J . Phys. Chem. 1988, 92. 4052-4056
4052
chlorotoluene molecules varied linearly with the concentration of naphthalene, and the plot of the decay rate against the naphthalene concentrations also gave straight lines with slopes similar to those in Figure 7 . From the slopes of the plots in Figure 7, the quenching rate constants of the triplet chlorotoluenes by naphthalene (k,') can be determined. The values of k,' for p - , and m-, and o-chlorotoluene were evaluated to be 8.3 X los, 9.8 X lo8, and 5.3 X lo8 M-I s-l, respectively. The biacetyl quenching rate constant (8.3 X lo8 M-I s-l) obtained previously for p-chlorotoluene is similar to the present results. Knowing the kinetics of the energy-transfer reactions, the lifetime of the triplet states involved, and the extinction coefficient of naphthalene triplet state, the value of the initial concentration of triplet chlorotoluene can be calculated. In consequence, the extinction coefficients of triplet chlorotoluenes (tT) at 305 nm was determined to be 11 000,6000, and 10 000 M-I cm-' for p - , m-, and o-chlorotoluene, respectively. These values may be compared with that for triplet chlorobenzene (6800 700 M-' cm-'), though these values have large errors (*20%) due to experimental uncertainties. The value of tT@T for chlorotoluene can be obtained in comparison with the value of tTaTfor chlorobenzene (4800 f 500 M-I cm-l),lI where @T stands for the triplet formation quantum yield and tT is the extinction coefficient of triplet molecules. The absorbance of the sample chlorotoluene solution at 248 nm, the excitation wavelength, was prepared to be about 0.3, which was very similar to that of chlorobenzene. Then the sample solutions were irradiated by the laser pulse under the same condition. Thus the absorbance was measured at 305 nm with low excitation intensities, giving the linear relation for the intensity. By taking the ratio of the slope for the chlorotoluene to that for chlorobenzene, the value of tT@T was derived. Those values of tT@T for p - , m-, and o-chlorotoluene were derived to be 5200, 2400, and 2000 M-' cm-I, respectively. Here the values of tT at 305 nm have already been determined, and the values of aTwere respectively determined to be 0.5, 0.4, and 0.2 for p - , m-, and o-chlorotoluene. These values tT and @T, however, may have large errors due to the accumulation of various uncertainties. Using the values of aT,we can estimate the formation rate of methylanisole ( k 2 )from the relation (IV) @ST = @Tk2/(kl + k2) Thus the values of k2 are estimated to be 3 X lo4, 9 X lo4, and 6 X lo4 for triplet p - , m-, and o-chlorotoluene, respectively. These values are only estimates since aTmay be different in
*
methanol. The difference, however, may be small since the triplet yield is believed to be insensitive to the solvent polarity.I6 The value for chlorobenzene was indeed reported to be 0.7 in methanol," while the value is 0.6 in c y ~ l o h e x a n e .Therefore, ~~~ the formation rate seems to have the order of lo4 s-l. Thus the value is 2 orders of magnitude less than the decay rate of the chlorotoluene triplet state. This result indicates that the formation reaction of methylanisole should have some activation energy from the lowest excited triplet state of chlorotoluene. To estimate the activation energy, it will be necessary to measure the formation yield of methylanisole as a function of temperature. 4. Conclusions
Photochemical processes of the chlorotoluene molecules in methanol have been investigated. Absorption measurements in stationary photolyses of p - , m-, and o-chlorotoluene have shown that the photodecomposition process is major with the quantum yield range of 0.4-0.1 and that the p-isomer has the smallest value due to higher molecular symmetry. The formation yield of methylanisole (photosubstitution reaction) is also determined to be on the order of 10-2-10-3. By the addition of biacetyl it was found that the photosubstitution reaction takes place in the triplet state and also in the initial excited levels. Measurements of methylanisole formation yields as a function of biacetyl concentration gave the quantum yield of each process (Table I). Among the three isomers the para and ortho isomers have smaller yields in the triplet route than that of the meta isomer due to the electron-donating effect of the methyl substituent. Triplet states of chlorotoluenes have been studied by T-T absorption measurements. The transient absorption spectra of those triplet states were observed with the peak at -305 nm, and the formation of photoproduct dimethylbiphenyl was confirmed. The decay rates of those triplet states are on the order of lo6 s-l in methanol, and the quenching rate by biacetyl is approximately 1 X lo9 M-' s-l. The sensitized triplet-state formation of naphthalene by the triplet chlorotoluenes was also studied in cyclohexane solution, and the T-T absorption coefficients of chlorotoluenes at 305 nm were estimated to be around lo4 M-I cm-I. Triplet yields were also determined to be 0.5, 0.4, and 0.2 for p - , m-, and o-chlorotoluene, respectively. Given these values, the formation rate of methylanisole in the triplet state was derived to be on the order of lo4 s-I. ~
(16) Compton, R. H.; Grattan, K T. V.; Morrow, T J . Photochem. 1980, 14, 61.
