On the Assignment of Optically Pumped Far-Infrared Laser Emission from CH 3 OH

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Journal of Molecular Spectroscopy196,220–234 (1999)Article ID jmsp.1999.7876, available online at http://www.idealibrary.com on

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On the Assignment of Optically Pumped Far-Infrared Laser Emissionfrom CH3OH

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 CH3OH in the 930–1450 cm21 region has led to assignments,confirmations, or new insights for a number of far-infrared laser (FIRL) transition systems optically pumped by CO2 lasers.Many of the systems involve FIRL transitions among the CO-stretching, CH3-rocking, OH-bending, and CH3-deformationvibrational 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 harisen. Altogether, 45 CH3OH IR-pump/FIR-laser systems are examined in light of the new spectroscopic information; abouthalf of the system assignments are new and half have been previously reported in the literature and are here confirmextended, or revised.© 1999 Academic Press

Key Words:far-infrared laser; methanol; infrared spectra; internal rotation; torsion–vibration interaction; optically pumpedlasers.

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I. INTRODUCTION

This work reports assignments, confirmations, or newights for a variety of optically pumped far-infrared laFIRL) transition systems of CH3OH. The results are basedecent progress in the analysis of high-resolution Fourier torm infrared (IR) spectra of normal methanol in the 930–1m21 region.Since the first discovery of FIRL emission from CH3OH in

970 (1), observations of FIRL lines have provided importindows into the torsion–rotation structure of the excitedrational energy manifold of methanol. Traditionally, mos

he FIRL emission has been associated with IR pumping itrong CO-stretching band, but growing numbers of transystems are being found to involve levels of the CH3-rocking,H-bending, and CH3-deformation modes as well (2–4).Current understanding of the FIRL emission from CH3OH is

ummarized in several recent reviews (4–7). A substantiaraction of the catalog of known FIRL lines is now assignnd most of the proposed IR-pump/FIR-laser system ideations have been spectroscopically checked. Howeveystem assignments were still reported with question marhe latest compilation by Moruzziet al. (4), so had not beeigorously confirmed. Over half of these involve the non-Ctretch vibrational states mentioned above, providing aional motivation for the present work in investigatingeaker spectral bands associated with these modes.In this paper, we examine assignments of reported F

mission from CH3OH, utilizing our newly established Ipectroscopic data together with accurate calculationround state energies (4, 8). Many of the transition system

220022-2852/99 $30.00opyright © 1999 by Academic Pressll rights of reproduction in any form reserved.

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nvolve FIRL transitions between different vibrational stao provide particularly important signposts for the IR spessignments. In Section II of the paper, a brief discussion oH3OH torsion–vibration energy structure and IR spectriven. Our new FIR-laser information is presented in Sec

II, with a listing of the assigned IR pump and FIRL-transituantum numbers along with FIRL wavenumbers derivedccuracy of60.001 cm21 from spectroscopic combinatioifferences. We review features of interest for the pumpitions in Section IV, followed by comments on specific sems in Section V highlighting details of particular signance. Energy level and transition diagrams with suppopectroscopic data are shown for four of the systems torate confirmation of the transition schemes through combion loops as well as the extensive coupling among diffeorsion–vibration states via the FIRL emission. The paoncludes in Section VI with a summary of the resultsemarks on interesting spectral anomalies and unsolvedions about the CH3OH vibrational energy structure whiave been revealed by the assignments.

II. CH3OH TORSION–VIBRATION ENERGIESAND INFRARED SPECTRA

The notation adopted in this work is as follows. An eneevel is denoted asE(n, K, J) v Ts, wheren is the torsionauantum number,K is the component of rotational anguomentumJ along the moleculara axis, v is the vibrationa

tate, andTs is the torsional symmetry.Ts is eitherA or E, withositive K values corresponding toE1 levels and negativeKalues toE2 levels (9). ResolvedK doublets ofA symmetry

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221ASSIGNMENT OF FIR LASER EMISSION FROM CH3OH

ave an additional1/2 superscript onK to distinguish theA1

r A2 component of the doublet (10). The vibrational statabels (4) arev 5 gr for the ground state,v 5 co for the COtretch,v 5 ri for the in-plane CH3 rock, v 5 ro for theut-of-plane CH3 rock,v 5 oh for the OH bend, andv 5 sb for

he symmetric CH3 deformation (“umbrella bend”) mode.CH3OH has an interesting torsion–vibration energy struc

n the region of the bending vibrations and the CO stretch,any possibilities for torsion-mediated coupling amongodes. Perturbations and state mixing induced by suchling have proven to be important with respect to FIRL emion in CH3OH (11). PotentialDK 5 0 Fermi-type interactionan be seen from Fig. 1, in which calculatedK-reduced tor

FIG. 1. CalculatedK-reduced torsion–vibration energy curves for there calculated with a barrier height of 557 cm21 (12); all others employ the

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ion–vibration energies are plotted against rotationalK valuen Dennison’s t curves (13) for various torsion–vibratiotates. Thet index is an alternative torsional symmetry laelated toTs by the rule [12 (t 1 uKu)mod 3] 5 0 for Aevels,11 for E levels withK . 0, and21 for E levels with

, 0 (10). When curves of the same symmetry approachther, anharmonic resonances lead to energy perturbationvoided crossings (14). Figure 1 shows there are likely toignificant resonances betweenn 5 0 levels of the OH benndn 5 1 levels of the CO-stretch and CH3-rock modes, anetweenn 5 0 levels of the CH3 symmetric bend andn 5 2

evels of the CO stretch and CH3 rock. The origin of the knowermi resonances coupling the (n, K) vTs 5 (0,0)coA t 5 1

er vibrational modes of CH3OH. Curves for the in-plane (ri) CH3-rocking modeund state value of 373 cm21 (10).

