Fourier transform spectra and inverted torsional structure for a CH 3 -bending fundamental of CH 3 OH

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1 Fourier transform spectra and inverted torsional structure for a CH 3 -bending fundamental of CH 3 OH R.M. Lees, Li-Hong Xu, Anna K. Kristoffersen, Michael Lock, B.P. Winnewisser, and J.W.C. Johns 435 Abstract: The high-resolution Fourier transform spectrum of CH 3 OH has been investigated in the cm 1 CH 3 -bending region, and perpendicular K = 1 subbands forming a consistent pattern have been identified with origins from 1490 to 1570 cm 1. The location of the subbands as the only significant spectral features towards the upper edge of the CH 3 - bending absorption favours their assignment to the ν 4 in-plane A asymmetric CH 3 -bending mode. The upper state term values have been fitted to J(J + 1) power-series expansions to obtain substate origins and effective B-values. The origins exhibit a linear K-dependence as well as the normal variation with K 2. The mean effective B-value of 0.82 cm 1 is higher than that of the ground state, consistent with a bending vibration. The pattern of K-reduced torsion vibration energies is anomalous. It appears to be inverted relative to the customary picture for n = 0 torsional levels, in agreement with a recent prediction, but has unusual periodicity significantly different from the ground state. A simple Fourier cosine series model for the energy curves gives a vibrational band origin of cm 1 for this CH 3 -bending mode, close to the best current calculated value for ν 4. PACS Nos.: 33.20E, 33.80B Résumé : Nous étudions le spectre à transformée de Fourier de haute résolution du CH 3 OH dans la région cm 1 de flexion du CH 3 et identifions des sous-bandes perpendiculaires K = 1, avec des origines allant de 1490 à 1570 cm 1. Le fait que les sous-bandes constituent le seul élément significatif de la tranche supérieure du spectre dû à la flexion du CH 3 suggère qu on les assigne au mode ν 4 planaire asymétrique A de flexion du CH 3. Nous ajustons à une série de puissance en J(J + 1) les termes des états supérieurs pour obtenir l origine des sous-états et les valeurs efficaces des coefficients B. Les origines ont une dépendance linéaire en K, aussi bien que que l habituelle dépendance en K 2. La valeur moyenne efficace de B = 0, 82 cm 1 est plus élevée que celle du fondamental, ce qui est cohérent avec une vibration de flexion. La structure des niveaux de vibration torsion est anomale. Elle semble inversée par rapport à l image habituelle pour les niveaux de Received July 20, 2000.Accepted December 1, Published on the NRC Research Press Web site on May 10, R.M. Lees. 1 Department of Physics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada. L.-H. Xu and A.K. Kristoffersen. Department of Physical Sciences, University of New Brunswick, Saint John, NB E2L 4L5, Canada. M. Lock and B.P. Winnewisser. Physikalisch-Chemisches Institut, Justus-Liebig-Universität, Heinrich-Buff- Ring 58, D Giessen, Germany. J.W.C. Johns. Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, ON K1A 0R6, Canada. 1 Corresponding author ( Can J. Phys 79: (2001) DOI: /cjp-79-2/ NRC Canada

2 436 Can J. Phys Vol. 79, Introduction torsion n = 0, en accord avec de récentes prédictions, mais avec une périodicité inattendue significativement différente de celle du fondamental. Une simple analyse de Fourier en cosinus pour les courbes d énergie donne une origine de la bande de vibration à 1477,6 cm 1 pour ce mode de flexion CH3, proche de la meilleure valeur calculée pour ν 4. [Traduit par la Rédaction] In the last few years, significant progress has been achieved in analysis of the torsion rotation structure of high-resolution infrared (IR) absorption spectra of CH 3 OH in the cm 1 region containing the CH 3 -rocking and OH-bending fundamental bands [1,2], and also in the 3 µm region containing the CH- and OH-stretching fundamentals [3,4]. The present work is the first phase of a high-resolution investigation of the cm 1 region in which the CH 3 -bending fundamentals are located. At low resolution, as shown in Fig. 1, the CH 3 OH IR absorption extending above the strong COstretching band to about 1600 cm 1 is broad and relatively weak and, despite numerous studies, information on the exact locations and detailed structures of absorption bands in this region has been sparse [5,6]. At high resolution, in contrast, the spectrum springs to life with a wealth of detail, and many clear line series become apparent whose lower levels can be confidently assigned from ground-state combination differences [2]. However, this region contains six vibrational fundamentals and numerous torsional combination bands, with a network of interactions coupling and mixing the modes. Thus, although the energies of the upper levels of the observed IR subbands can be accurately determined, the problem of correctly labelling their vibrational parentage from the complex mixture of interacting states is a challenging one and many uncertainties still remain [7]. In this situation, one must proceed spectroscopically by continuing to build a detailed map of the torsion rotation energy manifold in the excited vibrational region to seek systematic patterns that can be related to specific modes. A number of recent developments in the high-resolution vibrational spectroscopy of methanol have provided particular motivation for a study of the CH 3 -bending fundamentals. In 1997, the first clear sign for methanol of a major breakdown in the traditional picture of effective 0ne-dimensional torsional Hamiltonians for the excited vibrational states surfaced with the discovery of an inverted torsional energy pattern for the ν 2 asymmetric A CH-stretching mode of CH 3 OH [3]. (There had been some earlier indications of anomalous structure for the CD 3 -rocking mode of 13 CD 3 OH [8].) Subsequently, in 1998, inversion was reported by Wang and Perry [9] for the ν 9 A asymmetric CH stretch. They showed that this unexpected inverted torsional structure arose naturally in a local-mode internal coordinate picture, and conjectured that it represented a general phenomenon that would be observable for other vibrational fundamentals over a wide class of torsional molecules. Indeed, an inverted torsional pattern was observed shortly afterwards in 1999 for a quite different mode of vibration, namely, the ν 11 A out-of-plane CH 3 rock [1]. Around the same period, theoretical investigations by Halonen and Quack and their co-workers [10 12] were showing that the 3 µm CH-stretching region of the spectrum would be complicated by strong coupling among the CH 3 -bending overtones and the CH-stretching modes, increasing the need for better understanding of the torsion rotation structure of the bending fundamentals. Very recently, ab-initio-based local-mode calculations have been performed for the torsional patterns of the methylbending modes [13]; an inverted structure is predicted for the ν 4 A and ν 10 A asymmetric bends and normal structure for the ν 5 A symmetric bend, but with quite different torsional E A splittings. Thus, our principal aims in undertaking an investigation of the cm 1 Fourier transform (FTIR) spectrum of CH 3 OH were (i) to analyze the torsion rotation structure of this region in detail to seek to identify the bending fundamentals and look for inverted torsional energy patterns to test the above predictions [13]; (ii) to determine accurate vibrational frequencies for the bending fundamentals to provide a better

