The rotational spectrum of tertiary-butyl alcohol

Journal of Molecular Spectroscopy 260 (2010) 77–83

Contents lists available at ScienceDirect

Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms

The rotational spectrum of tertiary-butyl alcohol E.A. Cohen a,*, B.J. Drouin a, E.A. Valenzuela b,1, R.C. Woods b, W. Caminati c, A. Maris c, S. Melandri c a

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099, USA Department of Chemistry, University of Wisconsin, Madison, WI 53706-1322, USA c Dipartimento di Chimica ‘‘G. Ciamician”, dell’Università, Via Selmi 2, I-40126 Bologna, Italy b

a r t i c l e

i n f o

Article history: Received 21 October 2009 In revised form 16 November 2009 Available online 4 December 2009 Keywords: tertiary-Butyl alcohol Rotational spectrum Internal rotation

a b s t r a c t The rotational spectrum of tertiary-butyl alcohol has been recorded in selected regions between 8 and 500 GHz. Early data from the University of Wisconsin in the 8–40 GHz region have been combined with recent measurements from the University of Bologna and the Jet Propulsion Laboratory in the millimeter and submillimeter wavelength regions. The spectrum was fit over a wide range of J’s and K’s using a common set of parameters for both the A and E states. This paper describes the initial assignment at Wisconsin and the final procedure used to assign and fit the higher rotational states. The resulting molecular constants and their interpretation are discussed. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction

2. Experimental details

tertiary-Butyl alcohol (TBA) presents a particularly interesting internal rotation problem. It is a nearly spherical rotor with a moderately low barrier to internal rotation about the C–O bond. Effects due to internal rotation about the C–C bonds are not observable in the ground state. The tert-butyl symmetric internal top is nearly the entire molecule with the axis of internal rotation nearly coincident with the c axis in the ac plane as shown in Fig. 1. The rotational spectrum of TBA was first reported by Valenzuela [1] as part of a study which also included tert-butyl mercaptan [2]. At that time, only the E state transitions between 8 and 40 GHz were fit using eight parameters and a data set which was limited by the available computing capability. The spectrum was again observed between 60 and 78 GHz in the Bologna laboratory as part of a study of the TBA-NH3 complex [3]. In order to properly assign and predict the TBA spectrum in the higher frequency region, the original data set was refit using Pickett’s SPFIT program [4]. Eventually, the predictions became sufficiently adequate to assign and fit spectra up to 500 GHz. At present 1539 features are fitted with a single set of parameters which describes both the A and E state spectra. Although the primary purpose for the re-examination of this spectrum was to precisely predict previously unobserved features, this paper also reports some of the procedures used in the original assignment, the fitting method used, and the newly derived parameters. The parameters are compared with those derived from ab initio calculations and those of related compounds.

The data used in this analysis was obtained at the University of Wisconsin (UW) between 8 and 40 GHz with a Stark modulated spectrometer and data acquisition system described by Woods and Dixon [5], between 58 and 78 GHz at the University of Bologna (UB) with a free jet spectrometer described by Melandri et al. [6], and in selected regions between 160 and 508 GHz at the Jet Propulsion Laboratory (JPL) with a spectrometer utilizing a microwave synthesizer and amplifier–multiplier chains [8–10]. The sample in the UW experiment was cooled to a point below 273 K which was sufficient to enhance low J transitions while still maintaining sufficient vapor pressure for observation. The UB experiment utilized a jet cooled sample at 10 K. The JPL experiments were done at room temperature. Two lc , J ¼ 1  0 transitions were measured with high accuracy at Bologna with a Fourier transform (FT), molecular beam spectrometer [11]. For the analysis, uncertainties of 100 kHz were assigned to the measurements below 40 GHz and above 200 GHz , 3 kHz to the two FT measurments, 20 kHz to most of the free jet measurements, and 50 kHz to the remaining lines.

