Fourier transform spectroscopy of CH 3 OH: rotation torsion vibration structure for the CH 3 -rocking and OH-bending modes

Transcription

1 Journal of Molecular Spectroscopy 228 (2004) Fourier transform spectroscopy of CH 3 OH: rotation torsion vibration structure for the CH 3 -rocking and OH-bending modes R.M. Lees, a,* Li-Hong Xu, a J.W.C. Johns, b Z.-F. Lu, b B.P. Winnewisser, c,d M. Lock, d and R.L. Sams e a Department of Physical Sciences,University of New Brunswick, Saint John, NB, Canada E2L 4L5 b Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ont., Canada K1A 0R6 c Department of Physics, The Ohio State University, 174 W. 18th Avenue, Columbus, OH 43210, USA d Physikalisch-Chemisches Institut, Justus-Liebig-Universit at, Heinrich-Buff-Ring 58, D Giessen, Germany e Pacific Northwest National Laboratory, P.O. Box 999, Mail Stop K8-88, Richland, WA 99352, USA Received 5 April 2004; in revised form 13 June 2004 Available online 13 July 2004 Abstract High-resolution Fourier transform spectra of CH 3 OH have been investigated in the infrared region from 930 to 1450 cm 1 in order to map the torsion rotation energy manifolds associated with the m 7 in-plane CH 3 rock, the m 11 out-of-plane CH 3 rock, and the m 6 OH bend. Upper-state term values have been determined from the assigned spectral subbands, and have been fitted to powerseries expansions to obtain substate origins and effective B-values for the three modes. The substate origins have been grouped into related families according to systematic trends observed in the torsion vibration energy map, but there are substantial differences from the traditional torsional patterns. There appears to be significant torsion-mediated spectral mixing, and a variety of forbidden torsional combination subbands with jdt t j > 1 have been observed, where t t denotes the torsional quantum number (equivalent to t 12 ). For example, coupling of the ðt 6 ; t t Þ¼ð1; 0Þ OH bend to nearby torsionally excited ðt 7 ; t t Þ¼ð1; 1Þ CH 3 -rock and ðt 8 ; t t Þ¼ð1; 1Þ CO-stretch states introduces ðt 6 ; t t Þ¼ð1; 0Þ ð0; 1Þ subbands into the spectrum and makes the m 7 þ m 12 m 12 torsional hot band stronger than the m 7 fundamental. The results suggest a picture of strong coupling among the OH-bending, CH 3 - rocking, and CO-stretching modes that significantly modifies the traditional energy structure and raises interesting and provocative questions about the torsion vibration identity of a number of the observed states. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Methanol; CH 3 OH; Infrared spectra; Methyl rock; OH bend; Internal rotation; Torsion vibration term values; Torsion-mediated vibrational coupling 1. Introduction * Corresponding author. Fax: address: lees@unb.ca (R.M. Lees). This paper reports identification and analysis of spectral subbands in Fourier transform infrared (FTIR) spectra of CH 3 OH in the cm 1 region, with interesting implications for the question of intermode coupling among the lower vibrations. The region of the CH 3 OH IR spectrum lying above the strong m 8 COstretching fundamental at 1034 cm 1 [1] has long presented significant problems and challenges. Viewed at low-resolution, the IR absorption is broad and relatively weak and lacks distinct band structure, despite the fact that it contains six vibrational fundamentals [2,3] and a number of torsional combination bands. However, progress in the analysis of the CH 3 -rocking and OH-bending bands for the O-18 [4,5], C-13 [6,7], and normal 12 CH 3 16 OH [8 10] methanol isotopomers has shown that torsionally mediated interactions among the modes strongly perturb the excited state energy manifolds and thus the shapes and widths of the infrared band profiles /$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi: /j.jms

2 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) There is a rich body of literature on the spectroscopy of methanol. The foundations for our understanding that were originally laid in a classic series of papers by Dennison and co-workers (see [11] as the latest of the series) have now evolved to sophisticated multiparameter models [12 15] which can fit the microwave (MW) and far-infrared (FIR) spectra of the ground vibrational state to within experimental uncertainty. The accurate CH 3 OH ground-state torsion rotation energies obtained from the MW and FIR studies [1,14] then provide a platform from which to launch spectroscopic investigations of the excited vibrational modes. The strong m 8 CO-stretching band has been extensively studied and analyzed [1,16] along with several subbands of the m 7 inplane CH 3 -rocking band that are enhanced by Coriolis resonance with the CO stretch [1,17]. In recent years, analyses of optically pumped FIR laser emission [18 20] as well as continuing FTIR studies have also provided high-resolution information for the other low-frequency modes, highlighted by the discovery of inverted torsional structure in the m 11 out-of-plane CH 3 -rocking band [9] and the m 4 in-plane asymmetric CH 3 -deformation band [21,22]. These latter results paralleled the original finding of inverted splitting for the m 2 CHstretching mode of CH 3 OH [23], and have helped to stimulate a variety of recent approaches to the torsion vibration Hamiltonian that have had some striking successes in modeling the observed structures [22,24 27]. In the current work we have analyzed high-resolution Fourier transform (FTIR) spectra of 12 CH 16 3 OH from 930 to 1450 cm 1, with particular interest in the regions of the m 7 and m 11 CH 3 -rocking and m 6 OH-bending vibrational bands. Brief descriptions of some of the results have been presented earlier in connection with related studies [8 10]. Our spectroscopic goal was to map the excited-state rotation torsion vibration (R T V) energy structure in as much detail as possible, identifying individual torsion K rotation subbands and determining excited-state energy term values and effective substate parameters. The present paper reports assignments and term-value analysis for a variety of CH 3 -rocking and OH-bending subbands, both allowed and perturbation-induced, for the vibrational fundamentals as well as torsional hot and combination bands. First, we give an overview of the spectral region from 1100 to 1450 cm 1, with a catalog of assigned subband origin wavenumbers to show their distribution and grouping across the spectrum. We then present a listing of the upper substate origins and effective B-values obtained from fitting the excited-state term values, classified into related families as far as possible, together with a map of the K-reduced energy manifold. The question of the torsional and vibrational parentage of the substate families is discussed next and systematic trends in the substate energy patterns are illustrated for several of the more complex and crowded regions. Finally, in the concluding remarks, we point out the urgent need for extension of the promising Hamiltonian model developed by Hougen [25] to bring in excited torsional states and K-dependence of the energies to seek to meet the interesting spectroscopic challenges and puzzles emerging from the torsion vibration energies in this region. 