Low resolution microwave spectroscopy. I. The structural significance of the bandspacingMaya Swamy Farag and Robert K. Bohn Citation: The Journal of Chemical Physics 62, 3946 (1975); doi: 10.1063/1.430315 View online: http://dx.doi.org/10.1063/1.430315 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/62/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Demonstration and interpretation of significant asymmetry in the low-resolution and high-resolution Q yfluorescence and absorption spectra of bacteriochlorophyll a J. Chem. Phys. 134, 024506 (2011); 10.1063/1.3518685 Bolometric technique for high-resolution broadband microwave spectroscopy of ultra-low-loss samples Rev. Sci. Instrum. 75, 124 (2004); 10.1063/1.1633001 Verylowtemperature Xband electronspinresonance spectroscopy with small slowwave resonant structures Rev. Sci. Instrum. 61, 2354 (1990); 10.1063/1.1141363 Characteristics of low resolution Qbranch microwave bands: Applications to 2,2,2trifluoroethyl vinyl ether and 7methylbicyclo[2.2.1]hept2ene5one J. Chem. Phys. 75, 3238 (1981); 10.1063/1.442473 Low resolution microwave spectroscopy. II. The conformation of 2,2,2trifluoroethyl vinyl ether J. Chem. Phys. 62, 3951 (1975); 10.1063/1.430316

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Low resolution microwave spectroscopy. I. The structural significance of the band spacing

Maya Swamy Farag and Robert K. Bohn

Department of Chemistry and Institute of Materials Science, University of Connecticut, Storrs, Connecticut 06268 (Received 26 September 1974)

Compounds which are nearly symmetric tops. have ~ 20 mtorr vapor pressure, and have a sizeable dipole moment along the a axis display band microwave rotational spectra under low resolution conditions. The frequencies of the band maxima are adequately represented by a symmetric rotor type equation, v = (B + C)(J + 1). From calculated spectra it is shown that the B + C value defined above exceeds the ground state effective rotational constant B 0 + Co. Low resolution B + C values and high resolution B 0 + Co values are compared for nineteen species. B + C differs from B 0 + Co by less than 2% in all cases and less than 0.8% for molecules with K < -0.8. Empirically it is found that (B + C)/(Bo + Co) - I = vivo - I = O.02S(±O.OOS)(1 + K), where k is the asymmetry parameter and Vo is the hypothetical symmetric rotor frequency, (B 0 + C o)(J + I). This empirical relation allows B 0 + Co to be estimated from B + C with an uncertainty of only a few tenths of a percent.

Scharpen1 first observed that the microwave rotational spectra of molecules which are nearly symmetric rotors display simple band spectra under low resolution condi­tions, fast frequency sweep coupled with a heavily damped detector. The bands are due to pileups of many nearly degenerate K components of each J + 1-J transi­tion. The spectra require only about a half hour to run, are simple to interpret, and can be used to unambiguously determine molecular conformations. Nevertheless, ex­cept for preliminary work for high resolution studies, little direct application has been made of low resolution microwave spectroscopy (LRMW). References l-S are a complete bibliography of such applications of the LRMW technique. A single conformational species displays a spectrum of equally spaced bands whose spacing will be called B + C (unsubscripted). Thus, only one parameter is obtained. For this lone value to provide Significant structural information it is necessary to establish the relationship between it and the molecule's structure and to ascertain confidence limits for this relationship. This is accomplished below by considering some theoretical aspects of the spectra and by comparing empirical low resolution and high resolution spectral parameters for nineteen compounds. An accompanying paper8 applies the LRMW method to the determination of the conforma­tion of 2, 2, 2-trifluoroethyl vinyl ether.

