On the Assignment of Optically Pumped Far-Infrared Laser Emission from CH3OH

Journal of Molecular Spectroscopy 196, 220 –234 (1999) Article ID jmsp.1999.7876, available online at http://www.idealibrary.com on

On the Assignment of Optically Pumped Far-Infrared Laser Emission from CH 3OH R. M. Lees* and Li-Hong Xu† *Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada; and †Department of Physical Sciences, University of New Brunswick, Saint John, New Brunswick, E2L 4L5, Canada Received February 22, 1999

Progress in the analysis of the infrared spectrum of CH 3OH in the 930 –1450 cm 21 region has led to assignments, confirmations, or new insights for a number of far-infrared laser (FIRL) transition systems optically pumped by CO 2 lasers. Many of the systems involve FIRL transitions among the CO-stretching, CH 3-rocking, OH-bending, and CH 3-deformation vibrational modes, giving useful information on the torsion–rotation structure of the methanol vibrational energy manifold. Some anomalies and mysteries concerning the identity of the lasing levels have been resolved, but several new ones have arisen. Altogether, 45 CH 3OH IR-pump/FIR-laser systems are examined in light of the new spectroscopic information; about half of the system assignments are new and half have been previously reported in the literature and are here confirmed, extended, or revised. © 1999 Academic Press Key Words: far-infrared laser; methanol; infrared spectra; internal rotation; torsion–vibration interaction; optically pumped lasers. I. INTRODUCTION

This work reports assignments, confirmations, or new insights for a variety of optically pumped far-infrared laser (FIRL) transition systems of CH 3OH. The results are based on recent progress in the analysis of high-resolution Fourier transform infrared (IR) spectra of normal methanol in the 930 –1450 cm 21 region. Since the first discovery of FIRL emission from CH 3OH in 1970 (1), observations of FIRL lines have provided important windows into the torsion–rotation structure of the excited vibrational energy manifold of methanol. Traditionally, most of the FIRL emission has been associated with IR pumping in the strong CO-stretching band, but growing numbers of transition systems are being found to involve levels of the CH 3-rocking, OH-bending, and CH 3-deformation modes as well (2– 4). Current understanding of the FIRL emission from CH 3OH is summarized in several recent reviews (4 –7). A substantial fraction of the catalog of known FIRL lines is now assigned, and most of the proposed IR-pump/FIR-laser system identifications have been spectroscopically checked. However, 17 system assignments were still reported with question marks in the latest compilation by Moruzzi et al. (4), so had not been rigorously confirmed. Over half of these involve the non-COstretch vibrational states mentioned above, providing additional motivation for the present work in investigating the weaker spectral bands associated with these modes. In this paper, we examine assignments of reported FIRL emission from CH 3OH, utilizing our newly established IR spectroscopic data together with accurate calculations of ground state energies (4, 8). Many of the transition systems

involve FIRL transitions between different vibrational states, so provide particularly important signposts for the IR spectral assignments. In Section II of the paper, a brief discussion of the CH 3OH torsion–vibration energy structure and IR spectra is given. Our new FIR-laser information is presented in Section III, with a listing of the assigned IR pump and FIRL-transition quantum numbers along with FIRL wavenumbers derived to an accuracy of 60.001 cm 21 from spectroscopic combination differences. We review features of interest for the pump transitions in Section IV, followed by comments on specific systems in Section V highlighting details of particular significance. Energy level and transition diagrams with supporting spectroscopic data are shown for four of the systems to illustrate confirmation of the transition schemes through combination loops as well as the extensive coupling among different torsion–vibration states via the FIRL emission. The paper concludes in Section VI with a summary of the results plus remarks on interesting spectral anomalies and unsolved questions about the CH 3OH vibrational energy structure which have been revealed by the assignments. II. CH 3OH TORSION–VIBRATION ENERGIES AND INFRARED SPECTRA

The notation adopted in this work is as follows. An energy level is denoted as E(n, K, J) v T s , where n is the torsional quantum number, K is the component of rotational angular momentum J along the molecular a axis, v is the vibrational state, and T s is the torsional symmetry. T s is either A or E, with positive K values corresponding to E 1 levels and negative K values to E 2 levels (9). Resolved K doublets of A symmetry

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FIG. 1. Calculated K-reduced torsion–vibration energy curves for the lower vibrational modes of CH 3OH. Curves for the in-plane (ri) CH 3-rocking mode are calculated with a barrier height of 557 cm 21 (12); all others employ the ground state value of 373 cm 21 (10).

have an additional 1/2 superscript on K to distinguish the A 1 or A 2 component of the doublet (10). The vibrational state labels (4) are v 5 gr for the ground state, v 5 co for the CO stretch, v 5 ri for the in-plane CH 3 rock, v 5 ro for the out-of-plane CH 3 rock, v 5 oh for the OH bend, and v 5 sb for the symmetric CH 3 deformation (“umbrella bend”) mode. CH 3OH has an interesting torsion–vibration energy structure in the region of the bending vibrations and the CO stretch, with many possibilities for torsion-mediated coupling among the modes. Perturbations and state mixing induced by such coupling have proven to be important with respect to FIRL emission in CH 3OH (11). Potential DK 5 0 Fermi-type interactions can be seen from Fig. 1, in which calculated K-reduced tor-

sion–vibration energies are plotted against rotational K value in Dennison’s t curves (13) for various torsion–vibration states. The t index is an alternative torsional symmetry label related to T s by the rule [1 2 ( t 1 uKu)mod 3] 5 0 for A levels, 11 for E levels with K . 0, and 21 for E levels with K , 0 (10). When curves of the same symmetry approach each other, anharmonic resonances lead to energy perturbations and avoided crossings (14). Figure 1 shows there are likely to be significant resonances between n 5 0 levels of the OH bend and n 5 1 levels of the CO-stretch and CH 3-rock modes, and between n 5 0 levels of the CH 3 symmetric bend and n 5 2 levels of the CO stretch and CH 3 rock. The origin of the known Fermi resonances coupling the (n, K) v T s 5 (0,0) coA t 5 1

