Far-Infrared Laser Assignments for Methylamine

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1 Int J Infrared Milli Waves (2008) 29:8 6 DOI /s Far-Infrared Laser Assignments for Methylamine R. M. Lees & Zhen-Dong Sun & Li-Hong Xu Received: May 2007 / Accepted: 6 November 2007 / Published online: 24 November 2007 # Springer Science + Business Media, LLC 2007 Abstract Reported far-infrared laser lines for five different transition systems of CH 3 NH 2 optically pumped by a CO 2 laser have been identified spectroscopically through a highresolution Fourier transform infrared study of the C-N stretching band together with CO 2 - laser/microwave-sideband broad-scan and Lamb-dip measurements. From the infrared analysis plus previous far-infrared (FIR) results for the ground vibrational state, quantum numbers have been assigned for seven methylamine FIR laser transitions and their C-N stretching pump absorptions coincident with the CO 2 laser lines. The assignments are confirmed through the use of closed frequency combination loops that also provide improved FIR laser frequencies to spectroscopic accuracy. Keywords FIR lasers. Methylamine. CH 3 NH 2. FTIR. Microwave sideband spectrometer. Lamb dips. Infrared spectroscopy 1 Introduction The C-N stretching infrared band of methylamine, reported fifty years ago at low resolution by Gray and Lord [1], is centred around 1044 cm -1 and displays the P, Q and R branch structure characteristic of a parallel vibration. This overlaps well with the 9.6 μm band of the CO 2 laser, and optically pumped far-infrared laser (FIRL) emission from CH 3 NH 2 was detected early on by Dyubko et al. in 1972 [2] and Plant et al. in 1973 [3]. Subsequently, further FIRL transition systems were reported by Radford [4, 5], Landsberg [6] and Dyubko et al. [7]. During the same period, an optoacoustic study by Walzer et al. [8] revealed a rich spectrum of signals, showing that a substantial number of CO 2 laser lines coincide with methylamine infrared (IR) absorption lines. R. M. Lees (*) : Z.-D. Sun : L.-H. Xu Department of Physics, Centre for Laser, Atomic and Molecular Sciences (CLAMS), University of New Brunswick, Saint John, N.B., Canada E2L 4L5 lees@unb.ca

2 Int J Infrared Milli Waves (2008) 29:8 6 9 The identification of the quantum numbers for the IR pump and FIR lasing transitions, however, presents a difficult spectroscopic problem for methylamine. In addition to the complex structure introduced into the spectrum by the internal rotation (torsion) of the CH 3 group, there is also a substantial and irregular splitting of the energy levels into doublets due to the inversion or wagging motion of the NH 2 group, analogous to the well-known inversion of ammonia. The two levels of an inversion doublet can be labeled as a or s for antisymmetric and symmetric rotational states, and have spin weights of 3 and 1, respectively, as they correspond to the spins of the two H nuclei being parallel or antiparallel. [From Fermi-Dirac statistics, the overall wavefunction must be antisymmetric to the inversion operation so that the symmetric spin functions combine with the antisymmetric rotational functions, and vice-versa.] Since the internal rotation also splits the energies into sublevels of A and E torsional symmetry with a 2:1 ratio of spin weights, the resulting energy structure and spectra are very complicated, with intensity ratios 6:3:2:1 among the four possible A-a, E-a, A-s and E-s combinations. As absorption lines from excited torsional states are also present, the Doppler-limited spectra are very dense and highly overlapped, making the problem of transition assignment extremely challenging. In the present study, we have employed a high-resolution Fourier transform spectrum of CH 3 NH 2 together with measurements taken in both the broad-scan Doppler-limited and Lamb-dip sub-doppler modes [9 11] of our CO 2 -laser/microwave-sideband spectrometer to assign structure in the C-N stretching band and thereby identify a number of the reported FIRL lines. So far, five IR-pump/FIR-laser transition systems have been assigned via closed-loop combination relations employing our new IR data together with previous ground-state FIR observations [12 ] and calculated energies (Ohashi, private communication). The combination loops also serve to provide improved frequencies for the FIRL lines to the spectroscopic accuracy. 2 Experimental aspects Originally, the Fourier transform spectrum of CH 3 NH 2 was recorded from 990 to 1100 cm 1 at cm 1 resolution on the modified Bomem DA3.002 spectrometer at the National Research Council of Canada in Ottawa. A total of 25 scans were coadded, employing a pressure of 80 mtorr and a path length of 2.0 m in four transits of an 0.5-m absorption cell at room temperature. To improve the resolution to the Doppler limit, we also recorded the spectrum again using the broad-band mode of our CO 2 -laser/microwave-sideband spectrometer. The features and operation of this instrument have been described previously in some detail [9, 10] so we will just review them briefly here. The principal components of the infrared source are illustrated in Fig. 1, showing the evolution of the radiation from the original CO 2 carrier through to a single tunable microwave sideband. The beam from our line-tunable Evenson-type CO 2 laser, with power of order 8 W, is focused into a Cheo-type modulator described in detail in [9]. Here, it is mixed with the W output from a traveling-wave-tube amplifier driven by a microwave synthesizer in order to add tunable sidebands on both sides of the CO 2 carrier. The carrier plus sidebands are then focused into a piezoelectrically tuned Fabry-Perot filter that allows just one of the sidebands to pass through. The final output is a single sideband beam of power of order 1 mw that can be tuned over a GHz range, giving substantial spectral coverage. In operation, the CO 2 laser is locked to line centre via the Lamb-dip in the fluorescence from an external low-

