JOURNAL OF MOLECULAR SPECTROSCOPY
ARTICLE NO.
185, 158–172 (1997)
MS977367
Sub-Doppler Infrared Spectra and Torsion–Rotation Energy Manifold
of Methanol in the CH-Stretch Fundamental Region
Li-Hong Xu,* Xiaoliang Wang,† Thomas J. Cronin,† David S. Perry,† Gerald T. Fraser,‡ and Alan S. Pine‡
*Department of Physical Sciences, University of New Brunswick, Saint John, New Brunswick, Canada E2L 4L5;
†Department of Chemistry, University of Akron, Akron, Ohio 44325; and ‡Optical Technology Division,
National Institute of Standards and Technology, Gaithersburg, Maryland 20899
Received May 6, 1997
The infrared spectrum of jet-cooled methanol in the CH-stretch fundamental region has been investigated by two
sub-Doppler laser techniques: optothermally detected molecular-beam electric resonance and direct-absorption slit-jet
spectroscopy. With the aid of microwave-infrared double resonance and ground state combination differences, 27
subbands in the frequency range 2967 to 3027 cm01 have been assigned to the n2 fundamental. Perturbation systems in
the K * Å 0 E, 01 E, and 02 E symmetry subbands have been analyzed to yield matrix elements of 0.013, 0.041, and
0.75 cm01 , respectively. The A–E torsional tunneling splitting for J Å 0 of the n2 vibration of 03.26 cm01 is of opposite
sign and a factor of three smaller in magnitude than the ground state value of /9.12 cm01 . q 1997 Academic Press
I. INTRODUCTION
This work reports molecular-beam investigations of the
infrared (IR) absorption spectrum of CH3OH in the 3 mm
region of the CH-stretching fundamental bands. Methanol
has been of interest to high-resolution spectroscopists for
many years, yet still remains a challenge to understand because of the large amplitude hindered internal rotation and
its interaction with the small amplitude vibrations (Fig. 1).
Of the 12 normal fundamental modes, the torsion ( n12 , A 9
symmetry in Cs ) is the lowest in frequency and has been
studied extensively in the microwave (MW), millimeterwave (MMW) (1–7), and far-infrared (FIR) (8–14) regions of the spectrum. This body of work has been an important testing ground for internal-rotor models (1, 3, 15–
20). Recently this region has been revisited by Xu and
Hougen (21, 22) using a one-dimensional torsional Hamiltonian (3) with an extended internal axis method (IAM). An
extensive set of pure rotation and rotation–torsion transitions
have been fit to a global Hamiltonian to within experimental
precision, establishing the groundwork for the spectroscopic
studies of the excited vibrational states.
The CO-stretch fundamental ( n8 , A * symmetry), centered
near 1033 cm01 , has been studied extensively (23–28) because of interest in the rich optically pumped FIR laser emission observed from methanol. An additional question of interest is the interaction between the CO-stretch fundamental
and the large amplitude torsion. Even though n8 is the second
lowest frequency mode, the observed CO-stretch torsion–
rotation energy structure is still not properly accounted for
by existing models. The weak CH3-rock fundamental bands
( n7 , A * and n11 , A 9 ) are located close to the strong COstretch band and create difficulties for systematic assignment. There is evidence (29–32) to suggest that the in-plane
(A * ) CH3 rock is in Coriolis resonance with the CO stretch
and has a torsional potential barrier approximately 50%
higher than the ground state value.
To gain more information on the interactions of the low
amplitude vibrations with the torsion, Lees et al. have undertaken high-resolution studies of the OH-bend band ( n6 , A * )
(33). The observed OH-bend torsion–rotation energy-level
pattern is inverted in comparison with the ground state, possibly because of interaction with the first excited torsion of
the CO stretch as suggested from the calculated vibration–
torsion–rotation energy. Also, the OH-stretch fundamental
( n1 , A * ) near 3672 cm01 has been investigated extensively
(34–36) under both room temperature and molecular-beam
conditions. The effective torsional barrier from a global fit
to the OH-stretch levels (36) was 439(13) cm01 , or about
18% higher than the ground state barrier (22) of
373.594(14) cm01 . (The numbers in parentheses refer an
expanded uncertainty with a coverage factor k Å 2 in units
of the least significant digit.) The anharmonic extension of
the OH bond might be expected to decrease the effective
barrier; so the increase was attributed to a possible nonlinear
coupling between the OH stretch and torsion (35) or a harmonic mixing of the displacement coordinates of other vibrations of the same symmetry (36).
Similar to the OH stretch, the CH-stretch modes ( n2 , A *,
n3 , A *, and n9 , A 9 ) have fundamentals in the 3 mm region
and might be extensively mixed with ‘‘dark’’ background
bath states arising from numerous lower-lying vibrations and
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159
FIG. 1. Vibrational and torsional energy levels of methanol.
their combination states. (The density of bath states is about
0.3 per cm01 ). Detailed high-resolution Fourier-transform
infrared studies at room temperature have been carried out
in this region by Hunt, Bignall, Shelton, and collaborators
(37, 38). Because of heavy congestion in the room temperature spectra, they were only able to establish subband assignments at low K for the parallel symmetric CH-stretch band
( n3 , A * ) and at high K for the perpendicular asymmetric
CH-stretch bands ( n9 , A 9 and n2 , A * ). Their analysis indicates that a treatment which does not consider interactions
between vibrational bands will give poor results.
