured. This problem is eliminated when samples undergo supersonic expan-
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(7) Robin, M. B.; Kuebler, N. A. J. Chem. Phys. 1979,70, 3362-3368. (8) Lias, S.G.; Bartrness, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R D.; Mallard, W. G. J. Phys. Chem. Ref: Data 1988,17. 262. (9) Shang, Q. Y.: Bemstein, E. R J. Chem. Phys. 1994,100, 862558632, (10) Whetten, R. L.; Grant, E. R J. Chem. Phys. 1984,80, 1711-1728. (11) Parker, D. H. In Utrasemitiue Loser Spectroscopy: Niger, D. S., Ed.; Academic Press: New York, 1983; Chapter 4. (12) Parker, D.H.; Berg, J. 0.;El-Sayed. M. A In Advances in Loser Chemistry; Zewail. A H., Ed.; Springer Verlag: Berlin, 1978 pp 320-335. (13) Weickhardt, C.; Zimmermann, R.; Boesl, U.; Schlag, E. W. Rapid Commun. IWUS Spectrom. 1993,7, 182-185. (14) Seeman, J. I.; Paine, J. B.; Secor, H. V.; Im, H.; Bernstein. E. R.] A m . Chem. SOC.1992,114. 5269-5280. (15) Tubergen, M. J.; Cable, J. R; Levy, D. H. J. Chem. Phys. 1990,92, 51-60. (16) Li, L.; Lubman. D.M. Appl. Spectrosc. 1989,43, 543-549. (17) Li, L.; Lubman, D.M.Appl. Spectrosc. 1988,42. 418-424. (18) Cable, J. R: Tubergen, M. J.; Levy, D. H. Faraday Discuss. Chem. SOC.1988, 86, 143 -152. (19) Imasaka, T.: Tashiro, K; Ishibashi, N. Anal. Chem. 1986,58, 3242-3244. (20) Tembreull, R.; Sin, C. H.; Li, P.; Pang, H. M.; Lubman, D. M. A d . Chem. 1985,57,1186-1192. (21) Dunn, T. M.; Tembreull, R.; Lubman. D. M. Chem. Phys. Lett. 1985,121, 453-457. (22)Tembreull, R.; Lubman, D.M. Anal. Chem. 1984,56, 1962-1967. 0003-270019510367-4322$9.0010 0 1995 American Chemical Society
sion because the internal energy of the seed molecules is converted into translational energy. The rotational and vibrational degrees of freedom normally step out of the expansion with temperatures in the ranges of 1-10 and 30-100 K,23-25 respectively. Therefore, in the cold molecular beam, very few rotational states and only the lowest vibrational state are significantly populated, greatly reducing spectral congestion. The fwhm of the vibrational bands observed in the REMPI spectra of substituted five- and six-membered rings are usually on the order of a few
wave number^.^^-^^ In previous studies we obtained the 3s n 2 1 REMPI spectra of methylcyclohexanones (MCHOs) ?6-28 ethylcyclohexanones (ECHOs),29 methylcyclopentanones (MCPOs) ethylcyclopentanones (ECPOs),29 and methyltetrahydropyrans (MTHPs),27.31which were then used to perform stereochemical and conformational analysis on these compounds. In each case, the 3s n transition origins lie between 49 000 and 52 OOO cm-1 and can be pumped via simultaneous absorption of two 385-41G nm photons. Since the fwhm of the vibrational bands are -5 cm-I, the relatively large energy differences (100's cm-I) between 0-0 transitions for different stereoisomers and conformations permit them to be easily distinguished. The 0-0 transitions for these molecules are very sensitive to both the positions and orientations of their substituents. For instance, consider the MCHOs, where substitution of an equatorial 2-methyl group red shifts the 0-0 transition 543 cm-1 with respect to the 0-0 transition for the unsubstituted parent compound. Equatorial substituents in the 3- and 4-positions cause blue shifts, with the largest shift of 147 cm-1 occumng for 3sub~titution.~~ The magnitude and direction of the shifts also depend strongly on whether the substituent is in an equatorial or axial orientation. Axial methyl groups cause large red shifts relative to their equatorial counterparts. In addition, we also discovered that the 0-0 transition energies for the methyl-substituted compounds could be quantitatively predicted from a series of additive shift parameters for each unique position of substitution and orientation of the methyl groups. For example, the predicted transition origin energy of truns-2,3dimethylcyclohexanone can be calculated by adding the shift parameters for equatorial 2- and 3-methyl groups to the 0-0 transition energy for unsubstituted cyclohexanone to give 50 318 f 21 cm-1.26This number compares very well with the observed transition origin at 50 311 cm-' and is fairly representative of the results obtainable with the MCHOs and M C P O S . ~ ~ , ~ ~ In this paper, we extend this approach to the stereochemical analysis of the methyl-substituted cyclohexanes. We will experimentally show that 3s 0 transition origins for methylcyclohexanes are sensitive to the relative position of substitution in di- and trimethylcyclohexanes. Likewise, the differences between 0-0 transitions for stereoisomers of the same constitutional isomer
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,28s30
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(23)DePaul, S.;Pullman, D.; Friedrich, B. J. Phys. Chem. 1993,97,2167-2171. (24)Hayes, J. M.;Small, G . J. Anal. Chem. 1983,55,565A-574A. (25)Weitzel, K M.;Booze, J. A; Baer, T. Chem. Phys Lett. 1991, 150, 263273. (26)Driscoll, J. W.; Baer, T. Anal. Chem. 1992,64, 2604-2609. (27)Cornish, T..I.Baer, ; T. 1.Phys. Chem. 1990,94,2852-2857. (28) Cornish, T.J.; Baer, T. /. Am. Chem. SOC.1988, 110,3099-3106. (29) Nesselrodt, D.R; Potts, A R.; Baer, T. J. Phys. Chem. 1995,99,44584465. (30)Potts, A R;Nesselrodt, D. R; Baer T.; Driscoll, J. W.; Bays, J. P. J. Phys. Chem. 1995,99,12090-12098. (31) Cornish, T.J.; Baer. T. Anal. Chem. 1990,62, 1623-1627. (32) Nesselrodt, D. R.; Baer, T. Anal. Chem. 1994,66, 2497-2504. (33)Cornish, T.J.; Baer, T. J. Am. Chem. Suc. 1987, 109,6915-6920.
