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Barriers to Internal Rotation in β-Methyl-γ-Butyrolactone, 3-Methylcyclopentanone, and γ-Valerolactone from Fourier Transform Microwave Spectroscopy
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
176, 251–257 (1996)
0084
Barriers to Internal Rotation in b-Methyl-g-Butyrolactone, 3-Methylcyclopentanone, and g-Valerolactone from Fourier Transform Microwave Spectroscopy M. Elena Charro1 and Jose´ L. Alonso Departamento de QuıB mica-Fisica, Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain Received June 29, 1995; in revised form November 20, 1995
The microwave spectrum of b-methyl-g-butyrolactone has been analyzed using Stark modulation microwave spectroscopy in the frequency range 26.5–40 GHz. Spectra of the ground vibrational state and the first excited states of the ring bending, ring twisting, and methyl torsion have been assigned. The rotational constants are consistent with the molecule having a conformation similar to that of g-butyrolactone, and with the methyl group occupying an equatorial position. A reinvestigation of the microwave spectrum of 3-methylcyclopentanone has led to a reassignment of the first excited states of the ring twisting and methyl torsion vibrations. Measurements have been made in the frequency range 8–18 GHz using Fourier transform microwave spectroscopy on the ground vibrational state and the first excited state of the methyl torsion for b-methyl-g-butyrolactone, 3methylcyclopentanone, and g-valerolactone in order to determine the barriers to internal rotation. No A–E splittings have been observed in the ground vibrational state. Analyses of A–E splittings in the first excited state of the methyl torsion using the IAM method give the following barrier heights (in kJ mol01): for b-methyl-g-butyrolactone V3 Å 17.2, for 3-methylcyclopentanone V3 Å 14.76, and for g-valerolactone V3 Å 14.75. q 1996 Academic Press, Inc. INTRODUCTION
EXPERIMENTAL DETAILS
The barrier to internal rotation of a methyl group is very sensitive to the group (R) it is attached to. By making small changes in R it is possible to study variations in the methyl barrier in a systematic way. We have chosen to study the methyl barrier in a series of related saturated ring molecules. In this type of molecule the barriers are high and the A–E splittings in the ground vibrational state are small. Because of the possibility of interactions between the methyl torsion and the low-frequency large-amplitude ring-puckering vibrations, it is important, if possible, to measure these splittings in the ground vibrational state (1). The development of Fourier transform microwave spectroscopy (2) makes it possible to achieve very high sensitivity and resolution, compared to Stark spectroscopy. The high sensitivity makes it possible to work at low pressures in order to minimize collisional broadening, and low temperatures in order to minimize Doppler broadening. In this paper an attempt to measure the barriers to internal rotation is described. It has been carried out for b-methyl-g-butyrolactone (I), 3-methylcyclopentanone (II), and g-valerolactone (III) in order to compare their barriers with those in a-methyl-g-butyrolactone (IV) and 2methylcyclopentanone (V) (see Fig. 1), which have been previously measured (3). 1
To whom correspondence should be addressed.
The sample of b-methyl-g-butyrolactone was purchased from Fluka-Chimica, and those of 3-methylcyclopentanone and g-valerolactone from Janssen-Chimica. All of them were used without further purification. Measurements of the rotational spectra of b-methyl-gbutyrolactone and 3-methylcyclopentanone in the frequency range 26.5–40 GHz were made at 260 K and Ç15 mTorr using a computer-controlled Stark modulation microwave spectrometer (4). Radio frequency–microwave double resonance experiments (5, 6) were made in order to assign the spectrum of b-methyl-g-butyrolactone. The Esbitt–Wilson method (7) was used for relative intensity measurements in this molecule. Measurements in the 8–18 GHz region were made using a Fourier transform microwave spectrometer (FTMW) (2, 8) in order to observe internal rotational A–E splittings. These measurements were made at about 220 K with pressures lower than 1 mTorr. Frequencies were obtained by fitting the time domain spectra (9). Tables of the observed line frequencies are available from M. E. Charro on request. MICROWAVE SPECTRUM OF b-METHYL-gBUTYROLACTONE
Ground Vibrational State Model calculations, based on reasonable bond lengths and angles, indicated that b-methyl-g-butyrolactone is a prolate
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torial or axial). The observed rotational constants can be compared with those calculated for these four conformers from reasonable bond lengths and angles. In this way, the following assumptions were made concerning the structure and taking some parameters from a-methyl-g-butyrolactone (4) (the atom numbering scheme for a-methyl-g-butyrolactone is shown in Fig. 2):
FIG. 1. (I) b-methyl-g-butyrolactone, (II) 3-methylcyclopentanone, (III) g-valerolactone, (IV) a-methyl-g-butyrolactone, and (V) 2-methylcyclopentanone.