Proton Spin-Lattice Relaxation in Gaseous Furan Boris E. Weiss-Lopez, Eric D. Winegar, and Nancy S. True* Department of Chemistry, The University of California. Davis, California 95616 (Received: October 15, 1987; In Final Form: January 13, 1988)
The nuclear spin-lattice relaxation time, T I ,measured for the 01 and fl protons of gaseous furan at pressures between 7 and 425 Torr at 300 K, exhibits a characteristic nonlinear pressure dependence. The T I is about 12% shorter for the a protons at the pressures studied. Nuclear Overhauser enhancement measurements at pressures between 100 and 400 Torr demonstrate that the contribution to relaxation from dipole-dipole interactions is negligible in this pressure range. Analysis of the pressure-dependent T I data using a single relaxation time approximation yields a spin-rotation coupling constant, lCeffl,of 306 (2) Hz and an angular momentum reorientation cross section of 143 (1) A* for the 01 protons. Corresponding values are 336 (2) Hz and 136 (1) A* for the p protons.
Introduction In the present paper we report pressure-dependent gas-phase T I data for the a and fl protons of furan which establish that proton spin-lattice relaxation in this molecule occurs predominantly via spin-rotation interactions. Analysis of the pressure0022-3654/88/2092-4052$01.50/0
dependent TIdata yielded effective spin-rotation coupling constants and angular momentum reorientation cross sections. These results demonstrate that a single relaxation time symmetric top aPproximation analysis can be successfully applied to a nearly oblate asymmetric mOleCUle.
0 1988 American Chemical Society
Proton Spin-Lattice Relaxation in Gaseous Furan
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4053
Spin-rotation interactions provide the most efficient mechanism TABLE I: Pressure-Dependent Spin-Lattice Relaxation Times of for nuclear spin-lattice relaxation in the gas phase.' Studies of Gaseous Furan at 300 K O relaxation of linear?-5 spherical:' and symmetric top m ~ l e c u l e s ~ ~ ~ have been reported. With few exceptions, these analyses have 6.84 8.88 (0.18) 8.74 (0.24) assumed that spin-rotation interactions provide the only important 9.26 6.32 (0.08) 6.44 (0.07) relaxation mechanism for protons. T I measurements for methane 5.02 (0.1 1) 9.96 4.81 (0.11) I 45(0.09) temperature dependence, conwere consistent with a T 14.74 4.71 (0.03) 4.40 (0.05) firming the dominance of spin-rotation relaxation.6 A small 4.06 (0.04) 20.65 3.65 (0.11) amount of dipole-dipole relaxation could not be ruled out, however. 3.00 (0.08) 23.30 2.56 (0.04) 2.92 (0.02) By assuming that the molecular reorientation correlation time, 25.73 2.66 (0.04) 2.54 (0.03) 29.56 2.27 (0.02) T ~ is, comparable to the angular momentum correlation time, T ~ , 2.46 (0.01) 32.80 2.16 (0.02) it was estimated that dipolar relaxation contributes ca. 8% to the 2.05 (0.02) 41.20 1.79 (0.02) total IH spin-lattice relaxation rate of methane gas at 300 K at 1.87 (0.01) 51.30 1.57 (0.01) high densities.6 Moreover, calculations have predicted, and ex1.65 (0.01) 64.04 1.39 (0.01) periments confirmed, an almost equal contribution in H2gas from 1.40 (0.01) ?0.10 1.61 (0.01) both dipolar and spin-rotational interaction^.