are on the order of 700 cm-I or more, which permits the stereoisomers to be distinguished by their transition origin energies. In addition, we will demonstrate that a total of three empirical shift parameters will permit us to predict the transition origins for most di- and trimethylcyclohexanes. Finally, correlations between REMPI and 13C NMR spectroscopy will be demonstrated, suggesting that the ground-state steric properties of the molecule are largely responsible for the 3s u transition origin shifts.
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EXPERIMENTALSECTION Experimental Apparatus. The apparatus used to obtain the 2 1 REMPI spectra has been described in detail el~ewhere?~ and only a short description follows. A Lumonics excimer pumped dye laser (Model EPD-330) operated at 10 Hz was used to generate tunable W radiation in the wavelength range of 350370 nm. Photons in this wavelength range have only half the energy needed to pump the 3s (7 transitions of methylcyclohexanes, which lie between 54 000 and 57 000 cm-'. This light was focused by a 25 cm focal length lens into the ionization region of an electron and ion time-of-flight (TOF) spectrometer, where it perpendicularly intersects a seeded supersonic molecular beam. The molecular beams were composed of 1-5% analyte vapor in 400-Torr argon carrier gas and were produced with a Lasertechnics Model LW pulsed valve. Background interference from pump oil and trace organics was minimal when the base pressure in the ionization region was less than Torr with the pulsed valve off. At slightly higher baseline pressures, significant background interference was encountered. REMPI spectra were obtained by monitoring the total electron signal as a function of laser wavelength. The electrons were accelerated with a 1000 V/cm electric field into a l k m field free drift tube before striking a 25" chevron microchannel plate assembly. The output of the microchannel plates was amplified and integrated over a 3 ns window with a Stanford Research Systems Model SR-245gated integrator. The laser power at each wavelength was monitored with a Scientech calorimeter. Both the electron signals and the laser power readings were digitized and transferred to a 286ATmicrocomputer where the signals were stored. The spectra could have been collected by monitoring the ion signal; however, extensive fragmentation due to the high laser intensity required for the 2-photon excitation step, makes this a less desirable option. All the spectra were power normalized to the square of the laser intensity to compensate for power differences due to the dye's wavelength-dependent gain. Since the 2-photon absorption step is rate limiting, the REMPI signal is proportional to the square of the laser intensity. The monochromator wavelength reading on the excimer pumped dye laser was calibrated against several 0-0 transition energies obtained on a Nd:YAG pumped dye laser system. Indirect calibration was performed because the Nd:YAG laser system uses red dyes mixed with the 1064-nm fundamental to give light in the desired UV wavelength range. The red dyes can be calibrated to less than fl cm-l against neon transitions in an optogalvanic cell. Neon has 18 strong transitions at the wavelengths of the red dyes used in the Nd:YAG pumped ~ystem.3~ Reagents. Cyclohexane with 97%purity was purchased from Aldrich. All other analytes were obtained from Wiley Organics
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(34)Smyth, K. C.; Schenk, P. K. Chem. Phys. Lett. 1978,55, 466-472.
Analytical Chemistry, Vol. 67, No. 23, December 1, 1995
4323
with '99% isomeric purity. No attempts were made to further puri@ the samples. 13C NMFt Spectra. 13C NMR spectra for 1,1,4trimethylcyclohexane, l-cis-2-cis-3-trimethylcyclohexane,and 1-cis-3-cis-5 trimethylcyclohexane were obtained with a Varian W O O NMR spectrometer. All the spectra were collected using deuterated chloroform as the solvent and were externally referenced to TMS. Peak assignments were made using well-known chemical shift parameter^.^^^^^ The 13C NMR chemical shifts for the other compounds have been taken from the literature.36 Calculations. Molecular mechanics calculations have been performed with the commercial software package PCMODEL for Windows, which uses the MMX force field.37 Calculations were performed to determine the relative stability of different conformations. These energy differences were then used in the Boltzmann equation to determine the 298 K relative population ratios of the conformations.