RESULTS AND DISCUSSION

Theory of LRMW spectra

steinmetz 7 has succinctly presented the relevant theo­ry. We will reproduce only that necessary for coherence and make additional comments. For a prolate symmet­ric top (Ia < II> '" Ie) the rotational energy levels are given by\)

( B+C) 2 (B+C) E J ,K_l'" A--2- K_1 + -2- J(J+1), (1)

where A", h2 /Srr-I., etc. If the dipole moment along the a or symmetry axis is nonzero, the allowed absorption transitions (a type spectra) are governed by the selection rules t..K -1 = 0 and t..J", 1. The frequencies for these transitions are

(2)

where Bv and C" are the effective rigid rotor rotational constants in the vth vibrational state. It will be shown (vide infra) that variations of Bv and Cv with vibrational state are usually unimportant in low resolution applica-

-1 J=15~14

-95 (x 10)

-.90

-.85

- 0

91 95 GHz 275 GHz

J=10~9 -1~-'-~~'--~-~~-1f-_'-1IItf-,-~~~ __ _

(x 2) - 95

- 90

-85

- 80

185 GHz

FIG. 1. Dependence of microwave spectra on J and K. In the upper left quadrant are shown the calculated a-type transition frequencies for J = 5 - 4 for a molecule (like bromobenzene) with Ao = 5670 MHz and Bo + Co = 1823 MHz. The top spectrum is for the symmetric rotor case, K = -1. The spectrum on the second line was calculated for a molecule in which Bo and Co were changed maintaining their sum at 1823 MHz but changing K to - O. 95'. Similarly, the third, fourth, and fifth lines show the spectra for similar systems with K = - O. 90, - O. 85, and - O. 80, respectively. The remaining quadrants display calcu­lated spectra for the identical set of hypothetical molecules for J=10-9, 15-14, and 20-19. Some low K transitions, particularly for the less symmetric mOdels, lie outside the frequency range displayed. Spectral frequencies separated by less than 5 MHz are considered degenerate in this diagram.

3946 The Journal of Chemical Physics, Vol. 62, No. 10, 15 May 1975 Copyright © 1975 American I nstitute of Physics

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M. S. Farag and R. K. Bohn: Low resolution microwave spectroscopy. I 3947

tions and we will only be concerned with the ground state rotational constants, Bo and Co. Since all of the useful low resolution band spectra we have observed are a type spectra, only a type transitions will be discussed.

Microwave spectral frequencies were calculated10 for hypothetical molecules with spectral characteristics similar to those of bromobenzene, AD = 5670 MHz and Bo +Co= 1823 MHz. The results are summarized in Fig. 1. The frequencies for a J = 5 - 4 transition are shown in the upper left quandrant. On the top line is shown the sym­metric top frequency given by II = (1823)(4 + 1) = 9115 MHz which is 2J + 1 = ninefold degenerate. On the second line are shown the frequencies for the hypothetical molecule in which Bo and Co have been changed to maintain Bo + Co = 1823 but to achieve an asymmetry parameter value of - O. 95 where the asymmetry parameter is given by K

= (2B -A - C)/(A - C). In the prolate rotor limit K = -1. The calculations were repeated for other hypothetical molecules with Bo and Co changed to obtain K values of - O. 90, - O. 85, and - O. 80 as shown in the figure. With decreasing molecular symmetry the various K compo­nents of the transition are seen to spread farther from the symmetric top frequency. In the lower left quadrant are shown the frequencies for the J = 10 - 9 transition for the same set of hypothetical molecules. The remaining two quadrants display the results of similar calculations for the J = 15 -14 and J = 20 -19 transitions for the same set of hypothetical molecules. Four characteristic fea­tures can be noticed. One is that under low resolution conditions, the clusters of lines could be observed as broad bands. This is most obvious in the high J spectra of the more symmetric species. Band spectra are ob­served even in cases where the calculations displayed in Fig. 1 do not predict them. For example, deuterated methyl trifluoroacetate, CF3COOCD3, has K = - O. 870 and the J = 10 - 9 band at 26.32 GHz is relatively intense and smoothly contoured (see Fig. 2). This must arise from numerous vibrationally excited species which contribute their characteristic J = 10 - 9 lines in the 26.3 GHz re­gion resulting in a large number of lines which are not resolved under low resolution conditions, e. g., 10 MHz/