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222 LEES AND XU

nd (0,25)co E t 5 3 CO-stretch levels with high-lyingn 5and n 5 4 ground state levels (14) is also evident from

ig. 1.In addition to theDK 5 0 anharmonic resonances, there

lso Coriolis and asymmetry-induced resonances whichouple near-degenerate levels of differentK (11). Here, Heningsen’s “X-state” Coriolis resonances strongly mixing0,5)co A with the (0,4)ri A state and the (0,7)co A with the (0,6)ri

state are the best-known examples (15). WeakerJ-localizedevel-crossing resonances withuDKu . 1 can also arise wheevels of givenK of one torsion–vibration state start out at ljust above levels of differentK of a second state with a larg

otationalB value. With the higherB value, the levels of thecond state will rise faster withJ and eventually cross ovhose of the first. Substantial perturbations and state-m

TABAssignments, Confirmations, and New Information for C

a Pump wavenumbers in brackets are calculated from combinationb IR pump lines areDn 5 0, DK 5 0 a-type transitions unless otherw

r or p prefix, respectively. Transitions withDn 5 21 or Dn 5 22 are s2 pump transition is shown asK 5 2 4 0.

c The vibrational label h for the 9P(10), 9P(26), and 13-9R(26) systeidentity yet to be established; the labels hu and hd refer to upper anddifferent (0,0)oh A states, labeled as (0,0)oh A/hi and (0,0)oh A/lo, respectiv

d Relative polarizations in brackets are not observed but predictede Loop wavenumbers in brackets have reduced accuracy due either

J using spectroscopic combination differences, or inclusion of smallf Assignment code is: N, new; C, confirmed; R, revised; I, extendeg Mean wavenumber of closeK-doublet line pair; predicted splittings

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 o


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an then occur for severalJ values in the vicinity of thevel-crossing point.

III. FIR-LASER SYSTEM ASSIGNMENTS FOR CH3OH

The results obtained in this work on new assignmeonfirmations, or further insights for IR-pump/FIR-laser trition systems of CH3OH are presented in Table 1. Our sproscopic analysis has provided additional support for manhe other system assignments already established in theure, but only those systems for which specific new informaas been obtained are discussed in the present paper. Wlso that, along with the new system identifications, weeadily generate accurate wavenumber predictions for nuus unreported but potentially observable FIRL lines defi

1

3OH FIR Laser Lines Optically Pumped by CO2 Lasers

ferences or as the CO2 laser wavenumber1 offset.indicated;uDKu 5 11 or 21 b-type transitions are denoted by a superscripn asn 5 0 4 1 andn 5 0 4 2; for the 9P(16)–56system, theDK 5

indicates levels believed to be hybridized, with the exact torsion–vibrawer components of a hybrid doublet. The 9P(22) and 10R(16) systems involve. [See text.]

overlap of IR transitions, extrapolation of excited or ground state energiulated highK doublet splittings.ith new information; ?, still not fully confirmed spectroscopically.0.0015 cm21 for the 9P(36) 1 184 system, and 0.0036 and 0.0069 cm21 for

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TABLE 1—Continued

Copyright © 1999 by Academic Press

224 LEES AND XU

TABLE 1—Continued


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y all of the many possible transitions allowed by the selecules. We have refrained from including these predictions hut they can be made available on request.In Table 1, the FIR-laser systems are listed by decreaavenumber of the pump line, first for normal CO2 pumping,

hen sequence and hot-band pumping, and lastly for isoO2 pumping. The CO2 pump line is given in the first columith offset in megahertz where known, followed by the waumber of the IR pump absorption as determined frompectrum. Where this pump absorption was not clearlyolved, thenpump value was calculated either from combinatifferences or from the CO2 laser wavenumber plus offset a

s shown in brackets in Table 1.The following five columns contain the IR pump assients, the FIRL transition assignments, the reported Favenumbers, the relative polarization of the IR and

adiation, and the spectroscopic FIRL wavenumbers dined from combination loop relations using our observeata together with accurate ground state energies (4, 8). These

oop wavenumbers are estimated conservatively to havccuracy of60.001 cm21. For some cases in which we hadxtrapolate either the IR series or the ground state eneeyond their measured ranges, generally by using combinifferences, the resulting FIRL loop wavenumbers are ouced accuracy and are shown in brackets.The next column gives an assignment code, in whicN

enotes a new assignment,R a revised assignment,I a previousartial assignment with additional information given here (ss theA1 or A2 K-doublet labeling), andC a confirmation oknown assignment for which a rigorous spectroscopic c

ad not been previously available. A question mark in the Column indicates that some aspect of the assignment isncertain, often involving the exact torsion–vibration idenf the upper level of the laser transition. The final two coluive references for the best reported experimental waveers and previous assignments. Most of the sources areere directly, but the reader is also directed on occasion teviews of the FIRL literature in Refs. (4–7) for references the original reports.

IV. FEATURES OF THE IR-PUMP TRANSITIONS

Studies of the IR spectrum and FIR-laser emissionH3OH are relatively mature, so that new system assignmow tend to involve interesting and unexpected aspects o

orsion–vibration energy manifold. It can be seen in Tabhat a wide variety of IR-pumping transitions is responsiblehe FIRL emission discussed here, ranging over highJ andorsionally excited CO-stretch transitions, botha- andb-typeH3-rocking transitions, and OH-bending and CH3-deforma-

ion transitions of nontraditionalDn 5 1 andDn 5 2 typesikely arising from state mixing. In a number of cases,umping line is shifted from its expected position by perations in the excited state due to anharmonic resonances


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ubband-wide Coriolis resonances, or smallerJ localized resnances. The perturbed spectral subbands involving the

eractions are often difficult to identify with confidence, hehe FIRL systems can give crucial information for the speccopic assignments. Several CH3OH torsionally excited subands were assigned in this work directly through the crovided by the FIRL pumping. Analysis of the perturbati

eads to important information about the channels for viional coupling among the various modes, notably for thnteractions mediated by changes in torsional state. The df the spectroscopic results associated with these systemutlined only briefly here, but will be treated more fully

uture separate communications describing the spectral aes.