In the present work, the 3 mm region has been reinvestigated with greater accuracy, higher instrumental resolution,
and at a very low temperature in two different molecular-
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XU ET AL.
beam instruments. Motivation for this work comes from
three perspectives:
(i) From the theoretical point of view, the interactions
between the torsion and the low-amplitude vibrations are of
fundamental interest (39). Spectra in the excited CH-stretch
region are part of the effort to build up a comprehensive
energy-level pattern for methanol which will assist in understanding the molecular dynamics and torsion–vibration interactions.
(ii) Infrared-assisted photofragment spectroscopy (IRLAPS) experiments in the nOH Å 2 through 6 regions of
methanol have revealed a hierarchy of intramolecular relaxation pathways and time scales (40). The strongest interaction is a one-to-one resonance between the OH and CH
stretches (40, 41). At nOH Å 5, the OH stretch is anharmonically shifted to lower frequency to bring the nOH Å 5 state
(5 n1 ) into resonance with the nOH Å 4 plus nCH Å 1 combination (4 n1 / n2 ). Detailed information on the CH-stretch
fundamental is essential in order to build an understanding
of the structure of the lower regions of the torsion–vibration
energy manifold which might be extended to the highly excited vibrational states.
(iii) From the astrophysical point of view, methanol is
an important species widespread in interstellar clouds (42)
which has also recently been observed in comets in both the
microwave and the 3 mm regions (43, 44). The cometary
community requires data that will permit simulation of the 3
mm methanol emission spectrum under cometary conditions.
The present paper reports sub-Doppler spectra of jetcooled methanol covering mainly the n2 , A *, CH-stretch
fundamental band. Altogether, about 19 b-type ( DK Å {1)
and 8 a-type ( DK Å 0) n2 subbands have been identified
involving K * up to 3 for A and from 03 to 4 for E. Three
subbands of the n9 , A 9, CH-stretch fundamental band have
also been identified. In contrast to the n1 OH stretch and the
n3 symmetric CH stretch which are normal in terms of the
ordering of the A and E levels, we find the n2 asymmetric
CH stretch to have a torsion– K–rotation energy-level pattern that is inverted relative to the ground state.
II. EXPERIMENTAL 1
The results reported here are based on separate molecularbeam spectra recorded on two different spectrometers, one at
the National Institute of Standards and Technology (NIST)
1
Certain commercial instruments and materials are identified in this paper
in order to specify adequately the experimental procedure. In no case does
such identification imply recommendation or endorsement by the National
Institute of Standards and Technology, nor does it imply that the instruments
or materials identified are necessarily the best available for the purpose.
and one at the University of Akron. Figure 2 shows a segment
of sample spectra in a similar spectral region obtained from
the two spectrometers. The initial work was carried out independently, but the data have now been combined for more
comprehensive analysis. Both spectrometers employ a colorcenter laser pumped by Ç1.6 W of 647-nm light from a krypton
ion laser to produce 8 to 9 mW of single frequency tunable
infrared radiation in the 3 mm region. In both cases the methanol
was cooled in a nozzle expansion, and spectra were recorded
at sub-Doppler resolution. Nonetheless, as indicated below, the
detection techniques were rather different and the two spectra
contain complementary information.
The first spectrum was recorded from 2977 to 3027 cm01
at the University of Akron using direct absorption detection.
The apparatus included a pulsed 2 1 0.01 cm slit nozzle
system (45) and a multi-reflection cell (46) to enhance the
absorption of the infrared radiation by the free jet. A mixture
of about 6% by volume methanol (Aldrich, 99.9%) in argon
(Union Caribide, 99.997%) was expanded through the slit
nozzle operated piezoelectrically at 34.5 Hz with a pulse
duration of 400 msec and a stagnation pressure of 65 kPa.
The laser beam crossed through the jet about 1.5 cm from
the nozzle 25 times. The use of two matched InSb infrared
detectors enabled noise reduction by baseline subtraction.
The regular pattern of absorption intensities corresponded
to a 17 K rotational temperature. In the planar expansion,
the residual Doppler linewidth was about 75 MHz. A further
reduction in the linewidth could be obtained under more
vigorous expansion conditions but this would result in a
lower rotational temperature with a corresponding loss of
spectral information. Only a few lines were blended under
the experimental conditions employed. The overview of the
spectrum, shown in Fig. 3, is a composite spliced together
from many short sections.
Three signals were recorded simultaneously: (i) the transmitted laser intensity through the jet, (ii) the transmitted
intensity through a reference gas cell containing ethylene
for absolute frequency calibration, and (iii) the transmitted
intensity through a 150 MHz marker étalon (Burleigh
CFT100P) for relative frequency calibration. The spectrum
was recorded in 0.15 cm01 sections which were spliced utilizing marker étalon fringes. The digitized signal from a
temperature-controlled and pressure-sealed 7.5 GHz (Burleigh FCL975) spectrum analyzer provided a check on the
identity of the marker étalon fringes at which splices were
made. A strong methanol line at 3001.0249 cm01 was used
as the reference line for a daily reproducibility check of line
intensities and frequency calibration. The frequency calibration was accomplished by fitting 139 ethylene lines (46) to
the marker étalon fringe number to obtain
frequency Å 0.004989832(12)
1 fringe number / 2976.9924(5).