I 25

I 20

I GHz

HOD HOD

FIG. 2. The low resolution microwave spectrum of CF3COOCDa. The spectrum was scanned at 10 MHz/sec with a recorder time constant of 0.3 sec. The band markers are calculated from 2632.0"'+1).

sec sweep rate and 1 sec detector time constant. The second feature is that the frequency of the band maximum shifts to higher frequency relative to (Bo + Co)(J + 1). Therefore, the B +C value obtained by dividing the fre­quency of the LRMW band maximum by J + 1 will exceed Bo + Co, the effective rigid rotor constants of the vibra­tional ground state molecule. The remaining two fea­tures are that the intensities of the lines increase with J due to a frequency squared factor in the intensity and the density of nearly degenerate lines increases with J due to the increasing number of high K lines which are shifted relatively little from the symmetric rotor frequency.

Band spectra have usually been observed at room tem­perature so that vibrationally excited species contribute to the spectrum weighted by the appropriate Boltzmann factors. Effective rotational constants vary with vibra­tional state so that the observed band is typically a super­position of overlapping bands from the various vibration­al states. Bv + Cv may be greater or less than Bo + Co de­pending on the vibrational mode which is excited.

Since all LRMW spectra thus far observed have been obtained on Stark modulated spectrometers with phase sensitive detection, the effect of the extent of Stark mod­ulation on the spectra must be considered. Band spectra which have been observed have bandwidths at half-height on the order of 50 to 300 MHz, at least two orders of magnitude wider than individual lines. Thus, the shifts required for most of the Stark lobes to be shifted out of a band are large. The symmetry of the molecules helps to provide large Stark shifts. For nearly symmetric rotors ± IKI levels for higher values of K and a given J are nearly degenerate. The Stark effects for such nearly degenerate levels are effectively first order and typically large. 9 The Stark shifts are then proportional to the component of the dipole moment along the symmetry axis of the molecule, Jla• On the other hand, the Stark shifts decrease with increasing J. Thus, a molecule which displays a weak band spectrum around J = 20 may not near J = 40 due to diminishing Stark modulation at higher J.

Thus, it is evident that the frequency of a LRMW band maximum depends on many factors, including K, J, the degree of Stark modulation (i, e., the product of Jla and the Stark voltage), the vibrational characteristics of the molecule, the temperature, and the distortion caused by sweeping the spectrum rapidly (10 MHz/sec) and detect­ing with a heavily damped recorder (time constant 1-3 sec).

COMPARISON OF LOW AND HIGH RESOLUTION EXPERIMENTAL RESULTS

In spite of the formidable array of complex factors af­fecting LRMW band frequencies we have looked for and found a simple, quantitative relationship between B + C and the ground state parameter, Bo +Co,

Let one define a low resolution B + C value according to

(3)

where II is the frequency of the band maximum and J is an integer. Table I summarizes the spectral charac-

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3948 M. S. Farag and R. K. Bohn: Low resolution microwave spectroscopy. I

TABLE 1. Comparison of low resolution B + C with B 0 + Co.