asymmetric rotor (k É 00.79), with the electric dipole moment mainly oriented along the inertial axis a. Low-resolution scans of the spectrum showed the presence of a prominent aR-branch band structure characteristic of a near-prolate asymmetric rotor. In order to identify the aR K01 doublets, initial assignments were made performing low Stark modulation voltage scans and radiofrequency microwave double resonance experiments in the regions where the low resolution bands occur. In this way, the first lines to be assigned were those doublets with K01 Å 4 and 5, for the bands with J Å 9 R 8 and 10 R 9. The ground state microwave spectrum of b-methyl-g-butyrolactone was then readily assigned and the aR and aQ type transitions up to J Å 38 were measured. Using FTMW spectroscopy, measurements in the range 8–18 GHz showed no A–E splittings, indicating that the barrier hindering methyl group internal rotation should be high. The spectrum was fitted using the A-reduced semirigid rotor Hamiltonian of Watson (10), using Ir representation. The results of the fitting are given in Table 1. Conformational Analysis The microwave spectrum of only one conformer of bmethyl-g-butyrolactone has been observed. The experimental data obtained from this study are not sufficient to determine a complete structure for it. However, some conformational aspects can be elucidated. There are four possible conformers, depending on the configuration of the ring (twisted or bent) and the position of the methyl group (equa-
(i) All the HCH angles are assumed to be 1107 with C{H ˚ for the methylene and methyl groups. The Å 1.095 A H{C{H planes, the CH3{C{H plane, and the carbonyl C|O bond have been taken to bisect the corresponding ring angles. (ii) The following bond lengths have been used: C|O ˚ , C2{O2 Å 1.38 A ˚ , C1{C5 Å 1.53 A ˚ , C2{C1 Å 1.195 A ˚ ˚ Å 1.52 A, and C5{CH3 Å 1.52 A. (iii) A twisted angle of 207 was assumed for the twist form and a bending angle of 217 was assumed for the bent form, and slightly different ring angles have been considered for each of the ring configurations: twisted form: O{C2{C1 Å 1117, C4{O{C2 Å 107.57, C5{C1{C2 Å 102.57; bent form: O{C2{C1 Å 1117, C4{O{C2 Å 1087, C5{C1{C2 Å 1037. The calculated rotational constants are listed in Table 2. A comparison between the observed and calculated values reveals that the observed microwave spectrum of b-methylg-butyrolactone is due to molecules with the methyl group in an equatorial position, but does not determine whether the ring is in a twisted or in a bent form. However, the twisted equatorial form could be expected to be the most stable one by analogy with related molecules such as gbutyrolactone (11, 12), g-valerolactone (13, 14), and amethyl-g-butyrolactone (3, 4), for which a twisted equatorial form has been reported. Excited States Assignment Several satellite lines corresponding to vibrational excited states of low frequency vibrations were observed close to the ground state R-branch transitions. The most intense satellite series occurs on the high frequency side, forming a progression with regular frequency and intensity patterns. This progression was assigned to successive quanta £a of the ringbending vibration, which is expected to be the lowest frequency mode of the molecule. Two more satellite lines occur very close to the ground state lines one on the high frequency side and the other on the low frequency side. The vibrational satellite lines should belong to the first excited states of the ring-twisting vibration, £b Å 1, and of the methyl torsion vibration, £g Å 1. In order to identify the first excited state of the methyl torsion vibration £g Å 1, a search for internal rotation A–E splittings was made in the frequency range 8–18 GHz using
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BARRIERS TO METHYL GROUP ROTATION
253
TABLE 1 Rotational and Centrifugal Distortion Constants and Quantity Dc for the Ground and Excited States of b-Methyl-g-butyrolactone (A) and 3-Methylcyclopentanone (B)
a
Standard error in units of the last digit in parentheses. Number of transitions fitted. c Fixed at the ground state value. d Standard deviation of the fit. e Vibrational energy relative to the ground vibrational state. b
FTMW spectroscopy. Measurements were made only for both unassigned states, and for £a Å 1. In this way, splittings were found only for transitions corresponding to the vibrational satellite appearing on the low frequency side of the ground state R-branch lines. Thus, we can conclude that the
other unassigned satellite must belong to the first excited state of the ring-twisting vibration £b Å 1. The A–E splittings observed for the £g Å 1 state, together with the frequencies for the A-level spectrum, are collected in Table 3. TABLE 2 Calculated Rotational Constants (MHz) of b-Methyl-gbutyrolactone for Four Possible Conformers and Experimental Values
FIG. 2. Ring-atom numbering scheme for b-methyl-g-butyrolactone.
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All the vibrational excited states have been fitted to the same semirigid rotor Hamiltonian, as used for the ground state. For the £g Å 1 state, the frequencies for the A-level spectrum have been used in the semirigid rotor fitting. The results of these fittings are collected in Table 1. This table also gives the values of the quantity Dc Å Ic 0 Ia 0 Ib, and of the energies above the ground vibrational states determined from relative intensity measurements. The values of Dc observed for the ring-bending and ring-twisting excited states are more negative than the ground state values, as expected for out-of-plane vibrations. The centrifugal distortion constant DK for the second quanta of ring-bending (£a Å 2), the twisting (£b Å 1) and torsional (£g Å 1) vibrational states, was kept fixed to the ground state value, given that few lines have been measured for these states.