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FIG. 2. Sample spectra for the K Å 1 R 0 A Q-branch region obtained from University of Akron and the National Institution of Standards and
Technology.
The uncertainties indicated in parentheses are one standard
deviation in units of the last digit. A measure of the relative
accuracy of the transition frequencies is provided by the distribution of upper state energies when the same upper state is
reached by several different selection rules ( DK Å {1, D J Å
0, {1). A typical standard deviation is 2 1 10 04 cm01 .
The second spectrum was recorded from 2965 to 3027
cm01 on the molecular-beam electronic resonance optothermal spectrometer (EROS) at NIST (47). Here, a mixture
of a few percent methanol in He carrier was introduced into
the beam chamber through a 60-mm pinhole nozzle with
Ç100 kPa backing pressure, giving a rotational temperature
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XU ET AL.
FIG. 3. Stick representation of the central part of the slit-jet spectrum of methanol. The vibrational assignments and A/E symmetry are indicated by
horizontal lines, and the subband K values are shown at the positions of the lowest- J member of the Q branch marked by vertical lines. The b-type DK
Å {1 subbands are marked by solid lines and the a-type DK Å 0 subbands by dashed lines. The two dashed lines with asterisks locate the origins of
the K Å 0 A and E a-type subbands, for which there is zero Q-branch intensity.
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CH STRETCH OF METHANOL
near 10 K. The molecular beam was focused onto a liquidHe-cooled bolometer using quadrupole focusing in the flight
chamber between the skimmer and the detector. The use
of the quadrupole focusing/defocusing field enhances the
detection sensitivity, but the observed intensities are more
complicated than the transition absorption strengths since
they also reflect the Stark tuning of the probed levels which
may vary both in magnitude and sign as shown in the bottom
part of the Fig. 2. A few spectral gaps were encountered in
which H2O absorption obscured the methanol spectrum and
spoiled control of the laser scan. Calibration methane traces
were recorded at the beginning and end of a day to minimize
errors due to gaps and drifts. On a given day the calibration
interferometer drift was typically less than Ç10 MHz, defining the overall precision. Separations of close lines in a
single scan should have precision better than 1 MHz. The
internal consistency in frequency calibration between the
Akron and NIST spectra was typically Ç0.0005 cm01 .
A comparison of the two spectra showed the EROS
method to have very high peak sensitivity that yielded more
lines in a given spectral region than did the direct absorption
method. However, the complicated intensity behavior from
the Stark focusing caused many lines to be missing in the
EROS experiment that were quite intense in the direct absorption experiment. Frequently, the EROS method produced a strong Q branch without showing the corresponding
P-branch and R-branch lines.
In addition to the spectra of jet-cooled methanol, highresolution Fourier-transform (FT) spectra in the CH-stretch
region (2700–3150 cm01 ) were recorded. Traces were taken
at 0.003 cm01 resolution at both room temperature and 190 K
on a modified DA8.002 Bomem spectrometer at the Steacie
Institute for Molecular Sciences of the National Research
Council of Canada in Ottawa. Although these FT spectra
are extremely crowded, they give a broad spectral view and
have provided some checks on the assignments. The FT
work will be the subject of a separate communication.
III. ASSIGNMENTS
The molecular-beam spectra between 2965 and 3027 cm01
cover mainly the n2 , A * asymmetric CH-stretch fundamental.
The predominant subbands are those with perpendicular btype selection rules, but a number of weaker parallel a-type
subbands are found as well. Some initial line assignments
were established by infrared–microwave double resonance
(IR–MW DR); others were found by pattern recognition
and polynomial fits of the line positions within individual
subbands. Assignments were then confirmed using the stringent combination loop tests detailed below.
If methanol were constrained to be a rigid molecule, its
energy levels could be categorized in the Cs point group as A *
or A 9. However, to account for the large amplitude torsional
coordinate and tunneling between the three equivalent positions of the methyl group, the G6 molecular symmetry group,
with representations G Å A1 , A2 , and E, is used. The rigid
rotor basis functions and all the normal modes other than
the torsion are either A1 (A * ) or A2 (A 9 ). Like the vibrational
ground state, the n2 vibration is split by torsional tunneling
into A1 and E components.
The rotational levels of the A tunneling component can
be categorized as A1 and A2 and these symmetries can be
related to the traditional labels, A / and A 0 (16). All of the
rotational levels of the E component have E symmetry but
are often labeled for convenience by E1 (for K § 0) or E2
(for K õ 0) according to the relative orientations of the
torsional and K-rotational angular momenta (1). It is important to note that E1 and E2 levels, having the same symmetry, are coupled by the asymmetry of the molecule and may
be mixed by perturbations. In this paper, we will mainly use
the signed K notation for E levels, but will occasionally
employ E1 and E2 when convenient.