2. Experimental details For this work, a variety of CH 3 OH FTIR spectra were recorded under different conditions to optimize different spectral features. The original spectra were obtained at room temperature on the modified DA3.002 Bomem FTIR spectrometer at the National Research Council of Canada (NRC). Our first spectrum covered the cm 1 region at cm 1 resolution in 75 coadded scans, with a pressure of 13.5 Pa and 2.0 m pathlength. This was originally aimed at the strong COstretching fundamental, but several of the subbranches of the weaker CH 3 -rocking m 7 þ m 12 m 12 torsional hot band could also be identified. Thus, a further spectrum from 930 to 1301 cm 1 was recorded with 94 scans coadded at cm 1 resolution using a higher 100 Pa pressure and 2.0 m path length in order to bring up the weaker features and extend the rocking-band analysis. Also, a spectrum of the cm 1 region containing the m 6 OH-bending band was recorded at cm 1 resolution with 100 scans coadded using 72 Pa pressure and 2.0 m path length. The NRC spectra were calibrated against known offsets for CH 3 OH absorption lines pumped by CO 2 lasers in the lower region [1], and against standard wavenumbers [28] for the residual water lines observed in the spectrum in the higher region. To improve our coverage of the entire region with a greater range of optical densities, three spectra were recorded from 1100 to 1800 cm 1 on the Bruker IFS 120 instrument at Giessen at a resolution (1/MOPD) of cm 1. The respective pressures were 7.0 Pa with 104 coadded scans, 25 Pa with 250 coadded scans, and 280 Pa with 321 coadded scans. A path length of 16.3 m in a 1-m White cell operated at room temperature was employed in each case. KBr optics, a globar source and a Ge:Cu detector were used in the spectrometer. External calibration against a group of 15 standard OCS lines in the cm 1 region [29] gave a standard error of cm 1, representing the statistical uncertainty in a single measurement. As well, in order to isolate subbands of low quantum number to assist the analysis and help confirm the assignments, cooled-beam spectra in the cm 1 region were recorded with the FTIR-jet spectrometer at the Pacific Northwest National Laboratory. This system was designed to produce the highest quality at the highest resolution possible. A Bruker 120HR with a

3 530 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) maximum resolution of cm 1 was coupled to a 12 cm by 50 lm slit nozzle pumped by a stack of four Roots blowers combined to produce a pumping speed of greater than 6 m 3 /s. The light from the FTIR was coupled into the slit compartment by a Gregorian telescope, producing a 6 mm diameter beam, and made a total of 5 passes through the molecular jet before exiting the slit compartment to the detector. The low temperature (about 10 K) spectrum of methanol was obtained at a resolution (full width at half height) of cm 1 by expanding a 7% mixture of CH 3 OH in helium at a total backing pressure of kpa. 3. Notation and torsion vibration energy structure The rotation torsion vibration energy levels of methanol can conveniently be labeled by the set of quantum numbers (r; t; t t ; K; J), where r is the A or E torsional symmetry, t is the vibrational state, t t is the torsional quantum number (equivalent to t 12 ), and K is the a-component of the rotational angular momentum J. The vibrational modes are denoted by t ¼ gr, co, ri, ro, oh, sb, andab for the ground, m 8 CO-stretching, m 7 in-plane and m 11 out-of-plane CH 3 -rocking, m 6 OHbending, and m 5 symmetric and m 4 asymmetric CH 3 -deformation modes, respectively [1]. In some of the figures we have also used the convenient shorthand m 6 þ m 12, m 7 þ m 12, m 8 þ m 12, m 8 þ 2m 12, and 4m 12 to label the ðt 6 ; t t Þ¼ð1; 1Þ, ðt 7 ; t t Þ¼ð1; 1Þ, ðt 8 ; t t Þ¼ð1; 1Þ, ðt 8 ; t t Þ¼ð1; 2Þ, and ðt; t t Þ¼ð0; 4Þ torsionally excited states, respectively. For levels of E symmetry, a signed K is used, with K > 0 corresponding to levels often labeled as E 1 and K < 0toE 2 [30]. States of A symmetry with K > 0 can also display K-doubling, hence an additional superscript is added to distinguish resolved doublet components as A þ or A [31]. The energy term values of different J for a vibrational substate of given t t, K, and r can normally be well represented [1] as a series expansion in powers of J ðj þ 1Þ with state-specific coefficients EðJÞ ¼W 0 þ BJðJ þ 1Þ DJ 2 ðj þ 1Þ 2 þ HJ 3 ðj þ 1Þ 3 þ LJ 4 ðj þ 1Þ 4 þ MJ 5 ðj þ 1Þ 5 þ NJ 6 ðj þ 1Þ 6 þ ð1þ The first two series coefficients in Eq. (1), W 0 and B, represent the substate origin and the effective B-value, respectively. By subtracting the K-rotational energy of ½A ðbþcþ=2šk 2 from W 0, where A, B, andc are the effective rotational constants, one obtains K-reduced torsion vibration energies. In the customary one-dimensional model of the torsional Hamiltonian, these energies are periodic functions of K that can conveniently be plotted in s-curves of the form shown in Fig. 1 of [9]. The s index [11] is DennisonÕs useful alternative specification for r defined by: ðk þ sþ mod 3 ¼ 1(A), 0 ðe 1 or K > 0Þ, 2ðE 2 or K < 0Þ. Fig. 1. Schematic calculated s-curves of K-reduced torsion vibration energies for CH 3 OH in the neighborhood of the OH-bending fundamental state, showing predicted close proximity between ðt 6 ; t t Þ¼ð1; 0Þ OH-bend [m 6 ], ðt 7 ; t t Þ¼ð1; 1Þ in-plane CH 3 -rock [m 7 þ m 12 ], ðt 8 ; t t Þ¼ð1; 1Þ CO-stretch [m 8 þ m 12 ], and ðt 11 ; t t Þ¼ð1; 1Þ out-of-plane CH 3 -rock [m 11 þ m 12 ] levels and possible accidental near-degeneracies with ðt; t t Þ¼ð0; 4Þ ground-state [4m 12 ] levels. The K-reduced energy is given by subtracting K-rotational energy of 3.45K 2 from the K-rotation torsion vibration energy, where 3.45 cm 1 is an effective value of the K-rotational constant, [A ðb þ CÞ=2]. The s ¼ 1 points are shown as open circles, s ¼ 2 as filled circles, and s ¼ 3 as open triangles.