TABLE 3 Observed A-State Frequencies and E–A Splittings and Differences between the Observed and Calculated Splittings (in MHz) for the First State of the Methyl Torsion of b-Methyl-gbutyrolactone, 3-Methylcyclopentanone, and g-Valerolactone
TABLE 4 Parameters from IAM Analysis of the First Excited State of the Methyl Torsion of b-Methyl-g-butyrolactone (A) and 3-Methylcyclopentanone (B)
a
Moment of inertia of the methyl group. Reduced internal rotation constant calculated from the structural parameters. b
c
r Å ÉrÉ,
d,e
S
r
r Å la
D
Ia Ia Ia , lb , lc . Ia Ib Ic
Euler angles g and b (angle between a axis and r): g Å arccos
S
q
lbIa
D
Ib lbIa/Ib / lcIa/Ic
b Å arccos
,
laIa . Iar
f
Reduced barrier height S Å 4V3/9F. Barrier height. h Standard errors in units of the last digit. They do not reflect the errors introduced by the assumed structure. i These parameters are defined dependent on the moments of inertia Ig (g Å a, b, c), the moment of inertia of the methyl group Ia, and the direction cosines that connect internal rotation and inertial axes lg (g Å a, b, c). g
Internal Rotational Analysis The internal rotational splittings observed for the £g Å 1 state have been fitted using the internal axis method (IAM) (15–17) in the form of the high barrier approximation of the Woods program (18). As the splittings were only slightly dependent on r, b, and g, these parameters were constrained to be the values calculated from the twisted equatorial structure ˚ 2. given above. Ia was fixed to the standard value 3.19 AMU A In this way, only the reduced barrier s was determined from the experimental data. The results are shown in Table 4, along with the other parameters relevant to the internal rotation of
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the methyl group. The differences between the observed and calculated splittings are reported in Table 3. MICROWAVE SPECTRUM OF 3-METHYLCYCLOPENTANONE
A comparison of the vibrational satellite patterns observed here for b-methyl-g-butyrolactone with those reported by Li (19) for 3-methylcyclopentanone show the same features. However, from the reported values of the quantity Dc for the second molecule, it seems that the proposed assignment of the £b Å 1 and £g Å 1 vibrational excited states to the first excited states of methyl torsion and ring-twisting, respectively, should be changed. No splittings due to methyl group internal rotation were observed by Li (19), and a lower limit of 10.04 kJ/mol was suggested for the barrier to internal rotation. In the present work, in order to determine the centrifugal distortion constants, we have extended the measurements of the rotational spectra of 3-methylcyclopentanone to higher values of J, for the R and Q branch, for both a and b-type spectra. FTMW measurements in the frequency range 8–18 GHz have been carried out for the ground vibrational state, the first excited state of the ring-bending vibration (£a Å 1), and the £b Å 1 and £g Å 1 states. Internal rotational splittings have been observed only for the £g Å 1 state. The A-level frequencies and the A–E splittings are shown in Table 3. These results indicate that £g Å 1 should be assigned to the methyl torsion vibration, and £b Å 1 should belong to the ring-twisting motion, as expected from the Dc values reported for these states (19). The spectra for all observed states has been fitted to the A-reduced semirigid rotor Hamiltonian of Watson (10) in the Ir representation. The frequencies for the A-level have been used in the fitting for the £g Å 1 state. The results are given in Table 1. For the second and third quanta of the ring-bending vibration, the DK and dK centrifugal distortion constants have been fixed at the ground state value, given that no Q-lines were measured for these states. The internal rotational splittings observed for the £g Å 1 state of 3-methylcyclopentanone have been fitted to the same model used for b-methyl-g-butyrolactone. The parameters r, b, and g have been constrained to the values calculated from the structure reported by Li (19). The results of the fitting are collected in Table 4. Table 3 shows the differences between the observed and calculated splittings. BARRIER TO INTERNAL ROTATION IN g-VALEROLACTONE
The microwave spectrum of g-valerolactone was previously studied (14) using a Stark modulation spectrometer (4). Internal rotational splittings were observed for the first
excited state of the methyl torsion for some bQ lines. In the present work, we have studied the FTMW spectrum of this vibrational state, in order to observe better resolved internal rotational splittings and to obtain a more accurate value of the barrier to hindering internal rotation in g-valerolactone. Splittings have been observed for several aQ and bQ transitions. The A–E splittings have been fitted with the Woods program by the internal axis method (IAM). The structural parameters r, b, and g have been constrained to the values reported previously (14), r Å 0.0302, b Å 0.211 rad, and g Å 0.774 rad, and the barrier height obtained with these new measurements is more accurate, 14.75(5) kJ/mol. The frequencies for the A-level transition, the corresponding splittings, and the calculated values are listed in Table 3. DISCUSSION
A series of different methylcycloderivatives have been studied in order to give a value for the barrier height of the internal rotation of the methyl group. A comparison among the values of V3 reveals that similar results have been obtained when the environment of the methyl group is the same. This is the case of a-methyl-g-butyrolactone and 2methylcyclopentanone, with the same environment of the {CH3 group (see Fig. 1), where values of 10.92 and 10.09 kJ/mol, respectively, have been calculated (3) for such barriers. The same feature is shown by 2-methyl-4,5-dihydrofuran (20), with V3 Å 8.2 kJ/mol, and a-angelicalactone (21), with almost the same value, V3 Å 8.8 kJ/mol; both molecules present this environment, {O{C(CH3) Å CH{. On this basis, attending to the methyl’s environment, the values of the barrier height of the internal rotation calculated in this work can be analyzed and compared with each other. In this way, the V3 value for the g-valerolactone, 14.76 kJ/mol, is consistent with the values for noncyclic methylcycloderivatives CH3{CH2OH and CH3{CHOH{CH3, 13.93 and 14.2 kJ/mol, respectively (22), with the same immediate environment for the methyl group. However, very different values of the barrier height to the internal rotation of the methyl group for b-methyl-g-butyrolactone (17.2 kJ/mol) and for 3-methylcyclopentanone (14.76 kJ/mol) have been determined. In both molecules, the immediate environment of the methyl group is the same (see Fig. 1) and very similar values for V3 might be expected. In order to elucidate which is the most reliable value we can compare these results with the barrier height of propane (CH3{CH2{CH3), V3 Å 13.6 kJ/mol (23), where the methyl group has the same immediate environment as in our rings. Comparing these values, only the 3-methylcyclopentanone has a value of V3 similar to propane’s, and an anomalous value of V3 (17.2 kJ/mol) is found for b-methyl-g-butyrolactone. Although the V3 value for b-methyl-g-butyrolactone has been well determined, the difference found between our val-
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TABLE 5 Summary of the Frequencies (in cm01) of Methyl Torsion and of Ring-Bending and Ring-Twisting Motions from Intensity Measurements and the Value of the Methyl Torsion Frequency from V3.