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TABLE 1 Assignments, Confirmations, and New Information for CH 3OH FIR Laser Lines Optically Pumped by CO 2 Lasers

Pump wavenumbers in brackets are calculated from combination differences or as the CO 2 laser wavenumber 1 offset. IR pump lines are Dn 5 0, DK 5 0 a-type transitions unless otherwise indicated; uDKu 5 11 or 21 b-type transitions are denoted by a superscript r or p prefix, respectively. Transitions with Dn 5 21 or Dn 5 22 are shown as n 5 0 4 1 and n 5 0 4 2; for the 9P(16)–56 system, the DK 5 2 pump transition is shown as K 5 2 4 0. c The vibrational label h for the 9P(10), 9P(26), and 13-9R(26) systems indicates levels believed to be hybridized, with the exact torsion–vibration identity yet to be established; the labels hu and hd refer to upper and lower components of a hybrid doublet. The 9P(22) and 10R(16) systems involve different (0,0) oh A states, labeled as (0,0) oh A/hi and (0,0) oh A/lo, respectively. [See text.] d Relative polarizations in brackets are not observed but predicted. e Loop wavenumbers in brackets have reduced accuracy due either to overlap of IR transitions, extrapolation of excited or ground state energies to high J using spectroscopic combination differences, or inclusion of small calculated high K doublet splittings. f Assignment code is: N, new; C, confirmed; R, revised; I, extended with new information; ?, still not fully confirmed spectroscopically. g Mean wavenumber of close K-doublet line pair; predicted splittings are 0.0015 cm 21 for the 9P(36) 1 184 system, and 0.0036 and 0.0069 cm 21 for J 5 13 and 14 lower levels, respectively, in the 9HP(18) system. h Predicted FIRL transition. i Partial suggested assignment with rotational quantum numbers of pump absorption. a

b

and (0,25) co E t 5 3 CO-stretch levels with high-lying n 5 3 and n 5 4 ground state levels (14) is also evident from Fig. 1. In addition to the DK 5 0 anharmonic resonances, there are also Coriolis and asymmetry-induced resonances which can couple near-degenerate levels of different K (11). Here, Henningsen’s “X-state” Coriolis resonances strongly mixing the (0,5) co A with the (0,4) ri A state and the (0,7) co A with the (0,6) ri A state are the best-known examples (15). Weaker J-localized level-crossing resonances with uDKu . 1 can also arise when levels of given K of one torsion–vibration state start out at low J just above levels of different K of a second state with a larger rotational B value. With the higher B value, the levels of the second state will rise faster with J and eventually cross over those of the first. Substantial perturbations and state-mixing

can then occur for several J values in the vicinity of the level-crossing point. III. FIR-LASER SYSTEM ASSIGNMENTS FOR CH 3OH

The results obtained in this work on new assignments, confirmations, or further insights for IR-pump/FIR-laser transition systems of CH 3OH are presented in Table 1. Our spectroscopic analysis has provided additional support for many of the other system assignments already established in the literature, but only those systems for which specific new information has been obtained are discussed in the present paper. We note also that, along with the new system identifications, we can readily generate accurate wavenumber predictions for numerous unreported but potentially observable FIRL lines defined

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ASSIGNMENT OF FIR LASER EMISSION FROM CH 3OH

TABLE 1—Continued

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TABLE 1—Continued

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by all of the many possible transitions allowed by the selection rules. We have refrained from including these predictions here, but they can be made available on request. In Table 1, the FIR-laser systems are listed by decreasing wavenumber of the pump line, first for normal CO 2 pumping, then sequence and hot-band pumping, and lastly for isotopic CO 2 pumping. The CO 2 pump line is given in the first column with offset in megahertz where known, followed by the wavenumber of the IR pump absorption as determined from our spectrum. Where this pump absorption was not clearly resolved, the n pump value was calculated either from combination differences or from the CO 2 laser wavenumber plus offset and is shown in brackets in Table 1. The following five columns contain the IR pump assignments, the FIRL transition assignments, the reported FIRL wavenumbers, the relative polarization of the IR and FIR radiation, and the spectroscopic FIRL wavenumbers determined from combination loop relations using our observed IR data together with accurate ground state energies (4, 8). These loop wavenumbers are estimated conservatively to have an accuracy of 60.001 cm 21. For some cases in which we had to extrapolate either the IR series or the ground state energies beyond their measured ranges, generally by using combination differences, the resulting FIRL loop wavenumbers are of reduced accuracy and are shown in brackets. The next column gives an assignment code, in which N denotes a new assignment, R a revised assignment, I a previous partial assignment with additional information given here (such as the A 1 or A 2 K-doublet labeling), and C a confirmation of a known assignment for which a rigorous spectroscopic check had not been previously available. A question mark in the Code column indicates that some aspect of the assignment is still uncertain, often involving the exact torsion–vibration identity of the upper level of the laser transition. The final two columns give references for the best reported experimental wavenumbers and previous assignments. Most of the sources are cited here directly, but the reader is also directed on occasion to the reviews of the FIRL literature in Refs. (4 –7) for references to the original reports. IV. FEATURES OF THE IR-PUMP TRANSITIONS

Studies of the IR spectrum and FIR-laser emission for CH 3OH are relatively mature, so that new system assignments now tend to involve interesting and unexpected aspects of the torsion–vibration energy manifold. It can be seen in Table 1 that a wide variety of IR-pumping transitions is responsible for the FIRL emission discussed here, ranging over high J and torsionally excited CO-stretch transitions, both a- and b-type CH 3-rocking transitions, and OH-bending and CH 3-deformation transitions of nontraditional Dn 5 1 and Dn 5 2 types, likely arising from state mixing. In a number of cases, the pumping line is shifted from its expected position by perturbations in the excited state due to anharmonic resonances, large