3 0 Int J Infrared Milli Waves (2008) 29:8 6 Fig. 1 Source section of the CO 2 -laser/microwave-sideband spectrometer, showing the radiation path from the laser through the modulator in which the microwave sidebands are added to the CO 2 carrier and then through the Fabry-Perot filter which isolates a single tunable sideband [9, 10]. The accessible microwave tuning range is GHz. 1 mw Tunable IR SB Fabry-Perot Filter Microwave Synthesizer W MW CO 2 Laser 8W CO 2 laser Modulator pressure CO 2 cell. Thus, the microwave frequency is precisely known and measurements with this instrument have intrinsically high accuracy without needing additional calibration. In the present study, we first ran full-sideband sweeps using CO 2 lines of the 9.6 μm P and R branches, employing a multipass 0.6-m absorption cell with total path length of m. We then switched to the spectrometer sub-doppler mode by inserting a reflecting mirror at the cell output window to produce counter-propagating beams inside the cell and shifting the Fabry-Perot filter to a position following the cell in order to maximize the sideband power in the cell. In this mode, we obtained saturation-dip spectra for a substantial number of the CH 3 NH 2 IR lines. The Lamb-dip resolution is of order 0.4 MHz with absolute accuracy of about 200 khz, as determined from a study of the methanol C-O stretching spectrum []. 3 Energy level notation and spectral structure The energy levels of methylamine can be characterized by a set of quantum numbers defining the vibrational state v, the torsional state v t, the torsional symmetry σ, the inversion symmetry I, the overall rotational angular momentum J, and the component K of the angular momentum along the molecular a-axis nearly parallel to the C-N bond. Here, the excited C-N stretching vibrational state will be denoted as cn. The torsional symmetry σ can be either A or E and the inversion symmetry I can be a or s. We use a signed K for the E levels, with positive K corresponding to levels sometimes labeled as E 1 [12] and negative K corresponding to E 2. For A symmetry, the levels with K>0 are split by the effects of molecular asymmetry into K-doublets, and we label the components of a resolved K-doublet with a superscript as K + or K. The C-N stretching mode of methylamine is a parallel band with an a-type transition moment, so that the infrared transitions follow a ΔK=0 selection rule. The J-selection rule is ΔJ= 1, 0 or +1, corresponding to IR transitions labeled as P, Q or R, respectively. The FIRL transitions occur within the excited C-N stretching state and arise through μ a and μ c components of the permanent molecular dipole moment, giving the selection rules ΔK=0 or ±1, respectively. However, μ a has a relatively low value for methylamine, compared for example to methanol, so that the a-type FIRL laser lines are weak and one does not see the typical triad patterns of lines that are such a help to assignments in methanol [].