a b
Frequency calculated using the Mathieu equation. No measured value.
ues for these two rings, b-methyl-g-butyrolactone and 3methylcyclopentanone, indicates that it might correspond to an anomalous value. This result may be attributed to an interaction between the methyl torsion and other low frequency motion. It has been demonstrated (1) that when the methyl group torsion is influenced by another vibration the most reliable value for the barrier height is the one obtained from the ground state A–E splittings. This effect occurs when low frequency vibrational modes are close in frequency. In some of the molecules pointed out above, 2methylcyclopentanone and a-methyl-g-butyrolactone, these interactions have been detected between ring-puckering and methyl torsion vibrations, and different V3 values have been obtained from measurements in the ground state and in other vibrational excited states. The barrier heights reported here have been obtained by fitting A–E splittings corresponding to transitions of the first quanta of the methyl torsion vibration, and no split lines were observed in the ground state. However, we can suspect that the methyl group is affected by other motions if the frequency of methyl torsion is close to ring-bending or twisting motion frequencies. In order to analyze this possibility, the 1–0 separation for the methyl torsion has been calculated from the eigenvalues of the appropriate Mathieu equation (24) for the molecules in this work, and these can be compared with the values corresponding to the other motions in Table 5. Given that the n values obtained from the relative intensity measurements are not affected by the interactions between the motions, a comparison of the two frequencies of the methyl torsion, n and n*, calculated from different methods, can be a proof of the existence or nonexistence of interactions. For 3-methylcyclopentanone, these two values of the frequency of the methyl torsion, 220 and 244 cm01, are very close, and the same feature can be observed for gvalerolactone, with 233 and 245 cm01 (see Table 5). This analysis of the closeness of the frequencies of the methyl torsion is consistent with the absence of interactions, and
gives a reliable value for the barrier height for these two rings. Unfortunately, no measurement by the relative intensity method of £g Å 1 has been done for b-methyl-g-butyrolactone; given the low intensity of the observed lines, smaller than the ring twisting vibration lines, a higher value of the frequency for £g Å 1 than the ntwisting might be expected. However, the frequencies of ring-twisting vibration and methyl torsion for b-methyl-g-butyrolactone, collected in Table 5, reflect that the torsional motion can be influenced by the twisting motion, given their closeness. In several molecules (3, 20, 21), the values of V3 in the ground state have been found to be lower than the calculated values in other excited states due to the presence of some interaction; because of this fact, lower values of the frequency and the barrier height of the methyl torsion for b-methyl-g-butyrolactone can be expected. Other evidence of this plausible interaction might be the strange value Dc of £g Å 1 in b-methyl-g-butyrolactone, which does not show the same behavior as the value Dc of £g Å 1 for 3-methylcyclopentanone with respect to the ground state value. It is also possible to estimate the barrier height for the methyl torsion according to the environment of the methyl group by ordering the barriers from low to high values: (I) V3 Ç 8–9 kJ/mol, when {CH3 is attached to a double bond (20, 21). (II) V3 Ç 10–11 kJ/mol, when {CH3 is next to a C|O group (3). (III) V3 Ç 14 kJ/mol, when the environment is {CH2, and also {O{ (in this work). Finally, it is interesting to notice that the inclusion of an O atom in the ring lightly increases the V3 value in cases (I) and (II). In this way, a value of V3 between 14.7 and 17.2 kJ/mol for 3-methyl-g-butyrolactone may be expected to be more realistic. ACKNOWLEDGMENTS We thank the DGICYT (Spain) for financial support (Project PB900345). M. E. Charro also thanks D. G. Lister for useful discussions.
REFERENCES 1. H. Dreizler, in ‘‘Molecular Spectroscopy: Modern Research’’ (K. N. Rao and C. N. Mathews, Eds.), Vol. I, pp. 59–72. Academic Press, New York, 1972. 2. M. Kru¨ger and H. Dreizler, Z. Naturforsch. A 45, 986–988 (1990). 3. J. L. Alonso, N. Heineking, H. Dreizler, A. G. Lesarri, and J. C. Lopez, Z. Naturforsch. A 47, 761–764 (1992). 4. J. C. Lo´pez, J. L. Alonso, and F. J. Pelae´z, J. Mol. Spectrosc. 131, 9– 20 (1988). 5. F. J. Wodarczyk and E. B. Wilson, Jr., J. Mol. Spectrosc. 37, 445– 463 (1971).
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BARRIERS TO METHYL GROUP ROTATION 6. F. J. Pela´ez, J. L. Alonso, and J. M. Mun˜oz, Opt. Pura Apl. 16, 83– 89 (1983). 7. A. S. Esbitt and E. B. Wilson, Jr., Rev. Sci. Instrum. 34, 901–907 (1963). 8. L. A. Leal, Ph.D. Thesis. Valladolid University, 1994. 9. J. Haekel and H. Ma¨der, Z. Naturforsch. A 43, 202–206 (1988). 10. J. K. G. Watson, ‘‘Vibrational Spectra and Structure’’ (J. R. Durig, Ed.), Vol. 6, pp. 1–89. Elsevier, Amsterdam, 1977. 11. J. C. Lo´pez, J. L. Alonso, R. Cervellati, A. Degly Esposti, D. G. Lister, and F. Palmieri, J. Chem. Soc. Faraday Trans. 86, 453–458 (1990). 12. A. Degly Esposti, J. L. Alonso, R. Cervellati, D. G. Lister, J. C. Lo´pez, and P. Palmieri, J. Chem. Soc. Faraday Trans. 86, 459–466 (1990). 13. R. Kewley, J. Mol. Spectrosc. 89, 548–555 (1981). 14. J. L. Alonso, E. Gonzalez, W. Caminati, and B. Velino, J. Mol. Spectrosc. 122, 247–258 (1987).
