Int J Infrared Milli Waves (2008) 29:148–156
DOI 10.1007/s10762-007-9309-6
Far-Infrared Laser Assignments for Methylamine
R. M. Lees & Zhen-Dong Sun & Li-Hong Xu
Received: 14 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 CH3NH2
optically pumped by a CO2 laser have been identified spectroscopically through a highresolution Fourier transform infrared study of the C-N stretching band together with CO2laser/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 CO2 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 . CH3NH2 . 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 CO2 laser, and optically pumped far-infrared laser (FIRL) emission from CH3NH2 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 CO2 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
e-mail: [email protected]
Int J Infrared Milli Waves (2008) 29:148–156
149
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 CH3
group, there is also a substantial and irregular splitting of the energy levels into doublets
due to the inversion or wagging motion of the NH2 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
CH3NH2 together with measurements taken in both the broad-scan Doppler-limited and
Lamb-dip sub-Doppler modes [9–11] of our CO2-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 [12–14] 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 CH3NH2 was recorded from 990 to 1100 cm−1
at 0.002 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 CO2-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 CO2
carrier through to a single tunable microwave sideband.
The beam from our line-tunable Evenson-type CO2 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 15 W
output from a traveling-wave-tube amplifier driven by a microwave synthesizer in order to
add tunable sidebands on both sides of the CO2 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 7–18.5 GHz range, giving substantial spectral coverage. In operation, the CO2
laser is locked to line centre via the Lamb-dip in the fluorescence from an external low-
150
Fig. 1 Source section of the
CO2-laser/microwave-sideband
spectrometer, showing the radiation path from the laser through
the modulator in which the microwave sidebands are added to
the CO2 carrier and then through
the Fabry-Perot filter which isolates a single tunable sideband [9,
10]. The accessible microwave
tuning range is 7–18.5 GHz.
Int J Infrared Milli Waves (2008) 29:148–156
1 mW Tunable IR SB
Microwave Synthesizer
Fabry-Perot
Filter
15W MW
CO2 Laser
8W CO2 laser
Modulator
pressure CO2 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 CO2 lines of the 9.6 μm P
and R branches, employing a multipass 0.6-m absorption cell with total path length of 16 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 CH3NH2 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 [15].
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 vt, 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 E1 [12] and negative K
corresponding to E2. 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 μa and μc
components of the permanent molecular dipole moment, giving the selection rules ΔK=0
or ±1, respectively. However, μa 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 [16].
Int J Infrared Milli Waves (2008) 29:148–156
151
4 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 CH3NH2. 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.
4.1 9R(4) transition systems (a) and (b)
The 9R(4) CO2 laser line is reported to pump two FIRL lines at 288 and 314 μm [4]. The
288 μm wavelength corresponds to a wavenumber of 34.7 cm−1, while the frequency of the
314 μm line has been measured accurately as 952185.0 MHz [5], corresponding to a
wavenumber of 31.76147 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 qR
(0,−2,16) and qR(0,2,16) 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 33:3419 1066:2797 ¼ 34:6014 cm1
¼ a þ α b ¼ 1015:8936 þ 36:7879 1018:0798 ¼ 34:6017 cm1
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=34.6016 cm−1 represents a significant improvement in accuracy over
the original wavelength measurement.
Table 1 Assignments for optically pumped far infrared laser lines of CH3NH2.
CO2 Line
IR Assgta
(vt,K,J)v σ-I
FIRL Assignment
0
00
(vt′,K′,J′)v → (vt′′,K′′,J′′)v
νloopb (cm−1)
νobsc (cm−1)
[Ref]
9R(4)
9R(4)
9P(24)
R(0, −2,16)cn E-a
R(0,2,16)cn E-a
Q(0,−9,15)cn E-a
9P(46)
9P(46)
P(0,2+,15)cn A-a
P(0,7,15)cn E-a
(0,−2,17)cn → (0,−1,16)cn
(0,2,17)cn → (0,1,16)cn
(0,−9,15)cn → (0,−8,15)cn
(0,−9,15)cn → (0,−8,14)cn
(0,2+,14)cn → (0,1−,13)cn
(0,7,14)cn → (0,6,14)cn
(0,7,14)cn → (0,6,13)cn
34.6016
31.7616
45.7147
67.6375
28.2086
34.8916d
55.3613d
34.7
31.76147
45.714
67.63855
28.5
35.3
55.6
[4]
[5]
[7]
[5]
[6]
[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).
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Int J Infrared Milli Waves (2008) 29:148–156
17
La
34.7
(a)
Pump P
9R(4)
31.76147
16
16
17
Lb
Excited C-N Stretch
a
f
b
c
d
(b)
Pump P
9R(4)
e
J
18
γ
α
Ground State
17
16
β
(0,-2) E-a
(vt ,K ) σ-I
(0,-1) E-a
17
17
16
16
15
15
(0,0) E-a
18
17
16
δ
(0,2) E-a
(0,1) E-a
Fig. 2 CH3NH2 energy level and transition systems for the FIRL lines at wavelengths of (a) 288 μm and (b)
314 μm optically pumped by the 9R(4) CO2 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=1067.5392, a=1015.8936, b=1018.0798, c=
1066.2797, α=[36.7879], β=[33.3419] cm−1. For system (b), P=1067.5392, d=1066.381024, e=
1017.244164, f=1015.53790, γ=[33.4677], δ=[30.6036] 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=31.76147 cm−1, the analogous two loops in
Fig. 1 determine the Lb values as:
Lb ¼ P þ δ d ¼ 1067:5392 þ 30:6036 1066:3810 ¼ 31:7618 cm1
¼ f þ γ e ¼ 1015:5379 þ 33:4677 1017:2442 ¼ 31:7614 cm1
Both loop values are in excellent agreement with the frequency-measured value, confirming
the assignment.