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subband-wide Coriolis resonances, or smaller J localized resonances. The perturbed spectral subbands involving these interactions are often difficult to identify with confidence, hence the FIRL systems can give crucial information for the spectroscopic assignments. Several CH 3OH torsionally excited subbands were assigned in this work directly through the clues provided by the FIRL pumping. Analysis of the perturbations leads to important information about the channels for vibrational coupling among the various modes, notably for those interactions mediated by changes in torsional state. The details of the spectroscopic results associated with these systems are outlined only briefly here, but will be treated more fully in future separate communications describing the spectral analyses. V. FEATURES OF SPECIFIC CH 3OH FIR-LASER SYSTEMS

As discussed above, new FIRL assignments now frequently involve novel insights into the excited state energy structure. Thus, in the following we present comments on the spectroscopy and background for specific FIRL systems, grouped by common features where appropriate, to show the basis for the assignments along with other relevant details. To illustrate combination–loop confirmation of the assignments, we also give four examples of energy level and transition diagrams for the FIRL systems with spectroscopic data included. In these diagrams, individual FIR transitions between the ground state levels no longer need be shown because the ground state energies are now available directly from recent accurate termvalue analysis (4) and global-fit modeling (8), simplifying the loop procedure. 9R(34) The R(0,0,45) co E absorption pumped by the 9R(34) CO 2 line is close to the high J limit of detectability for the COstretch band in our present spectrum. The observed IR line is overlapped, hence the pump wavenumber is given in brackets in Table 1. The ground state energies were extrapolated up to J 5 45 with the use of [R( J) 2 P( J 1 2)] IR combination differences. With only a single FIRL line, the assignment is tentative, and a question mark is included in the assignment code. Observation of the (n, K, J) v 5 (0,0,46) co 3 (0,0,45) co E a-type FIRL line at a calculated wavenumber of 71.821 cm 21 would confirm the system identification. 9R(32) 1 90, 9R(30) 2 162, 9R(12) 2 25, 9P(44) 2 31, 10R(34) 2 46, and 9HP(18) These systems all involve Henningsen’s X-state Coriolis resonances coupling the (n, K) v 5 (0,4) ri, (0,5) ri, and (0,6) ri A states of the CH 3 rock with the (0,5) co, (0,6) co, and (0,7) co A states of the CO stretch, respectively (15). Because we could resolve K doubling in relevant subbands linking to the (0,3) ri,

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(0,4) ri, (0,5) ri, (0,5) co, and (0,6) co states, we were able to establish the A 1 and A 2 labeling for the 9R(32), 9R(12), 9P(44), and 10R(34) systems. The splittings for the (0,5) ri, (0,5) co, and (0,6) co A states are much larger than the ground state values, while the (0,5) co K doublets are inverted, likely due to strong Coriolis mixing with the (0,4) ri levels. For the 9R(30) system, the r R(0,6,9) co A pump line was found originally by combination-difference prediction from the known (0,7) co subband, for which the (0,7) co A upper levels are strongly hybridized with the (0,6) ri A levels due to the Coriolis mixing. Combination differences were also the source of the p Q(0,6 1 ,32) ri A wavenumber which led to the assignment of the 9P(44) system. This high J Q-branch pump transition is not directly visible in our spectrum. For the 9R(12) system, the K doubling of the (0,3) ri A lower levels of the FIRL transitions is sufficient to tie down the A 1 /A 2 labeling and establish that the upper pumped level must be (0,4 1,19) ri A. The Q-branch pump transition is therefore A 1 4 A 2 . The 6 labeling is also well determined for the 10R(34) system pumped at 246 MHz offset. The three FIRL frequencies have all been accurately measured by heterodyne techniques, and Table 1 shows the loop-calculated wavenumbers to be in close agreement. This agreement would have been visibly affected if the experimental K doubling of 0.0044 cm 21 for the (0,5,25) ri A levels, for example, had not been accounted for in the loops. The 9HP(18) system assignment was previously based on approximate wavenumbers (35), but observation of the (0,3) ri subband has now supplied confirming values. Since the (0,4) ri asymmetry splitting will only be about 3 MHz at J 5 14, both A 1 and A 2 upper state levels will be pumped by the 9HP(18) CO 2 line. Thus, each of the two reported FIRL lines should actually be a close pair split by the K doubling of the (0,3) ri lower levels. Calculated wavenumbers for the centers of the pairs are given in Table 1 with the predicted splittings included in a footnote. 9R(28), 9R(20) 2 140, and 10R(20) 1 147 These systems involve pumping from (n, K) v 5 (0,4) gr A ground levels. In the 9R(20) system, the (0,2) ri A state had not been spectroscopically observed earlier and the FIRL transition down to the (0,2 1,16) ri A level was the key to identifying IR subbands to that state and thereby confirming the system assignment. The 10R(20) system has been an elusive problem for some time (20, 23, 32, 33), but we have finally succeeded in nailing it down. Despite opinion to the contrary (33), the FIRL emission does arise from the CO-stretching state, occurring through an unsuspected perturbation. As was originally surmised (20, 32), it is the P(0,4,31) co A absorption which coincides with the 10R(20) CO 2 line but the A 2 rather than the A 1 component is pumped, opposite to the earlier proposal (20). The difficulty with this system arises from a J-localized level-