* Corresponding author. E-mail address: [email protected] (E.A. Cohen). 1 Present address: 4901 Oakridge Dr. Midland, MI 48640, USA. 0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2009.11.010

3. The spectrum and its assignment 3.1. Initial assignment The original work on TBA is reported in Ref. [1] and the procedure leading to the assignment is reviewed here. The most striking features of the microwave spectrum of TBA in the traditional 8–40 GHz microwave region are the many strong lines with partially resolved first order Stark effects. These

78

E.A. Cohen et al. / Journal of Molecular Spectroscopy 260 (2010) 77–83

mercaptan [2]. Although more than one of the possible J assignments gave equally good fits to the data, only the one shown in Fig. 2 gave reasonable values for the molecular parameters. From the value of ðA þ BÞ determined in this fitting procedure, we were able to locate the R-branch transitions due to changes in the parallel component of the dipole moment, lc . These confirmed the initial assignment since none of the other four possible choices yielded ðA þ BÞ values in agreement with experiment. These R-parallel transitions were obscured by neighboring lines but we were able to confirm the 1–0 and some of the 2–1 transitions by their Stark effects. Another least squares fit to the expanded data along with double resonance experiments to locate Q-branch transitions served to further confirm the assignment. Ref. [1] reports 218 assigned transitions between 8 and 40 GHz. 3.2. Millimeter and submillimeter spectra

Fig. 1. tert-Butyl alcohol. The arrow shows the direction of the dipole moment with the tail positive.

provided the first clues which eventually led to the spectral assignment. In that region more than 200 strong lines showing partially resolved Stark effects of a first-order nature were eventually identified. Due to the complexity of the spectrum with consequent crowding of lines and the general weakness of the individual Stark lobes, the exact number of Stark lobes and therefore the J value for each line was difficult to determine. Some of these lines exhibited from 10 to 20 such Stark lobes. From the intensity patterns of the individual Stark components these lines were identified as Rbranch transitions. The seemingly random pattern of these lines suggested that they were due to DK ¼ 1 transitions allowed by the perpendicular component of the dipole moment, la . By counting Stark lobes for the resolved members of a transition within a given J family it proved possible to assign the J quantum numbers involved in the transitions to within 2. From an examination of the spectra and by extrapolation of first differences, the last member of a family for which K ¼ J could be determined. The first sequences of transitions which were identified are shown in Fig. 2. These families are similar to the ‘‘b-type chains” of Lees and Baker [12] and the ‘‘s-families” of Hershbach and Swalen [13]. With the five possible J assignments some of the transitions shown in Fig. 2 were fit to the six parameters characteristic of the IAM Hamiltonian using a nonlinear least squares fitting procedure [14]. Initial guesses were chosen from information extrapolated from the previously studied methanol [12] and tert-butyl

The available computational capability limited the analysis of the data in Ref. [1] to an eight parameter fit of selected E state transitions with J 6 15. These parameters fit the selected transitions with an RMS of 2.05 MHz and were accurate enough to provide a new prediction using the program SPCAT [4]. Once this was done the energy level labels could be converted to those appropriate for SPFIT and most of the previously reported transitions could be accurately fit using higher order centrifugal and torsion–rotation parameters. The fitting procedure is similar to that employed for perchloric acid, HClO4 [7]. The program SPFIT was run using symmetric rotor quantum number notation and what is referred to in the program description as ‘‘full projection ordering” to label the energy levels [4]. Both TBA and HClO4 are near spherical rotors with moderately low barriers to internal rotation leading to energy ordering which is dominated by the K dependent solutions of the Mathieu equation. Fig. 3 shows the Mathieu energy for the torsional ground state of TBA as a function of K. The lower series is for states with jK  rj ¼ 3n, the center series is for states with jK  rj ¼ 3n þ 1, and the top series is for states with jK  rj ¼ 3n  1, where r ¼ 0 for A and 1 for E states. The reduced energy E  ðA þ BÞJðJ þ 1Þ=2 is plotted as a function of J in Fig. 4 for the A states. The E states show similar behavior but have not been plotted to avoid clutter. States with K ¼ 3n are seen to be at lower energy and interact only weakly at low K with K ¼ 3n  1 states. The K ¼ 3n  1 states interact more strongly with each other. For the E states, K is replaced by K  r. This produces a characteristic pattern for the parallel lc transitions in which the jK  rj ¼ 3n levels give rise at low K to a symmetric rotor like pattern at multiples of A þ B with a group of lines from the levels with jK  rj ¼ 3n þ 1 to low frequency and another group with jK  rj ¼ 3n  1 to high. At high J the spectrum becomes

Fig. 2. Initially assigned sequences. The ’s represent the A state, the ’s represent the E state with K r > 0, and the ’s represent states with K r < 0.