4 Int J Infrared Milli Waves (2008) 29: IR-Pump/FIR-laser transition system assignments Analysis of our high-resolution spectroscopic results for the C-N stretch band together with previous FIR information for the vibrational ground state has now yielded transition identifications for five FIRL emission systems from CH 3 NH 2. The assignments are presented in Table 1, and the relevant data and interesting features for the different transition systems are discussed individually in the following text R(4) transition systems (a) and (b) The 9R(4) CO 2 laser line is reported to pump two FIRL lines at 288 and 3 μm [4]. The 288 μm wavelength corresponds to a wavenumber of 34.7 cm 1, while the frequency of the 3 μm line has been measured accurately as MHz [5], corresponding to a wavenumber of cm 1. By an interesting coincidence, the two FIRL lines turn out to belong to two distinct but very similar emission systems, pumped respectively by the q R (0, 2,) and q R(0,2,) E-a transitions that overlap almost exactly in our FTIR spectrum. Thus, as illustrated in Fig. 2, the energy level and transition diagrams are identical for the two systems, but with opposite signs for all of the K values. We refer to the system with K<0 as system (a), corresponding to La=34.7 cm 1. With the IR and FIR data given in the caption to Fig. 2, La can be determined from two independent combination loops as follows: La ¼ P þ β c ¼ 1067:5392 þ 33: :2797 ¼ 34:60 cm 1 ¼ a þ α b ¼ 10:8936 þ 36: :0798 ¼ 34:60 cm 1 The close agreement between the two La values gives strong support for the line assignments and also the quality of the ground-state energies. The average FIRL wavenumber of La=34.60 cm 1 represents a significant improvement in accuracy over the original wavelength measurement. Table 1 Assignments for optically pumped far infrared laser lines of CH 3 NH 2. CO 2 Line IR Assgt a (v t,k,j) v σ-i FIRL Assignment ν b loop (cm 1 ) ν c obs (cm 1 ) [Ref] (v t,k,j ) v0 (v t,k,j ) v00 9R(4) R(0, 2,) cn E-a (0, 2,) cn (0, 1,) cn [4] 9R(4) R(0,2,) cn E-a (0,2,) cn (0,1,) cn [5] 9P(24) Q(0, 9,) cn E-a (0, 9,) cn (0, 8,) cn [7] (0, 9,) cn (0, 8,) cn [5] 9P(46) P(0,2 +,) cn A-a (0,2 +,) cn (0,1,) cn [6] 9P(46) P(0,7,) cn E-a (0,7,) cn (0,6,) cn d 35.3 [6] (0,7,) cn (0,6,) cn d 55.6 [4] a The assigned infrared pump transitions are all to the excited C-N stretching state, denoted as cn. b FIRL wavenumbers calculated from the spectroscopic data using closed-loop combination relations. c Experimental FIRL wavenumbers derived from the reported wavelengths or frequencies in the indicated references. d Tentative values, based on IR wavenumbers for the subband believed to be the (0,6) E-a subband but not yet rigorously confirmed (see text).

5 2 Int J Infrared Milli Waves (2008) 29:8 6 (a) 9R(4) J 18 a (0,-2) E-a (v t,k ) σ-i La 34.7 α β Excited C-N Stretch b c d e Ground State (0,-1) E-a (0,0) E-a (0,1) E-a Lb γ δ f (0,2) E-a (b) 9R(4) 18 Fig. 2 CH 3 NH 2 energy level and transition systems for the FIRL lines at wavelengths of (a) 288 μm and (b) 3 μm optically pumped by the 9R(4) CO 2 laser line [4]. System (a) on the left refers to K<0, while system (b) on the right has the same diagram but K>0. Wavenumber Lb (in cm 1 ) is derived from the frequency reported in Ref. [5]. The IR and FIR data for system (a) are: P= , a= , b= , c= , α=[ ], β=[ ] cm 1. For system (b), P= , d= , e= , f= , γ=[ ], δ=[ ] cm 1. IR wavenumbers given to 4, 5 or 6 decimal places are FTIR, broad-scan sideband or Lamb-dip sideband measurements, respectively. FIR wavenumbers in brackets are calculated from ground-state energies kindly provided by Prof. N. Ohashi. For the second system (b) with K>0 and Lb= cm 1, the analogous two loops in Fig. 1 determine the Lb values as: Lb ¼ P þ δ d ¼ 1067:5392 þ 30: :3810 ¼ 31:7618 cm 1 ¼ f þ γ e ¼ 10:5379 þ 33: :2442 ¼ 31:76 cm 1 Both loop values are in excellent agreement with the frequency-measured value, confirming the assignment P(24) transition system The 9P(24) CO 2 laser line falls within the dense Q branch of the C-N stretching band and produces a particularly strong optoacoustic signal [8]. Of the six FIRL lines that are known to be pumped by 9P(24) [2, 3], we have been able to arrive at positive identifications for two of them from our analysis. As given in Table 1 and illustrated in the energy level and transition diagram for this system in Fig. 3, the IR pump is assigned as the q Q(0, 9, ) E- a transition. FIRL lines La (reported at a wavelength of μm [3, 7] with parallel polarization) and Lb (with reported frequency of MHz [5] and perpendicular polarization) are then assigned to the (v t, K, J) v =(0, 9, ) cn (0, 8, ) cn and (0, 9, ) cn (0, 8, ) cn E-a transitions, respectively. The experimental IR and FIR wavenumbers in the caption to Fig. 3 confirm the transition assignments through combination relations going around closed loops of lines,