(B+C) Compound B+C Bo+Co

--- -1 K B o" Co

t-propargyl formate - O. 99 3372.3±1& 3372.35a 0.0000(3) t-propyl bromide8! -0.99 3204.6 ± 6b 3205.2c - 0.0002(2) t-propyl bromide19 -0.99 3228.0 ± 1. 8b 3228.0c 0.0000(6) t-propyl chloride31 -0.98 4549±2.2b 4548.2 ± O. 4d 0.0002(5) t-propyl chloride35 -0.98 4652.4±1.4b 4651.4 ± O. 4d 0.0002 (3) iodobenzene - O. 965 1414.5 ± O. 2" 1412.9 ± O. 21 0.0011 (2) 8!bromobenzene -0.940 1826.5±0.6& 1822.81h 0.0020(3) 79bromobenzene - O. 938 1844.2 ± O. 68 1841.14h 0.0017(3) p-fluoroanisole - O. 923 1792 ± 11 1788.021 0.0022(5) methyl trifluoroacetate (-CD3) - O. 870 2632±0.5 2625.66' 0.0024(2) 31chlorobenzene -0.853 2751.6±2.28 2739.36k 0.0045(8) methyl35chloroformate - 0.85 4850 ± 31 4830.25 1 0.0041 (6) 35chlorobenzene - O. 846 2825. 0±2. 38 2810. 446k 0.0052(8) methyl trifluoroacetate -G.834 2859.7 ± 0.98 2853.37' 0.0022(3) benzaldehyde - O. 822 2785.3± 1.0· 2768. 940m 0.0059(4) phenyl boron difluoride - 0.82 1956±2D 1946.63" 0.0046(10) nitrobenzene - O. 796 2274 ± 1. 48 2258.1 ± O. 6° 0.0071 (5) aniline - 0.575 4438 ± 58 m - fluoroaniline (- NDz) -0.56 2894 ± 10q

aD. C. Lister and N. L. Owen (unpublished work). bReference 2. CT. N. Sarachman, as quoted in Ref. 2. d.r. N. Sarachman, J. Chern. Phys. 39, 469 (1963). "Reference 7.

4370. O' 0.0155(11) 2845.72Q 0.0172(35)

fK. Johannson, H. Oldeberg, and H. Selen, Ark. Fys. 29, 531 (1965). 'This work. hE. Rosenthal and B. P. Dailey, J. Chern. Phys. 43, 2093 (1965). ID. G. Lister and N. L. Owen, J. Chern. Soc. Faraday II 69, 1304 (1973). IReference 11. kR. L. poynter, J. Chern. Phys. 39, 1962 (1963). ID. G. Lister and N. L. Owen, J. Chern. Soc. Faraday II 69, 1036 (1973). mR. K. Kakar, E. A. Rinehart, C. R. Quade, and T. KOjima, J. Chern. Phys. 52, 3803

(1970). "D. Christen and D. G. Lister (unpublished work), OK. E. Reinert, Z. Naturforsch. A 15, 85 (1960). PD. G. Lister and J. K. Tyler, Chern. Comm. 1966, 152. qG. Cazzoli, D. Damiani, and D. G. Lister, J. Chern. Soc. Faraday II, 69, 119 (1973).

teristics of nineteen compounds whose high resolution spectra have been assigned and whose LRMW band spec­tra have also been observed. They are listed in order according to increasing asymmetry. The A rotational constants of compounds 1-5 were not determined in the high resolution studies. Values for the A constants were calculated from reasonable assumed geometrical param­eters in order to calculate the asymmetry parameters K.

The uncertainties in their K values are estimated to be considerably less than 0.01. The third column lists the low resolution B + C values obtained by dividing the fre­quencies of the band maxima by appropriate J + 1 values and averaging over the observed bands. The frequencies are averages of those obtained from up and down fre­quency scans. The uncertainties are the larger of the standard deviation of the B + C values from the mean or an estimated uncertainty of the frequency of the band maximum divided by an average J + 1 value appropriate for that spectrum. The fourth column lists the corre­sponding ground state effective rigid rotor constants de­termined from the assigned high resolution microwave spectra. The last column shows the difference between the low and high resolution values divided by their re-

spective Bo + Co values. The uncertainties in the last significant figure are shown within parentheses. It can be seen that these relative differences generally increase with increasing asymmetry in agreement with the trend displayed in the theoretical spectra shown in Fig. 1. The differences are not large in any case. B + C differs from Bo + Co by less than 2% in all cases and by less than 0.8% for compounds with - O. 8:S K:S - 1. The relative differences are plotted vs K in Fig. 3. The relationship is Simple. The dimensionless difference parameter is adequately given by

(B + C)/(Bo + Co) - 1 = O. 025(± 0.005)(1 + K) . (4)

The slope was determined by a least squares procedure with each point weighted by the inverse square of its un­certainty. The quoted uncertainty in the slope is 2.50". The dashed lines in Fig. 3 represent the error limits quoted in (4). The correlation coefficient is 0.977.