E.A. Cohen et al. / Journal of Molecular Spectroscopy 260 (2010) 77–83

79

Fig. 3. Mathieu energy as a function of K. The ’s represent the A state, the ’s represent the E state with K r > 0, and the ’s represent states with K r 6 0.

Fig. 4. Reduced energy vs J for the A states. The K value for an approximately horizontal line of points is given by the J value at which it starts.

Fig. 5. Jet cooled spectrum of the parallel J ¼ 8  7 transitions. The features at the far ends of the figure are the asymmetry split jKj ¼ 1, A state transitions. The two features marked with a  are not TBA.

80

E.A. Cohen et al. / Journal of Molecular Spectroscopy 260 (2010) 77–83

Fig. 6. A portion of the jK  rj ¼ 3n transitions near the center of the J ¼ 47  46 parallel band with a simulation at the bottom. See text for details.

a bit cluttered with excited state lines and at higher K some unusual mixing of states is possible. However, the pattern is quite clear in the jet cooled spectrum of the parallel J ¼ 8  7 transitions shown in Fig. 5. These and other 60–78 GHz UB data were then included leading to predictions of still higher frequency spectra. Initially, the E state transitions were better predicted than the ones arising from the A state. Many of the high frequency A state transitions were found by interpolating between unambiguously assigned E state members of high J sequences similar to those shown in Fig. 2. Finally 1539 features up to 507 GHz were included in the fit with an RMS of 87 kHz and a reduced RMS of 0.93. Thirty two other measurements were rejected because the observed minus calculated frequencies were greater than three times the estimated experimental uncertainty. A portion of the center of the J ¼ 47  46 parallel band is shown in Fig. 6. In the figure, the three lowest frequency lines are those with jK  rj ¼ 21 and jKj ¼ 22; 21; 20 counting from low to high frequency. The next group of three is for jK  rj ¼ 18 and so forth. Eventually the individual lines become difficult to distinguish at the band origin. One of the asymmetry split A state jKj ¼ 3 lines is isolated at the high

end of the scan. A plot of K vs. J for the fitted A state energy levels is shown in Fig. 7. The E state plots are similar and are included in the supplementary material. The output file of the fitting program which has been deposited with the Journal contains the full list of transitions. 3.3. The molecular parameters We have adopted a phenomenological approach to derive the set of molecular parameters which describe the spectrum. Rather than using Kivelson–Kirtman parameters [15,16] we have taken advantage of the fact that the molecular parameters may be expressed as Fourier expansions in terms of cos½2pnðqK  rÞ=3 where r ¼ 0; 1 for A and E states respectively. Here K ¼ ðK 0 þ K 00 Þ=2 when the operator connects K 0 with K 00 . Among the reasons for using this method are that the coefficients of the expectation values of ðp  qKÞ2 and cosð3aÞ are highly correlated leading to uncertain and misleading values and that the calculation would involve continued re-evaluation of torsional integrals for the off-diagonal elements as the fit was refined. The torsional en-

Fig. 7. Observed A state energy levels.

81

E.A. Cohen et al. / Journal of Molecular Spectroscopy 260 (2010) 77–83 Table 1 Molecular parameters in MHz except for unitless q. SPFIT id.