^ This dipolar re1.36 (0.01) 83.28 1.65 (0.01) laxation is due in large part to the relatively short interatomic 1.30 (0.01) 87.80 1.57 (0.01) distance in H,. The symmetry of most molecules studied to date 1.32 (0.01) 92.53 1.51 (0.02) in the gas phase, however, has precluded nuclear Overhauser 1.28 (0.01) 93.00 1.57 (0.01) 1.27 (0.01) 95.67 1.54 (0.01) enhancement (NOE) measurements to determine the magnitude 1.62 (0.04) 1.32 (0.04) 99.30 of dipoledipole contributions to the relaxation. High symmetry 1.30 (0.01) 111.4 1.60 (0.05) also ensured that all of the spectral density was centered in the 124.8 1.54 (0.01) 1.28 (0.01) zero-frequency transition and no contributions from other rota1.38 (0.02) 140.0 1.71 (0.02) tional transitions affected the spectral density at the nuclear 1.52 (0.03) 152.0 1.69 (0.02) Larmor frequencies. Furan is a nearly prolate asymmetric 160.8 1.44 (0.02) 1.83 (0.02) molecule whose spectral density in the radio frequency region 169.7 1.42 (0.03) 1.86 (0.03) consists of a series of Q-branch transitions. The chemical shift 180.5 1.47 (0.01) 1.87 (0.01) difference between the a and p protons allows NOE measurements 190.0 1.53 (0.01) 1.96 (0.01) 198.3 1.64 (0.01) 1.98 (0.02) to be made, permitting a determination of the relative contributions 209.7 1.51 (0.06) 1.98 (0.01) to the overall relaxation from the dipolar and spin-rotation in218.1 1.65 (0.01) 2.16 (0.03) teractions.
Experimental Section Furan (99+%) was obtained from Aldrich Chemical Co. and was purified by vacuum distillation and subsequently degassed using five freeze-pumpthaw cycles. Gas-phase N M R samples were prepared in 10.95 mm 0.d. Wilmad coaxial inserts cut to a length of 17 mm with a short section of 3 mm tubing attached. Tubes were constructed with flat termini on the top and bottom to maximize the sample volume while at the same time confining the sample to the active volume region inside the probe in order to minimize diffusional contributions to the observed T,s. Each sample was prepared by filling a vacuum line with the appropriate pressure and sealing the attached N M R sample tube with a torch. The tubes were sealed as close as possible to the top in order to minimize the volume in the stem. Each sample was immediately immersed in liquid N2 to minimize thermal decomposition at the sealing site. The resulting restricted volume tubes were inserted into standard 12 mm 0.d. Wilmad N M R tubes having a indentation ca 1 cm from the tube bottom. This arrangement enabled precise positioning of the tube in the center of the receiver. All N M R measurements were made with a G.E. NT-300 WB spectrometer with IH observation at 300.068 MHz. Spectra were obtained for spinning samples without a frequency lock. Spectrometer drift was negligible on the time scale of most of these experiments. For experiments of duration longer than 24 h, a previously determined drift constant for the magnet was used to provide a current ramp to the main coil, thus compensating for residual drift. The temperature was regulated at 300 f 1 K. To (1) Bloom, M. In M T P International Review of Science, Physical Chemistry Series One; McDowell, C. A,, Ed.; Butterworth: London, 1972; Vol. 4, pp 1-42. (2) Bloom, M.; Oppenheim, I. Can. J . Phys. 1963, J4, 1583-1590. (3) Lemaire, C.; Armstrong, R. L. J . Chem. Phys. 1984.81, 1626-1631. (4) Courtney, J. A,; Armstrong, R. L. Can. J . Phys. 1972, 50, 1252-1261. (5) Kalechstein, W.; Lemaire, C.; Armstrong, R. L. J . Chem. Phys. 1977, 66, 1586-1588. (6) Bloom, M.; Bridges, F.; Hardy, W. N. Can. J . Phys. 1967, 45, 3533-3554. (7) Pandey, L.; Lalita Sarkar, K. Chem. Phys. Lett. 1978, 58, 375-378. (8) Folkendt, M. M.; Weiss-Lopez, B. E.; True, N. S . J . Phys. Chem., in press. (9) Dong, R. Y . ;Bloom, M. Can. 3. Phys. 1970, 48, 793-840.