An alternative notation often used denotes a torsion–rotation–vibration level as ( nttK, J) n where nt is the torsional
quantum number, t is the torsional index associated with
the torsional symmetry, and n is the quantum number of a
vibration of interest other than the torsion. In this notation,
K, the projection of the overall rotational angular momentum
J along the molecular symmetry axis, is indicated without
a sign. K and t may be combined to obtain A, E1 , or E2
according to the rule: mod(K / t )/3 Å 0 is E1 ; 1 is A;
and 2 is E2 . The torsional index is particularly useful for
examining the dependence of the torsional energy on K.
A. Infrared–Microwave Double Resonance
The initial assignments for four of the subbands were
made with the aid of infrared–microwave (IR–MW) threelevel double-resonance experiments on the EROS machine
at NIST (48). In this case, infrared radiation was tuned to
coincide with a strong feature in the NIST spectrum, and
then a microwave synthesizer was scanned through a series
of known ground state transition frequencies. When the infrared signal varied due to a resonance with a specific microwave transition, that transition was recorded in the computer.
To confirm that the double resonance indeed involved the
lower infrared level, the infrared radiation was masked to
check that some absorption due to the ground state microwave transition still remained. The relevant level schemes
are shown in Fig. 4 and the assignments are discussed individually below.
(a) K Å 1 R 0 A system (Fig. 4a). The infrared radiation was first tuned to the strong transition at 3008.6389
cm01 , which was clearly identified as the first line of a Q
branch. To search for infrared–microwave double resonance, a microwave synthesizer was stepped through the
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XU ET AL.
FIG. 4. Infrared–microwave double-resonance schemes (a) K Å 1 R 0 A, (b) K Å 0 R 1 A, (c) K Å 2 R 1 A, and (d) K Å 2 R 1 E.
known ground state transitions and a strong double-resonance signal was found at the 48 372.456 MHz frequency
of the J Å 1 R 0, K Å 0 A ground state a-type microwave
transition. This result indicates that the infrared transition is
the Q(1) member of the K Å 1 R 0 A subband.
(b) K Å 0 R 1 A system (Fig. 4b). Another Q branch
around 2996.87 cm01 was examined with the double-resonance experiment. In this case, the infrared radiation was
set to coincide with the first line of the Q branch at
2996.8701 cm01 and the microwave synthesizer was scanned
through ground state transitions. A double-resonance signal
was found at 834.267 MHz, corresponding to the J Å 1, K
Å 1 A 0 R A / transition across the levels of the lowest K Å 1
ground-state asymmetry doublet. The observation of doubleresonance signals at 2502.778 and 5005.321 MHz for the
second and third Q lines respectively confirmed that the
lower state of this infrared Q branch is K Å 1 A.
(c) K Å 2 R 1 A system (Fig. 4c). The third Q branch
for which a double-resonance search was performed is near
3006.27 cm01 . The first two members of the Q branch gave
double-resonance signals with microwave frequencies of
2502.778 and 5005.321 MHz. These were clearly the same J
Å 2 and 3, K Å 1 ground state asymmetry doublet transitions
as for the previous system above, implying the lower state of
the Q branch was K Å 1 A and that the upper state had to be
K Å 2 from the absence of a J Å 1 line. Then, by combining
the schemes of Figs. 4b and 4c with knowledge of the general
energy level structure, it was deduced that the previous Q
branch around 2996.87 cm01 belonged to the K Å 0 R 1
A / R A 0 subband and the present Q branch around 3006.27
cm01 to one of the two components of the K Å 2 R 1 A
subband. To further confirm these assignments, the microwave source was then scanned to search for the upper state K
Å 2 asymmetry doublets, and indeed three double-resonance
signals were found at frequencies of 29.60, 88.79, and 206.68
MHz in resonance with Q(3) at 3006.2334 cm01 , Q(4) at
3006.1848 cm01 , and Q(5) at 3006.1257 cm01 , respectively.
The expected quadrupole focusing behavior for these Kdoublet systems suggested that this stronger Q-branch shading to low frequency corresponds to the K Å 2 R 1 A / R
A 0 component, while a weaker observed Q branch moving
to higher frequency is the K Å 2 R 1 A 0 R A / component.
R-, P- and Q-branch assignments for the above three systems were then extended by using ground state combination
differences.
(d) K Å 2 R 1 E system (Fig. 4d). A strong infrared
absorption at 3013.5259 cm01 was examined with the double-resonance technique and found to give a double-resonance signal with the second harmonic of the microwave
synthesizer set to 12 466.74 MHz. This corresponds to the
J Å 4 member of the K Å 2 R 1 E ground state Q branch
at 24 933.47 MHz, as shown in Fig. 4d.
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CH STRETCH OF METHANOL
n(K / 1 R K) IR 0 n(K / 1 R K / 2) IR
B. Subband Assignments Using Ground State
Combination Differences
Å n(K / 2 R K) 0 ,
Altogether, 19 DK Å {1 b-type subbands for 0 £ K £
3 for A and 03 £ K £ 4 for E have been identified using
ground state energies calculated from the parameters reported in Ref. (22). All of these assignments are attributed
to the n2 , A * asymmetric CH-stretch fundamental. This vibrational identification is based on lower resolution spectra
of methanol and its isotopomers (49, 50). Table 1 lists all
the assigned transitions arranged according to K * R K 9 subbands and is divided into two parts according to A/E symmetry. The majority of the lines were first recognized as series
and classified into R, P, and Q subbranches by performing
polynomial fits in m (m Å J / 1, J, and 0 J for R-, Q-, and
P-branch transitions, respectively). The subbranches were
then linked into subbands and the full quantum number assignments determined by applying two stringent checks described separately below.
