Lamb-dip spectroscopy of the C−N stretching band of methylamine by using frequency-tunable microwave sidebands of CO2 laser lines

Lamb-dip spectroscopy of the C−N stretching band of methylamine has been systematically extended to P-, Q-, and R-branch by using microwave sidebands of a large number of CO2 laser lines as frequency-tunable infrared sources in a sub-Doppler spectrometer. Lamb-dip signals of more than 150 spectral lines have been observed with a resolution of 0.4 MHz and their frequencies have been precisely measured with an accuracy of ±0.1 MHz. More than 30 closed combination loops have been formed, which unambiguously confirm the assignments. For over 150 vibrational excited levels in 27 substates, refined term values have been determined and expanded in J(J + 1) power-series to determine the substate origins and the effective rotational constants. For transitions with Aa torsion-inversion symmetry in torsional state υt = 0, 57 K-doublet lines displaying asymmetry splittings have been observed and the splitting constants for levels with K = 1, 2, and 3 in the excited states have been determined. Our results provide accurate experimental information for spectroscopic studies of the interesting vibrational perturbations and intermode interactions related to the C−N stretching mode, directly support astronomical surveys, and are very relevant in practice to identification and frequency determination of the CO2-laser-pumped far-infrared laser lines of methylamine.

Methylamine (CH 3 NH 2 ) is the simplest primary amine in chemistry. Its CH 3 group is connected to the NH 2 group by the C− N bond that exhibits a vibrational stretching motion. As for the two groups themselves, the CH 3 group has an internal torsional motion while the NH 2 group has an inversion motion, which makes the CH 3 NH 2 a prototype in molecular physics for non-rigid molecules having two coupled large-amplitude internal motions. The torsion splits the rotational energy levels into a threefold pattern of E and A symmetry components with an E/A spin statistical weight ratio of 1/2, and inversion produces a further splitting into s and a doublets with spin weight ratio of 1/3. Thus, each vibration-rotation level of CH 3 NH 2 has Aa, As, Ea and Es sublevels, resulting in a complex vibration-rotation-torsion-inversion energy structures and rich but highly crowded spectra with a wide range of relative line intensities. Therefore, the interesting microwave 1-10 , far-infrared [11][12][13][14][15][16][17] , and infrared [18][19][20][21][22][23] spectra of CH 3 NH 2 have been extensively studied for many years to explore the splittings and the symmetry species, leading to the valuable application in the detection of interstellar methylamine [24][25][26][27] . In contrast, despite the fact that it is of great practical interest related to optically pumped far-infrared laser lines and interstellar detection, spectroscopic study by the sub-Doppler technique on the stretching of the C− N bond that connects the CH 3 and NH 2 groups has remained rare until recently 28 .
Study of the C− N stretching band of CH 3 NH 2 has been of great spectroscopic, practical, and astrophysical interest for decades. The C− N stretching band of CH 3 NH 2 , earlier studied and reported sixty years ago at the relatively low resolution of 1 cm −1 and an accuracy of about 0.1 cm −1 by Gray and Lord 19 , displays strong characteristic absorptions in the infrared region around 1044 cm −1 . It is characterized by a parallel structure with vibrational P, Q, and R branches, which overlaps well with the CO 2 laser bands. Thus, CH 3 NH 2 has been an important member of the class of laser media employed to generate far-infrared laser lines by optically pumping with CO 2 laser transitions. However, few of the CH 3 NH 2 lines have so far been identified as to their quantum numbers due

Results and Discussion