e - (AH"/RT)
ratio = Kes = e- ( A G c / R n
Because equatorial and axial conformations have similar vibrational frequencies and moments of inertia, the AS' associated with the equilibrium is very small so that the equilibrium could be approximated by use of the A W s from the MMX calculations. The total MMX energy and the individual contributions to this energy were also determined for each compound in this study.
a m
55000
56000
57000 ENERGY (cm-')
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58000
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Figure 1. 3s u 2 1 REMPI spectra of cyclohexane and methylcyclohexane. The inset showing the transitions for axial methylcyclohexane has been expanded by a factor of 20. The combs mark the first few vibrational transitions for both conformers. Table 1. Comparlson of 2.Photon Transltion Wavelengths, 3s u Transition Origin Energies, and Relative Transition Origin Shifts for Methyl-Substituted Cyclohexanes
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RESULTS
2 + 1 REMPI Spectra of Cyclohexanes. (A) Cyclohexane and Methylcyclohexane. The 3s u 2 + 1 REMPI spectra of cyclohexane (CH) and methylcyclohexane (MCH) are displayed in Figure 1. They were collected using linear polarized light. The overall electronic symmetry of the 3s u transition in the DSd CH is E, Alg.7,9J0The 0-0 transition is thus allowed in a 2-photon transition but not allowed by 1-photon excitation. Under D3d symmetry, vibronic transitions to vibrational states having E, or AI, symmetry are allowed for 2-photon transition^.^^ Vibronic transitions to both symmetry states are observed and can be distinguished by their relative fwhm. As pointed out by Shang and Bernsteing and Whetten and Grant,l0the narrow peaks (fwhm < 1 cm-l) are assigned to Alg vibronic states arising from eg x E, vibronic coupling, while the broader peaks with fwhm of 5 cm-l are due to vibronic states of E, symmetry. The energy of the 3s u 0-0 transition energy for cyclohexane and all the other compounds in this study are listed in Table 1. Shang and Bernstein reported a CH 0-0 transition at 56 758 ~ m - ' ,while ~ Whetten and Grant obtained a value of 56766 cm-l.1° Our transition origin for CH occurs at 56 769 & 4 cm-l, showing better agreement with Whetten and Grant's value. The uncertainty in our number is due to the indirect calibration method.
unsubstituted eq-methyl =-methylb 1,l-dimethyl cis-1,2-dimethylb truns-1,2-dimethylb cis-1,3-dimethylb trans-1,3-dimethylb cis-1,4-dimethylb trans-1&dimethylb l,l,Ztrimethyl 1,l,Ptrimethyl 1,1,4(ed-trimethyl 1,1,4(ax)-trimethyl l-cis-2-cis-3-trimethyhylb l-cis-2-truns-3-trimethylb l-trum-2-cis-3-trimethylb l-trum-2-cis-4-trimethylb l-truns-2-truns-4-~methylt l-cis-5cis-5trimethylb l-cis-3-truns-5trimethylb
(35) Dalling, D. K.; Grant, D. M. J. Am. Chem. Soc. 1972,94, 5318-5324. (36) Strothers, J. B. Curbon-13 NMR Spectroscopy; Academic Press, Inc.: New York, 1972; p 62. (37) PCMODEL for Windows is available from Serena Software, Box 3076, Bloomington, IN, 47402-3076. The MMX force field is an extension of Allinger's MM2 force field (Allinger. N. L.; Yoh, Y. H. QCPE 1977,No. 395) and includes pi-VESCF routines from his MMPl (Allinger, N. L.; et al. QCPE 1976,No. 318). Changes were made by J. J. Gajewski and K. E. Gilbert. (38) Hams, D. C.; Bertolucci, M. D. Symmety and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy; Oxford University Press: New York, 1978; Appendix A.
The 3s u REMPI spectrum for MCH (see bottom of Figure 1) differs from that of the unsubstituted parent compound because addition of the methyl group lowers the molecular symmetry so that many more vibronic transitions are allowed. All of the baseline resolved peaks have approximately the same fwhm. The spectrum is also more complex because the methyl group may occupy either equatorial or axial orientations in the chair conformation of the cyclohexane ring. No other ring conformations are significantly populated at the pulsed valve temperature (298 K)
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4324 Analytical Chemistry, Vol. 67, No. 23, December 7, 7995
compd
2-photon 3s u transition transition transition wavelength origin energy origin shift" (nm) (cm-l) (cm-1) 352.305 356.633 361.494 365.571 369.918 361.252 356.716 361.566 361.657 356.182 365.484 364.398 364.817 367.013 370.240 367.134 360.627 365.424 360.653 356.544 361.840
56 769 56 080 55 326 54 709 54 066 55 363 56 067 55 315 55 301 56 151 54 722 54 885 54 822 54 494 54 019 54 476 55 459 54 731 55 455 56 094 55 273
698 0 -754 -1371 -2014 -717 - 13 -765 -779 71 -1358 -1195 -1258 -1586 -2061 - 1604 -621 - 1349 -625 14 -807
Relative to the 0-0 transition for equatorial methylcyclohexane. Compounds used to determine optimized shift parameters.