15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
K. T. Hecht, and D. M. Dennison, J. Chem. Phys. 26, 31–47 (1957). L. C. Lin and I. D. Swalen, Rev. Mod. Phys. 31, 841–892 (1959). H. Dreizler, Fortschr. Chem. Forsch. 10, 59–155 (1968). R. C. Woods, J. Mol. Spectrosc. 21, 4–24 (1966). Y. S. Li, J. Mol. Spectrosc. 104, 302–307 (1984). J. L. Alonso, J. C. Lo´pez, R. Cervellati, and D. G. Lister, J. Mol. Spectrosc. 112, 26–38 (1985). J. L. Alonso, F. J. Pela´ez, J. C. Lo´pez, D. G. Lister, and R. Cervellati, J. Mol. Spectrosc. 124, 199–208 (1987). D. G. Lister, J. N. Macdonald, and N. L. Owen, ‘‘Internal Rotation and Inversion.’’ Academic Press, San Diego, 1978. J. R. Durig, P. Groner, and M. G. Griffin, J. Chem. Phys. 66, 3061– 3065 (1977). W. Gordy and R. L. Cook, ‘‘Microwave Molecular Structure,’’ Chap. 12, pp. 428–436. Wiley, New York, 1970.
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0084
Barriers to Internal Rotation in b-Methyl-g-Butyrolactone, 3-Methylcyclopentanone, and g-Valerolactone from Fourier Transform Microwave Spectroscopy M. Elena Charro1 and Jose´ L. Alonso Departamento de QuıB mica-Fisica, Facultad de Ciencias, Universidad de Valladolid, E-47005 Valladolid, Spain Received June 29, 1995; in revised form November 20, 1995
The microwave spectrum of b-methyl-g-butyrolactone has been analyzed using Stark modulation microwave spectroscopy in the frequency range 26.5–40 GHz. Spectra of the ground vibrational state and the first excited states of the ring bending, ring twisting, and methyl torsion have been assigned. The rotational constants are consistent with the molecule having a conformation similar to that of g-butyrolactone, and with the methyl group occupying an equatorial position. A reinvestigation of the microwave spectrum of 3-methylcyclopentanone has led to a reassignment of the first excited states of the ring twisting and methyl torsion vibrations. Measurements have been made in the frequency range 8–18 GHz using Fourier transform microwave spectroscopy on the ground vibrational state and the first excited state of the methyl torsion for b-methyl-g-butyrolactone, 3methylcyclopentanone, and g-valerolactone in order to determine the barriers to internal rotation. No A–E splittings have been observed in the ground vibrational state. Analyses of A–E splittings in the first excited state of the methyl torsion using the IAM method give the following barrier heights (in kJ mol01): for b-methyl-g-butyrolactone V3 Å 17.2, for 3-methylcyclopentanone V3 Å 14.76, and for g-valerolactone V3 Å 14.75. q 1996 Academic Press, Inc. INTRODUCTION
EXPERIMENTAL DETAILS
The barrier to internal rotation of a methyl group is very sensitive to the group (R) it is attached to. By making small changes in R it is possible to study variations in the methyl barrier in a systematic way. We have chosen to study the methyl barrier in a series of related saturated ring molecules. In this type of molecule the barriers are high and the A–E splittings in the ground vibrational state are small. Because of the possibility of interactions between the methyl torsion and the low-frequency large-amplitude ring-puckering vibrations, it is important, if possible, to measure these splittings in the ground vibrational state (1). The development of Fourier transform microwave spectroscopy (2) makes it possible to achieve very high sensitivity and resolution, compared to Stark spectroscopy. The high sensitivity makes it possible to work at low pressures in order to minimize collisional broadening, and low temperatures in order to minimize Doppler broadening. In this paper an attempt to measure the barriers to internal rotation is described. It has been carried out for b-methyl-g-butyrolactone (I), 3-methylcyclopentanone (II), and g-valerolactone (III) in order to compare their barriers with those in a-methyl-g-butyrolactone (IV) and 2methylcyclopentanone (V) (see Fig. 1), which have been previously measured (3). 1
To whom correspondence should be addressed.