6 Int J Infrared Milli Waves (2008) 29:8 6 3 Fig. 3 CH 3 NH 2 energy level and transition system for FIRL lines optically pumped by the 9P(24) CO 2 laser line. FIRL wavenumbers La and Lb (in cm 1 ) are derived from results in Refs. [7] and [5], respectively. IR and FIR wavenumbers are: P= , a= , b= , c= , d= , e= , f= , g= , α= , β= 68.07, γ= cm 1.IR data given to 4 decimal places are FTIR observations; data to 5 places are CO 2 -laser/microwavesideband measurements. FIR data are from Ref. [12]. Excited C-N Stretch Ground State J a b c d e (0,-8) E-a La 45.7 Lb α β γ f g (0,-9) E-a (v t,k) σ-i 9P(24) whose frequencies should sum to zero. The closure defects δ for three sample combination loops are as follows: δ 1 ¼ P Lb d þ β ¼ 1043:43 67: :5366 þ68:07 ¼ 0:0029 cm 1 δ 2 ¼ P f α þ e d þ β ¼ 1043: : :4840 þ1021: :5366 þ 68:07 ¼ 0:0039 cm 1 δ 3 ¼ f g γ þ c e þ α ¼ 1019: : :5421 þ1064: :3805 þ 69:4840 ¼ 0:0019 cm 1 The defects are close to zero to within the net estimated uncertainties for the IR and FIR wavenumbers in the loops, supporting the assignments. Combination loops can also be used to obtain the FIRL wavenumber La as follows: La ¼ P þ β a ¼ 1043:43 þ 68: :4631 ¼ 45:79 cm 1 ¼ f þ α b ¼ 1019:5340 þ 69: :3036 ¼ 45:74 cm 1 The two values are in good agreement with each other and also with the value of 45.7 cm 1 derived from the experimental wavelength of μm reportedin[7] P(46) transition systems The 9P(46) CO 2 laser line pumps three FIRL lines at wavelengths of 180, 283 and 351 μm [4, 6] which belong to two different systems according to our spectroscopic results. Looking at the 351 μm line first, we identify its IR pump as the q P(0, 2 +, ) A-a transition, so that this system involves asymmetry-split A-a K-doublet levels. In Fig. 4, we show the energy level and transition diagram, with the supporting IR and FIR data given in the caption. The wavenumbers in parentheses for the IR Q-branch transitions were obtained from their P and R branch partner lines using ground-state combination differences.