The point in Fig. 3 lying farthest below the correla­tion line belongs to methyl trifluoroacetate (K'" - O. 834). Among the compounds listed in Table I, this compound has the largest number of low frequency torsional and

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M. S. Farag and R. K. Bohn: Low resolution microwave spectroscopy. I 3949

( B+C )-1 13,+ Co

0020

0015

0010

0005

-06 -07 -08 -09 )(

FIG. 3. Comparison of low resolution B + C and high resolution Bo + Co values. (8 + e)1 (80 + Co) -1 is plotted vs K. The straight line is the function 0.025(1 + K) and the dashed lines indicate the limiting slopes represented by (0.025 ± O. 005) (1 + K).

skeletal Vibrations. 11 The low resolution band spectrum observed from the room temperature vapor consists of overlapping bands of many vibrationally excited species. If Bv+Cv is less than Bo+Co for a majority of these states, the low resolution B + C value would decrease accordingly. To test this rationalization the band spec­trum of methyl trifluoroacetate was observed at 25°, - 25°, and - 78 °C yielding B + C values of 2859.7 ±O. 9 MHz, 2860.1 ± 0.5 MHz, and 2860.8 ± 0.4 MHz, respec­tively. Thus, at - 78°C with vibrationally excited spe­cies contributing less to the observed spectra, the rela­tive difference between B + C and Bo + Co increased to a value, 0.0026(2), vs a value, 0.0022(3) at 25°C. The - 78 ° C value is more consistent with the results from the other more rigid compounds considered in this study. Deuterated methyl trifluoroacetate was synthesized and its spectrum observed as a further test of the contribu­tion of vibrationally excited species. In general, the energy levels of the more massive deuterated compound lie deeper in the potential wells of the methyl trifluoro­acetate vibrational potential function with smaller vibra­tional amplitudes and hence rotational constants not as sensitive to vibrational state. This expectation is justi­fied by the relative B + C difference, 0.0024(2) plotted on Fig. 3 at K = - O. 870, which lies closer to the correla­tion line than does the corresponding value of the un­deuterated species. If one used Eq. (4) to calculate Bo + Co from the room temperature B + C of methyl trifluoro­acetate, one obtains 2847.8 MHz, an error of 5.6 MHz or 0.2%.

Figure 3 demonstrates that the relationship between B + C and Bo + Co is dominated by the asymmetry param­eter, K. Equation (4) can be interpreted in another way. Since B + C = II/(J + 1), where II is the frequency of the band maximum and defining 110 = (J + l)(Bo + Co), the hypo­thetical symmetric rotor frequency, then

(4a)

Thus, it is the ratio, v /110, which is prinCipally deter­mined by K.

Application of Eq. (4) to a molecule of unknown struc­ture requires an estimate of the asymmetry parameter K. The accuracy with which one can estimate K depends on the accuracy of the assumed molecular structural pa­rameters and also on the rotational difference, A - C. Thus, for molecules with a single heavy atom, e. g. , propyl bromide or iodobenzene, the heavy atom lies very close to the a axis insuring a large A and small B and C rotational constants. Molecules with no or several heavy atoms, e. g., benzaldehyde or methyl trifluoro­acetate, usually have A, B, and C values more nearly equivalent and their K values are more sensitive to mo­lecular structure uncertainties.