229.9 240.2 246.9 250.0 260.4 270.7 290.7 302.2 325.7 349.6 376.9' 398.0 424.9
2.22 2.21 2.26 2.30 2.34 2.45 2.61 2.74 2.79 3.00 3.20 3.48 3.58
(0.07) (0.01) (0.03) (0.03) (0.02) (0.01) (0.01) (0.02) (0.06) (0.01)
(0.05) (0.05) (0.08)
1.74 (0.05) 1.76 (0.02) 1.77 (0.03) 1.77 (0.04) 1.88 (0.01) 1.93 (0.01) 2.05 (0.01) 2.22 (0.01) 2.15 (0.05) 2.39 (0.01) 2.53 (0.08) 2.82 (0.08) 2.85 (0.02)
'Results of additional measurements at 323 K are Tl(cu) = 3.00 (0.04) s and TI@) = 2.39 (0.05) s. At 348 K, T , ( a ) = 2.71 (0.02) s and TI@) = 2.14 (0.03) s.
minimize the effects of B1 inhomogeneity, each T , measurement was performed using the inversion-recovery method with a composite inversion pulse sequence.1° Between 1 and 180 transients were acquired for each delay time and their sum was stored in 8K of memory. The sweep width was 800 H z and the corresponding digital resolution was 10.2 points/Hz. Each T1 determination used at least 12 delay times, the longest of which was greater than 8 T,s in order to ensure complete recovery. In order to improve S/N, each transient was multiplied by an exponentially decaying apodization function corresponding to a 2-Hz line broadening. The resulting spectrum in each case had a S / N of at least 25/ 1. Intensity data from each series of inversion recovery measurements were analyzed to obtain a three-parameter fit of the equation Z ( T ) = Z,[1 - 2 exp(-~/T,)] where T is the delay time. T , values reported in Table I obtained from this analysis are at the 99.5% confidence limit. Pressure-dependent T , values were fit to the function
TI = AP
+ B/P
(1)
where P is the pressure in Torr and A and B are constants which correspond to the quantities (a/4~~)(C,$)-l((w, uJ)/pmn),and (a/47r2)(Cef~)-'(uI - uJ)pmln,respectively. The quantity a is
+
(10) Freeman, R.; Kempsell, S. P.; Levitt, M. H. J . Magn. Reson. 1980, 38, 453-479.
4054
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
h2/4r2210kTfor a symmetric top. Furan is a nearly oblate asymmetric top (Ray's asymmetry parameter K = 0.91) and the quantity 21, can be replaced with ( I A + 1,). From the rotational kg m2, constants reported in ref 18, ( I A + I,) is 17.95 X and a is 1.496 X w , and w J are the nuclear and molecular Larmor angular velocities and pmlnis the minimum pressure. A weighted nonlinear Fletcher Powell minimization routine was used to obtain the values of A and B for each proton from which Cef: and pmlnwere obtained. Errors in the pressure determination for each sample along with uncertainties in T I derived from the inversion-recovery data were used to determine the weight of each data point in the least-squares analysis. Curve-fitting parameters and the associated spectroscopic and kinetic constants are reported at the 95% confidence limit. In order to determine if dipole-dipole interactions contribute to the observed T , of gaseous furan, NOE measurements were made at pressures between 200 and 350 Torr. To improve the S/N for these measurements, 30 mm long N M R tubes with rounded bottoms were used. These tubes maximized the amount of sample in the active volume and improved shimming capabilities. Each NOE experiment involved collection of three data sets, one with the decoupler set at a frequency corresponding to one of the proton resonances, one with the decoupler set off resonance from the observed resonance by a frequency difference equal to the resonance frequency difference between the a and p resonances in order to test for decoupler leakage, and a third measurement was obtained with the decoupler set 1 kHz off resonance to serve as a control. Typical decoupler power levels employed in these experiments were on the order of 300 mW. The NOE was allowed to build for a period of I O Tls. Spectra were collected sequentially into three blocks to compensate for long time changes in the system. Digitized spectra were transferred to a microcomputer for integration and analysis. All spectra used to determine NOE enhancement factors had S / N in excess of 1000.