7 4 Int J Infrared Milli Waves (2008) 29:8 6 Excited C-N Stretch J - + La P(46) Ground State a b c For this system, we obtain three estimates of the FIRL wavenumber La from loop combination relations as follows: La ¼ P þ α c ¼ 1021:0590 þ 29: :42 ¼ 28:2090 cm 1 ¼ d þ β b ¼ 1043:7356 þ 30: :9433 ¼ 28:2084 cm 1 ¼ e þ γ a ¼ 1064:0970 þ 26: :6640 ¼ 28:2084 cm 1 The average value of La= cm 1 is a substantial improvement in accuracy, while the close agreement among the three values serves to confirm the line assignments as well as the good quality of the ground-state energies. For the other two FIRL lines at 180 and 283 μm pumped by 9P(46), we have a secure assignment of the q P(0,7,) E-a IR pump transition as shown in Fig. 5, but there is still some ambiguity about exactly which lines in the spectrum correspond to the (0,6) E-a transitions. The problem is that the ground-state combination differences that are our main assignment tool are almost identical for the K=+6 and K= 6 E-a levels. Thus, while we have identified two K =6 subbands in the spectrum, they are both strongly affected by line overlapping over large sections of their ranges and it is not yet possible to differentiate confidently between them with the combination differences being so similar. The caption to Fig. 5 gives the IR wavenumbers for what looks to be the most likely choice, but we note that this is still tentative. With the data from Fig. 5, the FIRL wavenumbers are given from the following combination loops: La ¼ P þ α d ¼ 1021:0565 þ 35: :65 ¼ 34:8918 cm 1 ¼ e þ γ b ¼ 1043:2181 þ 55: :0207 ¼ 34:89 cm 1 La ¼ P þ β c ¼ 1021:0565 þ 57: :86 ¼ 55:36 cm 1 ¼ f þ δ a ¼ 1063:9040 þ 54: :7637 ¼ 55:3610 cm 1 d e (0,2) A-a (0,1) A-a (v t,k) σ-i Fig. 4 CH 3 NH 2 energy level and transition system for FIRL line optically pumped by the 9P(46) CO 2 laser line. FIRL wavenumber La is derived from the wavelength given in Ref. [6]. IR and FIR data are: P= , a= , b=( ), c= , d=( ), e= , α=[ ], β=[30.41], γ= [ ] cm 1. IR wavenumbers given to 4, 5 or 6 decimal places are FTIR, broad-scan sideband or Lamb-dip sideband measurements, respectively. Values for Q-branch lines b and d in parentheses are obtained from P and R branch partners via ground-state combination relations. FIR wavenumbers in brackets are calculated from ground-state energies (Ohashi, private communication). The asymmetry splittings of the energy levels are exaggerated for clarity. α β γ

8 Int J Infrared Milli Waves (2008) 29:8 6 5 Excited C-N Stretch J La 35.3 Lb P(46) a b c d e f Ground State 12 (0,6) E-a (v t,k) σ-i Fig. 5 CH 3 NH 2 energy level and transition system for FIRL lines optically pumped by the 9P(46) CO 2 laser line. FIRL wavenumbers La and Lb are derived from wavelengths reported in Refs. [6] and [4]. IR and FIR data are: P=( ), a= , b=( ), c=( ), d= , e= , f= , α=[ ], β=57.66, γ= , δ= cm 1. The parentheses indicate an overlapped IR absorption for which the wavenumber has been refined on the basis of series trends and/or ground-state combination differences. FIR data are from Ref. [12], except for α in brackets which is calculated from ground-state energies (Ohashi, private communication). Note that the (0,6) E-a wavenumbers are still tentative, as discussed in the text. α γ β δ (0,7) E-a The good consistency for each of the pairs of loop values for La and Lb supports the energy level picture of Fig. 5 and the FIRL transition assignments. [The alternative choice in the spectrum for the (0,6) E-a subband would lead to slightly different mean loop values of and cm -1 for La and Lb. Thus, measurement of accurate frequencies or wavelengths for the two FIRL lines could resolve the ambiguity and tie down the IR assignments definitively.] 5 Conclusion In this work, we have applied the results of spectroscopic analyses of high-resolution Fourier transform and CO 2 -laser/microwave-sideband measurements for methylamine to identify IR pump and FIRL transitions for five FIRL transition systems of CH 3 NH 2. Closed loops of transitions could be formed for each system that confirm the assignments through consistency of the closure relations for different combination loops. FIRL wavenumbers were obtained to a net spectroscopic closure uncertainty of about ±0.002 cm 1 from the combination loops, representing a substantial improvement in accuracy for those lines previously measured only in wavelength. The present results not only identify the FIRL transitions but also serve to confirm the associated IR line assignments. This is valuable support for the spectroscopic analysis given the extensive subband overlapping that occurs in the very crowded CH 3 NH 2 spectrum. Since each identified FIRL transition system provides a stringent test of the assignments of specific lines for two different IR subbands, confidence in the correctness of the spectroscopy is greatly enhanced.