4.2 9P(24) transition system
The 9P(24) CO2 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 qQ(0, −9, 15) Ea transition. FIRL lines La (reported at a wavelength of 218.75 μm [3, 7] with parallel
polarization) and Lb (with reported frequency of 2027752.6 MHz [5] and perpendicular
polarization) are then assigned to the (vt, K, J)v =(0, −9, 15)cn → (0, −8, 15)cn and (0, −9,
15)cn → (0, −8, 14)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,
Int J Infrared Milli Waves (2008) 29:148–156
Fig. 3 CH3NH2 energy level and
transition system for FIRL lines
optically pumped by the 9P(24)
CO2 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=1043.1643,
a=1065.46306, b=043.3036, c=
1064.22248, d=1043.53660, e=
1021.38051, f=1019.5340,
g=1065.31980, α=69.4840, β=
68.0137, γ=66.5421 cm−1. IR
data given to 4 decimal places are
FTIR observations; data to 5
places are CO2-laser/microwavesideband measurements. FIR data
are from Ref. [12].
Excited
C-N Stretch
153
15
La
45.714
J
Lb
67.638546
15
Pump P
9P(24)
14
a
f
b
c
d
g
e
16
α
Ground
State
15
β
15
14
γ
14
(0,-9) E-a
13
(0,-8) E-a
(vt ,K) σ -I
whose frequencies should sum to zero. The closure defects δ for three sample combination
loops are as follows:
δ1 ¼ P Lb d þ β ¼ 1043:1643 67:6385 1043:5366
þ68:0137 ¼ 0:0029 cm1
δ2 ¼ P f α þ e d þ β ¼ 1043:1643 1019:5340 69:4840
þ1021:3805 1043:5366 þ 68:0137 ¼ 0:0039 cm1
δ3 ¼ f g γ þ c e þ α ¼ 1019:5340 1065:3198 66:5421
þ1064:2225 1021:3805 þ 69:4840 ¼ 0:0019 cm1
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 1043:1643 þ 68:0137 1065:4631 ¼ 45:7149 cm1
¼ f þ α b ¼ 1019:5340 þ 69:4840 1043:3036 ¼ 45:7144 cm1
The two values are in good agreement with each other and also with the value of
45.714 cm−1 derived from the experimental wavelength of 218.75 μm reported in [7].
4.3 9P(46) transition systems
The 9P(46) CO2 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 qP(0, 2+, 15) 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.
154
Int J Infrared Milli Waves (2008) 29:148–156
Excited
C-N Stretch
+ 14
La
28.5
-
J
Pump P
9P(46)
13 +d
a
e
b
c
+ 15
-
α
Ground
State
14 +13 +-
+
- 14
+ 13
β
γ
-
(0,2) A-a
12 +-
(vt ,K) σ -I
(0,1) A-a
Fig. 4 CH3NH2 energy level and transition system for FIRL line optically pumped by the 9P(46) CO2 laser line.
FIRL wavenumber La is derived from the wavelength given in Ref. [6]. IR and FIR data are: P=1021.0590, a=
1062.664047, b=(1045.9433), c=1022.4142, d=(1043.7356), e=1064.09697, α=[29.5642], β=[30.4161], γ=
[26.7754] 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.
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 29:5642 1022:4142 ¼ 28:2090 cm1
¼ d þ β b ¼ 1043:7356 þ 30:4161 1045:9433 ¼ 28:2084 cm1
¼ e þ γ a ¼ 1064:0970 þ 26:7754 1062:6640 ¼ 28:2084 cm1
The average value of La=28.2086 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 qP(0,7,15) 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 35:0018 1021:1665 ¼ 34:8918 cm1
¼ e þ γ b ¼ 1043:2181 þ 55:6940 1064:0207 ¼ 34:8914 cm1
La ¼ P þ β c ¼ 1021:0565 þ 57:1666 1022:8616 ¼ 55:3615 cm1
¼ f þ δ a ¼ 1063:9040 þ 54:2207 1062:7637 ¼ 55:3610 cm1
Int J Infrared Milli Waves (2008) 29:148–156
Excited
C-N Stretch
155
14
La
35.3
J
Lb
55.6
14
13
a
Pump P
9P(46)
e
b
c
f
d
15
α
14
β
Ground
State
13
15
14
γ
δ
(0,7) E-a
13
12
(0,6) E-a
(vt ,K) σ -I
Fig. 5 CH3NH2 energy level and transition system for FIRL lines optically pumped by the 9P(46) CO2 laser
line. FIRL wavenumbers La and Lb are derived from wavelengths reported in Refs. [6] and [4]. IR and FIR
data are: P=(1021.0565), a=1062.7637, b=(1064.0207), c=(1022.8616), d=1021.1665, e=1043.2181, f=
1063.9040, α=[35.0018], β=57.1666, γ=55.6940, δ=54.2207 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.
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 35.0401 and 55.5099 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 CO2-laser/microwave-sideband measurements for methylamine to
identify IR pump and FIRL transitions for five FIRL transition systems of CH3NH2. 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 CH3NH2 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.
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Int J Infrared Milli Waves (2008) 29:148–156
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 CH3NH2.
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