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Table 2. MMX AY0's,Predicted Boltzmann Population Ratios for Conformations at 298 K, and Observed Relative Transition Origin Intensities for Various Methyicyciohexanes
compound
MMX AHfo conformtn (kcal/mol)
2-ax
-37.03 -35.26 -48.58 -47.39
4eq
-50.93
methyl
1-eq 1-ax
1,1,2-trimethyl
2-eq
1,1,4-trimethyl
4-ax l-cis-2-trans-3-trimethyl 1-ax,2eq, 3-eq 1-eq,2-ax, 3-ax l-trans-2-cis-4-trimethyl 1-eq,2eq, 4ax 1-ax,2-=, 4-eq
-49.14 -47.96
MMX
popultn ratioat 298 K
1.00 0.05 1.00 0.13 1.00 0.05
!A
c-1.2
obsdrel transtn
origin intens
1.00 0.05 1.00 u
1.00
1.00
0.04 1.00
-47.14
0.25
a
-49.06
1.00
1.00
-48.42
0.34
u
+
N
L 54000
Not observed.
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55000
56000
57000
58000
ENERGY (cm-')
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Figure 2. 3s u 2 1 REMPI spectra of dimethylcyclohexanes. The 0-0 transitions for each isomer have been marked with a dot.
so that only two conformations can be frozen out with appreciable number densities in the molecular beam. The conformation with an axial methyl substituent is known to constitute 5% of the total population at 298 K,39 a fraction confumed by our MMX calculations in Table 2. Work by Gutowsky and co-workers suggests that if the barriers to interconversion are in excess of -1 kcal/ mol, the higher energy structure will not conformationally relax during supersonic e x p a n s i ~ n . This ~ ~ . ~is~true as long as the rate of cooling is much faster than the rate of interconversion between conformations during the initial supersonic expansion. Our previous studies with M C H O S , ~MCPOS,~~~~O ~-~~ and some of their ethyl-substituted have shown that the conformations can be trapped in their ambient temperature ratios in the molecular beam. Some of the transitions for the two different MCH conformations are marked with combs in Figure l. The strong transition at 56 080 cm-1 is assigned to the transition origin for the equatorial conformation, while the peak furthest to the red at 55 326 cm-' is assigned to the axial conformation's 0-0 transition. These assignments are based on the relative intensities of the peaks and the similarity in the vibrational structure (as marked with combs) to the blue of each assigned 0-0 transition. In addition, transitions for structures with axial methyl groups appear to the red of those corresponding to conformations with equatorial substituents, as shown below for the dimethylcyclohexanes. (B) Dimethylcyclohexanes. The 3s u REMPI spectra for three pairs of dimethylcyclohexane (DMCH) stereoisomers are shown in Figure 2. These spectra are similar to that for MCH. Although, the stereoisomers with diequatorial methyl groups can exist in a higher energy diaxial conformation, the energy difference between the two is so large that only the diequatorial conformation has a significant number density in the molecular beam. The stereoisomers with equatorial and axial substituents
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(39)Carey, F. A Organic Chemisty; McGraw-Hill Book Co.: New York, 1987; Chapter 3. (40) Ruoff, R S.; Klots, T. D.; Emilsson,T.; Gutowsky, H. S.J. Chem. Phys. 1990, 93,3142-3150. (41) Klots, T. D.; Ruoff, R. S.; Gutowsky, H. S.J. Chem. Phys. 1989,90,42174221.
can exist in only a single chair conformation. Therefore, all the peaks in each spectrum are due to a single structure. The transition origin in each spectrum is marked with a dot. No other peaks are observed further to the red of the assigned 0-0 transitions. Values for all the DMCH transition origins can be found in Table 1. Like CH and MCH, the 0-0 transition is one of the largest peaks in the spectrum, except for cases of vicinal methyl substitution. The transition origins for cis- and truns-1,2DMCH are smaller than many other peaks in their REMPI spectra. Evidently, a substantial geometry change takes place upon exciting compounds with vicinal methyl groups to the 3s Rydberg state. This geometry change enhances the Franck-Condon factors for excitation to higher energy vibrational states so that the dominant peaks in these spectra appear at more than 1000 cm-' to the blue of the transition origins. The most striking and analytically useful feature of these spectra is that the transition origins for each stereoisomeric pair are separated by hundreds of wavenumbers. This fact permits differentiation of stereoisomers on the basis of their transition origin energies. The 0-0 transition energies for cis- and trans1,2-DMCH,cis- and trans-1,3-DMCH, and cis- and tram-1,CDMCH are separated by 1297, 752, and 850 cm-', respectively. It is interesting to note that the 0-0 transitions for the trans isomers of 1,2-DMCH and 1,CDMCH lie at higher energy than their cis counterparts, while the opposite is true for the 1,3DMCH stereoisomers. In each case, the stereoisomer with the higher energy transition origin contains diequatorial methyl groups, while the lower energy 0-0 transition belongs to the stereoisomer with axial and equatorial substituents. Therefore, axial methyl groups cause large red shifts in the transition origins relative to the 0-0 transitions for the stereoisomers containing only equatorial methyl substituents. This observation is consistent with those we have previously noted for cyclic ketones and ethers. (C) Trimethylcyclohexanes with Geminal Methyl Substituents. The 3s u REMPI spectra of 1,l-DMCHand trimethylcyclohexanes (?'MCHs) with geminal methyl groups are displayed in Figure 3. The transition origin in each spectrum is marked
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Analytical Chemistry, Vol. 67, No. 23, December 1, 1995
4325
I-C-2-1-3
L@,
I-c-3-1-5
54500
-
55000 55500 ENERGY (cm-')
56000
54000
-
55000 56000 ENERGY (cm-I)
57000
Figure 3. 3s u 2 + 1 REMPI spectra of 1 , l-dimethylcyclohexane and trimethylcyclohexanes containing geminal methyl groups. Their 0-0 transitions are marked with dots or combs. The combs above the 1,1,4-trimethylcyclohexane spectrum differentiate the transitions for the conformations with axial and equatorial 4-methyl groups.