crossing resonance in which the (0,1 2) ri A levels rise from below and cross over the (0,4 2) co A stack between J9 5 28 and 29. (The analogous level crossing occurs for 13CH 3OH (42) but between J9 5 21 and 22 for the A 1 component.) Due to the perturbation, the (0,4 2,30) co A level is shifted downward by about 0.018 cm 21, resulting in a K-doublet splitting of 0.083 cm 21 for J 5 30. This is larger than expected and explains the failure to observe a triple resonance signal below 2 GHz (32). 9R(26) 1 25 The (0,1 1) co A pumping subband for this system is locally perturbed around J9 5 35, and the R(34) and P(36) members are split due to an interaction with an unknown partner. We were able to pick up the R subbranch again after the perturbation and follow it through the coincidence with the 9R(26) CO 2 line at R(39). Petersen and Henningsen report an IR absorption at 25 MHz offset in their laser–Stark study (43) and assign it as the R(0,2,38) co E transition. However, this does not seem consistent with our results so far for the (0,2) co E subband, although we have only been able to follow the R subbranch up to R(37) and there are signs of perturbation at that point. 9R(24) 1 6 This system is not fully confirmed because we have not yet found subbands connecting to the (0,23) ri E rocking state. Thus, the identity of the upper pumped level cannot be definitively checked. However, our results accurately locate the (0,22) ri E levels and confirm the lower level assignments of the two FIRL lines in Table 1 with the use of the IR pump wavenumber determined from the CO 2 line plus offset. The good agreement between reported and calculated FIRL wavenumbers shows the high quality of Henningsen’s more careful wavelength measurements (2). So far, we have been unable to shed any light on the lower torsion–vibration state for two further FIRL lines at 28.77 and 41.62 cm 21, which were given the same rotational assignments by Henningsen (2) as the 21.72 and 34.58 cm 21 pair in Table 1. The lower levels for these lines must lie 7.04 cm 21 below their (0,22) ri E counterparts, placing them only 0.84 cm 21 below the (0,1) ri E levels of corresponding J on the basis of our spectral data. Thus, their identity is an intriguing mystery. 9R(16) 2 8 The assignment for this system was originally proposed by Mollabashi et al. in 1987 (20) but was not included in previous reviews (4 – 6). However, in the present work, we have revised high J assignments for the (1,26) co E subband, modifying the calculated FIRL wavenumbers. Our current calculated wavenumber for the 52 cm 21 FIRL line is in excellent agreement with the recent frequency measurement by Carelli et al. (19), as seen in Table 1, confirming the system identification. The assignment of the refilling transition in the ground state is

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ASSIGNMENT OF FIR LASER EMISSION FROM CH 3OH

mildly speculative, but is consistent with the reported wavenumber. 9R(10) 1 52, 9P(16) 2 56, 9SP(21) 1 16, 9HR(23), and 9HP(13) These systems each involve in some way the “giant K doubling” caused by interaction between the (1,2 1) ri and (1,0 1) co A substates (44, 45). Only one a-type FIRL line is reported for the 9R(10) 1 52 MHz system, but its wavenumber is sensitive to the anomalous K doubling and the assignment appears solid. For the 9P(16)–56 MHz system, the pump is reassigned to the perturbation-induced R(1,2 4 0,16) ri A 1 transition (44) but Henningsen’s original identification of the lower laser levels is correct (22). Here, the accurate frequency measured by Zerbetto et al. (26) for the 238.8 cm 21 FIRL line was the initial clue to finding the (0,1) ri A subbands in the spectrum and thereby confirming the assignment for that line. For the 9SP(21) system, the influence of the giant K doubling is indirect, with the wide splitting of the (1,2) ri A doublets partially fed through the (0,2) oh A levels by anharmonic Fermi coupling and inverting the normal A 6 ordering (44). The pump assignment is confirmed by the close agreement for the 123.8 cm 21 FIRL line in Table 1 between calculation and frequency measurement (with correction of a typographical error for the frequency in Ref. (7)). However, an unexplained 0.385 cm 21 discrepancy for the 173 cm 21 line still leaves some question about the (0,2) oh A level identification. For the 9HR(23) system, the pumping occurs within the same (1,2 1) ri A stack as for 9R(10) 1 52 MHz, with lasing down to the CO-stretching mode as found for the 9P(16) system (2, 22, 24). Lastly, the 9HP(13) system samples the other side of the giant K-doubling interaction since it is the partner (1,0 1) co A levels that are involved. 9R(10) 1 3 This system is doubly perturbed, in that the (0,9) co E levels show a small J-localized level-crossing resonance between J9 5 26 and 27, while the (0,10) co E levels have a similar but larger resonance between J9 5 24 and 25. The interaction partners have not been identified in either case. The consequences for the FIRL system are that the (0,9,26) co and (0,9,27) co E levels are perturbed by 20.001 and 10.009 cm 21, respectively, while the (0,10,25) co, (0,10,26) co, and (0,10,27) co E levels are downshifted by approximately 20.168, 20.076, and 20.043 cm 21. Nevertheless, the agreement between measured and calculated FIRL wavenumbers in Table 1 shows that the IR assignments are under control. A minor change for this system reassigns the J 5 26 3 25 cascade transition at 41.29 cm 21 as K 5 9 instead of the previous K 5 10 (4 – 6, 24). With the perturbations, the K 5 10 line would lie 0.082 cm 21 higher than the K 5 9 line, hence we believe our K 5 9 assignment in Table 1 better matches the reported wavenumber.