4 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) When the vibrational energies are added in, a complex torsion vibration energy manifold results (see Fig. 1 of [20], for example) in which there are numerous possibilities for anharmonic or Coriolis resonances between near-degenerate levels. Fig. 1 illustrates the general situation to be expected in the region of the OHbending state, showing schematic K-reduced s-curves obtained by simply adding calculated ground-state torsional energies onto predicted vibrational energies. The region is evidently an interesting one, with multiple interactions likely to occur among the t t ¼ 0 OH-bending and t t ¼ 1CH 3 -rocking and CO-stretching levels as well as the possibility of Fermi resonance with t t ¼ 4 groundstate levels [32]. Because the overlapping ladders of torsional states greatly enhance the possibilities for intermode resonance, torsionally mediated vibrational coupling is undoubtedly an important factor in determining mechanisms and rates for intramolecular vibrational energy redistribution (IVR). 4. Subband assignments, torsion vibration substate origins, and effective B values 4.1. Overview of the spectrum and torsion vibration energy structure Because large energy changes occur in jdt t j¼1 and jdt t j¼2 torsional combination transitions, the origin wavenumbers of all of the observed subbands that are associated with CH 3 -rocking and OH-bending upper states cover a very wide range from 958 up to 1418 cm 1. Those origins lying below 1100 cm 1 are reported in a companion paper on the 10 lm spectrum dealing principally with assignments and analysis for the strong m 8 COstretching band [33]. The region below 1100 cm 1 contains, in addition to the m 8 band, the t t ¼ 0 fundamental of the m 7 in-plane CH 3 -rock plus several t t ¼ 1 m 7 subbands and a variety of Dt t ¼ 1 and Dt t ¼ 2 torsional combination subbands from the m 5, m 6, and m 7 modes. In the present work, we have moved our focus up to the next region of the CH 3 OH spectrum extending from 1100 to 1450 cm 1. Table 1 presents the origins of the subbands identified so far in this region, illustrating the extent and distribution of the spectral structure. In general, the subbands fall into characteristic groupings in different regions of the spectrum. Further t t ¼ 1 torsionally excited m 7 subbands are found from 1100 to 1125 cm 1, mingling with subbands of the ðt 6 ; t t Þ¼ð1; 0Þ ð0; 1Þ OH-bending torsional combination band that extends from 1107 to 1142 cm 1. The m 11 out-of-plane CH 3 -rocking fundamental then takes over from 1142 to 1165 cm 1. The region from 1180 to 1263 cm 1 is an interesting but puzzling one containing numerous DK ¼ 0 a-type subbands that originate from Table 1 Observed subband origins (in cm 1 ) in the spectral region from 1100 to 1450 cm 1 for CH 3 OH a r t 0 t 0 t t 00 t K 0 K 00 Origin b E ri E co E oh 0 1 )8 ) A oh A ri E oh E ri A ri A co A ro E oh 0 1 )2 ) A ri E ri A ri E ri 1 1 )3 ) E oh A oh E ri 1 1 )4 ) E ri E oh 0 1 )4 ) A oh E oh 0 1 )6 ) A oh E oh E oh E oh A oh A oh E oh E oh 0 1 )7 ) A oh E ro 0 0 )7 ) E ro A ro A ro A ro E ro 0 0 )10 ) A ro E ro 0 0 )4 ) E ro 0 0 )6 ) A ro E ro E ro A ro E ro E ro 0 0 )8 ) A ro A ro E ro 0 0 )9 ) A ro E ro E U E U )5 ) A ro A ro A ro A U A oh E U )4 ) E U )5 ) E U E U A U E U E U A ro A U c A co c E U

5 532 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) Table 1 (continued) r t 0 t 0 t t 00 t K 0 K 00 Origin b A co E U E U )9 ) E U )2 ) A U E U E U E U )4 ) A U E U A U E U )2 ) E U A U E U )1 ) A U E U A U E U )8 ) E U A sb A U E U E U )5 ) E U A U E U )5 ) A ri E ri A ri E ri 1 0 )4 ) E co E ri E ri E co A co E co A ri A ri A ri A co ) E ri E oh A ri E ri 1 0 )6 ) E ri 1 0 )2 ) E ri E co E co 1 0 )1 ) A co E ri E ri A ri A oh A ri E oh 0 0 )3 ) A oh E co 1 0 )5 ) E oh A oh E oh A ri E ri 1 0 )5 ) E ri 1 0 )1 ) E oh 0 0 )7 ) E ri 1 0 )9 ) E oh E ri E oh 0 0 )10 ) A oh A U Table 1 (continued) r t 0 t 0 t t 00 t K 0 K 00 Origin b A oh E oh E oh A oh E oh 0 0 )6 ) E oh 0 0 )1 ) A U A? A oh E oh E oh 0 0 )4 ) E ri E oh A oh E ri E oh A oh E oh E oh 0 0 )2 ) A oh A oh E oh E oh 0 0 )8 ) A U B? E oh 1 1 )3 ) E oh A oh E oh A oh E oh A U A oh A oh A oh A U E oh 1 1 )2 ) E U )1 ) E U A oh E U A oh A U E U A U C? E U )4 ) E U E U a The lower levels of the subbands are established from ground-state combination differences, but the vibrational and/or torsional labeling of the upper levels is tentative in a number of cases. The U 0, U 1,andU 2 entries for the upper levels refer to groupings of substates that appear to follow systematic patterns associated with t t ¼ 0, 1, and 2 torsional levels, respectively, but which have not yet been vibrationally assigned. Labels U A, U B, and U C refer to individual unidentified torsion vibration substates that are not associated with other substate groupings. b Origin wavenumbers listed to only 1 or 2 decimal place have correspondingly greater uncertainties than those listed to 3 places. Origins marked with asterisks indicate subbands for which one or more of the initial lines are observed in the 10 K cooled-beam slit-jet spectrum, confirming that the subband originates from a t t ¼ 0 lower level of low energy and low quantum number. c The strongly interacting (A; U2 ; 2; 4) and (A,co,2,5) upper states of these two hybridized subbands are the states labeled as (A,co,2,5), hd, and hu, respectively, in [20,33]. t t ¼ 1 and t t ¼ 2 levels of the ground vibrational state, but whose upper states have not yet been confidently labeled either vibrationally or torsionally. From 1280 to 1313 cm 1, t t ¼ 1 0 torsional combination subbands of the CO stretch and in-plane CH 3 rock dominate the spectrum. The t t ¼ 0 subbands of the m 6 OH-bending