V. FEATURES OF SPECIFIC CH3OH FIR-LASERSYSTEMS

As discussed above, new FIRL assignments now frequnvolve novel insights into the excited state energy struchus, in the following we present comments on the specopy and background for specific FIRL systems, groupeommon features where appropriate, to show the basis fossignments along with other relevant details. To illusombination–loop confirmation of the assignments, weive four examples of energy level and transition diagram

he FIRL systems with spectroscopic data included. In tiagrams, individual FIR transitions between the ground

evels no longer need be shown because the groundnergies are now available directly from recent accurate talue analysis (4) and global-fit modeling (8), simplifying theoop procedure.

R(34)

The R(0,0,45)co E absorption pumped by the 9R(34) CO2

ine is close to the highJ limit of detectability for the COtretch band in our present spectrum. The observed IR liverlapped, hence the pump wavenumber is given in bra

n Table 1. The ground state energies were extrapolated5 45 with the use of [R( J) 2 P( J 1 2)] IR combinationifferences. With only a single FIRL line, the assignmen

entative, and a question mark is included in the assignode. Observation of the (n, K, J) v 5 (0,0,46)co 30,0,45)co E a-type FIRL line at a calculated wavenumber1.821 cm21 would confirm the system identification.

R(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’sX-state Coriolisesonances coupling the (n, K) v 5 (0,4)ri, (0,5)ri, and (0,6)ri Atates of the CH3 rock with the (0,5)co, (0,6)co, and (0,7)co Atates of the CO stretch, respectively (15). Because we couesolveK doubling in relevant subbands linking to the (0,3ri,

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226 LEES AND XU

0,4) , (0,5) , (0,5) , and (0,6) states, we were able to estaish theA1 andA2 labeling for the 9R(32), 9R(12), 9P(44),nd 10R(34) systems. The splittings for the (0,5)ri, (0,5)co, and0,6)co A states are much larger than the ground state vahile the (0,5)co K doublets are inverted, likely due to strooriolis mixing with the (0,4)ri levels.For the 9R(30) system, therR(0,6,9)co A pump line was

ound originally by combination-difference prediction fromnown (0,7)co subband, for which the (0,7)co A upper levels artrongly hybridized with the (0,6)ri A levels due to the Coriolixing. Combination differences were also the source o

pQ(0,61,32)ri A wavenumber which led to the assignmenhe 9P(44) system. This highJ Q-branch pump transitionot directly visible in our spectrum.For the 9R(12) system, theK doubling of the (0,3)ri A lower

evels of the FIRL transitions is sufficient to tie down1/A2 labeling and establish that the upper pumped levele (0,41,19)ri A. The Q-branch pump transition is therefo1 4 A2. The 6 labeling is also well determined for t0R(34) system pumped at246 MHz offset. The three FIR

requencies have all been accurately measured by heterechniques, and Table 1 shows the loop-calculated waveers to be in close agreement. This agreement would haveisibly affected if the experimentalK doubling of 0.0044 cm21

or the (0,5,25)ri A levels, for example, had not been accounor in the loops.

The 9HP(18) system assignment was previously basedpproximate wavenumbers (35), but observation of the (0,3ri

ubband has now supplied confirming values. Since the (ri

symmetry splitting will only be about 3 MHz atJ 5 14, both1 andA2 upper state levels will be pumped by the 9HP(18)O2 line. Thus, each of the two reported FIRL lines shoctually be a close pair split by theK doubling of the (0,3)ri

ower levels. Calculated wavenumbers for the centers oairs are given in Table 1 with the predicted splittings inclu

n a footnote.

R(28), 9R(20)2 140, and 10R(20)1 147

These systems involve pumping from (n, K) v 5 (0,4)gr Around levels. In the 9R(20) system, the (0,2)ri A state had noeen spectroscopically observed earlier and the FIRL tranown to the (0,21,16)ri A level was the key to identifying Iubbands to that state and thereby confirming the systeignment.The 10R(20) system has been an elusive problem for s

ime (20, 23, 32, 33), but we have finally succeeded in nailit down. Despite opinion to the contrary (33), the FIRL emision does arise from the CO-stretching state, occurring thrn unsuspected perturbation. As was originally surmised20,2), it is the P(0,4,31)co A absorption which coincides wi

he 10R(20) CO2 line but theA2 rather than theA1 compo-ent is pumped, opposite to the earlier proposal (20). Theifficulty with this system arises from aJ-localized level


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rossing resonance in which the (0,1) A levels rise fromelow and cross over the (0,42)co A stack betweenJ9 5 28 and9. (The analogous level crossing occurs for13CH3OH (42) butetweenJ9 5 21 and 22 for theA1 component.) Due to therturbation, the (0,42,30)co A level is shifted downward bbout 0.018 cm21, resulting in aK-doublet splitting of 0.08m21 for J 5 30. This is larger than expected and explainsailure to observe a triple resonance signal below 2 GHz32).