Figure 4. 3s u 2 + 1 REMPI spectra of seven trimethylcyclohexanes without geminal methyl substituents. The insets in the spectra for the compounds with vicinal methyl groups have been expanded by a factor of 10. All assigned transition origins are marked with dots.
with a dot or a comb. With the exception of 1,1,4TMCH, the transition origin is not the dominant peak in the spectrum. A series of vibrational bands appear at energies greater than -150 cm-' to the blue of the 0-0 transitions and coalesce into broad unresolved bands at higher energy. The 1,1,%TMCHspectrum has the best signal-to-noise ratio and displays the most highly resolved vibrational structure, clearly distinguishing it from the other geminally substituted compounds. 1,1,4-TMCH exists in two low-energy conformations in the molecular beam. The large peak at 54 822 cm-I is assigned to the transition origin for the structure with an equatorial 4methyl group, while the peak at 54 494 cm-' is the transition origin for the conformation with an axial 4methyl substituent. On the basis of the molecular mechanics results listed in Table 2, we predict that, at 298 K (the pulsed valve temperature), the population ratio of the higher energy conformation to the most stable structure is -0.05. The supersonic expansion conditions used to collect this spectrum were identical to those for obtaining the MCH spectrum. Therefore, we expect to see transitions for two conformations in a -1:20 ratio in the REMPI spectrum. As shown in Table 2, this ratio is approximately the observed value. What about conformations with axial methyl groups for the other TMCHs? MMX calculations predict that the fraction of the population in the 1,1,3(ax)-TMCHconformation is less than 0.002 and thus will not be detected. On the other hand, the roomtemperature ratio of the less stable to most stable 1,1,2-TMCH conformer is 0.13 (see Table 2). However, we are not able to assign any transitions to the 1,1,2(ax)-TMCH conformation at this time. The calculated energy differences between axial and equatorial methyl groups follow an interesting and expected pattern. Axial methyl substitution at the %position is very unstable because of the 1,3-diaxial steric repulsion. The other two axial isomers have their axial methyl groups on opposite sides of the ring so that they do not interfere.
(D) Other Trimethylcyclohexanes. The 3s o REMPI spectra for seven additional trimethylcyclohexanes are presented in Figure 4. The trends observed for the DMCHs are repeated for these compounds. The 0-0 transitions for vicinally substituted TMCHs are small because of poor Franck-Condon factors; therefore, some of them have been enlarged by a factor of 10 in the insets. Because of these weak onsets, the transition origins for some of these spectra are dif6cult to assign. Those with the weakest peaks were assigned in part with the aid of the shift parameters discussed in the following section. Like the DMCHs, different stereoisomeric pairs can be distinguished by their transition origin energies. For instance, the energy difference between 0-0 transitions for l-cis-3-cis-5TMCH and 1-cis-3-trans5TMCH is 821 cm-l. The TMCH structures with all equatorial methyl groups appear to the blue of those containing axial substituents. Based on our molecular mechanics calculations, only l-cis-2trans-3-, and l-truns-2-cis-4TMCH should have higher energy conformations that constitute more than -1% of the roomtemperature population (see Table 2). This is because all of the conformations with tri-axial methyl groups as well as those with 1,3 di-axial methyl groups are unstable. On the other hand, the higher energy conformations of 1-cis-2-trans-%and l-truns-2-cis-3TMCH are quite stable so that they should constitute 20-25% of the population at 298 K. The transition origin for the higher energy l-cis-2-trans-3-TMCH conformation is calculated (as shown in the next section) to be at 53 339 cm-', which is -1140 cm-l to the red of the more stable conformation origin. The combination of a weak transition origin as well as low laser power in this wavelength region does not permit us to identify the transition origin for this conformation. On the other hand, the weak peaks to the red of the l-cis-2-trans-3-TMCHspectrum in Figure 4 are undoubtedly due to vibronic transitions from the less stable conformation. However, they are much less intense than expected
4326 Analytical Chemistry, Vol. 67, No. 23, December 1, 7995
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on the basis of the large room-temperature population of this conformation. A similar analysis holds for the l-truns-2-cis-4TMCH isomer. The higher energy conformation should appear -1420 cm-' to the red of the very weak origin at 54 731 cm-I. While we do not expect to observe the weak origin of the higher energy conformation, we should observe moderately intense vibronic peaks at -54 300 cm-'. However, we see nothing there. This lack of signal from the higher energy conformation is puzzling. The barriers to interconversion in the cyclohexane system (-10 kcal/ m o P 4 ) are among the largest in six-membered ring compounds. Our previous work with rotational barriers of 3-4 kcal/mol in ethylcyclohexanones and ethylcyclopentanones provided nearquantitative agreement between predicted and observed peak i n t e n s i t i e ~ . ~It~is thus very unlikely that the higher energy conformations of the methylcyclohexanes equilibrate during the molecular beam expansion. A possible explanation for the nonobservance of the higher