A frequency-tunable infrared source for Lamb-dip observation. Although the C− N stretching band center of CH 3 NH 2 overlaps well with the CO 2 laser bands, it is difficult to observe many absorption lines of CH 3 NH 2 by using just a grating CO 2 laser, because the available spectral coverage between the CO 2 laser and CH 3 NH 2 absorption lines is limited to the overlap in Doppler widths of only about 60-100 MHz for each laser line. This situation was recently improved greatly by the application of a frequency-tunable infrared source in a dual-mode sideband spectrometer to CH 3 NH 2 28 . The schematic of the experimental setup used in the present work for the Lamb-dip spectroscopy of CH 3 NH 2 is shown in Fig. 1, and has been described in detail previously 28 . The tunable radiation is generated by adding microwave sidebands to the CO 2 laser lines in a GaAs waveguide modulator. In the modulator, the added microwave radiation with a frequency f MW produces a periodic variation of the refractive index of the GaAs crystal and a corresponding small phase change of Δφ to the incident CO 2 laser field. Therefore, the laser output from the modulator includes both the input field of the CO 2 laser plus microwave-modulated field components. The latter are called microwave sidebands of the CO 2 laser lines. In practice, the output from the modulator shows three spectral signals at f L (frequency of CO 2 laser carrier), f L + f MW (upper sideband), and f L − f MW (lower sideband), respectively. These upper and lower microwave sidebands of CO 2 laser lines provide a powerful radiation source for precision spectroscopy, operating at room-temperature with narrow linewidths and continuously tunable and precisely controlled frequencies in the 9-11 μm region. Our infrared source has the three main features of 1) a tunability range about 23.6 GHz (± 6.7 to ± 18.5 GHz) for each CO 2 laser line by sweeping the microwave frequency f MW ; 2) a typical microwave-modulated CO 2 laser power about 10 mW for either the upper or lower sideband; 3) accurate radiation frequency. In operation, the CO 2 laser is stabilized to the center of a 4.3 μm fluorescence Lamb-dip signal and has an estimated frequency uncertainty of 33 kHz 29 . High-resolution observation and precise measurement of the spectral Lamb-dips. A Lamb-dip signal has a much narrower spectral linewidth than that of the Doppler-broadened spectral line. The Lamb-dip spectroscopic technique can thus enable blended lines in the Doppler-limited spectrum to be fully resolved and the centers of these resolved absorption lines to be determined very precisely. Figure 2 shows a Lamb-dip spectrum for a blended line in the extremely congested Q-branch of the C− N stretching band center of CH 3 NH 2 around 1044.5930 cm −1 in the FT spectrum. A 50 MHz scan of the lower microwave sideband of the 9P22 CO 2 laser line was recorded at a pressure of 10 mTorr in 2nd derivative (2f) detection mode using a lock-in amplifier time constant of 30 ms. We can see that two spectral lines with an interval of just 30 MHz have been clearly resolved. This shows the usefulness of the high power and wide frequency-tunability of the CO 2 -microwave sidebands for resolving the overlapped features by Lamb-dip observations. Furthermore, in order to precisely measure the absolute transition frequencies for each of the individual line, we narrowed the microwave scanning range down to 3 MHz and swept the microwave sideband both upward and downward 5 times for each line with a frequency step-size of 10 kHz to record their saturation-dip 2f signals. Figure 3 displays the result for signal I of Fig. 2, recorded at 14 mTorr pressure with a lock-in time constant of 30 ms. We then fitted the experimental trace (black) to determine the center transition frequency by a least-squares fit to the second derivative of a Gaussian profile 29 where G 0 is a baseline constant, G 1 is the integrated intensity, ν 0 is the center frequency, and Δν pp is the frequency separation between positive and negative peaks of the first-derivative G'(ν ). The fitting trace is shown as a red solid curve in Fig. 3. From this fit, the microwave frequency at line center was determined to be 12839.477 MHz, which yields an infrared transition frequency as 9P22-12839.477 MHz, giving 31 316 122.019 MHz with an accuracy of 0.1 MHz when the known frequency of the 9P22 CO 2 laser line 30 is added. In the current study, we have measured more than 150 saturated absorption dips for spectral lines which belong to 27 C− N stretching substates. The assignments of these transitions, the measured transition frequencies, and the determined upper-state energy term values are presented in Table 1.