R(26)1 25

The (0,11)co A pumping subband for this system is locaerturbed aroundJ9 5 35, and theR(34) andP(36) membersre split due to an interaction with an unknown partner.ere able to pick up theR subbranch again after the pertation and follow it through the coincidence with the 9R(26)O2 line at R(39). Petersen and Henningsen report anbsorption at 25 MHz offset in their laser–Stark study (43) andssign it as theR(0,2,38)co E transition. However, this doeot seem consistent with our results so far for the (0,2)co Eubband, although we have only been able to follow thRubbranch up toR(37) andthere are signs of perturbationhat point.

R(24)1 6

This system is not fully confirmed because we have noound subbands connecting to the (0,23)ri E rocking statehus, the identity of the upper pumped level cannot be d

tively checked. However, our results accurately locate0,22)ri E levels and confirm the lower level assignmentshe two FIRL lines in Table 1 with the use of the IR puavenumber determined from the CO2 line plus offset. Theood agreement between reported and calculated FIRL wumbers shows the high quality of Henningsen’s more caavelength measurements (2).So far, we have been unable to shed any light on the l

orsion–vibration state for two further FIRL lines at 28.771.62 cm21, which were given the same rotational assignmy Henningsen (2) as the 21.72 and 34.58 cm21 pair in Table. The lower levels for these lines must lie 7.04 cm21 below

heir (0,22)ri E counterparts, placing them only 0.84 cm21

elow the (0,1)ri E levels of correspondingJ on the basis of oupectral data. Thus, their identity is an intriguing mystery

R(16)2 8

The assignment for this system was originally proposeollabashiet al. in 1987 (20) but was not included in previou

eviews (4–6). However, in the present work, we have reviigh J assignments for the (1,26)co E subband, modifying thalculated FIRL wavenumbers. Our current calculated wumber for the 52 cm21 FIRL line is in excellent agreemeith the recent frequency measurement by Carelliet al.(19), aseen in Table 1, confirming the system identification.ssignment of the refilling transition in the ground stat

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R(10)1 52, 9P(16)2 56, 9SP(21)1 16, 9HR(23), and9HP(13)

These systems each involve in some way the “gianKoubling” caused by interaction between the (1,21)ri and1,01)co A substates (44, 45). Only onea-type FIRL line iseported for the 9R(10) 1 52 MHz system, but its wavenumer is sensitive to the anomalousK doubling and the assigent appears solid. For the 9P(16)–56 MHzsystem, the pum

s reassigned to the perturbation-inducedR(1,24 0,16)ri A1

ransition (44) but Henningsen’s original identification of tower laser levels is correct (22). Here, the accurate frequen

easured by Zerbettoet al. (26) for the 238.8 cm21 FIRL lineas the initial clue to finding the (0,1)ri A subbands in thpectrum and thereby confirming the assignment for thator the 9SP(21) system, the influence of the giantK doubling

s indirect, with the wide splitting of the (1,2)ri A doubletsartially fed through the (0,2)oh A levels by anharmonic Fermoupling and inverting the normalA6 ordering (44). The pumpssignment is confirmed by the close agreement for the 1m21 FIRL line in Table 1 between calculation and frequeeasurement (with correction of a typographical error for

requency in Ref. (7)). However, an unexplained 0.385 cm21

iscrepancy for the 173 cm21 line still leaves some questiobout the (0,2)oh A level identification. For the 9HR(23) sys-

em, the pumping occurs within the same (1,21)ri A stack as foR(10) 1 52 MHz, with lasing down to the CO-stretchiode as found for the 9P(16) system (2, 22, 24). Lastly, the

HP(13) system samples the other side of the giantK-dou-ling interaction since it is the partner (1,01)co A levels that ar

nvolved.

R(10)1 3

This system is doubly perturbed, in that the (0,9)co E levelshow a smallJ-localized level-crossing resonance betweeJ9

26 and 27, while the (0,10)co E levels have a similar buarger resonance betweenJ9 5 24 and 25. The interactioartners have not been identified in either case. The cuences for the FIRL system are that the (0,9,26)co and0,9,27)co E levels are perturbed by20.001 and10.009 cm21,espectively, while the (0,10,25)co, (0,10,26)co, and (0,10,27)co

levels are downshifted by approximately20.168,20.076,nd20.043 cm21. Nevertheless, the agreement between mured and calculated FIRL wavenumbers in Table 1 showshe IR assignments are under control. A minor change forystem reassigns theJ 5 263 25 cascade transition at 41.m21 as K 5 9 instead of the previousK 5 10 (4–6, 24).ith the perturbations, theK 5 10 line would lie 0.082 cm21

igher than theK 5 9 line, hence we believe ourK 5 9ssignment in Table 1 better matches the reported waveer.


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R(8)1 28

This system was originally assigned by Petersen thrR–IR double-resonance experiments (25). Although we haveot yet succeeded in identifying the (0,213)co E pumpingubband, the CO2 pump wavenumber plus the known frequies for the two FIRL lines serve to accurately locate theJ9 55 and 26 levels of the (0,212)co E state. With this informa

ion, we were then able to find and follow the (0,212)co Eubband and confirm Petersen’s assignments.

R(2)1 25

This system has been well understood from Henningsriginal work (22), but an incorrect calculated wavenumberersisted in the literature for the particular 94.8 cm21 FIRL line

n Table 1 (4–6). Since the frequency of this line was acately measured by Zerbettoet al. recently (26), we decided tonclude it here to show that our present loop calculation agith the measurement. Four other FIRL lines are known

his system (22, 26) and are correctly reported in the literat4–6, 46).

P(6) 1 73

The (2,7)co A subband is highly perturbed forJ9 . 12 ande lose track of it aboveJ9 5 16. Fortunately, theQ sub-ranch is strong and well isolated so permits confident idcation of the subband at lowJ. The consistency betwebserved and calculated FIRL wavenumbers gave cruciaort for the IR assignments in the perturbed region forystem.