energy conformation in the two spectra of Figure 4 may be related to the rather strange intensity patterns in these spectra. A number of the molecules in Figure 4 have very weak origin bands followed at higher energies by anomalously large vibronic peaks. In order to observe a strong REMPI signal, it is essential to have a stable intermediate state. The lifetime must be on the order of the laser pulse width, which in this case is 5-6 ns. Could it be that the origin and the lower energy vibrational levels of the 3s Rydberg state are depleted rapidly by predissociation or by internal conversion while some of the higher energy levels are more stable? Such a depletion mechanism would not necessarily follow a regular pattern and could even deplete one conformation more rapidly than another one. DISCUSSION (A) Additivity EfTect. Least-SquaresAnalysis. The number of variables needed to formulate an optimized set of shift parameters can be determined by examining the transition origin shifts in Table 1 for MCH and the DMCHs. The shifts due to ax-MCH, truns-1,2-DMCH, truns-l,3-DMCH, and cis-1,CDMCH which contain 1-axial, 2-equatorial, 3-axial, and 4axial methyl groups, respectively, have an average value of -754 f 27 cm-' and can therefore be described by a single shift parameter. cis1,3-DMCH and truns-1,CDMCH give very small red shifts, suggesting that 3-, and Cequatorial substituents can be described by a second shift parameter. This leaves only the 2-axial substitution to be described by a third shift parameter with a magnitude of --2014 cm-'. Comparison of the shifts for the 1,3,5TMCH stereoisomers reveals that 3- and 5substitution are essentially equivalent. We should thus be able to predict the transition origins for most of the compounds in this study with just three shift parameters. Since no MCHs with &substitution are commercially available, we were not able to determine whether substitution in the 2- and &positions produces equivalent shifts. As discussed later, substitution in these two positions is probably not equivalent. The optimized values for the REMPI shift parameters relative to eq-MCH are obtained by simultaneously fitting the following ~~~~
~~~~
(42) Eliel, E. L.; Wilen, S. H.: Mander, L. N. Stereochemisty of Organic Compounds; Wiley & Sons: New York, 1994; Chapter 11. (43) Leong, M. K: Mastryukov, V. S.; Boggs, J. E. /. Phys. Chem. 1994,98, 6961. (44)Ross, B. D.; True, N. S. J. Am. Chem. SOC.1983,105, 4817.
Table 3. Optimized Shift Parameters for Methyl Substituents
substituent
shift parameter (cm-l)
3-eq,4 e q 1-ax,2-eq, 3-ax, 4-ax 2-ax
7 f 23 -734 It 54 -2041 It 15
equation:
where .SPEDis the predicted energy shift relative to eq-MCH, the m's refer to the number of substituents in each unique orientation, and the scs', are the optimized shift parameters. A nonlinear leastsquares Levenberg-Marquardt fitting procedure was used to determine the best shift parameters such that
S=sxM
(3)
where M is a 3 x 14 matrix containing row vectors of the form [mo ml m2l in which the elements are the occupation number of the three nonequivalent methyl group orientations for the 14 MCH structures marked in Table 1. For example, the form of the row corresponding to cis-1,BDMCH is [O 0 11 where the compound has a 2-axial methyl group. Likewise, l-truns-2-truns-4-TMCHhas the form [l 1 01. S is a 1 x 14 matrix containing the observed transition origin shifts relative to eq-MCH. Optimized shift parameters were obtained by adjusting s, the 1 x 3 matrix of shift q) S ( Z . ~ ) ]in order to minimize x2 parameters [ ~ ( 3 ~ ~ , kS(l.ax,
[email protected],4-a) where 14
(4)
Optimized shift parameters can be found in Table 3, and a plot of predicted versus observed transition origins for all 14 compounds used in the analysis is shown in Figure 5. A best fit gives uncertainties in the range of 15-54 cm-1 for the three shift parameters. On average, the error associated with predicting the transition origins with respect to eq-MCH is -58 cm-I over a range of observed shifts of 2100 cm-'. The differences between the predicted and observed 0-0 transition energies are listed in Table 4. The compounds containing geminal methyl groups were excluded from the above analysis since doing so increases the correlation coefficient for the observed and predicted 0-0 transitions from 0.965 to 0.994. The shift parameters derived from the other compounds gives predicted transition origin energies of 55 346, 54 612, 55 353, 55 353, and 54 612 cm-l for l,l-DMCH, 1,1,2-TMCH,1,1,3-TMCH,1,1,4(eq)-TMCH,and 1,1,4(ax)-TMCH, respectively. These results give an average discrepancy of 373 cm-I between the predicted and observed transition origins compared to an average error of only 82 cm-I for the other TMCHs. The steric effects associated with gem-methyl groups require additional terms to accurately model the transition origin shifts. However, the deviation of thegem-TMCH transition origins Analytical Chemistry, Vol. 67, No. 23, December 1, 1995
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h
56000
-
/
v
h