EXPERIMENTAL SECTION

All microwave measurements were made on a Hew­lett-Packard model 8460A microwave spectrometer. Bromo- and chlorobenzene were run in R band while ni­trobenzene, aniline, methyl trifluoroacetate, and deu­terated methyl trifluoroacetate were run in K band. Scan rates of 10 MHz/sec with time constants of 0.3-1 sec were usually used. Samples were directly injected or distilled into the wave guide and run at about 60 mtorr pressure with a Stark voltage of 3200 V /cm. Frequency measurements are frequencies of band maxima averaged over forward and reverse scans. Frequency accuracy depended on the width and shape of the bands and varied from 10-20 MHz. Bromo-, chloro-, and nitrobenzene and aniline were all commercial samples, were distilled prior to use and were identified by their microwave spectra. Methyl trifluoroacetate was prepared from trifluoroacetic anhydride and methanol. Deuterated methyl trifluoroacetate was similarly prepared using methanol (d4 ). Carefully distilled samples of each showed only one peak in vapor phase chromatograms using a SE - 30 column and infrared absorption spectra indistinguishable from literature spectra. 10 Methyl tri­fluoroacetate displayed only an intense methyl singlet in the proton nmr spectrum.

CONCLUSION

LRMW band spectra are observed for species which are nearly symmetric ( I K I~ O. 7), sufficiently volatile (~20 mtorr vapor pressure at room temperature) and have a suffiCiently large J.J.a (about 1 D for lighter mole­cules and larger for heavier ones). The band spacing can be- converted to an effective rigid rotor Bo + Co with an uncertainty of several tenths of one percent. This rotational constant information usually allows one to ar­rive at definitive conclusions concerning conformation in systems whose B + C values are sensitive to conforma­tional change.

ACKNOWLEDGMENTS

The authors are extremely grateful to Professor E. Bright Wilson, Jr., of Harvard University for granting use of his microwave spectrometer supported by NSF

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3950 M. S. Farag and R. K. Bohn: Low resolution microwave spectroscopy.

Grant GP-37066X and for his interest and stimulating comments. Ms. Nancy S. True prepared and characterized the trifluoroacetate esters. Dr. Richard Suenram as­sisted in obtaining the spectra and contributed innumer­able insights and suggestions. Mr. E. M. Bellott's in­terest and comments were very helpful. We are indebted to Professor Noel Owen for communicating many of his results prior to publication. This research was funded by the University of Connecticut Research Foundation. Computations were carried out at the University of Con­necticut Computer Center.

IL . H. Scharpen, Paper 09, 24th Symposium of Molecular Structure and Spectroscopy, The Ohio State University, Co­lumbus, OH, 1969. Also, Paper Tl, 3rd Austin Symposium on Gas Phase Molecular Structure, University of Texas,

Austin, TX, March 1970. 2S. Armstrong, Appl. Spectrosc. 23, 575 (1969). 3V. W. Laurie, Acc. Chern. Res. 3, 331 (1970). 4L. H. Scharpen and V. W. Laurie, Anal. Chern. 44, 378R

(1972). 5W. Ralowski, G. Wettermark, and S. Ljunggren, Acta Chern.

Scand. 27, 1565 (1973); but see also, L. Nygaard, ibid. A28, 118 (1974).

6W. E. Steinmetz, Ph. D. thesis, Harvard University (1973). 7W. E. Steinmetz, J. Am. Chern. Soc. 96, 685 (1974). 8N. S. True and R. K. Bohn, J. Chern. Phys. 62, 3951 (1975),

followi ng paper. 9C. H. Townes and A. L. Schawlow, Microwave Spectroscopy

(McGraw-Hill, New York, 1955). IOThe calculations were carried out using the program MODTOP

obtained from Professor Wilson's group. ItG. 1. C. Jones, T. D. Summers, and N. L. Owen, J. Chern.

Soc. Faraday IT 70, 100 (1974).

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