6 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) fundamental then appear, extending over a wide range from 1315 to 1350 cm 1, followed by torsionally excited t t ¼ 1 OH-bending subbands up to 1400 cm 1. Six further mysterious subbands lie between 1400 and 1420 cm 1 whose upper states are vibrationally unassigned. Beyond 1450 cm 1, one then enters the domain of the m 5, m 10, and m 4 CH 3 -deformation modes that have been reported previously [21,22]. Our overall data set currently includes about 4600 assigned absorption lines accessing torsion rotation levels of the in-plane CH 3 rock, 900 for the out-of-plane CH 3 rock, 3400 for the OH bend, and 2800 whose upper levels are still vibrationally unidentified. We will not report the details of the spectra here, but plan to include them in the near future as supplementary data to accompany a study in progress on the J-dependent level patterns of the (r; t; t t ; K) substates and the numerous level-crossing interactions among them. From the spectroscopic data, upper-state term values were obtained by adding ground-state energies from Moruzzi et al. [1] to the wavenumbers of the assigned line. For each identified (r; t; t t ; K) substate, the substate origin and effective B value were then determined by fitting the term values of the sequence of substate J- levels to the power-series expansion of Eq. (1). In each case, fits were performed with maximum powers of JðJ þ 1Þ ranging from 3 to 6, and the order giving the minimum standard error in the substate origin W o was adopted as the optimum. Our results are collected in Table 2, grouped in families of related substates. For each substate, we give the origin W o, the effective B value, the order of the optimum fit, the weighted standard deviation of the optimum fit, and the difference dw o between minimum and maximum origin values obtained over the four fits from order 3 to 6. The dw o variation is a measure of how well the power-series model fits the term values for a substate, and we believe it gives a useful and realistic estimate of the likely accuracy of the substate origin. For substates of A torsional symmetry with resolved asymmetry K-doubling, the A þ and A components were fitted separately and the resulting constants, which were always very close, were averaged to give the values in Table 2. As mentioned above, an informative pictorial synthesis of the experimental information on the excited energy manifold is given by plotting the K-reduced energies as a function of the K quantum number. Fig. 2 shows our current map of known CH 3 OH torsion vibration substate energies up to 1950 cm 1, in which the new results from Table 2 are combined with previous results for the m 8 CO stretch [1,33], the m 11 out-of-plane rock [9,10] and the m 4, m 5 and m 10 CH 3 -deformation modes [21,22]. The challenge now is to connect the dots in order to classify the substates into a consistent picture with full torsional and vibrational labeling, and this is discussed in Section 5 below. Table 2 CH 3 OH (r; t; t t ; K) substate W o origins and effective B values (in cm 1 ) from power-series fitting of experimental term values a Substate b Origin W o B Value Ord c SD d dw o e (A,ri,0,0) (A,ri,0,1) f f (A,ri,0,2) f f (A,ri,0,3) f f (A,ri,0,4) g f f (A,ri,0,5) g (A,ri,0,6) g (A,ri,0,8) (E,ri,0,0) (E,ri,0,1) (E,ri,0,2) (E,ri,0,3) (E,ri,0,)1) (E,ri,0,)2) (E,ri,0,)4) (E,ri,0,)5) (A,oh,0,0) (A,oh,0,1) f f (A,oh,0,2) f f (A,oh,0,3) f f (A,oh,0,4) f f (A,oh,0,5) (A,oh,0,6) (A,oh,0,7) (A,oh,0,8) (A,oh,0,10) (E,oh,0,0) (E,oh,0,1) (E,oh,0,2) (E,oh,0,3) (E,oh,0,4) (E,oh,0,5) (E,oh,0,6) (E,oh,0,7) (E,oh,0,8) (E,oh,0,9) (E,oh,0,)1) (E,oh,0,)2) (E,oh,0,)3) (E,oh,0,)4) (E,oh,0,)6) (E,oh,0,)7) (E,oh,0,)8) (E,oh,0,)10) (A,U 0,0,0) (A,U 0,0,4) (E,U 0,0,2) (E,U 0,0,5) (E,U 0,0,6) (E,U 0,0,)1) (E,U 0,0,)4) (A,U 1,1,0) (A,U 1,1,2) f f (A,U 1,1,3) f f (A,U 1,1,4) (A,U 1,1,7) (A,U 1,1,8) (E,U 1,1,0) (E,U 1,1,1) (E,U 1,1,2) (E,U 1,1,3) (E,U 1,1,6)

7 534 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) Table 2 (continued) Substate b Origin W o B Value Ord c SD d e dw o (E,U 1,1,)1) (E,U 1,1,)2) (A,oh,1,1) f f (A,oh,1,2) f f (A,oh,1,3) (A,oh,1,4) (A,oh,1,5) (A,oh,1,6) (A,U A,1,2) f f (A,U B,1,2) f f (A,ro,0,4) (A,ro,0,5) (A,ro,0,6) (A,ro,0,7) (A,ro,0,8) (A,ro,0,9) (A,ro,0,10) (A,ro,0,11) (E,ro,0,7) (E,ro,0,8) (E,ro,0,9) (E,ro,0,10) (E,ro,0,11) (E,ro,0,)6) (E,ro,0,)7) (E,ro,0,)8) (E,ro,0,)9) (E,ro,0,)10) (A,ri,1,1) f f (A,ri,1,2) f f (A,ri,1,3) f f (A,ri,1,4) (A,ri,1,5) (A,ri,1,6) (A,ri,1,7) (A,ri,1,8) (A,ri,1,9) (A,ri,1,10) (E,ri,1,0) (E,ri,1,1) (E,ri,1,2) (E,ri,1,3) (E,ri,1,4) (E,ri,1,5) (E,ri,1,6) (E,ri,1,7) (E,ri,1,8) (E,ri,1,)1) (E,ri,1,)2) (E,ri,1,)3) (E,ri,1,)4) (E,ri,1,)5) (E,ri,1,)6) (E,ri,1,)9) (E,U 1,1,)5) (E,U 1,1,)8) (A,U 2,2,0) (A,U 2,2,1) f f (A,U 2,2,3) (A,U 2,2,4) h (A,U 2,2,5) (A,U 2,2,7) (E,U 2,2,0) (E,U 2,2,1) Table 2 (continued) Substate b Origin W o B Value Ord c SD d e dw o (E,U 2,2,2) (E,U 2,2,3) (E,U 2,2,4) (E,U 2,2,6) (E,U 2,2,7) (E,U 2,2,)1) (E,U 2,2,)2) (E,U 2,2,)4) (E,U 2,2,)5) (E,U 2,2,)9) (E,oh,1,0) (E,oh,1,1) (E,oh,1,4) (E,oh,1,)2) (E,oh,1,)3) (A,U C,2,3) (A,sb,0,1) f f a Term values were determined by adding ground-state energies from Moruzzi et al. [1] to observed wavenumbers. Thus, they are referenced to the values of and cm 1 from [1] for the (r; t; t t ; K; J) ¼ (A,gr,0,0,0) and (E,gr,0,0,0) levels. Note that these torsional zero-point energies are model dependent, and are slightly lower than the values of and cm 1 calculated with the global fit parameters of Xu and Hougen [14]. b The torsional and vibrational labeling is not yet fully established for substates other than the t t ¼ 0 CH 3 -rocking ri and ro modes. Substates of a given classification are believed to belong to a group following a systematic pattern, but the patterns do not