Not included in Table 1 are a great many unassigned
lines. The number is particularly great in the molecular beam
electric resonance spectrum because it extends further on
the low frequency side and because it picks up many lines
not seen in the slit jet spectrum. Below 3000 cm01 , many
of the unassigned lines probably belong to the n9 band.
Above 3000 cm01 , the most intense unassigned lines in the
slit jet spectrum are about 5% of the largest peak in Fig. 3.
(a) Confirmation of J 9, K 9, and t9 for a single subband.
R, P, and Q transitions within a subband originating from
a (K 9, t9 ) lower state must satisfy the ground state combination differences
where n(K * R K 9 ) IR refers to the transition K * R K 9 going
from the ground state to the n2 excited vibrational state, and
n(K / 2 R K) 0 refers to an energy difference within the ground
state. As the n(K / 2 R K) 0 values are extremely sensitive to
K and t, this test puts each subband assignment on a solid
footing. Because only a few K states were populated in the
cold molecular beam, some of the ‘‘higher’’ K subbands, such
as K * Å 3 or 4, were confirmed with a second (K * R K 9 ) IR
subband taken from the Fourier-transform spectra.
(c) a-type transitions in the n2 band. In addition to the
b-type transitions discussed above, systematic searches for
a-type transitions were performed and eight a-type subbands
were found with ÉK *maxÉ Å 2 for both A and E torsional
symmetries. The a-type transition frequencies are calculated
precisely from the observed b-type transitions. The ratios of
the observed b-type to a-type subband intensities vary between 5 and 10 to 1, suggesting an a/b hybrid transition
moment for the n2 asymmetric CH-stretch vibrational mode.
(d) Transitions in the n9 band. Three DK Å {1 subbands attributable to the n9 A2 (A 9 ) asymmetric CH stretch
were also assigned as described in Section (a) above and
are centered at frequencies below 2989 cm01 . These subbands are marked in Fig. 3 but an additional investigation
of the n9 region is planned and these results will be presented
in a subsequent publication.
IV. PERTURBATIONS
R(J) 0 Q(J / 1) Å Q(J) 0 P(J / 1)
Å n(J / 1 R J) 0 ,
where n(J / 1 R J) 0 is a ground state a-type frequency.
The latter are accurately known from ground-state studies
(21, 22) and are generally sufficiently sensitive to K 9 and
t9 to distinguish clearly between different possible assignments. Thus, the infrared combination difference formulas
could be used not only to connect the R-, P-, and Q-branch
series but also in most cases to assign t9 for a subband. For
an assignment to be considered verified, the combination
relations had to be satisfied to within the experimental uncertainty. Sometimes the a-type frequencies are similar for different K 9 and t9 possibilities, hence caution must be exercised in such cases.
(b) Confirmation of K* and t* for two subbands connected to the same upper state. Additional combinationdifference verification of assignments is obtained by noticing
for an upper state (K * Å K / 1, t* )
Several J-localized perturbations were observed in the n2
state in the subbands terminating on the K * Å 0 E and
01 E levels and confirmed by ground state combination
differences. For K * Å 0 E, the J * Å 1 line is shifted away
from its expected position by Ç0.009 cm01 while for K Å
01 E, the J * Å 5 line is shifted away from its expected
position by Ç0.033 cm01 . In both cases, the intensity borrowing of the perturbing (‘‘dark’’) state is sufficient to allow
its observation.
A stronger perturbation was found in the K Å 02 R 01
E subbands. The K * Å 02 E upper states are split by É1.7
cm01 so the K Å 02 R 01 E transitions appear in Fig. 3 as
two complete subbands near 3016.0 and 3017.8 cm01 , each
with P, Q, and R branches. The combination differences of
the type described above in Section B(a) were sufficient to
establish that the lower state is K 9 Å 01 E for both of these
subbands. The combination differences of the type described
in Section B(b) then confirmed that K * Å 02 E is the upper
state of the 3016.1 cm01 subband. Unfortunately, the K Å
02 R 03 E transitions corresponding to the 3017.8 cm01
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TABLE 1a
A Symmetry Transitions (in cm01 ) in the n2 CH-Stretch Fundamental Band of CH3OH
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TABLE 1b
E Symmetry Transitions (in cm01 ) in the n2 CH-Stretch Fundamental Band of CH3OH
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dark states must be less than or equal to 1 and 5, respectively;
(ii) from the assignments for each subband associated with
the perturbed levels, we find that the line series seem regular
once we move away from the perturbing region, suggesting
that the perturbation mechanism involves an anharmonic interaction rather than Coriolis forces. If this is the case, one
would expect the interacting states to carry the same K value.
The stronger interaction at K * Å 02 E has a matrix element
of about 0.75 cm01 which is approximately independent of
J *. Therefore, it could be anharmonic or possibly z-type
Coriolis in origin but definitely not x- or y-type Coriolis.
V. TORSIONAL AND ROTATIONAL STRUCTURE
OF THE n2 VIBRATION
FIG. 5. Deperturbation scheme. The bright and dark zeroth-order energy
levels are represented as dashed lines and the observed energy levels are
solid lines.