Parameter name

910099 199

ðA þ BÞ=2

q

1000000100 2000000100 1099

C  ðA þ BÞ=2

1000001000 2000001000 40009 1000040000 2000040000 410009 1000410000 2000410000

ðC  BÞ=4

Dac

430099

P 2þ þ P 2 ðc1  1Þ ðc2  1Þ Pa Pc þ Pc Pa ðc1  1Þ ðc2  1Þ

0.12382( 47) 5:09ð49Þ  103 178.93818( 36) 0.20820( 47) 0:72ð50Þ  103 7.111412( 62) 0.0540( 36) 0.0348( 35) 17.25171(104) 0.97730(59) 0:0289ð136Þ  103

2000430000

c2

1:804ð203Þ  106

410199

P 2 ðP a P c þ P c P a Þ c1

0:026608ð76Þ  103

½P 2c ; ðP a P c þ P c P a Þþ =2 c1

0:034217ð124Þ  103

DJ

P4 c1

1:179426ð125Þ  103

DJK

P 2 P 2c c1

0:43321ð51Þ  103

DK

P 4c c1

0:69472ð43Þ  103

dJ

9:9276ð244Þ  106

1000040100

P 2 ðP 2þ þ P 2 Þ c1

2000040100

c2

1:477ð187Þ  106 0:06397ð77Þ  103

1000041000

½P 2c ; ðP 2þ þ P 2 Þþ =2 c1

2000041000

c2

5:14ð100Þ  106

6

0:5592ð277Þ  109

1000411000 299 1000000200 1199 1000001100 2099 1000002000 40199

41099

dK

0:245703ð291Þ  103 2:613ð276Þ  106

0:604ð242Þ  106 3:67ð46Þ  106 2:675ð2Þ  106 0:55ð57Þ  106 3:77ð53Þ  106 1:012ð176Þ  106

0:01268ð233Þ  103

399

HJ

P

1299

HJK

P 4 P 2c

1:285ð116Þ  109

2199

HKJ

2:745ð119Þ  109

3099

HK

29 3000000009 600019

F V3

P 2 P 4c P 6c 2

601019

c

P 2c ðc1  1Þ ðc2  1Þ

0.993244247(fixed) 4688.626959(156)a

1000430000

411099

a

P2 ðc1  1Þb ðc2  1Þ

Fitted value

½Pc; ðP 3þ þ P 3 Þþ =21=2 c1

1000410100

b

Operator

p ð1  cos 3aÞ=2 pP c pP 3c

1:768ð112Þ  109 671350.3(fixed) 13287286.242(312) 0:0ð63Þc  103 5:4141ð140Þ  103

Numbers in parentheses are approximately 1r uncertainties in units of the least significant figure. The preceding operator is multiplied by the function shown with cn ¼ cosð2pnqK=3Þ. This term is minimized by varying q manually. The uncertainty corresponds to approximately 4 units of the least significant figure of q.

ergy as a function of K is expressed as a Fourier expansion of a solution of the modified Mathieu equation ½Fðp  qKÞ2 þ V 3 ð1  cos 3aÞ=2w ¼ Ew. The relative magnitudes of the Fourier coefficients are fixed by a preset value of s ¼ 4V 3 =9F. These are multiplied in the fitting program by a single fitted constant which is proportional to F. The constant q is not varied within the program but is reset manually until a minimum RMS is found for the selected s. The procedure is repeated for several s values until a minimum RMS is found as a function of both q and s. This method was used for the initial refinement of the fit. An alternative procedure requires the inclusion of the operators ðp  qKÞP c and ðp  qKÞP 3c . These are correlated with q and s respectively. The values of q and s may then be quickly adjusted to reduce the coefficients of these operators to values much smaller than their uncertainties. This procedure was used as data were added to the fit and gave parameters consistent with those derived by the method described in the paragraph above. Although this yielded a satisfactory fit to the data with the most compact set of parameters, the resulting value of F when the contribution of the ðp  qKÞP 3c term is set to zero is not in very good agreement with