The sample of b-methyl-g-butyrolactone was purchased from Fluka-Chimica, and those of 3-methylcyclopentanone and g-valerolactone from Janssen-Chimica. All of them were used without further purification. Measurements of the rotational spectra of b-methyl-gbutyrolactone and 3-methylcyclopentanone in the frequency range 26.5–40 GHz were made at 260 K and Ç15 mTorr using a computer-controlled Stark modulation microwave spectrometer (4). Radio frequency–microwave double resonance experiments (5, 6) were made in order to assign the spectrum of b-methyl-g-butyrolactone. The Esbitt–Wilson method (7) was used for relative intensity measurements in this molecule. Measurements in the 8–18 GHz region were made using a Fourier transform microwave spectrometer (FTMW) (2, 8) in order to observe internal rotational A–E splittings. These measurements were made at about 220 K with pressures lower than 1 mTorr. Frequencies were obtained by fitting the time domain spectra (9). Tables of the observed line frequencies are available from M. E. Charro on request. MICROWAVE SPECTRUM OF b-METHYL-gBUTYROLACTONE
Ground Vibrational State Model calculations, based on reasonable bond lengths and angles, indicated that b-methyl-g-butyrolactone is a prolate
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torial or axial). The observed rotational constants can be compared with those calculated for these four conformers from reasonable bond lengths and angles. In this way, the following assumptions were made concerning the structure and taking some parameters from a-methyl-g-butyrolactone (4) (the atom numbering scheme for a-methyl-g-butyrolactone is shown in Fig. 2):
FIG. 1. (I) b-methyl-g-butyrolactone, (II) 3-methylcyclopentanone, (III) g-valerolactone, (IV) a-methyl-g-butyrolactone, and (V) 2-methylcyclopentanone.
asymmetric rotor (k É 00.79), with the electric dipole moment mainly oriented along the inertial axis a. Low-resolution scans of the spectrum showed the presence of a prominent aR-branch band structure characteristic of a near-prolate asymmetric rotor. In order to identify the aR K01 doublets, initial assignments were made performing low Stark modulation voltage scans and radiofrequency microwave double resonance experiments in the regions where the low resolution bands occur. In this way, the first lines to be assigned were those doublets with K01 Å 4 and 5, for the bands with J Å 9 R 8 and 10 R 9. The ground state microwave spectrum of b-methyl-g-butyrolactone was then readily assigned and the aR and aQ type transitions up to J Å 38 were measured. Using FTMW spectroscopy, measurements in the range 8–18 GHz showed no A–E splittings, indicating that the barrier hindering methyl group internal rotation should be high. The spectrum was fitted using the A-reduced semirigid rotor Hamiltonian of Watson (10), using Ir representation. The results of the fitting are given in Table 1. Conformational Analysis The microwave spectrum of only one conformer of bmethyl-g-butyrolactone has been observed. The experimental data obtained from this study are not sufficient to determine a complete structure for it. However, some conformational aspects can be elucidated. There are four possible conformers, depending on the configuration of the ring (twisted or bent) and the position of the methyl group (equa-
(i) All the HCH angles are assumed to be 1107 with C{H ˚ for the methylene and methyl groups. The Å 1.095 A H{C{H planes, the CH3{C{H plane, and the carbonyl C|O bond have been taken to bisect the corresponding ring angles. (ii) The following bond lengths have been used: C|O ˚ , C2{O2 Å 1.38 A ˚ , C1{C5 Å 1.53 A ˚ , C2{C1 Å 1.195 A ˚ ˚ Å 1.52 A, and C5{CH3 Å 1.52 A. (iii) A twisted angle of 207 was assumed for the twist form and a bending angle of 217 was assumed for the bent form, and slightly different ring angles have been considered for each of the ring configurations: twisted form: O{C2{C1 Å 1117, C4{O{C2 Å 107.57, C5{C1{C2 Å 102.57; bent form: O{C2{C1 Å 1117, C4{O{C2 Å 1087, C5{C1{C2 Å 1037. The calculated rotational constants are listed in Table 2. A comparison between the observed and calculated values reveals that the observed microwave spectrum of b-methylg-butyrolactone is due to molecules with the methyl group in an equatorial position, but does not determine whether the ring is in a twisted or in a bent form. However, the twisted equatorial form could be expected to be the most stable one by analogy with related molecules such as gbutyrolactone (11, 12), g-valerolactone (13, 14), and amethyl-g-butyrolactone (3, 4), for which a twisted equatorial form has been reported. Excited States Assignment Several satellite lines corresponding to vibrational excited states of low frequency vibrations were observed close to the ground state R-branch transitions. The most intense satellite series occurs on the high frequency side, forming a progression with regular frequency and intensity patterns. This progression was assigned to successive quanta £a of the ringbending vibration, which is expected to be the lowest frequency mode of the molecule. Two more satellite lines occur very close to the ground state lines one on the high frequency side and the other on the low frequency side. The vibrational satellite lines should belong to the first excited states of the ring-twisting vibration, £b Å 1, and of the methyl torsion vibration, £g Å 1. In order to identify the first excited state of the methyl torsion vibration £g Å 1, a search for internal rotation A–E splittings was made in the frequency range 8–18 GHz using
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TABLE 1 Rotational and Centrifugal Distortion Constants and Quantity Dc for the Ground and Excited States of b-Methyl-g-butyrolactone (A) and 3-Methylcyclopentanone (B)
a
Standard error in units of the last digit in parentheses. Number of transitions fitted. c Fixed at the ground state value. d Standard deviation of the fit. e Vibrational energy relative to the ground vibrational state. b
FTMW spectroscopy. Measurements were made only for both unassigned states, and for £a Å 1. In this way, splittings were found only for transitions corresponding to the vibrational satellite appearing on the low frequency side of the ground state R-branch lines. Thus, we can conclude that the
other unassigned satellite must belong to the first excited state of the ring-twisting vibration £b Å 1. The A–E splittings observed for the £g Å 1 state, together with the frequencies for the A-level spectrum, are collected in Table 3. TABLE 2 Calculated Rotational Constants (MHz) of b-Methyl-gbutyrolactone for Four Possible Conformers and Experimental Values
FIG. 2. Ring-atom numbering scheme for b-methyl-g-butyrolactone.