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9R(8) 1 28 This system was originally assigned by Petersen through IR–IR double-resonance experiments (25). Although we have not yet succeeded in identifying the (0,213) co E pumping subband, the CO 2 pump wavenumber plus the known frequencies for the two FIRL lines serve to accurately locate the J9 5 25 and 26 levels of the (0,212) co E state. With this information, we were then able to find and follow the (0,212) co E subband and confirm Petersen’s assignments. 9R(2) 1 25 This system has been well understood from Henningsen’s original work (22), but an incorrect calculated wavenumber has persisted in the literature for the particular 94.8 cm 21 FIRL line in Table 1 (4 – 6). Since the frequency of this line was accurately measured by Zerbetto et al. recently (26), we decided to include it here to show that our present loop calculation agrees with the measurement. Four other FIRL lines are known for this system (22, 26) and are correctly reported in the literature (4 – 6, 46). 9P(6) 1 73 The (2,7) co A subband is highly perturbed for J9 . 12 and we lose track of it above J9 5 16. Fortunately, the Q subbranch is strong and well isolated so permits confident identification of the subband at low J. The consistency between observed and calculated FIRL wavenumbers gave crucial support for the IR assignments in the perturbed region for this system. 9P(10) 1 63 In the assignment put forward by Henningsen for this system (2), lasing was proposed from the (2,7,11) co E pumped level down to hybridized (1,6,11) h and (1,6,10) h E levels, with a further cascade from the latter down to the (1,5,9) co E level. We have identified both the (2,7) co and (1,6) h E subbands in the spectrum so we can confirm Henningsen’s energy level and transition scheme. However, as he notes, the origin for the (1,6) h E subband is anomalously high for n 5 1 CO-stretch substates, and in fact is more consistent with the n 5 0 OH bend. So far, we too have been unable to pin down the exact vibrational identity of the (1,6) h levels. 9P(14) 2 35 and 9P(24) 1 0 Both of these spectroscopically rich systems involve four different vibrational states in the FIRL emission. The basic transition schemes were correctly set out by Henningsen but with some uncertainty about the vibrational modes involved (22). We have been able to clarify the vibrational labeling through our OH-bending results and have revised the assignments as shown for the 9P(24) system in Fig. 2. The keys to the reassignment were the discoveries first that

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FIG. 2. Schematic energy level and transition diagram (not to scale) for the CH 3OH far-infrared laser system optically pumped by the 9P(24) CO 2 laser line. Ground state energies are obtained from the global-fit modeling of Ref. (8).

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the pump absorptions for the two systems, which had been assigned in the literature (2, 4, 22) as (1,25) co E transitions, belong to a subband with the same upper state as the (0,25) oh E subband, and second that the (0,24) oh E levels lie only 2 cm 21 below the (0,25) oh E levels. Our assignments for the (1,25) co E levels then put them just 2 cm 21 further below, so that they are expected to perturb and mix with the (0,25) oh E levels. With these observations, we could then assign the pump transitions to the perturbation-induced (0,25) oh 4 (1,25) gr E subband and identify the lower partners of Henningsen’s postulated hybridized pump doublets (22) as (0,24) oh E substates. The reassignment removes the troublesome requirement for a DK 5 22 FIRL transition noted by Henningsen, as all transitions in Fig. 2 now follow the normal rotational selection rules. Mixing among the close grouping of upper state levels may also contribute to the anomalous Stark effects observed for the pump transitions (25, 43). The FIRL assignments can be confirmed by comparing wavenumbers calculated by combination differences from closed four-level loops in Fig. 2 against the accurate experimental values given to five decimal places in Table 1, which were derived from heterodyne frequency measurements (18). For example, the a-type laser wavenumber La is given by independent loops containing IR wavenumbers and ground state energies from Fig. 2 as follows: La 5 R~1,25,8! oh 1 E~1,25,8! gr 2 E~1,25,9! gr 2 P~1,25,9! oh 5 1043.1630 1 565.6181 2 580.0985 2 1014.2775 5 14.4051 cm 21 La 5 R~0,25,8! oh 1 E~0,25,8! gr 2 E~0,25,7! gr 2 R~0,25,7! oh 5 1336.4117 1 272.3694 2 259.4675 2 1334.9085 5 14.4051 cm 21 . The agreement between the two independent loop calculations for La and the precise observed value in Table 1, to well within the net spectroscopic uncertainty of 60.001 cm 21, serves to confirm the assignments of both the FIRL line and the IR transitions in the loops. Analogous loop calculations can readily be carried out for other FIRL lines in Fig. 2 using the data included in the diagram. All loops give wavenumbers in excellent agreement with the measured values in Table 1 except for line Lf, the (0,25) oh 3 (1,24) co E transition at 108 cm 21, for which there is a difference of 0.5 cm 21. Currently, we have no explanation for this discrepancy, so we cannot definitively confirm the Lf assignment. The other unconfirmed transitions for these systems are the proposed FIRL lines connecting to ro out-of-plane CH 3-rock-

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ing levels. The ro band is expected to be weak and has not been detected in our spectrum. However, the data in Table 1 put the ro band origin at around 1152 cm 21, which corresponds closely to the values of 1155 cm 21 calculated by Serrallach et al. (47) and 1151.4 cm 21 by Cruz et al. (48) for certain choices of their force constants. The experimental band origin was reported (47) to be 1145 6 4 cm 21, but our results suggest that this feature in the low-resolution spectrum is more likely due to a pileup of n 5 1 in-plane CH 3-rocking and n 5 0 4 1 OH-bending subbands in that region. 9P(22) 1 17 This is another intriguing system involving the OH-bending mode. We are confident of the transition structure and the lower pumped level, but the exact vibrational identity of the upper pumped level is still in question. Originally, the scheme tentatively proposed by Henningsen had the P(1,1 2 ,19) ri A transition as the IR pump (2), but our spectroscopic observations for the (1,1) ri A subband show that this transition does not coincide with the 9P(22) CO 2 line. However, when calculating n 5 0 4 2 wavenumbers by combination differences from a subband we had labeled as “(0,0) oh A/hi”, we found unexpectedly that the predicted R(17) n 5 0 4 2 transition coincided with the 9P(22) line, leading to the revised assignments shown in Fig. 3. The new scheme removes the K-doubling problem hinted at by Henningsen (2) because the FIRL lines now terminate on (0,1) oh and (0,1) ro levels with large K 5 1 asymmetry splittings rather than the (1,2) ri and (0,2) ri levels suggested originally which have much smaller K 5 2 doubling. Because the FIR lasing occurs to the outer members of the widely split K 5 1 doublets, as shown in Fig. 3, the line separations (Lc 2 Lb) and (Le 2 Ld) are significantly greater than expected for normal J 5 18 4 17 or 19 4 18 a-type transitions, explaining the apparent anomaly. Note that the K 5 1 doubling is substantially smaller for the excited OH-bending state than the ground state, which is why the wavenumbers in Fig. 3 for the R(0,1 1 ,16) oh and R(0,1 2 ,17) oh A transitions are unexpectedly close. The A 1 3 2 labeling in Fig. 3 corresponds to b-type transitions for lines Lb and Lc, but to c-type for Ld and Le (where the c axis is out-of-plane). This provides additional justification for our assignment of A0 out-of-plane CH 3-rocking lower levels for the latter, since c-type rotational selection rules imply an A9 3 A0 vibrational transition. The positions of the presumed (0,1) ro levels in Fig. 3 are also consistent with the band origin of 1152 cm 21 proposed above for the out-of-plane rocking fundamental. The uncertainty in pump identity and the need for the “A/hi” designation arise from the fact that, about 49.1 cm 21 below the (0,0) oh A/hi subband, there is a second (0,0) oh A/lo subband which also originates from the (0,0) gr A ground state, also has a weak n 5 0 4 2 forbidden partner, and also is involved with