In this section, it will be shown that, with the exception
of the perturbations noted above, the energy levels of the n2
vibration follow an apparently regular pattern. However, the
pattern is not the one anticipated by the Hamiltonian (22)
which has been so successful in fitting the ground and first
torsionally excited states.
subband were too weak to be observed. It could be shown
that the 3017.8 cm01 subband is not a DK Å 3 subband, i.e.,
K Å /2 R 01 E, since the K * Å /2 upper state energies
are known from other transitions. Since the 3017.8 cm01
subband represents the only group of moderately intense
lines found in the slit jet spectra above 3000 cm01 which
have not otherwise been assigned, the K Å 02 R 01 E
assignment is reasonable.
Each of the perturbed systems has been treated as a twostate interaction with a 2 1 2 secular determinant containing
an interaction matrix element W12 . From the observed perturbed energy separation de and intensity ratio R for the
allowed and the perturbation-induced satellite transitions
(Fig. 5), we can obtain the unperturbed energy separation
de* and off-diagonal matrix element W12 using the relations
q
(R 0 1) de
de* Å
(R / 1)
and
W12 Å
TABLE 2
Perturbations in the n2 Band
ÉdeÉ2 0 Éde*É2
.
2
Table 2 collects all the transitions associated with the perturbation systems along with the calculated unperturbed energy
separations and off-diagonal matrix elements.
It is difficult at this stage to firmly identify the perturbing
states, because as seen in Fig. 1 the density of vibrational
states near 3000 cm01 is significant and current methanol
Hamiltonian models cannot give sufficiently reliable predictions to assign possible background perturbing states. However, for the two localized perturbation systems, the following information can be deduced about the dark background
states: (i) since the perturbations occur at J Å 1 for K Å 0
E and J Å 5 for K Å 01 E, the K values of the two perturbing
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169
TABLE 3
K Å 1 A and 2 A Asymmetry Splittings in the n2 Excited CH-Stretch Vibrational State and Splitting
Constants, D Å [(J / K)!/(J 0 K)!][S / TJ(J / 1)], for Methanol (in MHz)
A. Rotational Level Structure
The new information on the asymmetry splittings for K
Å 1 and 2 A doublets in the n2 excited CH-stretch state is
shown in the upper portion of Table 3. These experimental
asymmetry splittings allowed a determination of splitting
parameters S and T from the relation
DÅ
(J / K)!
[S / TJ(J / 1)].
(J 0 K)!
In the lower portion of Table 3, the asymmetry splitting
parameters, S and T, for the n2 state are compared to those
for the ground, CO-stretch, and OH-bend states. The K Å
1 A asymmetry splittings for the n2 CH-stretch state are
comparable with those of the ground state, but the K Å 2 A
asymmetry splittings are significantly larger, indicating a
possible interaction with one or more dark states.
B. Torsional Level Structure
To study the torsion– K–rotation energy structure in the
n2 excited CH-stretch state, we first fit the K subbands to
J(J / 1) Taylor series expansions in order to extract the Jindependent subband origins which are collected in the top
part of Table 4. The observed infrared subband origins in
Table 4 allow one to map the torsion– K–rotation energy
structure in the n2 excited CH-stretch state. To remove the
rigid-rotor contribution to the K dependence of the upper
state energies, we subtract [A 0 (B / C)/2]K 2 using ground
state rotation constants. Table 4 summarizes the relevant
information used to plot torsion– K–rotation energy curves
for each t value for the ground and n2 excited CH-stretch
states as functions of K in Fig. 6. Table 4 also includes
the subband origins reported in Ref. (38). It is somewhat
surprising to see that although the latter were assigned to
both the n2 and n9 vibrational bands, in fact all fall on extrapolations of our t curves along the threefold cosine functions
shown in Fig. 6. Therefore, it is likely that all of the upper
states represented in Fig. 6, including those previously assigned as n9 , can be attributed to the single vibrationally
excited state designated as n2 in previous low-resolution
studies (49, 50). This attribution is supported by our assignments of three clearly different subbands (Fig. 3) about 30
cm01 lower in frequency than their n2 counterparts, which
is indeed the approximate shift expected for the n9 band.
Comparison of the two sets of torsion– K–rotation curves
for the ground and the n2 excited CH-stretch states reveals
an interesting yet puzzling energy structure for the n2 CHstretch state. The torsional oscillation pattern in the excited
state seems regular and follows a threefold cosine function
for all three t curves with a slight alteration of oscillation
period possibly due to a difference in rotational structures
for the two states. However, the sign of the torsional splitting, namely the ordering of the E/A levels for K Å 0, is
reversed in going from the ground state to the n2 excited
CH-stretch state. The magnitude of the E/A splitting is quite
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XU ET AL.
TABLE 4
Observed Infrared Subband Origins and Excited State Torsion– K–Rotation Energies in cm01
different for the two states too, being equal to about 9.12
cm01 for the ground state and about 03.26 cm01 for the n2
CH-stretch state. Apart from this inversion and the change
in the magnitude of the splitting at K Å 0, the K dependence
of the torsional energies appears regular with only a few
points lying noticeably off the expected cosine pattern.