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All the vibrational excited states have been fitted to the same semirigid rotor Hamiltonian, as used for the ground state. For the £g Å 1 state, the frequencies for the A-level spectrum have been used in the semirigid rotor fitting. The results of these fittings are collected in Table 1. This table also gives the values of the quantity Dc Å Ic 0 Ia 0 Ib, and of the energies above the ground vibrational states determined from relative intensity measurements. The values of Dc observed for the ring-bending and ring-twisting excited states are more negative than the ground state values, as expected for out-of-plane vibrations. The centrifugal distortion constant DK for the second quanta of ring-bending (£a Å 2), the twisting (£b Å 1) and torsional (£g Å 1) vibrational states, was kept fixed to the ground state value, given that few lines have been measured for these states.
TABLE 3 Observed A-State Frequencies and E–A Splittings and Differences between the Observed and Calculated Splittings (in MHz) for the First State of the Methyl Torsion of b-Methyl-gbutyrolactone, 3-Methylcyclopentanone, and g-Valerolactone
TABLE 4 Parameters from IAM Analysis of the First Excited State of the Methyl Torsion of b-Methyl-g-butyrolactone (A) and 3-Methylcyclopentanone (B)
a
Moment of inertia of the methyl group. Reduced internal rotation constant calculated from the structural parameters. b
c
r Å ÉrÉ,
d,e
S
r
r Å la
D
Ia Ia Ia , lb , lc . Ia Ib Ic
Euler angles g and b (angle between a axis and r): g Å arccos
S
q
lbIa
D
Ib lbIa/Ib / lcIa/Ic
b Å arccos
,
laIa . Iar
f
Reduced barrier height S Å 4V3/9F. Barrier height. h Standard errors in units of the last digit. They do not reflect the errors introduced by the assumed structure. i These parameters are defined dependent on the moments of inertia Ig (g Å a, b, c), the moment of inertia of the methyl group Ia, and the direction cosines that connect internal rotation and inertial axes lg (g Å a, b, c). g
Internal Rotational Analysis The internal rotational splittings observed for the £g Å 1 state have been fitted using the internal axis method (IAM) (15–17) in the form of the high barrier approximation of the Woods program (18). As the splittings were only slightly dependent on r, b, and g, these parameters were constrained to be the values calculated from the twisted equatorial structure ˚ 2. given above. Ia was fixed to the standard value 3.19 AMU A In this way, only the reduced barrier s was determined from the experimental data. The results are shown in Table 4, along with the other parameters relevant to the internal rotation of
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the methyl group. The differences between the observed and calculated splittings are reported in Table 3. MICROWAVE SPECTRUM OF 3-METHYLCYCLOPENTANONE
A comparison of the vibrational satellite patterns observed here for b-methyl-g-butyrolactone with those reported by Li (19) for 3-methylcyclopentanone show the same features. However, from the reported values of the quantity Dc for the second molecule, it seems that the proposed assignment of the £b Å 1 and £g Å 1 vibrational excited states to the first excited states of methyl torsion and ring-twisting, respectively, should be changed. No splittings due to methyl group internal rotation were observed by Li (19), and a lower limit of 10.04 kJ/mol was suggested for the barrier to internal rotation. In the present work, in order to determine the centrifugal distortion constants, we have extended the measurements of the rotational spectra of 3-methylcyclopentanone to higher values of J, for the R and Q branch, for both a and b-type spectra. FTMW measurements in the frequency range 8–18 GHz have been carried out for the ground vibrational state, the first excited state of the ring-bending vibration (£a Å 1), and the £b Å 1 and £g Å 1 states. Internal rotational splittings have been observed only for the £g Å 1 state. The A-level frequencies and the A–E splittings are shown in Table 3. These results indicate that £g Å 1 should be assigned to the methyl torsion vibration, and £b Å 1 should belong to the ring-twisting motion, as expected from the Dc values reported for these states (19). The spectra for all observed states has been fitted to the A-reduced semirigid rotor Hamiltonian of Watson (10) in the Ir representation. The frequencies for the A-level have been used in the fitting for the £g Å 1 state. The results are given in Table 1. For the second and third quanta of the ring-bending vibration, the DK and dK centrifugal distortion constants have been fixed at the ground state value, given that no Q-lines were measured for these states. The internal rotational splittings observed for the £g Å 1 state of 3-methylcyclopentanone have been fitted to the same model used for b-methyl-g-butyrolactone. The parameters r, b, and g have been constrained to the values calculated from the structure reported by Li (19). The results of the fitting are collected in Table 4. Table 3 shows the differences between the observed and calculated splittings. BARRIER TO INTERNAL ROTATION IN g-VALEROLACTONE
The microwave spectrum of g-valerolactone was previously studied (14) using a Stark modulation spectrometer (4). Internal rotational splittings were observed for the first
excited state of the methyl torsion for some bQ lines. In the present work, we have studied the FTMW spectrum of this vibrational state, in order to observe better resolved internal rotational splittings and to obtain a more accurate value of the barrier to hindering internal rotation in g-valerolactone. Splittings have been observed for several aQ and bQ transitions. The A–E splittings have been fitted with the Woods program by the internal axis method (IAM). The structural parameters r, b, and g have been constrained to the values reported previously (14), r Å 0.0302, b Å 0.211 rad, and g Å 0.774 rad, and the barrier height obtained with these new measurements is more accurate, 14.75(5) kJ/mol. The frequencies for the A-level transition, the corresponding splittings, and the calculated values are listed in Table 3. DISCUSSION