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“down” members of hybridized doublets. The vibrational source for a K 5 4 state in this vicinity is by no means clear. The transition picture for the two FIRL systems is illustrated in Fig. 4. The lower levels for lines Lb and Lc of the 139R(26) system are well established (2, 38) but the pump identity is now uncertain. The FIRL emission in the 9P(26) system is puzzling, as the best match with the reported wavenumbers is obtained with line Ld going to the upper component of the J 5 6 doublet, but line Le going to the lower component for J 5 5. If the lower levels do have predominantly K 5 4 character, line Le would then represent a DK 5 22 transition. Also, we have found that the (1,7,7) co A level lies 7 cm 21 too low to explain Henningsen’s assignment of FIRL line Lf (2), but the (0,6,7) oh A level is a possible alternative candidate. 9P(36) 1 184 and 10R(48) 2 10

FIG. 3. Schematic energy level and transition diagram (not to scale) for the CH 3OH far-infrared laser system optically pumped by the 9P(22) CO 2 laser line at 17 MHz offset. The n 5 0 and 1 ground state energies are obtained from the model of Ref. (8), n 5 2 energies are taken from Ref. (4) with an 0.1314 cm 21 zero-point energy adjustment to match with Ref. (8). Identifications of the (0,0) oh A/hi and the (0,1) ro A excited-state levels are tentative. K doubling of the K 5 1 OH-bending levels is substantially smaller than for the ground state, hence the wavenumbers for the R(0,1 1 ,16) oh and R(0,1 2 ,17) oh A transitions are unusually close.

At first glance, these two systems would appear unrelated, but a level-crossing resonance couples the (2,4) co A and (1,7) co A states and provides an indirect link through perturbations to the FIRL pump absorption for 9P(36) and two potential laser

FIR lasing as described below for the 10R(16) system. The upper state of this second (0,0) oh A/lo subband is just above the (1,0) co A state, which itself is strongly mixed with the (1,2) ri A 1 state (44)! The identity problem would be resolved if the upper state of the (0,0) oh A/hi subband were actually the (1,0) ri A state, which we still have not located, but this choice would then contravene the A 1 3 2 selection rules in Fig. 3. Thus, there is an interesting mystery here which we have yet to unravel. 9P(26) 1 54 and 13-9R(26) These two systems also lead to an enigma in the excited state. The 9P(26) assignment (2) did not have direct spectroscopic support earlier, but that for the 13-9R(26) system (although incorrectly reported in Refs. (4) and (5)), appeared to be solidly confirmed (2, 38). Our spectroscopic results, however, have revealed that the levels originally assigned as (2,5) co A have close hybridized companions lying just above, with subbands connecting to both partners from both (2,5) gr and (2,4) gr A lower states! The starting J values and relative intensities for the quartet of subbands suggest that at low J the lower partner actually has greater K 5 4 character, but we have not yet resolved this question and so will label the partner levels for the moment as the (2,5) hu A “up” and (2,5) hd A

FIG. 4. Schematic energy level and transition diagram (not to scale) for the CH 3OH far-infrared laser systems optically pumped by the 9P(26) CO 2 laser line at 54 MHz offset and the 13-9R(26) CO 2 laser line. The n 5 0 ground state energy is obtained from the model of Ref. (8); n 5 2 and 3 energies are taken from Ref. (4) with an 0.1314 cm 21 zero-point energy adjustment to match with Ref. (8). The (2,5) h A upper (u) and lower (d) excited-state levels are components of hybrid doublets arising from mixing between the (2,5) co A state and an unidentified partner.