The observed infrared transitions and assignments of CH 3 NH 2 . In Table 1, the transition notation of P/Q/R(υ t S t−i K, J) expresses the assigned quantum numbers for each of the identified spectral lines belonging to the P-, Q-, and R-branch, respectively. Here, υ t is the torsional quantum number, S t-i is the torsion-inversion symmetry (A or E for torsional species and a or s for inversion species), and K is the projection along the molecular near-symmetry a-axis of the rotational angular momentum J. For asymmetry K-doubling levels of A torsional symmetry, we add a superscript + or − to K to indicate the resolved doublet components. The C− N stretching fundamental is a parallel a-type band, the transition selection rules are Δ υ t = 0, Δ K = 0, and Δ J = 0, ± 1. Other researchers 22 use another common notation of the G 12 or D 3h molecular symmetry group species A, B, E 1 , and E 2 , which corresponds here to As, Aa, Ea, and Es, respectively. The second and third columns list the determined transition frequencies in MHz and in wavenumbers, respectively, according to the specific CO 2 -microwave and as Q(0 As 5, 5) at 1044.592375 cm −1 , respectively. The latter was first observed and reported in our previous work 28 , and has been confirmed here. In Table 1, a letter U in the first column denotes a line that is still unassigned in the spectrum. As lines of s inversion symmetry are weak with only 1/3 the intensity of the corresponding a lines due to the relative spin statistical weights, our data are primarily for the a inversion species. For a substantial number of transitions, we could test our assignments and measurement accuracy via application of the Rydberg-Ritz combination principle to closed loops involving the observed lines. As an example for illustration, an energy-level diagram for the (υ t S t−i K) = (0 Aa 3) sub-band is shown in Fig. 4. For each pair of transitions sharing a common upper-state level in Fig. 4, we can form four closed loops involving the eight infrared transitions with labels a to h and the eight microwave transitions in the ground state. By using the predicted microwave frequencies 17 (uncertainty of 0.06 MHz) in Loops 1 and 2 and the observed microwave frequencies 17 (uncertainty of 0.06 MHz) in Loops 3 and 4, we calculate the loop closure defects (in MHz) as follows: Since each loop contains two infrared transitions, the fact that these loop defects are all so close to zero confirms the transition assignments in each of the loops and our experimental uncertainty of 0.1 MHz. Over 30 closed combination loops of transitions have been formed from the present and previous sub-Doppler observations. Line assignments shown with a letter L in Table 1 are confirmed from these frequency combination closure relations. Such calculations of loop defects are very useful for providing secure assignments for the resolved K-doublet lines and for the component lines in blended features, especially for those spectral lines located around the crowded band center. We noticed that when term values for the ground state (kindly provided by N. Ohashi from his microwave and FIR analyses 7,14 ) are used to calculate the related energy differences involved in the above mentioned loops, we found that the loop defects in MHz from Loop 1 to Loop 4 are − 1.05, − 2.25, − 0.72, and − 2.58, respectively. This indicates the estimated uncertainty of those term values to be about 1 MHz, consistent with the estimate from the microwave experimental study by Ilyushin et al. 9 .
Comparison of the measured transition frequencies with those in the FT spectrum. The last two columns of Table 1 show the frequency differences between the present Lamb-dip measurements and the data in the FT spectrum reported in Ref. 21 and Ref. 22, respectively. A blank space indicates either a new assignment or an unidentified U line. A histogram illustrating the distribution of these differences is given in Fig. 5. The inset shows the histogram for the FT infrared data reported in Ref. 21. We see that most of the deviations are less than several megahertz, but some of them are tens of megahertz. The mean value of the absolute deviation is about 5 MHz and 8 MHz for the FT data in Ref. 21 and Ref. 22, respectively, which reflects the frequency accuracy of the FT data estimated in these two works for infrared transitions in the C− N stretching band of CH 3 NH 2 .
Power-series expansions of the energy term values in the excited state. The fourth column of Table 1 lists energy term values W(υ t S t − i K, J) for the upper levels of the corresponding transitions in the first  column, obtained by adding our measured transition frequencies in wavenumbers to the Ohashi calculated ground-state energies, referenced to the (υ t S t−i K, J) = (0 As 0, 0) ground level as the energy zero. When two or three transitions were observed having a common upper level but giving independent values, the average of those term values was taken. In order to determine the J-independent origins of 27 C− N stretching substates, their term values were least-squares fitted to J(J+ 1) power-series expansions where a 0 is the J-independent substate origin, a 1 is an effective rotational constant, and a 2 and a 3 are effective centrifugal distortion constants. The obtained expansion coefficients a 0 , a 1 , a 2 , and a 3 for 27 substates are shown in Table 2, in which the 1-σ standard deviations are in units of the last quoted digit.

Asymmetry splittings and asymmetry-splitting constants of A symmetry levels in the excited state.