always conform to the traditional torsional model. The unknown vibrational states labeled as U 0, U 1, and U 2 are the upper states for families of subbands originating from t t ¼ 0, t t ¼ 1, and t t ¼ 2 ground-state levels, respectively, although a number of the upper substates are also accessed by nominally forbidden subbands with jdt t j > 0. c Order of the fit, i.e., the maximum power of JðJ þ 1Þ included. Fits of order 3 to 6 were compared for each substate; the optimum order shown here is the one giving the minimum standard error in the substate origin. d Overall unitless weighted standard deviation of the fit. The default uncertainty for a single term value was cm 1. e dw o is the (max ) min) spread of W o values over the four fits of order 3 to 6. This is a measure of how well the substate term values are represented by a power series, and thus of the reliability of the W o value. f Average of values from separate fits to A þ and A substates. g Substate affected by strong Coriolis resonance with (K þ 1) partner in the t 8 ¼ 1 CO-stretching state. h The (A,U 2,2,4) substate is strongly hybridized with the (A,co,2,5) substate lying just above it, and is labeled as the (A,co,2,5) hd state in [20,33]. In the following subsections, we consider the assignments and analyses for the various subband groupings in approximate order of increasing upper-state energy. We have endeavored to arrange the excited substate origins into systematic families as far as possible on the basis of their positions and patterns in the energy map of Fig. 2. We will discuss the rationale for this classification below in Section 5. However, we note that the ordering and vibrational labeling are tentative in a number of cases, as there are significant differences between the observed patterns and the regular oscillating s-curves

8 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) Fig. 2. K-reduced torsion vibration energy map showing the locations of currently known substates associated with the lower vibrational modes of CH 3 OH. Each point represents a K-reduced substate origin established from one or more identified subbands in the spectrum. The labeling on the right-hand side represents the expected approximate energy ordering of the indicated torsion vibration states. expected from the traditional model. The existence of so many nominally forbidden a-type subbands with jdt t j > 0 implies a large degree of torsion-mediated mixing among the modes. Furthermore, the dramatic departures from the traditional model, notably torsional inversion, that have been observed for the t t ¼ 0 ground torsional levels of certain of the CH 3 -rocking, CH 3 -deformation, and CH-stretching modes [9,10,21,23] imply that similar changes may be expected for their excited torsional states. Such states have not yet been explored for these modes within the framework of the new torsion vibration formalisms [22,24 27]; we hope that the present results may serve as a stimulus to do so The m 7 in-plane CH 3 -rocking fundamental The m 7 in-plane CH 3 -rocking fundamental (in the t t ¼ 0 torsional state) is a hybrid a=b band centered around 1072 cm 1. This is just 38 cm 1 above the much stronger m 8 CO-stretching band, so that much of the P and Q branch structure of the m 7 band is heavily obscured by the m 8 R branch. However, a number of subbands having (r; t; t t ; K) ¼ (A,ri,0,4), (A,ri,0,5), and (A,ri,0,6) upper states had been identified previously [1] due to intensity enhancement arising from strong Coriolis resonances between those levels and the corresponding (K þ 1) m 8 states [17]. The Coriolis-induced

9 536 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) mixing is almost 50:50 for the {4 ri /5 co } and {6 ri /7 co } pairs of states, hence intensity borrowing leads to a variety of readily observable DK ¼ 0 and DK ¼ 1 subbands accessing the hybridized levels. Our present assignments for new and weaker m 7 subbands were based principally on ground-state combination differences using known ground-state energies [1]. The CH 3 OH m 7 band differs from those of the O-18 and C-13 isotopomers [5,6] in having significant b-type character. The DK ¼1 subbands are as strong as the a-type DK ¼ 0 subbands in some cases, although the relative intensities do not follow a consistent pattern. The presence of both a-type and b-type subbranches then permits valuable combination loop checks of the assignments. A sample diagram is given in Fig. 3 for R(9) transitions of the (E,ri,0,)2), (E,ri,0,)1), and (E,ri,0,0) subbands. The closure defects for the numerous loops that can be formed among the transitions and the ground state levels are all well below the experimental uncertainty, confirming our identifications. Another interesting test comes from the mean term values of and cm 1 obtained for the upper K ¼ 1 and 0 levels from the data in Fig. 3. The difference of cm 1 corresponds to a frequency of GHz, in agreement with the microwave value of GHz for the Q(10) line of the K ¼ 0 1 EQbranch measured directly in the t 7 ¼ 1 excited state many years ago [34]. With the substantial change in torsional splitting in going from the ground state to the ðt 7 ; t t Þ¼ð1; 0Þ excited state [10], the origins of the a-type subbands are distributed over a relatively broad range from to cm 1. The b-type subbands are spread more widely, with origins from up to cm 1.As mentioned above, most of the m 7 subband origin wavenumbers lie below 1100 cm 1 so were listed in our companion paper on the FTIR spectrum in the 10 lm region [33]. The remainder are included here in Table 1. The narrow band of ðt 7 ; t t Þ¼ð1; 0Þ K-reduced energies around 1200 cm 1 in Fig. 2 follows a well-behaved oscillating s-curve pattern [10]. The notable feature is that the E A splitting between