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ASSIGNMENT OF FIR LASER EMISSION FROM CH 3OH

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lines for 10R(48). In the 9P(36) system, the upper level of the Q(2,4,21) co A pump transition is perturbed upward by about 0.005 cm 21 by the resonance. However, we determine the coupling matrix element to be only 0.022 cm 21, much smaller than the separation of 0.126 cm 21 between the interacting levels for J9 5 21, hence there is little state mixing. For the 10R(48) system, the (1,8) co A pumping subband is also perturbed starting around J9 5 20, and we lose track of it in the spectrum above J9 5 23. Although several FIRL lines are pumped at similar offsets by 10R(48), we have so far only been able to assign the one a-type line in Table 1, for which the frequency measurement of Vasconcellos et al. (30) gives confirmation. In particular, potential FIRL lines down to the perturbed (1,7,22) co and (1,7,21) co A levels have not been reported; we predict wavenumbers for these transitions of 44.2932 and 79.4373 cm 21, respectively. 9P(40) 2 11, 10R(16) 2 19, 13-9P(14), 13,18-9P(34) These systems all involve Henningsen’s proposal (2) of pumping from n 5 2 torsionally excited ground state levels to n 5 0 levels of the symmetric CH 3-bending mode. For the 9P(40) system, we confirm his assignment structure with the exception of the 136 cm 21 FIRL line, which goes to the (1,23,9) ri E lower level rather than the (1,21,9) ri E level originally proposed. However, the (0 4 2,22) sb E subband appears in our spectrum with an appreciable intensity that is more typical of an n 5 2 CO-stretch subband. As can be seen in Fig. 1, the calculated uKu 5 2, t 5 3 levels are quite close for the n 5 0 CH 3-bend and the n 5 2 CO-stretch modes; hence there may be significant anharmonic interaction and mixing. Thus, the vibrational identity of the pump transition is not clearcut, and it could have substantial (2,22) co E character giving enhanced strength through intensity borrowing. Henningsen’s picture for the 10R(16) system (2, 34) involves the (0,0) oh A/lo subband introduced earlier in the discussion of the 9P(22) system. We support his scheme in general, as seen from our energy level and transition diagram in Fig. 5, but have clarified an ambiguity between (1,0) co and (0,0) oh A lower laser levels and differ in our A 1 /A 2 labeling from that implied in Fig. 6 of Henningsen and Petersen’s IR-microwave double resonance study (34). The latter shows pumping from the lower component of the (2,1,10) gr A Kdoublet which would be an A 1 transition, opposite to our A 2 assignment with the upper component in Fig. 5. It is not clear from Ref. (34) whether the double-resonance results definitely establish that the pumping must be from the lower doublet component, but this is evidently a crucial question for the system assignment. In going from our n 5 2, K 5 1 A 2 upper pump level to K 5 0 A 1 lower laser levels, the A 6 selection rules permit only Q-branch transitions for Dn 5 0 but only R and P transitions for Dn 5 1. Thus, as shown in Fig. 5, the b-type FIRL lines divide unambiguously between the (1,0 1) co and (0,0 1) oh lower states which, contrary to previous sugges-

FIG. 5. Schematic energy level and transition diagram (not to scale) for the CH 3OH far-infrared laser system optically pumped by the 10R(16) CO 2 laser line at 219 MHz offset. The n 5 0 and 1 ground state energies are obtained from the model of Ref. (8); n 5 2 energies are taken from Ref. (4) with an 0.1314 cm 21 zero-point energy adjustment to match with Ref. (8). The K doubling in the K 5 1 upper-pumped state is inverted relative to the normal A 1 /A 2 ordering.

tions (2, 34, 44), cannot mix because they are of different parities. An interesting and unexplained anomaly for this system is that the K doubling in the upper (0,1) sb A state starts out with the normal A 1 /A 2 ordering, increases up to J 5 3, but then turns over and inverts by J 5 6. As well, we still have the existence of two K 5 0 subbands, (0,0 1) oh A/hi and (0,0 1) A/lo, to account for. For the 13-9P(14) and 13,18-9P(34) systems, the upper state identity is not yet clear. Both pump absorptions belong to a subband with very peculiar behavior that we can only follow from J9 5 11–22 and which deviates sharply at either end of this range from the normal regular trend. The combination differences in this abbreviated subband confirm the lower state to be (2,3) gr A within the assigned J range, but for intensity and other reasons we believe the upper state might well be (2,3) co A rather than (0,3) sb A. (These K 5 3, t 5 1 levels are very close in Fig. 1.) However, it is then difficult to account for the IR–RF double resonance signals observed by Petersen (39) for the 13-9P(14) system, given the small K doubling expected for an n 5 2, K 5 3 A upper state. Thus, there are unexplained anomalies for these two systems as well, concerning

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the nature of the upper pumped state and the odd character of the pumping subband. 10R(34) 2 30 A pump assignment of P(1,23,27) co E proposed earlier for this system (5, 6, 20), although plausible in several respects, has turned out to be wrong. The correct P(0,9,27) co A pump assignment had escaped prior detection due to level-crossing resonances between the (0,9) and (1,5) A levels in both excited and ground vibrational states (11, 49). Perturbations occur first in the excited state as the interacting levels approach each other with increasing J; we have determined the [(1,5) co–(0,9) co] separations to be 0.133 and 0.184 cm 21 for J9 5 25 and 26, respectively. As the levels start to converge in the ground state at higher J, however, the shifts become quite erratic and we lose track of the subbands in the spectrum. Note that the (0,9) co levels are also pumped by the 18-9P(22) isotopic CO 2 line at J9 5 24 (37), at which point the perturbation is just appearing.

assignment and the a-type laser wavenumber are supported by our observations for the (0,4) oh A subband. For the third 9SR(9) system, the FIRL line assigned here is a companion to two related transitions identified in our previous work (35). 18-10R(16) The 18-10R(16) pump absorption belongs to a subband that we assign as (1,25) co E, whose lines are shown as unidentified in the spectra of Moruzzi et al. (4). Their choice for the (1,25) co E subband derives from pump assignments originally proposed for the 9P(14) 2 35 and 9P(24) 1 0 systems (22) but, as discussed above, we now believe those pump transitions belong to the (0 4 1,25) oh E subband. With our present assignment, the pattern calculated for the reported FIRL triad is consistent with the observations in Table 1, although with relatively large discrepancies between observed and calculated wavenumbers for the two transitions down to (1,24) co E levels.