A rotational level with A symmetry of CH 3 NH 2 may split due to the higher-order vibration-rotation interactions. For the resolved K-doublet lines, the transition selection rules are K ± ↔ K ± for Δ J = ± 1 and K ± ↔ K ∓ for Δ J = 0. We have observed 57 Lamb-dip signals for resolved K-doublet lines resulting from the asymmetry splittings and precisely determined their transition frequencies. From the calculated level splittings in the ground state, asymmetry splittings for Aa levels with K = 1, 2, and 3 in the υ t = 0 excited state have been determined and are shown in Table 3. The observed asymmetry splittings Δ E(υ t S t−i K, J) can be approximately represented by  Table 3.

Conclusion
In this work for a molecule with the two strongly coupled large-amplitude internal motions of torsion and inversion, by using microwave sidebands of CO 2 laser lines as frequency-tunable infrared sources in a sub-Doppler spectrometer, Lamb-dip spectroscopy of the C− N stretching band of CH 3 NH 2 has been systematically studied. Many blended features and unresolved K-doublet lines involving wide variations in relative intensities in dense Doppler-limited spectra have been separated at high resolution. More than 50 K-doublet lines have been observed and the asymmetry-splitting constants for levels with K = 1, 2, and 3 in the excited state have been determined. Over 150 transitions have been assigned and identified into 27 substates and their transition frequencies have been precisely measured with an absolute accuracy of ± 0.1 MHz. Energy term values for the upper levels of these assigned transitions have been determined and have been fitted to J(J + 1) power-series expansions for each substate to determine the J-independent C− N stretching substate origins and effective rotational constants. The Rydberg-Ritz combination principle was fully used in calculations of the defects for closed combination loops involving our observed transitions for confirming, revising and extending the transition assignments from previously reported results. Our experiment demonstrates the capabilities of the current experimental setup to precisely study the sub-Doppler infrared spectroscopies of isotopic species of CH 3 NH 2 and of molecules with more than two internal motions. Our results constitute a high-accuracy database for frequency calibration in the 9-11 μm region, provide more accurate spectral information for excited vibrational states to clearly map the rich and complex energy structures, to reveal the complex interaction mechanisms relevant to the C− N stretching of CH 3 NH 2 , to support further possible astronomical detections of interstellar CH 3 NH 2 , and to assign more energy levels and transition systems for optically pumped far-infrared laser emissions of CH 3 NH 2 .  Substate (υ t S t−i K) a 0 a 1 a 2 × 10 6 a 3 × 10 10 Table 3. Asymmetry splittings ΔE(υ t S t−i K, J) and asymmetry-splitting constants b m (in MHz) for the resolved K-doublet levels of A torsional symmetry of CH 3 NH 2 . a Asymmetry splittings were calculated from the asymmetry-splitting constants in Table 3. The K-doublet levels are in the excited states with K = 1, 2, and 3 and in torsional state υ t = 0 with the torsion-inversion symmetry Aa.

Methods
The tunable microwave radiation is generated by a microwave synthesizer and is amplified by a traveling-wave-tube amplifier to a power of about 20W before being fed to the modulator. Under this condition, the typical conversion efficiency into the sidebands from the incident laser beam is about 0.8%. In order to saturate the transitions of CH 3 NH 2 at low pressures of several mTorr in this work, the full output radiation from the modulator is focused into our multi-reflection absorption cell with a total absorption path of 9.6 m in 16 transits. For observation of the saturation Lamb-dips by generating a counter-propagating beam inside the cell, a mirror M5 is placed at the exit of the cell window to reflect the radiation which has passed through the absorption cell back into the cell. This mirror is adjusted carefully so that the retro-reflected radiation nearly coincides with the incoming radiation but is slightly shifted and passes through a tunable Fabry-Pérot etalon filter for selecting only the desired sideband containing the CH 3 NH 2 absorption signal. In such an optical arrangement, only those molecules moving at zero velocity parallel to the beam can absorb both the two counter-propagating laser radiations which have the same frequency, creating a saturation dip at the center of the absorption curve. This narrow dip is then detected by a liquid-N 2 -cooled HgCdTe detector as a Lamb-dip signal. In order to increase the probing sensitivity for the spectral signals, we use 1 kHz modulation of the sideband laser frequency for source modulation and demodulate the detected signal with a digital lock-in amplifier operating in the second-derivative (2f) detection mode to display the spectral lines. The signals are then sent to a computer for recording and analysis. A commercial CH 3 NH 2 sample supplied by BOC Specialty Gases with a stated purity of 99.5% was used in the experiment without further purification. High attention should be taken for avoiding the possible confusion in the spectral analysis from NH 3 impurity lines.