P(10)1 63

In the assignment put forward by Henningsen for this sys2), lasing was proposed from the (2,7,11)co E pumped leveown to hybridized (1,6,11)h and (1,6,10)h E levels, with a

urther cascade from the latter down to the (1,5,9)co E level.e have identified both the (2,7)co and (1,6)h E subbands in th

pectrum so we can confirm Henningsen’s energy levelransition scheme. However, as he notes, the origin fo1,6)h E subband is anomalously high forn 5 1 CO-stretchubstates, and in fact is more consistent with then 5 0 OHend. So far, we too have been unable to pin down theibrational identity of the (1,6)h levels.

P(14)2 35 and 9P(24)1 0

Both of these spectroscopically rich systems involveifferent vibrational states in the FIRL emission. The b

ransition schemes were correctly set out by Henningseith some uncertainty about the vibrational modes invo

22). We have been able to clarify the vibrational labehrough our OH-bending results and have revised the asents as shown for the 9P(24) system in Fig. 2.The keys to the reassignment were the discoveries firs

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228 LEES AND XU


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e tp

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9

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d(w asa ith


he pump absorptions for the two systems, which hadssigned in the literature (2, 4, 22) as (1,25)co E transitionselong to a subband with the same upper state as the (0,25)oh

subband, and second that the (0,24)oh E levels lie only 2m21 below the (0,25)oh E levels. Our assignments for t1,25)co E levels then put them just 2 cm21 further below, sohat they are expected to perturb and mix with the (0,25)oh Eevels. With these observations, we could then assign theransitions to the perturbation-induced (0,25)oh 4 (1,25)gr Eubband and identify the lower partners of Henningsen’sulated hybridized pump doublets (22) as (0,24)oh E substateshe reassignment removes the troublesome requirementK 5 22 FIRL transition noted by Henningsen, as all tritions in Fig. 2 now follow the normal rotational selectules. Mixing among the close grouping of upper state leay also contribute to the anomalous Stark effects obse

or the pump transitions (25, 43).The FIRL assignments can be confirmed by compaavenumbers calculated by combination differenceslosed four-level loops in Fig. 2 against the accurate exental values given to five decimal places in Table 1, were derived from heterodyne frequency measurements18).or example, thea-type laser wavenumber La is given

ndependent loops containing IR wavenumbers and grtate energies from Fig. 2 as follows:

a 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 1043.16301 565.61812 580.09852 1014.2775

5 14.4051 cm21

a 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 1336.41171 272.36942 259.46752 1334.9085

5 14.4051 cm21.

he agreement between the two independent loop calculaor La and the precise observed value in Table 1, to well whe net spectroscopic uncertainty of60.001 cm21, serves toonfirm the assignments of both the FIRL line and theransitions in the loops. Analogous loop calculationseadily be carried out for other FIRL lines in Fig. 2 usingata included in the diagram. All loops give wavenumberxcellent agreement with the measured values in Tabxcept for line Lf, the (0,25)oh3 (1,24)co E transition at 108m21, for which there is a difference of 0.5 cm21. Currently, weave no explanation for this discrepancy, so we cannot d

tively confirm the Lf assignment.The other unconfirmed transitions for these systems ar

roposed FIRL lines connecting toro out-of-plane CH3-rock-


en

p

s-

r a-

lsed

g

ri-h

d

nsn

n

n1

n-

he

ng levels. Thero band is expected to be weak and haseen detected in our spectrum. However, the data in Taut thero band origin at around 1152 cm21, which correspondlosely to the values of 1155 cm21 calculated by Serrallachetl. (47) and 1151.4 cm21 by Cruzet al. (48) for certain choicef their force constants. The experimental band origineported (47) to be 11456 4 cm21, but our results suggest thhis feature in the low-resolution spectrum is more likely du

pileup of n 5 1 in-plane CH3-rocking andn 5 0 4 1H-bending subbands in that region.

P(22)1 17

This is another intriguing system involving the OH-bendode. We are confident of the transition structure and

ower pumped level, but the exact vibrational identity ofpper pumped level is still in question. Originally, the sche

entatively proposed by Henningsen had theP(1,12,19)ri Aransition as the IR pump (2), but our spectroscopic observions for the (1,1)ri A subband show that this transition doesoincide with the 9P(22) CO2 line. However, when calculang n 5 04 2 wavenumbers by combination differences fr

subband we had labeled as “(0,0)oh A/hi”, we found unexectedly that the predictedR(17) n 5 0 4 2 transitionoincided with the 9P(22) line, leading to the revised assigents shown in Fig. 3.The new scheme removes theK-doubling problem hinted a

y Henningsen (2) because the FIRL lines now terminate0,1)oh and (0,1)ro levels with largeK 5 1 asymmetry splittingather than the (1,2)ri and (0,2)ri levels suggested originalhich have much smallerK 5 2 doubling. Because the F

asing occurs to the outer members of the widely splitK 5 1oublets, as shown in Fig. 3, the line separations (Lc2 Lb) andLe 2 Ld) are significantly greater than expected for nor5 184 17 or 194 18 a-type transitions, explaining th

pparent anomaly. Note that theK 5 1 doubling is substanially smaller for the excited OH-bending state than the grotate, which is why the wavenumbers in Fig. 3 for(0,11,16)oh andR(0,12,17)oh A transitions are unexpectedlose.The A 1 3 2 labeling in Fig. 3 corresponds tob-type

ransitions for lines Lb and Lc, but toc-type for Ld and Lewhere thec axis is out-of-plane). This provides additionustification for our assignment ofA0 out-of-plane CH3-rock-ng lower levels for the latter, sincec-type rotational selectioules imply an A93 A0 vibrational transition. The positionshe presumed (0,1)ro levels in Fig. 3 are also consistent withand origin of 1152 cm21 proposed above for the out-of-plaocking fundamental.