the K ¼ 0 E and A levels in Table 2 is only cm 1, just under half of the ground-state value of cm 1 [1]. When interpreted according to the traditional one-dimensional torsional Hamiltonian, this would imply a much higher torsional barrier height [4,6] for the t 7 ¼ 1 state than for the ground state. However, HougenÕs recent model now suggests the reduction in splitting is more likely the result of torsion vibration interaction [10,25]. Note that the trend continues with a further sharp reduction in torsional splitting down to 2.29 cm 1 for the t 7 ¼ 2 second excited rocking state [10] The m 11 out-of-plane CH 3 -rocking fundamental Fig. 3. Sample transition diagram for the m 7 in-plane (ri) CH 3 -rocking band of CH 3 OH. FTIR wavenumbers are shown in the boxes on the transitions; term values from [1] are shown for the ground-state levels. Closure of combination loops on the diagram with near-zero wavenumber defects confirms a- and b-type assignments of R(9) transitions to K ¼ 0, )1, and )2 E levels. For example, starting at the lower left and going up and around, we find ) ) ¼ ) cm 1, well within the experimental tolerance. The m 11 fundamental was recently identified as a relatively weak and predominantly parallel band centered around 1154 cm 1 [9]. Analysis of the torsional structure showed that the E A splitting for t t ¼ 0 was inverted (A level above the E level) compared to the ground and CO-stretching states, as can be seen for the band of energies around 1285 cm 1 in Fig. 2. This feature was shown by Hougen [25] to arise naturally in his coupled torsion vibration formalism for those CH 3 OH modes, such as the in-plane and out-of-plane CH 3 rock, that correlate to degenerate E vibrations of the limiting symmetric top with a linear COH group. In a recent fulldimensional ab initio reaction-path treatment, Fehrensen et al. [26] interpret the inversion within the context of an adiabatically projected one-dimensional torsional Hamiltonian as arising from a torsional geometric phase for these E-like modes. However, they predict that all such modes should display inversion, unlike our above observations for m 7. Another recent full-dimensional ab initio treatment [27], on the other hand, calculates the splittings to be normal for m 7 and inverted for m 11 as we observe experimentally, so that there are still interesting

10 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) differences between theoretical models and the need for additional precise spectroscopic data. Because the strongest m 11 spectral features are the parallel DK ¼ 0 Q-subbranches, for which the relative intensities are proportional to K 2, our information on this band is primarily for levels of medium to high K, as seen in Table 2. So far, we have not identified transitions to the K ¼ 0 levels, so do not have a direct experimental E A splitting. However, the earlier Fourier fit of the substate origins to the periodic s-curve model gave a splitting of )7.50 cm 1, with the negative sign indicating the torsional inversion [9,10] The m 6 OH-bending fundamental and m 7 and m 8 torsional combination and hot bands As seen from the s-curves in Fig. 1, the calculated levels of the ðt 6 ; t t Þ¼ð1; 0Þ fundamental OH-bending state lie in the same energy region as those of the ðt 7 ; t t Þ¼ð1; 1Þ and ðt 11 ; t t Þ¼ð1; 1Þ in-plane and out-ofplane torsionally excited CH 3 -rocking states and also the higher levels of the (t 8 ; t t Þ¼ð1; 1Þ CO stretch. The close proximity of many of these levels results in strong mixing between them. The levels are then best described as hybridized eigenstates, and forbidden jdt t j¼1, DK ¼ 0 subbands appear in the spectrum through intensity borrowing [5,7,8]. This allows useful checks of the spectral assignments from combination relations among the interlocking subbands that connect the ground and excited states. A combination-loop diagram was presented in [8], for example, that confirmed assignments for K ¼ 2A K-doublet transitions and also showed the K ¼ 2 asymmetry splitting to be inverted for the ðt 6 ; t t Þ¼ð1; 0Þ OH bend as compared to the ground state. From Fig. 1, the highest-lying ðt 8 ; t t Þ¼ð1; 1Þ COstretching levels most likely to mix with ðt 6 ; t t Þ¼ð1; 0Þ and ðt 7 ; t t Þ¼ð1; 1Þ partners are those with jkj ¼1 2 for s ¼ 1 and jkj ¼3 7 for s ¼ 3. (The K ¼ 0, s ¼ 1 level is even higher, but does not mix with the OH bend because the A selection rules forbid t t ¼ 1 A þ levels from interacting with t t ¼ 0 A þ levels for vibrational states of the same symmetry.) This mixing lends intensity to ðt 6 ; t t Þ¼ð1; 0Þ ð0; 1Þ, ðt 7 ; t t Þ¼ð1; 1Þ ð0; 0Þ and ðt 8 ; t t Þ¼ð1; 1Þ ð0; 0Þ forbidden subbands that we have seen in the spectrum. It can also give rise to farinfrared laser (FIRL) emission into the three different vibrational states from a single optically pumped upper level, as was illustrated in Fig. 2 of [20] for the FIRL system pumped by the 9P(24) CO 2 laser line. An example of the three-way vibrational coupling, again with FIRL emission involved, is shown in Fig. 4 for the K ¼ 7A, s ¼ 3 substates. In this system, interlocking transitions are observed from both (A,gr,0,7) and (A,gr,1,7) lower levels up to each of the three interacting (A,oh,0,7), (A,ri,1,7) and (A,co,1,7) upper Fig. 4. CH 3 OH transition diagram showing allowed and forbidden K ¼ 7A transitions to hybridized ðt 6 ; t t Þ¼ð1; 0Þ, ðt 7 ; t t Þ¼ð1; 1Þ, and ðt 8 ; t t Þ¼ð1; 1Þ levels coupled by anharmonic interactions. Solid arrows represent allowed transitions; dashed arrows are forbidden. Far-infrared laser emission from optical pumping by the 18 9P(34) CO 2 laser line is also shown with associated spectroscopic data [20]. FIR laser wavenumbers are derived from the reported wavelengths in [35]; ground-state energies are from [1].