Results The gas-phase nuclear spin-lattice relaxation time, T I , was determined for the a(upfie1d) and @(downfield)protons" of furan at pressures between 7 and 425 Torr at 300 K. Below 5 Torr, experimental acquisition times are prohibitively long due to rapid polarization decay and associated broadening, poor S/N due to low sample concentrations, and the long delay times required to measure the long Tls which occur at pressures below the T I minimum. For example, measurement of the TI at 7 Torr, which is 8.88 s for the a protons, required 40 h of acquisition time. Experimental measurements were limited to pressures below 425 Torr by sample volatility. The observed chemical shift difference of 1.05 ppm is 0.02 ppm less than the reported value for the neat liquid, 1.07 ppm.I2 T I values obtained at 43 pressures appear in Table I and are plotted as a function of sample pressure in Figure 1. At all the pressures where measurements were performed, the p proton relaxes faster than the a proton. NOE factors were obtained for both the a and p protons of furan at 250 and 350 Torr. Intensity measurements obtained with a S/N in excess of 1000 are consistent with an NOE enhancement factor, 7, of 0.02 (0.01) for both the a and p protons at both pressures. Data quality was such to only suggest that there is neither a pressure nor spin site dependence to the NOE factor. Combined with the T I values obtained at these pressures, the corresponding dipole-dipole relaxation times, TIDD, for the a'H are ca. 57 and 7 5 s at 250 and 350 Torr, respectively. For the p 'H, T I D D is ca. 44 and 60 s at 250 and 350 Torr, respectively. Additional measurements were made using samples containing 30 Torr of furan and 400 Torr of helium with no discernible difference in the observed NOE factor. In order to investigate the relaxation characteristics of the 13C nuclei in furan, TI measurements were made at 363 K using a (1 1 ) Abraham, R. J . ; Loftus, P.Proton and Carbon-13 N M R Spectroscopy, An Integrated Approach; Heyden: London, 1978. ( 1 2 ) Srogl, J.; Jand, M.; Stibor, I.; Skala, V.; Trska, P.; Ruska, M. Collect. Czech. Chem. Commun. 1974, 39, 3109-31 12.
10
Weiss-Lopez et al.
,,
I
I
1
100
0
zoo
300
400
P(torr1
Figure 1. Pressure-dependent T,s of the o( and p protons of gaseous furan. The solid lines are calculated from the A and B parameters which appear in Table 11. Derived cross sections and spin-rotation coupling constants appear in Table 11.
sample containing ca. 700 Torr of furan and 300 Torr of TMS. The elevated temperature was necessary to allow measurements at a higher vapor pressure in order to obtain an acceptable signal/noise ratio. 13C T,s are 0.12 (0.02) s and 0.14 (0.02) s for the downfield ( a ) (142.6 ppm downfield from gaseous TMS) and the upfield (p) (109.6 ppm downfield from gaseous TMS) I3C nuclei, respectively. These Tl values are about 100 times shorter than those of the protons in furan under similar pressure and temperature conditions.
Discussion The lack of a significant NOE enhancement for the a and p protons of furan at modest pressures demonstrates that dipoledipole interactions do not contribute significantly to the observed relaxation times. An estimate of the relative importance of other mechanisms such as intermolecular dipoledipole interactions and chemical shift anisotropy demonstrates that these mechanisms are also unimportant. Relaxation via intermolecular dipole-dipole interactions may be estimated from13 1 /T,(intra-DD) = [(2y4h21(I+ 1))/u2] [ r M / k T ] ' / 2 p
(2)
where p is the gas density. Assuming a cross section, u, of 138 is 4.25 X lo4 s at 100 Torr. An estimate of the contribution to relaxation from chemical shift anisotropy can be obtained from the relationship
A2, T,(intra-DD)
l/TlCSA = (2/15)(WA(r)27cs~
(3)
The contribution from this mechanism is small since proton shielding anisotropy is small. Assuming a chemical shift anisotropy of 10 ppm, and a collision cross section of 138 A*, TICSAis ca. 162 s at 400 Torr for proton observation at 300 MHz. At 10 Torr, TICSA is estimated to be 4 s by using the above parameters. The calculated values are lower limits since the proton chemical shift anisotropy of this molecule is most likely considerably less than 10 ppm.I3 These results demonstrate that nuclear spin relaxation in gaseous furan is primarily the result of spin-rotation interactions. Thus a straightforward analysis of the pressure-dependent T,s of gaseous furan to yield effective spin-rotation coupling constants and cross sections can be performed. Since the T I minimum is well characterized, it is possible to obtain both the A and B parameters in eq 1 and to determine the effective spinrotation coupling constants, CeffZ,and angular momentum reorientation cross sections, u, for both the a and p protons. A single relaxation time approximation (SRTA) was used to model the experimental T I data obtained for the a and p protons of gaseous furan. The data listed in Table I were fit to eq 1 as (13) Chen, F. M.; Snider, R. F. J . Chem. Phys. 1967,46, 3937-3940. (14) Kitchlew, A.; Nageswara Rao, B. D. J . Chem. Phys. 1973, 58, 4033-4034.