The uncertainty in pump identity and the need for the “A/hi”esignation arise from the fact that, about 49.1 cm21 below the0,0)oh A/hi subband, there is a second (0,0)oh A/lo subbandhich also originates from the (0,0)gr A ground state, also hweakn 5 04 2 forbidden partner, and also is involved w

Academic Press

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230 LEES AND XU

IR lasing as described below for the 10R(16) system. Thepper state of this second (0,0)oh A/lo subband is just above t1,0)co A state, which itself is strongly mixed with the (1,2)ri A1

tate (44)! The identity problem would be resolved if the uptate of the (0,0)oh A/hi subband were actually the (1,0)ri Atate, which we still have not located, but this choice wohen contravene theA 1 3 2 selection rules in Fig. 3. Thuhere is an interesting mystery here which we have yenravel.

P(26)1 54 and 13-9R(26)

These two systems also lead to an enigma in the extate. The 9P(26) assignment (2) did not have direct spectrcopic support earlier, but that for the13-9R(26) systemalthough incorrectly reported in Refs. (4) and (5)), appeared te solidly confirmed (2, 38). Our spectroscopic results, hover, have revealed that the levels originally assigned as (co

have close hybridized companions lying just above,ubbands connecting to both partners from both (2,5)gr and2,4)gr A lower states! The startingJ values and relativntensities for the quartet of subbands suggest that at lowJ theower partner actually has greaterK 5 4 character, but wave not yet resolved this question and so will label the pa

evels for the moment as the (2,5)hu A “up” and (2,5)hd A

FIG. 3. Schematic energy level and transition diagram (not to scalehe CH3OH far-infrared laser system optically pumped by the 9P(22) CO2

aser line at 17 MHz offset. Then 5 0 and 1 ground state energies are obtarom the model of Ref. (8), n 5 2 energies are taken from Ref. (4) with an.1314 cm21 zero-point energy adjustment to match with Ref. (8). Identifica-

ions of the (0,0)oh A/hi and the (0,1)ro A excited-state levels are tentativeKoubling of theK 5 1 OH-bending levels is substantially smaller than forround state, hence the wavenumbers for theR(0,11,16)oh andR(0,12,17)oh

transitions are unusually close.


d

to

ed

)h

er

down” members of hybridized doublets. The vibratioource for aK 5 4 state in this vicinity is by no means cleThe transition picture for the two FIRL systems is illustra

n Fig. 4. The lower levels for lines Lb and Lc of the 1R(26) system are well established (2, 38) but the pump

dentity is now uncertain. The FIRL emission in the 9P(26)ystem is puzzling, as the best match with the reported wumbers is obtained with line Ld going to the upper compof theJ 5 6 doublet, but line Le going to the lower compon

or J 5 5. If the lower levels do have predominantlyK 5 4haracter, line Le would then represent aDK 5 22 transitionlso, we have found that the (1,7,7)co A level lies 7 cm21 too

ow to explain Henningsen’s assignment of FIRL line Lf (2),ut the (0,6,7)oh A level is a possible alternative candidate

P(36)1 184 and 10R(48)2 10

At first glance, these two systems would appear unrelut a level-crossing resonance couples the (2,4)co A and (1,7)co

states and provides an indirect link through perturbationhe FIRL pump absorption for 9P(36) and twopotential lase

FIG. 4. Schematic energy level and transition diagram (not to scalehe CH3OH far-infrared laser systems optically pumped by the 9P(26) CO2

aser line at 54 MHz offset and the13-9R(26) CO2 laser line. Then 5 0round state energy is obtained from the model of Ref. (8); n 5 2 and 3nergies are taken from Ref. (4) with an 0.1314 cm21 zero-point energdjustment to match with Ref. (8). The (2,5)h A upper (u) and lower (dxcited-state levels are components of hybrid doublets arising from metween the (2,5)co A state and an unidentified partner.

r

Academic Press

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ines for 10R(48). In the 9P(36) system, the upper level of th(2,4,21)co A pump transition is perturbed upward by ab.005 cm21 by the resonance. However, we determineoupling matrix element to be only 0.022 cm21, much smallehan the separation of 0.126 cm21 between the interactinevels forJ9 5 21, hence there is little state mixing. For0R(48) system, the (1,8)co A pumping subband is also pe

urbed starting aroundJ9 5 20, and we lose track of it in thpectrum aboveJ9 5 23. Although several FIRL lines aumped at similar offsets by 10R(48), we have so far onleen able to assign the onea-type line in Table 1, for which th

requency measurement of Vasconcelloset al. (30) gives conrmation. In particular, potential FIRL lines down to the purbed (1,7,22)co and (1,7,21)co A levels have not been rorted; we predict wavenumbers for these transition4.2932 and 79.4373 cm21, respectively.

P(40)2 11, 10R(16)2 19, 13-9P(14), 13,18-9P(34)

These systems all involve Henningsen’s proposal (2) ofumping fromn 5 2 torsionally excited ground state levels5 0 levels of the symmetric CH3-bending mode. For th