11 538 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) substates, consistent with mixing and hybridization of those states. The 18 9P(34) isotopic C 18 O 2 laser line coincides with the R(9) transition of the allowed (A,ri,1,7) (A,gr,1,7) subband and pumps FIRL emission down to (A,ri,1,6) and (A,co,1,6) levels [20]. From the line wavenumbers and ground-state energies given in Fig. 4, all loop closure relations are found to be satisfied to well within our measurement uncertainty, confirming the assignments. Furthermore, the spectroscopic FIRL line wavenumbers calculated by combination relations from the data in Fig. 4 are , , and cm 1 for lines L a L c, respectively, in good agreement with the values shown in Fig. 4 that are derived from the reported wavelength measurements [35]. In Table 2, the origin wavenumbers and effective B values for the substates labeled as ðt 6 ; t t Þ¼ð1; 0Þ and ðt 7 ; t t Þ¼ð1; 1Þ are presented. (Those for the ðt 8 ; t t Þ¼ ð1; 1Þ substates were included in our companion COstretching paper [33].) The ðt 7 ; t t Þ¼ð1; 1Þ CH 3 -rocking levels lie from about 15 to 50 cm 1 below their ðt 6 ; t t Þ¼ð1; 0Þ OH-bending counterparts, with the topmost ðt 8 ; t t Þ¼ð1; 1Þ CO-stretching levels a further 5 20 cm 1 below. Thus, the strength of the coupling interactions must be of comparable magnitude, given the substantial mixing that occurs. In general, this anharmonic coupling among the ðt 6 ; t t Þ¼ð1; 0Þ, ðt 7 ; t t Þ¼ ð1; 1Þ, and ðt 8 ; t t Þ¼ð1; 1Þ states acts to perturb and spread the OH-bending energy structure, contributing to the lack of observable detail in the low-resolution spectrum of the m 6 OH-bending fundamental. In addition to the main group of t t ¼ 0 subbands of the m 6 fundamental from 1310 to 1350 cm 1, there are eleven identified a-type subbands lying slightly higher that have t t ¼ 1 lower states. These are tentatively assigned in Table 1 to the m 6 þ m 12 m 12 OH-bending torsional hot band on the basis of their spectral positions and the location and patterns of the upper state energies Rotationally assigned subbands with unidentified upper torsion vibration states Lying between the m 11 and m 6 fundamentals in the spectral region from 1194 to 1247 cm 1 is a substantial group of a-type subbands with assigned lower levels belonging to the t t ¼ 1 torsional state and a second group with lower levels belonging to t t ¼ 2. As well, there is a small cluster of apparently related subbands with t t ¼ 0 lower states lying near 1370 cm 1, about 50 cm 1 above their OH-bending m 6 counterparts. Knowing the torsion rotation assignments of the lower levels for these groups of subbands, we could accurately determine the upper-state term values and obtain the substate origins and B values. However, the torsion vibration identity of the excited states is not obvious, and we have chosen simply to label the three groups as U 0, U 1, and U 2 in Tables 1 and 2. The subscripts refer to the t t values of the lower levels of the main defining subband groups, but we note that in a number of cases there are jdt t j > 1 torsional combination subbands accessing the upper levels from other torsional states, so that there is evidently considerable torsional mixing. The entries in Table 2 include three individual U substates and one that we assign to the m 5 symmetric CH 3 -deformation mode. Substates U A and U B both derive from K ¼ 2A subbands with t t ¼ 1 lower levels and show resolved asymmetry K-doubling, but neither appears to be related to other families. They lie close below the (A,oh,1,2) torsionally excited OH-bending substate, however, so there may be substantial interaction and mixing. The U C substate belongs to a K ¼ 3A subband with a t t ¼ 2 lower level, and lies at a high energy for which we have little information as yet. The final (A,sb,0,1) substate is interesting in that its origin of cm 1 is encouragingly close to the prediction of cm 1 from the CH 3 -deformation model in a previous work [22], raising the hope that further m 5 subbands may be located with the help of that model Guidance towards low-k substates from jet-cooled spectra Since the subband assignments frequently depend on observation of the Q subbranches as significant clues, and the a-type Q-branch relative intensities vary as K 2, identification of the low-k subbands in the crowded spectrum can be particularly challenging. It is here, therefore, that the jet-cooled supersonic beam spectra were of great value in simplifying the spectrum and exposing only those subbands originating from the low-k, low-j states populated in the cold 10 K beam. In the cooled spectra from 1275 to 1648 cm 1, we were able to identify a substantial number of low-energy subbands, as marked with asterisks in Table 1. While some of these had previously been seen and tentatively assigned, their observation in the jet provided important confirmation of the identification. In other cases, the jet results were crucial in locating the initial lines and determining the assignments of new low-k subbands that could then be followed to higher J in the room-temperature FTIR spectra. Currently, the cooled-beam observations support the assignments for all ðt 6 ; t t Þ¼ð1; 0Þ OH-bending subbands up to K ¼ 4 plus K ¼ 5A, all ðt 7 ; t t Þ¼ ð1; 1Þ ð0; 0Þ forbidden CH 3 -rocking subbands up to K ¼ 3 with the exception of the still-missing K ¼ 3E subband, and the K ¼ 1E, 2E, and 4A ðt 8 ; t t Þ¼ð1; 1Þ ð0; 0Þ subbands whose upper states are closest to the highly mixed peak regions of the t t ¼ 1 CO-stretching s-curves. The K ¼ 0A, 1E, 2E, and 4A subbands of the U 0 family are also seen. Thus, nearly all of the subbands that we could expect to find in the 10 K cooled spectrum have indeed been detected.