The internal-rotor Hamiltonians (1, 3, 15–22) used to
treat the ground and torsionally excited states of methanol
are all based on a torsional potential of the form
V (g) Å
V3
V6
(1 0 cos 3g ) /
(1 0 cos 6g ) / rrr,
2
2
where g is the torsional angle. At J Å 0, this is a 1-dimen-
sional torsional problem and the potential dictates that A is
always lower in energy than E for the lowest torsional state.
Therefore, no effective barrier can account for the observed
inversion of the torsional levels in an isolated vibrational
fundamental. Of course, it is conceivable that we have analyzed the first excited torsional vibration ( nt Å 1) of the n2
fundamental, but the small magnitude of the torsional splitting (3.26 cm01 ) observed compared to the ground vibrational state of the nt Å 1 torsional splitting (85.54 cm01 )
would imply an unrealistically high effective torsional barrier and a substantially lower vibrational energy for the n2
n
fundamental (V3 É 1800 cm01 and E vib2 É 2200 cm01 , Ref.
52). We note in passing, similar inverted A/E torsional splittings have been observed in Propene work (53).
The A/E inversion could be explained by a global differ-
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171
CH STRETCH OF METHANOL
FIG. 6. Torsion– K–rotation energy diagram for the ground and the n2 excited states.
ential perturbation of the n2 levels by background state(s)
with torsional components nt § 1. Since the K subband
origins are shifted, anharmonic or parallel Coriolis interactions, but not perpendicular Coriolis, are involved; so the
overall perturbing combination vibration must have A * symmetry. A simple linear combination model indicates a 13%
mixing arising from such a background state would be
enough to change the observed n2 fundamental to an inverted
A/E pattern. An alternative explanation of the A/E inversion
involves torsionally induced coupling among the CH
stretches (54). In either case, the present work suggests that
to properly account for the observed n2 fundamental energylevel pattern, some kind of interacting band analysis will be
required. Such approaches are now under investigation and
will be reported in future papers.
ACKNOWLEDGMENTS
One of us (LHX) is greatly indebted to Drs. J. T. Hougen and R. M.
Lees for numerous fruitful discussions and valuable comments on the manuscript. This work was financially supported in part by the Natural Sciences
and Engineering Research Council of Canada, the University of New Brunswick Research Fund, the NASA Upper Atmosphere Research Program, and
the Division of Chemical Sciences, Office of Basic Energy Sciences, Office
of University Research, U.S. Department of Energy under Grant No. DEAI02-94ER14411. The work at the University of Akron was supported by
the Division of Chemical Sciences, Office of Basic Energy Sciences, Office
of Energy Research, U.S. Department of Energy under Grant No. DEFG02-90ER14151. Support of this work does not constitute endorsement
by the DOE of views expressed in this paper.
REFERENCES
1. R. M. Lees and J. G. Baker, J. Chem. Phys. 48, 5299–5318 (1968).
2. H. M. Pickett, E. A. Cohen, D. E. Brinza, and M. M. Schaefer, J. Mol.
Spectrosc. 89, 542–547 (1981).
3. E. Herbst, J. K. Messer, F. C. DeLucia, and P. Helminger, J. Mol.
Spectrosc. 108, 42–57 (1984).
4. K. V. L. N. Sastry, R. M. Lees, and F. C. DeLucia, J. Mol. Spectrosc.
103, 486–494 (1984).
5. F. C. DeLucia, E. Herbst, T. Anderson, and P. Helminger, J. Mol.
Spectrosc. 134, 395–411 (1989).
6. T. Anderson, F. C. DeLucia, and E. Herbst, Ap. J. Suppl. Series 72,
797–814 (1990).
7. O. I. Baskakov and M. A. O. Pashaev, J. Mol. Spectrosc. 151, 282–
291 (1992).
8. F. Matsushima, K. M. Evenson, and L. R. Zink, J. Mol. Spectrosc. 164,
517–530 (1994).
9. H. Odashima, F. Matsushima, K. Nagai, S. Tsunekawa, and K. Takagi,
J. Mol. Spectrosc. 173, 404–422 (1995).
10. S. P. Belov, G. Winnewisser, and E. Herbst, J. Mol. Spectrosc. 174,
253–269 (1995).
11. G. Moruzzi, F. Strumia, P. Carnesecchi, B. Carli, and M. Carlotti,
Infrared Phys. 29, 47–86 (1989).
12. G. Moruzzi, P. Riminucci, F. Strumia, B. Carli, M. Carlotti, R. M.
Lees, I. Mukhopadhyay, J. W. C. Johns, B. P. Winnewisser, and M.
Winnewisser, J. Mol. Spectrosc. 144, 139–200 (1990).
Copyright q 1997 by Academic Press
AID
JMS 7367
/
6t1f$$$244
09-09-97 22:35:14
mspas
172
XU ET AL.
13. G. Moruzzi, F. Strumia, J. C. S. Moraes, R. M. Lees, I. Mukhopadhyay,
J. W. C. Johns, B. P. Winnewisser, and M. Winnewisser, J. Mol. Spectrosc. 153, 511–577 (1992).
14. N. Ioli, G. Moruzzi, P. Riminucci, F. Strumia, J. C. S. Moraes, B. P.
Winnewisser, and M. Winnewisser, J. Mol. Spectrosc. 171, 130–144
(1995).