Proton Spin-Lattice Relaxation in Gaseous Furan TABLE 11: Spectroscopic and Kinetic Constants of Gaseous Furan at 300 K 8.08 (0.10) 6.34 (0.1 1) 10-3A, s Torr-' B, s Torr 72.33 (0.52) 63.08 (0.59) 94.62 (0.55) 99.62 (0.16) Pmi,,Torr 6,A2
ICeifL
Hz
143 (1) 305 (2))' 367 (2)'
136 (1) 336 (2)' 336 (2)'
"This work. bCalculated from parameters in ref 16.
described in the Experimental Section. The parameter A is 8.08 (0.10) X and 6.35 (0.11) X s Torr-' for the a and /3 protons, respectively. B is 72.3 (0.5) and 63.08 (0.60) s Torr, respectively, for the (Y and /3 protons. The solid curves in Figure 1 were calculated from the best values of these parameters. The differences T,(calculated) - T,(observed) as a function of pressure for the a and /3 protons of furan were calculated. N o systematic deviations between the experimental and calculated values are observed at pressures above 10 Torr. Below 10 Torr the calculated TI values are longer than the experimental values. The discrepancy increases with decreasing pressure. This may be due to an increased diffusional or wall collisional contribution to the observed Tls or to increasing contributions to the observed relaxation from chemical shift anisotropy. A recent study of N H 3 and HC1 gas demonstrated that a multiple relaxation time approximation (MRTA) provided a better fit of the experimental pressure-dependent T I data.3 A threethe average correlation time, parameter fit of the data yielded Cef12, and a dispersion parameter. In the present case systematic deviations were not observed. This may be the result of limitations in the range and quantity of the experimental data obtained or the result of the molecules' greater rotational partition function and lower symmetry rendering the separate contributions from the various spin symmetries undetectable. The rotational partition function of furan is 212682 at 300 K calculated from the rotational constants reported in ref 18, and the average Jvalue is 33 at 300 K. We have analyzed similar pressure-dependent T I data for benzene gas and observed that the value of the spin-rotation coupling constant, Ceffz,is the same, within experimental uncertainty for the SRTA and MRTA analyses.8 Moreover, if the time scale for the allowed contribution from inelastic collisions in SRTA is orders of magnitude shorter than the experimentally determined relaxation time, then the experiment will be sensitive to only some average collision time and not to individual reorientation collision events.I5 In the case of furan at even the highest pressure, the measured T I is many orders of magnitude longer than the time scale for inelastic collisions and consequently the SRTA approach should suffice. The present results can be compared to the spin-rotation coupling constants obtained from the measurement and analysis of hyperfine structure in the rotational transitions of furan in a molecular beam.I6 The reported spin-rotation tensor elements (Hz), C,,, C,,, and C,, are -537 (31, 611 (5), and -548 (13) for the a proton and 253 (4), -189 (5), and -512 (17) for the /3 proton, respectively. These parameters are related to the Cer? value obtained frm the N M R relaxation data for a symmetric top according to9
C,,? = K1Ca2+ K2CaCd + K3C,j2 Kl = (1 - y2/3)
K2 = (4/9)Y2 K3 = (1/9)(9(1 -Y2/Y2)2(-1 - cv2/3) + (1/2Y) In ((1 + Y)/(l - y ) ) ) - 1 + (5Y2)/31 (4)
where y = (1 - 21c/(Ia+ Ib))'/2 = 1.0017i for furan, and C, and (15) McCourt, F. R. In N M R Basic Principles and Progress; Diehl, P., Fluck, E., Kosfeld, R., Eds.; Springer-Verlag: h e w York, 1976; Vol. 13, pp 55-70. (16) Tomasevich, G. R.; Tucker, K. D.; Thaddeus, P. J . Chem. Phys. 1973, 59, 131-135.
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4055
+ C,, + C,,)/3 and ((Cx, respectively. The spin rotation tensor elements correspond to Ceffvalues of 367 (2) and 336 (2) Hz for the a and protons, respectively (Table 11). The corresponding values obtained from our measurements are 1306 (2)l and 1336 (2)l Hz, respectively, for the a and /3 protons. Equation 4 has been modified for the case of asymmetric m0lecu1es.l~ The magnitudes of the differences depend on differences in the relative inertial and &/Ic for the asymmetric molecule. Furan is nearly ratios la/& oblate and these ratios are 0.492 and 0.506, respe~tively.'~Since these ratios are not significantly different, eq 4 was used to calculate Cefffrom the beam data. The estimated uncertainties in our measurements as well as those reported in the beam studies are small (