12 R.M. Lees et al. / Journal of Molecular Spectroscopy 228 (2004) Systematic s-curve energy patterns and substate grouping into families As seen in the energy map of Fig. 2, there are numerous overlapping torsion vibration states for CH 3 OH and individual s-curves can be difficult to pick out. In this section, we will focus more closely on specific regions of the energy manifold to look for systematics in the substate distributions. By isolating the energies for specific classes of substate, we find interesting regularities in behavior that form the basis for our choice of substate grouping and our torsion vibration labeling in Tables 1 and The (t 6 ; t t )¼(1; 0), (t 7 ; t t )¼(1; 1), and (t 8 ; t t )¼ (1; 1) region The energy region from 1350 to 1500 cm 1 contains the ðt 6 ; t t Þ¼ð1; 0Þ, ðt 7 ; t t Þ¼ð1; 1Þ, and ðt 8 ; t t Þ¼ð1; 1Þ trio of coupled states. In Fig. 5, we have plotted the experimental K-reduced substate origins for each value Fig. 5. K-reduced torsion vibration m 6, m 7 þ m 12, and m 8 þ m 12 energy s- curves for the coupled ðt 6 ; t t Þ¼ð1; 0Þ, ðt 7 ; t t Þ¼ð1; 1Þ, and ðt 8 ; t t Þ¼ð1; 1Þ states of CH 3 OH, plotted separately for each value of s. The dashed line in (A) for s ¼ 1 indicates a tentative connection of the ðt 6 ; t t Þ¼ð1; 0Þ curve to the K ¼ 0A þ levels, for which the repulsive interaction with the ðt 7 ; t t Þ¼ð1; 1Þ and ðt 8 ; t t Þ¼ð1; 1Þ states becomes forbidden and is switched off. of s separately in order to expose possible patterns in the energies. In general, apart from a few irregularities, the substates indeed appear to lie along systematic curves, drawn in as solid lines in Fig. 5 in our proposed grouping. The shapes of these s-curves differ markedly from the regular oscillation seen for the lower states [1,10,33], and in fact have a strong flavor of avoided crossings at the points near K ¼ 0 and 8 for s ¼ 1, near K ¼ 3 for s ¼ 2 and near K ¼ 5 for s ¼ 3. It is interesting that those are the very points in Fig. 1 where calculated curves from other states approach closely tangent to the OH-bending curves. The patterns suggest a general picture of mutually repelling states, with the ðt 7 ; t t Þ¼ð1; 1Þ CH 3 -rocking curves being squeezed in between the ðt 6 ; t t Þ¼ð1; 0Þ OH-bending and ðt 8 ; t t Þ¼ ð1; 1Þ CO-stretching curves, and yet-to-be-determined ðt 11 ; t t Þ¼ð1; 1Þ CH 3 -rocking curves possibly playing a role from above. Downward shifts of those ðt 8 ; t t Þ¼ð1; 1Þ levels located near the peaks of the COstretching curves have already been noted previously in the literature [36], and account for an apparent reduction in torsional barrier height for the ðt 8 ; t t Þ¼ð1; 1Þ state when treated according to the traditional one-dimensional torsional model [37]. In general, it appears that there is new perturbation physics at work in this energy region that is creating new energy patterns. The interesting thing will be to see whether these can be explained by treating the ðt 6 ; t t Þ¼ð1; 0Þ, ðt 7 ; t t Þ¼ ð1; 1Þ, ðt 8 ; t t Þ¼ð1; 1Þ, and ðt 11 ; t t Þ¼ð1; 1Þ states together as a coupled system with appropriate interaction terms in a unified torsion vibration Hamiltonian [22,24 27]. The irregularities in Fig. 5 are of significance, particularly for the K ¼ 0A þ states in the s ¼ 1-curves of Fig. 5A. The (A þ,co,1,0) state lies at cm 1 [1,33], just underneath a second K ¼ 0A þ state at cm 1, with a third lying rather higher at cm 1. K ¼ 0A þ states have definite parity, so torsion-mediated coupling to certain other levels can be symmetry-forbidden. The rule for A level interactions between vibrational states of the same symmetry is that an A þ level must couple to another A þ level for even changes Dt t in torsional state, but can only couple to an A level for interactions with odd Dt t. This was the origin of the giant K-doubling of the (A,ri,1,2) levels lying just below the (A þ,co,1,0) levels, for example, with strong interaction between the (A þ,co,1,0) and (A þ,ri,1,2) levels repelling the latter downwards but leaving the (A,ri, 1,2) levels untouched [8,38]. Similarly, while the (A þ,co,1,0) and (A þ,ri,1,0) states will repel each other, neither can influence the (A þ,oh,0,0) state which is thus free to find its own location unaffected by perturbation. Now given the apparent strong repulsion between the s- curves, it seems very unlikely that the close pair of K ¼ 0A þ states in Fig. 5A could both be t t ¼ 1, implying that the upper level should be the (A þ,oh,0,0)