P(40) system, we confirm his assignment structure withxception of the 136 cm21 FIRL line, which goes to th1,23,9)ri E lower level rather than the (1,21,9)ri E levelriginally proposed. However, the (04 2,22)sb E subbandppears in our spectrum with an appreciable intensity thore typical of ann 5 2 CO-stretch subband. As can be s

n Fig. 1, the calculateduKu 5 2, t 5 3 levels are quite closor the n 5 0 CH3-bend and then 5 2 CO-stretch modeence there may be significant anharmonic interactionixing. Thus, the vibrational identity of the pump transitionot clearcut, and it could have substantial (2,22)co E characteiving enhanced strength through intensity borrowing.Henningsen’s picture for the 10R(16) system (2, 34) in-

olves the (0,0)oh A/lo subband introduced earlier in the dussion of the 9P(22) system. We support his schemeeneral, as seen from our energy level and transition dia

n Fig. 5, but have clarified an ambiguity between (1,0)co and0,0)oh A lower laser levels and differ in ourA1/A2 labelingrom that implied in Fig. 6 of Henningsen and PeterseR-microwave double resonance study (34). The latter showumping from the lower component of the (2,1,10)gr A K-oublet which would be anA1 transition, opposite to ourA2

ssignment with the upper component in Fig. 5. It is not crom Ref. (34) whether the double-resonance results definstablish that the pumping must be from the lower douomponent, but this is evidently a crucial question forystem assignment. In going from ourn 5 2, K 5 1 A2 upperump level toK 5 0 A1 lower laser levels, theA6 selectionules permit onlyQ-branch transitions forDn 5 0 but onlyRnd P transitions forDn 5 1. Thus, as shown in Fig. 5, t-type FIRL lines divide unambiguously between the (1,01)co

nd (0,01)oh lower states which, contrary to previous sugg


te

f

e

isn

d

m

s

ryt

e

-

ions (2, 34, 44), cannot mix because they are of differarities. An interesting and unexplained anomaly for this

em is that theK doubling in the upper (0,1)sb A state starts ouith the normalA1/A2 ordering, increases up toJ 5 3, but

hen turns over and inverts byJ 5 6. As well, we still have thxistence of twoK 5 0 subbands, (0,01)oh A/hi and (0,01)/lo, to account for.For the 13-9P(14) and 13,18-9P(34) systems, the upp

tate identity is not yet clear. Both pump absorptions belonsubband with very peculiar behavior that we can only fo

rom J9 5 11–22 andwhich deviates sharply at either endhis range from the normal regular trend. The combinaifferences in this abbreviated subband confirm the lower

o be (2,3)gr A within the assignedJ range, but for intensity anther reasons we believe the upper state might well be (co

rather than (0,3)sb A. (TheseK 5 3, t 5 1 levels are verlose in Fig. 1.) However, it is then difficult to account forR–RF double resonance signals observed by Petersen (39) forhe 13-9P(14) system, given the smallK doubling expecteor an n 5 2, K 5 3 A upper state. Thus, there are unlained anomalies for these two systems as well, conce

FIG. 5. Schematic energy level and transition diagram (not to scalehe CH3OH far-infrared laser system optically pumped by the 10R(16) CO2

aser line at219 MHz offset. Then 5 0 and 1 ground state energiesbtained from the model of Ref. (8); n 5 2 energies are taken from Ref.4)ith an 0.1314 cm21 zero-point energy adjustment to match with Ref. (8). Thedoubling in theK 5 1 upper-pumped state is inverted relative to the no

1/A2 ordering.

Academic Press

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232 LEES AND XU

he nature of the upper pumped state and the odd charache pumping subband.

0R(34)2 30

A pump assignment ofP(1,23,27)co E proposed earlier fohis system (5, 6, 20), although plausible in several respeas turned out to be wrong. The correctP(0,9,27)co A pumpssignment had escaped prior detection due to level-croesonances between the (0,9) and (1,5)A levels in both excitend ground vibrational states (11, 49). Perturbations occur fir

n the excited state as the interacting levels approach eachith increasingJ; we have determined the [(1,5)co–(0,9)co]eparations to be 0.133 and 0.184 cm21 for J9 5 25 and 26espectively. As the levels start to converge in the groundt higherJ, however, the shifts become quite erratic and

ose track of the subbands in the spectrum. Note that the (co

evels are also pumped by the18-9P(22) isotopic CO2 line at9 5 24 (37), at which point the perturbation is just appear

0R(10)1 100

Although this system is well understood in general, theome confusion and inaccuracy in the literature. Correcignments were presented originally by Mollabashiet al. (20)nd Carelliet al. (23). However, the transition diagram in t

atter is ambiguous and all reports have too low a wavenuor the 80 cm21 FIRL line (4–6). The problem arises fro0,4)co E spectral misassignments due to a strong level-croesonance betweenJ9 5 31 and 32. This perturbs th0,4,32)co E level downward by20.25 cm21 and so raises thavenumber of the 80.2 cm21 FIRL line significantly. The

0,4,33)co E level is also downshifted by approximately20.14m21, hence we give a revised prediction in brackets in Tfor the potential 27.7 cm21 FIRL transition.

SR(9) and 9SP(13)

Three different systems are pumped by the 9SR(9) se-uence-band CO2 line at similar offsets, but all reported FIR

ines have now been assigned. The first system involve-type (1,13 2)ri E subband, which is also pumped aifferent J value by the 9SP(13) CO2 line. We have discovred that the (1,1)ri E upper levels of this subband lie juelow the (1,2)co E levels, with a separation of only aboum21 at low J. There appears to be substantial (1,1)ri/(1,2)co

oriolis mixing, which no doubt contributes to the anomaltark behavior of the (1,2)co E levels (43). The FIRL triad for

he 9SP(13) system is well fitted by our calculations in Ta, confirming the pumping subband identification.The pump transition for the 25.5 cm21 FIRL line in the

econd 9SR(9) system, speculated earlier (35) to be aQ(16)ri

ine, is now assigned instead asR(0 4 1,4,15)oh. This nom-nally forbidden Dn 5 1, DK 5 0 transition is inducehrough strong anharmonic coupling betweenn 5 0 OH-ending andn 5 1 CH3-rocking modes (11). Both the pump


r of

,

ing

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.

iss-

er

ng

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he

s

ssignment and thea-type laser wavenumber are supportedur observations for the (0,4)oh A subband. For the thirSR(9) system, the FIRL line assigned here is a companiowo related transitions identified in our previous work (35).