10R(10) 1 100 Although this system is well understood in general, there is some confusion and inaccuracy in the literature. Correct assignments were presented originally by Mollabashi et al. (20) and Carelli et al. (23). However, the transition diagram in the latter is ambiguous and all reports have too low a wavenumber for the 80 cm 21 FIRL line (4 – 6). The problem arises from (0,4) co E spectral misassignments due to a strong level-crossing resonance between J9 5 31 and 32. This perturbs the (0,4,32) co E level downward by 20.25 cm 21 and so raises the wavenumber of the 80.2 cm 21 FIRL line significantly. The (0,4,33) co E level is also downshifted by approximately 20.14 cm 21, hence we give a revised prediction in brackets in Table 1 for the potential 27.7 cm 21 FIRL transition. 9SR(9) and 9SP(13) Three different systems are pumped by the 9SR(9) sequence-band CO 2 line at similar offsets, but all reported FIRL lines have now been assigned. The first system involves the b-type (1,1 3 2) ri E subband, which is also pumped at a different J value by the 9SP(13) CO 2 line. We have discovered that the (1,1) ri E upper levels of this subband lie just below the (1,2) co E levels, with a separation of only about 1 cm 21 at low J. There appears to be substantial (1,1) ri/(1,2) co Coriolis mixing, which no doubt contributes to the anomalous Stark behavior of the (1,2) co E levels (43). The FIRL triad for the 9SP(13) system is well fitted by our calculations in Table 1, confirming the pumping subband identification. The pump transition for the 25.5 cm 21 FIRL line in the second 9SR(9) system, speculated earlier (35) to be a Q(16) ri line, is now assigned instead as R(0 4 1,4,15) oh. This nominally forbidden Dn 5 1, DK 5 0 transition is induced through strong anharmonic coupling between n 5 0 OHbending and n 5 1 CH 3-rocking modes (11). Both the pump

VI. DISCUSSION AND CONCLUSIONS

In this work, we have applied results from recent analysis of the Fourier transform infrared spectrum of CH 3OH to the assignment of the energy level and transition systems for optically pumped FIR laser lines. In all, 45 IR-pump/FIR-laser transition systems are considered in this paper, with new information on a variety of aspects of the assignments for 115 reported FIRL transitions. In addition to presenting 40 new line identifications, we have partially reassigned or extended the quantum number labeling for a number of other lines and have obtained rigorous spectroscopic support for previous unconfirmed assignments. With respect to the latter, we looked carefully at the 53 FIRL transition identifications appearing with question marks in the recent review by Moruzzi et al. (4) and were able to contribute new information for 34 of them. We believe that 21 are now well established spectroscopically while 13 still have unresolved details so they retain their question marks in our table. Many of the energy level and transition schemes for the new or reassigned systems involve unconventional pump absorptions, vibrational perturbations, and intermode FIR laser lines and so are very interesting spectroscopically. As suggested by the vibrational energy picture of Fig. 1, there is extensive coupling and mixing among the excited torsion–vibration states making identification of the precise vibrational character of the pumped levels a significant challenge in a number of cases. For example, the n 5 2 CO-stretch levels lie in the same energy region as the n 5 0 CH 3-deformation state, and we believe that the pumped levels for one or more of the systems identified as CH 3 deformation could well be mixed states better described as n 5 2 CO stretch instead. Several previous questions about the CH 3OH energy level structure in the excited vibrational manifold have been fully or

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ASSIGNMENT OF FIR LASER EMISSION FROM CH 3OH

partially resolved. For the 9P(14) and 9P(24) systems, we have reassigned the pumped levels to Fermi-mixed (0,25) oh/ (1,25) co E states and explained the postulated “hybrid (1,25) h E doublets” (22) as due to (0,24) oh E levels lying very close below the (0,25) oh/(1,25) co E levels. For the 9P(22) system, reassignment of the pumped level to a K 5 0 state removes previous problems with anomalous K doubling (2) by identifying the lower laser levels as widely split K 5 1 doublets rather than K 5 2. The puzzle of the 10R(20) assignment (33) has been solved with the discovery of a J-localized levelcrossing resonance between the (0,1 2) ri and (0,4 2) co A states which perturbs the pumped level and strongly modifies the (0,4) co K doubling. In the 10R(16) system, we have clarified ambiguity between (1,0) co and (0,0) oh A lower levels for the FIRL lines (2, 4, 34). In the 9SR(9) system, near degeneracy and strong mixing were discovered between the (1,1) ri and (1,2) co E states, which may account for the strange Stark effects observed for the latter (43). However, as each spectroscopic puzzle is solved for CH 3OH, another takes its place and numerous mysteries still remain. The new insights into the 9P(22) and 10R(16) systems come at the cost of having to explain the existence of two states, (0,0) oh A/hi and (0,0) oh A/lo, both of which appear to have similar characteristics. The 10R(16) system also presents the enigma of inverted K 5 1 doubling in the (0,1) sb A pumped state. In the 9P(10) system, we still need to identify the source of the vibrational coupling leading to the hybridized (1,6) h E state (2), as well as the interaction partners for a number of localized level-crossing resonances in other systems. The mystery of a nearby hybrid partner has also surfaced for the (2,5) co A levels in the 9P(26) and 13-9R(26) systems. It seems fair to say that, while the methanol molecule may gradually be lifting the veils on its secrets, it continues to guard them well and to display remarkable resilience in posing challenging problems for spectroscopic study. In conclusion, the present results represent significant progress in interpreting the FIRL emission observed from optically pumped CH 3OH, covering interesting new states and a wide variety of torsion–vibration interactions. While several formerly puzzling features of the FIRL transition systems have been explained, new mysteries have arisen. Thus, the IR spectra and FIRL observations from CH 3OH continue to provide fertile territory for spectroscopic exploration and motivation for further detective work in the ongoing effort to identify observed FIR laser lines. ACKNOWLEDGMENTS Financial support for this research from the Natural Sciences and Engineering Research Council of Canada and the University of New Brunswick Research Fund is gratefully acknowledged. We thank J. T. Hougen for interest in this project and partial financial support from the U.S. Department of Energy. We also express our appreciation to J. W. C. Johns and Zhengfang Lu of the Steacie Institute for Molecular Sciences for assistance in obtaining the high-resolution methanol Fourier transform spectra.

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