maintained. However, this is not quite the case. Consider the TMCH, l(eq) ,2(eq),3(ax), which according to the IUPAC convention could just as easily be named l(ax),2(eq),3(eq). Do the predicted shifts give the same values? Using the shift values from Table 3, we calculate shifts of (0) (-734) (-734) = 1468 cm-l for the first method of naming this 1,2,3-TMCH, and (-734) + (-734) + (+7) = -1461 cm-I for the reverse method of naming the compound. These values are essentially the same and close to the experimental value for l-cis-2-truns-3-TMCHof -1604 cm-I. (According to Table 4,this is actually the worst agreement among all of the compounds investigated.) But, we could just as easily have named this compound l(eq),2(ax),6(eq) or l(eq),2(eq),& (ax)-TMCH. This is not in accord with the IUPAC convention, which insists on minimizing the numbers. This is a convention that we should be free to use or not. However, in this case, the predicted shifts for both would be (0) + (-2041) (-734) = -2775 cm-l, assuming that substitution in the 2- and &positions are equivalent. (This was not actually tested in our set of compounds, but it seems most reasonable to assume that they are equivalent.) The predicted shift now is completely wrong. The interesting aspect is that the observed shifts consist of a sum of 1,2 and 1,3 interactions and not as two 4 2 interactions. Presumably, by chance, this happens to be consistent with the IUPAC convention for naming these compounds. (B) Correlations with 13C NMR Spectroscopy. Stereochemical analysis has generally been performed using I3C NMR spectroscopy. In our previous work with MCHOs and MCPOs, we noted that there exists an interesting correlation between the 13C NMR chemical shift of the carbonyl group and the REMPI These correlations have made it possible to predict the carbonyl 13CNMR shifts from the REMPI transitions and vice versa and to use these techniques in combination to assign REMPI transitions for mixtures that cannot be separated on a preparative GC column.26 A good correlation has been discovered between the 13CNMR chemical shifts for the methyl carbon and the 3s u REMPI transitions for those substituted cyclohexanes in which all the methyl groups are equivalent. It should be noted that all the methyl 13CNMR shifts for the DMCHs are equivalent because ring flipping occurs rapidly on the time scale of the NMR experiment. As a result, only one peak is observed for the DMCH methyl carbons. Likewise, all three methyl groups in 1-cis-3-cisSTMCH are equivalent and give rise to a single methyl transition at 22.7 ~ p m On . ~the~ other hand, none of the other TMCHs have three equivalent methyl groups and tend to fall off the correlation line. A correlation plot of 13CNMR chemical shift for the 1-methyl group versus the REMPI transition origin shift is displayed in Figure 6. The 1-methyl group was selected since all the MCHs have one. The gem-MCHs were excluded from the plot because their spectroscopic behavior in the REMPI experiment is different from the other MCHs. Eliel has noted that additivity for the gemMCHs breaks down for the 13CNMR experiment as well.42 The data points for all the compounds with equivalent methyl groups are marked as solid dots, while the data points for all the other compounds are marked with squares. The regression line through these points has a correlation coefficient of 0.992. The 95%confidence limits are shown as dotted lines to either side of the regression line. Ai1 the data points for the compounds with nonequivalent methyl groups fall outside of the 95% confidence
+
ti
&
5400054000 54500 55000
55500
56000
Observed 0-0 Transition Energy (cm-’)
Figure 5. Correlation plot of predicted versus observed 0-0 transitions for the methylcyclohexanes (solid circles). The gemTMCHs (open triangles) were not included in calculation of the regression line. Table 4. Comparison of Observed and Predicted 3s Transition Origin Energies for Methylcyclohexanes
compound eq-methyl ax-methyl cis-1,2-dimethyl truns-1,2-dimethyl cis-1,PdimethyI truns-l,3-dimethyl cis-l,Cdimethyl truns-1,4-dimethyl l-cis-2-cis-3-trimethy1 l-cis-2-truns-3-trimethyl l-truns-2-cis-3-trimethyl l-truns-2-cis-4-trimethyl l-truns-2-truns-4-tmethyl
l-cis-3-cis-5-trimethyl l-cis-3-truns-5-trimethyl
transition origin energy (cm-I) obsd pred
3s-u
56 080 55 326 54 066 55 363 56 067 55 315 55 301 56 151 54 019 54 476
55 459 54 731 55 455 56 094 55 273
3s-a
55 356 f 54 54 039 i 15 55 346 f 54 56 087 f 23 55 346 f 54 55 346 f 54 56 087 i 23 54 046 f 59 54 619 f 80 55 353 f 59 54 612 f 76 55 353 f 59 56 094 f 33 55 353 f 59
-u
obsd-pred (cm-’) -30 27 14 -20 -31 -45 64
-27 -143 106
119 102 0 -80
from the predicted line does not follow any obvious pattern (see Figure 5) so that no single parameter can account for these spectra. These results indicate that a better approach is to treat the gem-MCHs as a separate “class” of molecules, which is spectroscopically different from the other MCHs. Close examination of the transition origin energies for the gem-MCHs listed in Table 1 reveals that some signifcant differences exist between the shifts for these compounds and those for other MCHs. The shifts for thegem-TMCHs occur to the blue of 1,l-DMCH regardless of the position of substitution as long as the methyl group is equatorial. This is true even for 1,1,2-TMCH in which an equatorial methyl group in the 2-position shifts the transition origin by +13 cm-’. 1,l-DMCH is assumed to be the parent molecule for this “class” of compounds. This finding is in sharp contrast to that for the other MCHs in which such a methyl substitution shifts the origin by -752 cm-I. The relationship between the nomenclature convention and the shift parameters is an interesting one. One might expect that the derived shift parameters should not depend upon what system is used to name the compounds, as long as consistency is 4328 Analytical Chemishy, Vol. 67, No. 23, December 1, 7995
+
+
-
(45) Cornish, T. J.; Baer, T.]. Am. Chew. SOC.1988, 110, 6287-6291.