15. D. G. Burkhard and D. M. Dennison, Phys. Rev. 84, 408–417 (1951).
16. E. V. Ivash and D. M. Dennison, J. Chem. Phys. 21, 1804–1816
(1953).
17. K. T. Hecht and D. M. Dennison, J. Chem. Phys. 26, 48–69 (1957).
18. Y. Y. Kwan and D. M. Dennison, J. Mol. Spectrosc. 43, 291–319
(1972).
19. B. Kirtman, J. Chem. Phys. 37, 2516–2539 (1962).
20. K. Nakagawa, S. Tsunekawa, and T. Kojima, J. Mol. Spectrosc. 126,
329–340 (1987).
21. Li-Hong Xu and J. T. Hougen, J. Mol. Spectrosc. 169, 396–409
(1995).
22. Li-Hong Xu and J. T. Hougen, J. Mol. Spectrosc. 173, 540–551
(1995).
23. R. M. Lees, J. Chem. Phys. 57, 2249–2252 (1972).
24. J. P. Sattler, T. L. Worchesky, and W. A. Riessler, Infrared Phys. 18,
521–528 (1978).
25. J. P. Sattler, W. A. Riessler, and T. L. Worchesky, Infrared Phys. 19,
217–224 (1979).
26. J. O. Henningsen, J. Mol. Spectrosc. 85, 282–300 (1981).
27. H. Rudolph, J. Avery, and J. O. Henningsen, J. Mol. Spectrosc. 117,
38–45 (1986).
28. G. Moruzzi, F. Strumia, P. Carnesecchi, R. M. Lees, I. Mukhopadhyay,
and J. W. C. Johns, Infrared Phys. 29, 583–606 (1989).
29. R. M. Lees, J. Chem. Phys. 57, 824–826 (1972).
30. J. O. Henningsen, J. Mol. Spectrosc. 83, 70–93 (1980).
31. R. M. Lees, M. A. Walton, and J. O. Henningsen, J. Mol. Spectrosc.
88, 90–94 (1981).
32. J. O. Henningsen, J. Mol. Spectrosc. 91, 430–457 (1982).
33. R. M. Lees, Li-Hong Xu, and Z. F. Lu, ‘‘Fourier Transform Spectroscopy of the CH3-Rocking and OH-Bending Bands of CH3OH,’’ XIV
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
Colloquium on High Resolution Molecular Spectroscopy, Dijon,
France, Sept., 1995, paper Q30.
R. G. Lee, R. H. Hunt, E. K. Plyler, and D. M. Dennison, J. Mol.
Spectrosc. 57, 138–154 (1975).
P. Carrick, R. F. Curl, M. Dawes, E. Koester, K. K. Murray, M. Petri,
and M. L. Richnow, J. Mol. Struct. 223, 171–184 (1990).
I. Kleiner, G. T. Fraser, J. T. Hougen, and A. S. Pine, J. Mol. Spectrosc.
147, 155–172 (1991).
R. H. Hunt, W. N. Shelton, W. B. Cook, O. N. Bignall, J. W. Mirick,
and F. A. Flaherty, J. Mol. Spectrosc. 149, 252–256 (1991).
O. N. Bignall, R. H. Hunt, and W. N. Shelton, J. Mol. Spectrosc. 166,
137–146 (1994).
J. T. Hougen, J. Mol. Spectrosc. 181, 287–296 (1997).
L. Lubich, O. V. Boyarkin, R. D. F. Settle, D. S. Perry, and T. R. Rizzo,
Faraday Disc. Chem. Soc. 102, 167–178 (1995).
Lauri Halonen, J. Chem. Phys. 106, (19) 7931–7945 (1997).
F. J. Lovas, J. Phys. Chem. Ref. Data 21, 181–272 (1992). [see
references therein]
D. Bockelee-Morvan, J. Crovisier, P. Colom, and D. Despois, Astron.
Astrophys. 287, 647–665 (1994).
D. Bockelee-Morvan, T. Y. Brooke, and J. Crovisier, Icarus 116, 18–
39 (1995).
G. A. Bethardy and D. S. Perry, J. Phys. Chem. 98, 6651 (1993).
D. Kaur, A. M. de Souza, J. Wanna, S. A. Hammad, L. Mercorelli, and
D. S. Perry, Appl. Opt. 29, 119 (1990).
A. S. Pine and G. T. Fraser, J. Chem. Phys. 89, 100–109 (1988).
Li-Hong Xu, A. M. Andrews, and G. T. Fraser, J. Chem. Phys. 103,
14–19 (1995).
A. Serrallach, R. Meyer, and Hs. Günthard, J. Mol. Spectrosc. 52, 94–
129 (1974).
F. C. Cruz, A. Scalabrin, D. Pereira, P. A. M. Vazquez, Y. Hase, and
F. Strumia, J. Mol. Spectrosc. 156, 22–38 (1992).
Li-Hong Xu, A. S. Smith, R. M. Lees, and Z. F. Lu, unpublished results.
Li-Hong Xu and J. T. Hougen, unpublished results.
A. Ainetschian, G. T. Fraser, J. Ortigoso, and B. H. Pate, J. Chem.
Phys. 100, 729 (1994).
X.-L. Wang and D. S. Perry, manuscript in preparation.
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