q and the C rotational constant. F was than fixed to a value derived from other structural constants as described below while the barrier and the coefficient of ðp  qKÞP3c were allowed to vary. The value of q was chosen to minimize to coefficient of ðp  qKÞPc . The derivation of the rotational constants from SPFIT parameters requires some discussion. The constants derivable from the coefficients of operators which are diagonal in K are evaluated by summing their A state Fourier coefficients evaluated at K ¼ 0. The coefficients of operators which are off diagonal in K present a different problem. Here we will be concerned with only the coefficients of ðP2þ þ P 2 Þ and ðPa Pc þ P c P a Þ which are related to the constants ðB  AÞ=4 and Dac , respectively. The torsional integrals give a fair qualitative description of the behavior of the DK ¼ 2 coefficients due to asymmetry, but the cos½2pðqK  rÞ=3 term in the fitted Fourier expansion of the DK ¼ 1 coefficients due to the off-diagonal element of the inverse inertial tensor has the opposite sign and is larger than that of the torsional integral. A similar situation was encountered in the analysis of the HClO4 spectrum [7]. Effective rotational constants for the A state are extracted from the coefficients by defining them as follows:

82

Xhv t Kjjv t K 0 i þ

E.A. Cohen et al. / Journal of Molecular Spectroscopy 260 (2010) 77–83 2 X

an fcos½2npðqK  rÞ=3  1g;

1

where X is either ðB  AÞ=4 or Dac , and hv t Kjjv t K 0 i is the appropriate torsional integral. Since there is not a unique solution for F, q and V 3 from only the ground state spectrum, it is usual to fix F so that F and q are both consistent with the overall rotational constants. When q is close to unity as is the case here, problems arise since F is related to the rotational constant for the internal rotor by

F ¼ C a =ð1  kq qÞ where kq is the cosine of the angle between the q axis and the top axis and is itself very nearly one. C a may be determined by either of two methods, both of which assume three fold symmetry of the internal rotor. The first utilizes the relationship among the rotational constants

1=C a ¼ ðC þ AÞ=ðAC  D2ac Þ  1=B: The second uses the equation

kq fðAC  D2ac Þ=Ag ¼ qC a : The second of these equations is used here for reasons which were discussed in Ref. [7]. The determination of kq is somewhat uncertain since it is usually done using the assumption that the internal top maintains three fold symmetry and ab initio calculations show this to be not quite the case. It is, however, so close to unity that it is not a significant source of error. The constant Dac may not be uniquely determined from a fit to only the torsional ground state, and its contribution to the uncertainty of C a is difficult to quantify. However, D2ac  AC and contributes only about 10 MHz to the value of F. The resulting parameters with F 671350:3 MHz are given in Table 1. For J ¼ 0 the E state lies 113325.480(6) MHz above the A state. The output file from the fit is included in the supplementary material. We note that the P4þ þ P 4 operator produced no significant improvement in the quality of the fit and was not included in the final set of parameters. It had been anticipated that the near spherical nature of the molecule might require the inclusion of such a term as had been the case for HClO4 [7]. However, its coefficient

is not highly correlated with the other centrifugal distortion constants. It must be emphasized that inclusion of the ðp  qKÞP 3c term allows for considerable variation in the values of F, V 3 , and q with only minor variation in the rotational constants. Both V 3 and q show an almost linear variation with F. A representation of this is shown in Fig. 8. The ðp  qKÞPc term is minimized in the calculations from which the plot is derived. The lines are plotted from F ¼ 622—672 GHz. The coefficient of ðp  qKÞP 3c varies from approximately 0.00046 MHz for the lowest F to 0.00055 MHz for the highest. The dipole moment was determined in Ref. [1] and no further refinement was done in this study. The value determined there was fla ; lc g ¼ f1:47; 0:98gD with the direction as shown in Fig. 1. The rotational constants and dipole moment are compared with ab initio values in Table 2 and are in reasonably good agreement. The rotational constant for the internal tert-butyl top, C a calculated as described above is 4540.3 MHz which can be compared to 4544.3 MHz for Aa derived from a similar fit to all available data for the prolate tert-butyl mercaptan [1,2,17,18]. Crane and Smith [19] report similar values for the excited states of the symmetric rotor tert-butyl fluoride. The three fold barrier is approximately 18.6% higher than that recently reported for methanol [20] which is half the percent difference found in Ref. [2] between tert-butyl mercaptan and methyl mercaptan. Table 2 Comparison of experimental and Ab Initio parameters. Parameter

Experimenta

MP2/6-311++G**

A (MHz) B (MHz) C (MHz) V 3 (cm1) la (D) lc (D) ltot (D)

4704.38 4674.41 4508.16 443 1.47(2) 0.98(2) 1.77(2)

4724.17 4693.14 4526.09 454 1.43 0.99 1.74

a Numbers in parenthesis are reported in Ref. [1] as 95% confidence limits. Uncertainties in the rotational constants are in the fourth decimal place. The range of V 3 values is shown in Fig. 8.