A series of different methylcycloderivatives have been studied in order to give a value for the barrier height of the internal rotation of the methyl group. A comparison among the values of V3 reveals that similar results have been obtained when the environment of the methyl group is the same. This is the case of a-methyl-g-butyrolactone and 2methylcyclopentanone, with the same environment of the {CH3 group (see Fig. 1), where values of 10.92 and 10.09 kJ/mol, respectively, have been calculated (3) for such barriers. The same feature is shown by 2-methyl-4,5-dihydrofuran (20), with V3 Å 8.2 kJ/mol, and a-angelicalactone (21), with almost the same value, V3 Å 8.8 kJ/mol; both molecules present this environment, {O{C(CH3) Å CH{. On this basis, attending to the methyl’s environment, the values of the barrier height of the internal rotation calculated in this work can be analyzed and compared with each other. In this way, the V3 value for the g-valerolactone, 14.76 kJ/mol, is consistent with the values for noncyclic methylcycloderivatives CH3{CH2OH and CH3{CHOH{CH3, 13.93 and 14.2 kJ/mol, respectively (22), with the same immediate environment for the methyl group. However, very different values of the barrier height to the internal rotation of the methyl group for b-methyl-g-butyrolactone (17.2 kJ/mol) and for 3-methylcyclopentanone (14.76 kJ/mol) have been determined. In both molecules, the immediate environment of the methyl group is the same (see Fig. 1) and very similar values for V3 might be expected. In order to elucidate which is the most reliable value we can compare these results with the barrier height of propane (CH3{CH2{CH3), V3 Å 13.6 kJ/mol (23), where the methyl group has the same immediate environment as in our rings. Comparing these values, only the 3-methylcyclopentanone has a value of V3 similar to propane’s, and an anomalous value of V3 (17.2 kJ/mol) is found for b-methyl-g-butyrolactone. Although the V3 value for b-methyl-g-butyrolactone has been well determined, the difference found between our val-
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TABLE 5 Summary of the Frequencies (in cm01) of Methyl Torsion and of Ring-Bending and Ring-Twisting Motions from Intensity Measurements and the Value of the Methyl Torsion Frequency from V3.
a b
Frequency calculated using the Mathieu equation. No measured value.
ues for these two rings, b-methyl-g-butyrolactone and 3methylcyclopentanone, indicates that it might correspond to an anomalous value. This result may be attributed to an interaction between the methyl torsion and other low frequency motion. It has been demonstrated (1) that when the methyl group torsion is influenced by another vibration the most reliable value for the barrier height is the one obtained from the ground state A–E splittings. This effect occurs when low frequency vibrational modes are close in frequency. In some of the molecules pointed out above, 2methylcyclopentanone and a-methyl-g-butyrolactone, these interactions have been detected between ring-puckering and methyl torsion vibrations, and different V3 values have been obtained from measurements in the ground state and in other vibrational excited states. The barrier heights reported here have been obtained by fitting A–E splittings corresponding to transitions of the first quanta of the methyl torsion vibration, and no split lines were observed in the ground state. However, we can suspect that the methyl group is affected by other motions if the frequency of methyl torsion is close to ring-bending or twisting motion frequencies. In order to analyze this possibility, the 1–0 separation for the methyl torsion has been calculated from the eigenvalues of the appropriate Mathieu equation (24) for the molecules in this work, and these can be compared with the values corresponding to the other motions in Table 5. Given that the n values obtained from the relative intensity measurements are not affected by the interactions between the motions, a comparison of the two frequencies of the methyl torsion, n and n*, calculated from different methods, can be a proof of the existence or nonexistence of interactions. For 3-methylcyclopentanone, these two values of the frequency of the methyl torsion, 220 and 244 cm01, are very close, and the same feature can be observed for gvalerolactone, with 233 and 245 cm01 (see Table 5). This analysis of the closeness of the frequencies of the methyl torsion is consistent with the absence of interactions, and
gives a reliable value for the barrier height for these two rings. Unfortunately, no measurement by the relative intensity method of £g Å 1 has been done for b-methyl-g-butyrolactone; given the low intensity of the observed lines, smaller than the ring twisting vibration lines, a higher value of the frequency for £g Å 1 than the ntwisting might be expected. However, the frequencies of ring-twisting vibration and methyl torsion for b-methyl-g-butyrolactone, collected in Table 5, reflect that the torsional motion can be influenced by the twisting motion, given their closeness. In several molecules (3, 20, 21), the values of V3 in the ground state have been found to be lower than the calculated values in other excited states due to the presence of some interaction; because of this fact, lower values of the frequency and the barrier height of the methyl torsion for b-methyl-g-butyrolactone can be expected. Other evidence of this plausible interaction might be the strange value Dc of £g Å 1 in b-methyl-g-butyrolactone, which does not show the same behavior as the value Dc of £g Å 1 for 3-methylcyclopentanone with respect to the ground state value. It is also possible to estimate the barrier height for the methyl torsion according to the environment of the methyl group by ordering the barriers from low to high values: (I) V3 Ç 8–9 kJ/mol, when {CH3 is attached to a double bond (20, 21). (II) V3 Ç 10–11 kJ/mol, when {CH3 is next to a C|O group (3). (III) V3 Ç 14 kJ/mol, when the environment is {CH2, and also {O{ (in this work). Finally, it is interesting to notice that the inclusion of an O atom in the ring lightly increases the V3 value in cases (I) and (II). In this way, a value of V3 between 14.7 and 17.2 kJ/mol for 3-methyl-g-butyrolactone may be expected to be more realistic. ACKNOWLEDGMENTS We thank the DGICYT (Spain) for financial support (Project PB900345). M. E. Charro also thanks D. G. Lister for useful discussions.
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