9 6 Int J Infrared Milli Waves (2008) 29:8 6 Acknowledgements This research was financially supported by the Natural Sciences and Engineering Research Council of Canada. We express our gratitude to Dr. J.W.C. Johns for his help and hospitality during the recording of the methylamine FTIR spectrum at NRC in Ottawa. We thank Prof. N. Ohashi for kindly providing a table of accurate ground-state energies for CH 3 NH 2. References 1. A. P. Gray and R. C. Lord, Rotation-vibration spectra of methyl amine and its deuterium derivatives, J. Chem. Phys. 26, (1957). 2. S. F. Dyubko, V. A. Svich, and L. D. Fesenko, Submillimeterband gas laser pumped by a CO 2 laser, JETP Lett., (1972). 3. T. K. Plant, P. B. Coleman, and T. A. DeTemple, New optically pumped far-infrared lasers, IEEE J. Quantum Electron. QE-9, (1973). 4. H. E. Radford, New CW lines from a submillimeter waveguide laser, IEEE J. Quantum Electron. QE-11, 2 2 (1075). 5. H. E. Radford, F. R. Petersen, D. A. Jennings, and J. A. Mucha, Heterodyne measurements of submillimeter laser spectrometer frequencies, IEEE J. Quantum Electron. QE-, (1977). 6. B. M. Landsberg, New cw FIR laser lines from optically pumped ammonia analogues, Appl. Phys. 23, (1980). 7. S. F. Dyubko, L. D. Fesenko, A. S. Shevyrev, and V. I. Yartsev, New emission lines of methylamine and methyl alcohol molecules in optically pumped lasers, Sov. J. Quantum Electron. 11, (1981). 8. F. Walzer, M. Tacke, and G. Busse, Optoacoustic spectra of some far-infrared laser active molecules, Infrared Phys. 19, 5 7 (1979). 9. Z.-D. Sun, R. M. Lees, L.-H. Xu, M. Yu. Tretyakov, and I. Yakovlev, Precision tunable infrared source at 10 μm: CO 2 -Laser/microwave-sideband system with an Evenson CO 2 laser and a Cheo waveguide modulator, Int. J. Infrared Millimeter Waves 23, (2002). 10. Z.-D. Sun, Q. Liu, R. M. Lees, L.-H. Xu, M. Yu. Tretyakov, and V. V. Dorovskikh, Dual-mode CO 2 - laser/microwave-sideband spectrometer with broadband and saturation dip detection for CH 3 OH, Rev. Sci. Instrum. 75, (2004). 11. Z.-D. Sun, Q. Liu, R. M. Lees, L.-H. Xu, V. V. Dorovskikh, and M. Yu. Tretyakov, Saturation-Dip measurements in the 2ν 2 overtone band of OCS with a CO 2 -laser/microwave-sideband spectrometer, Appl. Phys. B 78, (2004). 12. M. S. Malghani, R. M. Lees, and J. W. C. Johns, Far infrared spectrum of methylamine, Int. J. Infrared Millimeter Waves 8, (1987).. N. Ohashi, K. Takagi, J. T. Hougen, W. B. Olson, and W. J. Lafferty, Far-infrared spectrum and ground state constants of methyl amine, J. Mol. Spectrosc. 126, (1987).. N. Ohashi, K. Takagi, J. T. Hougen, W. B. Olson, and W. J. Lafferty, Far-infrared spectrum of methyl amine: assignment and analysis of the first torsional state, J. Mol. Spectrosc. 2, (1988).. Z.-D. Sun, R. M. Lees, and L.-H. Xu, Saturation-dip measurements for the ν 8 C-O stretching band of CH 3 OH with a CO 2 -laser-microwave-sideband spectrometer, J. Opt. Soc. Am. B 23, (2006).. J. O. Henningsen, Molecular spectroscopy by far-infrared laser emission, in Infrared and Millimeter Waves, edited by K. J. Button (Academic Press, New York, 1982) Vol. 5, Coherent Sources and Applications, Part I, pp

Far infrared laser assignments and predictions for CO-stretching and CH3-rocking states of optically pumped 13CH3OH

INFRARED PHYSICS & TECHNOLOGY ELSEVIER Infrared Physics & Technology 37 (1996) 351-366 Far infrared laser assignments and predictions for CO-stretching and CH3-rocking states of optically pumped 13CH3OH