/
-2000
-1500 2+1
-500
-1000
0
REMPI SHIFT (cm-')
Flgure 6. Correlation plot of 13CNMR shift for the 1-methyl carbon versus the observed 0-0 transition shifts relative to equatorial methylcyclohexane. The compounds with all equivalent methyl groups are marked with solid circles, while those with nonequivalent methyl groups are marked with open squares.
van der Waals energy at the carbon atoms and the 13C NMR chemical shifts for a variety of compounds, including cyclohexa n e ~ > Repulsive ~ , ~ ~ van der Waals interactions are associated with deshielding effects, while attractive interactions tend to shield the resonant nucleus. While the total repulsive van der Waals energies are greater for the structures with axial methyl groups, the local repulsive van der Waals interactions at the carbon atoms are reduced for these structures, leading to increased shielding of the resonant nucleus. The increased shielding produces upfield shifts in the methyl carbon 13C NMR chemical shifts. In the REMPI experiment, the structures with axial methyl groups (and consequently increased shielding of the carbon nuclei) appear further to the red than structures with only equatorial methyl groups. If the correlations illustrated in Figure 7 are valid, then the 3s u transition origin shifts are strongly dependent upon the ground-state steric properties of the molecules. We should not be surprised then that some correlations exist between the observed REMPI and 13C NMR shifts.
-
CONCLUSIONS 2 1 REMPI provides an effective means to distinguish stereoisomers of methyl-substituted cyclohexanes. Because the samples have been cooled in a supersonic expansion and analyzed in the gas phase, vibrationally resolved absorption spectra with fwhm of less than 5 cm-I can be obtained. As a result, the several hundred wavenumber energy differences between the 3s u 0-0 transitions for different stereoisomers of the same constitutional isomer can be used to effectively differentiate them. Compounds containing vicinal methyl groups can be easily distinguished from other MCHs by the poor Franck-Condon factors for excitation of the 0-0 transition observed in their REMPI spectra. A set of empirical shift parameters has been derived and used to accurately predict the transition origins for most of the MCHs in this study. These shift parameters can be used to predict the 0-0 transitions for most di- and trimethylcyclohexanes to within an average error of f 5 8 cm-I. Because the gem-MCHs behave spectroscopically different from the other MCHs, they were excluded from this analysis. It may be possible to derive a set of shift parameters for the gem-MCHs, but additional spectra with the tetramethylcyclohexanes containing gem-methyl groups will have to be obtained. An experimental correlation between 13CNMR and REMPI has been discovered. It is believed that the correlation arises from the local van der Waals interactions at the carbon nuclei. Therefore, the relative 3s u transition energies reflect the ground-state steric properties of the molecule.
+
-
VanderXula
0 2
Stretch. Bend. & Stretoh-bnd
,
I
54000 54500 55000 55500 56000 56500 57000 0-0 Transition Energy (cm-l)
Figure 7. Correlation plot of MMX energy and its components versus the 0-0 transition energy for the methylcyclohexanes. The total MMX energy, the van der Waals energy, the torsional energy, and the sum of the stretch, bend, and stretch-bend energies are marked with diamonds, squares, triangles, and circles, respectively.
limits, except for l-truns-2-cis-3-TMCH. The 13C NMR shifts for its 1-methyl group is equal to 21.3 A plausible explanation for this apparent correlation might be that the 3s u transition energies are related to the groundstate steric properties of the molecule.45 This reasoning is consistent with the MMX energies obtained from molecular mechanics calculations. A plot of the total MMX energy (diamonds) and the van der Waals (squares), torsional (triangles), and the sum of the stretch, bend, and stretch-bend contributions (circles) to the MMX energy as a function of the 3s u transition energies are displayed in Figure 7. In all cases, the van der Waals interactionswere the major contributor to the MMX energy. This plot even correlates the gem-TMCH isomers. L6. and Chesnut have demonstrated a strong correlation between the calculated local
-
-
~
~
~~~~~~
(46) Li, S.; Chesnut, D. B. Magn. Reson. Chem. 1986,24,93-100. (47) Li, S.; Chesnut, D.B. Magn. Reson. Chem. 1985, 23, 625-638.
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ACKNOWLEDGMENT We gratefully acknowledge NSF for financial support of this project under Grant CHE-9409144. Received for review June 30, 1995. Accepted September
18, 1995.@ AC950646N *Abstract published in Advance ACS Abstracts, November 1, 1995
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