Fig. 8. V 3 and q versus F between 622 and 672 GHz. The solid line represents q.

E.A. Cohen et al. / Journal of Molecular Spectroscopy 260 (2010) 77–83

83

4. Conclusion

References

Using the program SPFIT, we have determined a single set of molecular parameters which reproduces the available data to within experimental uncertainty over a wide range of quantum numbers for both the A and E internal rotation states of the tert-butyl group. This is the first application of the program to a molecule with very large q and both A and E states and demonstrates its usefulness for heavy internal rotors. The parameters are consistent with those determined in the initial analysis of Ref. [1], ab initio calculations, and molecular parameters of related molecules.

[1] E.A. Valenzuela, Ph.D. thesis, Department of Chemistry, University of Wisconsin, 1975. [2] E.A. Valenzuela, R.C. Woods, J. Chem. Phys. 61 (1974) 4119–4128. [3] B.M. Giuliano, M.C. Castrovilli, A. Maris, S. Melandri, W. Caminati, E.A. Cohen, Chem. Phys. Lett. 463 (2008) 330–333. [4] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371–377. Current versions are described and available from: . [5] R.C. Woods, T.A. Dixon, Rev. Sci. Instrum. 45 (1974) 1122. [6] S. Melandri, W. Caminati, L.B. Favero, A. Millemaggi, P.G. Favero, J. Mol. Struct. 352/353 (1995) 253. [7] J.J. Oh, B.J. Drouin, E.A. Cohen, J. Mol. Spectrosc. 234 (2005) 10–24. [8] B.J. Drouin, C.E. Miller, H.S.P. Müller, E.A. Cohen, J. Mol. Spectrosc. 205 (2001) 128. [9] J.E. Oswald, T. Koch, I. Mehdi, A. Pease, R.J. Dengler, T.H. Lee, D.A. Humphrey, M. Kim, P.H. Siegel, M.A. Frerking, N.R. Erickson, IEEE Microw. Guided W. 8 (1998) 232. [10] B.J. Drouin, F.W. Maiwald, J.C. Pearson, Rev. Sci. Inst. 76 (2005) 093113. [11] W. Caminati, A. Millemaggi, J.L. Alonso, A. Lesarri, J.C. Lopez, S. Mata, Chem. Phys. Lett. 392 (2004) 1. [12] R.M. Lees, J.G. Baker, J. Chem. Phys. 48 (1968) 5299–5318. [13] D.R. Herschbach, J.D. Swalen, J. Chem. Phys. 29 (1958) 761–766. [14] R.C. Woods, J. Mol. Spectrosc. 21 (1966) 4–24. [15] D. Kivelson, J. Chem. Phys. 22 (1954) 1733–1739; D. Kivelson, J. Chem. Phys. 23 (1955) 2230–2235; D. Kivelson, J. Chem. Phys. 23 (1955) 2236–2243. [16] B. Kirtman, J. Chem. Phys. 37 (1962) 2516–2539. [17] L. Margulès, H. Hartwig, H. Mäder, H. Dreizler, J. Demaison, J. Mol. Struct. 517518 (2000) 387391. [18] E.A. Cohen, unpublished. [19] R. Crane, J.G. Smith, J. Mol. Spectrosc. 101 (1983) 229–244. [20] Li-Hong Xu, J. Fisher, R.M. Lees, H.Y. Shi, J.T. Hougen, J.C. Pearson, B.J. Drouin, G.A. Blake, R. Braakman, J. Mol. Spectrosc. 251 (2008) 305313.

Acknowledgments Portions of the research described in this paper were carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. W.C., A.M., and S.M. thank the University of Bologna for financial support. Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (http://library.osu.edu/sites/msa/ jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jms.2009.11.010.