8-10R(16)

The 18-10R(16) pump absorption belongs to a subbande assign as (1,25)co E, whose lines are shown as unidentifi

n the spectra of Moruzziet al. (4). Their choice for the1,25)co E subband derives from pump assignments originroposed for the 9P(14) 2 35 and 9P(24) 1 0 systems (22)ut, as discussed above, we now believe those pump transelong to the (04 1,25)oh E subband. With our presessignment, the pattern calculated for the reported FIRL trionsistent with the observations in Table 1, althoughelatively large discrepancies between observed and calcuavenumbers for the two transitions down to (1,24)co E lev-ls.

VI. DISCUSSION AND CONCLUSIONS

In this work, we have applied results from recent analyshe Fourier transform infrared spectrum of CH3OH to thessignment of the energy level and transition systemsptically pumped FIR laser lines. In all, 45 IR-pump/FIR-la

ransition systems are considered in this paper, with newormation on a variety of aspects of the assignments foreported FIRL transitions. In addition to presenting 40 newdentifications, we have partially reassigned or extendeduantum number labeling for a number of other lines andbtained rigorous spectroscopic support for previous unrmed assignments. With respect to the latter, we looarefully at the 53 FIRL transition identifications appeaith question marks in the recent review by Moruzziet al. (4)nd were able to contribute new information for 34 of the believe that 21 are now well established spectroscophile 13 still have unresolved details so they retain tuestion marks in our table.Many of the energy level and transition schemes for the

r reassigned systems involve unconventional pump abions, vibrational perturbations, and intermode FIR lasernd so are very interesting spectroscopically. As suggest

he vibrational energy picture of Fig. 1, there is extenoupling and mixing among the excited torsion–vibratates making identification of the precise vibrational charaf the pumped levels a significant challenge in a numbeases. For example, then 5 2 CO-stretch levels lie in the samnergy region as then 5 0 CH3-deformation state, and welieve that the pumped levels for one or more of the sys

dentified as CH3 deformation could well be mixed states beescribed asn 5 2 CO stretch instead.Several previous questions about the CH3OH energy leve

tructure in the excited vibrational manifold have been full

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artially resolved. For the 9P(14) and 9P(24) systems, wave reassigned the pumped levels to Fermi-mixed (0,25)oh/1,25)co E states and explained the postulated “hybrid (1,25)h

doublets” (22) as due to (0,24)oh E levels lying very closelow the (0,25)oh/(1,25)co E levels. For the 9P(22) systemeassignment of the pumped level to aK 5 0 state removerevious problems with anomalousK doubling (2) by identi-

ying the lower laser levels as widely splitK 5 1 doubletsather thanK 5 2. The puzzle of the 10R(20) assignment (33)as been solved with the discovery of aJ-localized levelrossing resonance between the (0,12)ri and (0,42)co A stateshich perturbs the pumped level and strongly modifies

0,4)co K doubling. In the 10R(16) system, we have clarifiembiguity between (1,0)co and (0,0)oh A lower levels for theIRL lines (2, 4, 34). In the 9SR(9) system, near degenerand strong mixing were discovered between the (1,1)ri and1,2)co E states, which may account for the strange Sffects observed for the latter (43).However, as each spectroscopic puzzle is solvedH3OH, another takes its place and numerous mysteries

emain. The new insights into the 9P(22) and 10R(16) sys-ems come at the cost of having to explain the existence otates, (0,0)oh A/hi and (0,0)oh A/lo, both of which appear tave similar characteristics. The 10R(16) system also presen

he enigma of invertedK 5 1 doubling in the (0,1)sb A pumpedtate. In the 9P(10) system, we still need to identify the souf the vibrational coupling leading to the hybridized (1,6)h Etate (2), as well as the interaction partners for a numbeocalized level-crossing resonances in other systems. Theery of a nearby hybrid partner has also surfaced for the (2co

levels in the 9P(26) and 13-9R(26) systems. It seems fao say that, while the methanol molecule may graduallyifting the veils on its secrets, it continues to guard themnd to display remarkable resilience in posing challenroblems for spectroscopic study.In conclusion, the present results represent signifi

rogress in interpreting the FIRL emission observed fptically pumped CH3OH, covering interesting new states awide variety of torsion–vibration interactions. While sev

ormerly puzzling features of the FIRL transition systems heen explained, new mysteries have arisen. Thus, the IR

ra and FIRL observations from CH3OH continue to providertile territory for spectroscopic exploration and motivator further detective work in the ongoing effort to identbserved FIR laser lines.

ACKNOWLEDGMENTS

Financial support for this research from the Natural Sciences and Engng Research Council of Canada and the University of New Brunsesearch Fund is gratefully acknowledged. We thank J. T. Hougen for in

n this project and partial financial support from the U.S. Departmennergy. We also express our appreciation to J. W. C. Johns and Zhengff the Steacie Institute for Molecular Sciences for assistance in obtaininigh-resolution methanol Fourier transform spectra.


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REFERENCES

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J. Infrared Millimeter Waves12, 449–471 (1991).4. B. Hartmann and L. Lindgren,Int. J. Infrared Millimeter Waves3,

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J. Infrared Millimeter Waves17, 1049–1054 (1996).7. M. Inguscio, G. Moruzzi, K. M. Evenson, and D. A. Jennings,J. Appl.

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On the Assignment of Optically Pumped Far-Infrared Laser Emission from CH 3 OH

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Transcript of On the Assignment of Optically Pumped Far-Infrared Laser Emission from CH 3 OH