3 Lees et al. 437 Fig. 1. Low-resolution infrared spectrum of CH 3 OH, showing absorption regions associated with the various vibrational fundamentals. Vertical scale is in arbitrary units, indicating relative absorption strength. The inset highlights the complex region from 1100 to 1650 cm 1 containing the six CH 3 -rocking, OH-bending, and CH 3 - bending fundamentals plus numerous torsional combination bands. The CH 3 -bending subbands observed in the present work are concentrated towards the upper edge of the broad absorption, above 1500 cm 1. foundation for normal-mode and harmonic-force-field calculations and remove the ambiguity due to the lack of solid information from low resolution studies [5,6]; (iii) to provide bending data to assist in the development, currently underway [14], of a complex multimode coupling picture of the 3 µm CH-stretching region. This latter spectral region is currently of considerable astrophysical interest due to progress in IR observations of methanol as a major component of ice mantles in both interstellar dust grains [15] and comets [16]. The present paper describes our current progress in the FTIR spectral analysis in assigning a consistent group of subbands with origins towards the upper edge of the CH 3 -bending spectral region in Fig. 1. The pattern of the K-reduced torsional energy curves for these subbands shows them to be clearly related and thus belonging to the same vibrational mode. However, the torsional pattern is distinctly anomalous. It indeed appears to be inverted as predicted [13], providing further support for the generality of this behaviour, but has an unusual K-periodicity very different from that of the ground vibrational state. The paper is set out as follows. In Sect. 2, the experimental conditions for the recording of the FTIR spectra are outlined briefly. The subband assignments and origin wave numbers are presented in Sect. 3, along with excited substate origin energies and effective B-values obtained by fitting the upper state term values to series expansions in powers of J(J + 1). In Sect. 4, the pattern of the K-reduced torsion vibration energy curves and the results of fitting these to a simple Fourier model are discussed. In Sect. 5, localized perturbations observed for two of the subbands are described. The vibrational identity of the assigned subbands is then considered in Sect. 6, followed by concluding remarks in Sect. 7.

4 438 Can J. Phys Vol. 79, 2001 Table 1. Extrapolated J = 0 origins (in cm 1 ) of n = 0 subbands of a CH 3 -bending fundamental of CH 3 OH. Transition CH 3 -bending subband origins 2. Experimental aspects K K A E 1 E The FTIR spectrum of CH 3 OH in the bending region was initially recorded from cm 1 at a resolution of cm 1 on the modified Bomem DA3.002 Fourier transform spectrometer then in the Herzberg Institute of Astrophysics at the National Research Council of Canada. The path length was 2.0 m in 4 transits of a 0.5 m White cell, the sample pressure was 540 mtorr (1 Torr = Pa) at room temperature, and 100 scans were coadded. Subsequently, the spectrum was recorded again at NRC at cm 1 resolution from cm 1 at 8.0 m path length and a pressure of 500 mtorr, with 56 scans coadded. This spectrum was calibrated using internal water impurity lines as reference standards [17], and was the workhorse for the initial classification of lines into subbranches. More recently, the spectrum was obtained from cm 1 at cm 1 resolution on the Bruker IFS 120 instrument at Justus-Liebig-Universität, Giessen, at a path length of 16.3 m and three different pressures to accentuate different classes of feature. Runs were carried out at room temperature with 250 scans averaged at a mean pressure of 2.6 mbar (2.0 Torr), 321 scans at 0.25 mbar (190 mtorr), and 104 scans at mbar (53 mtorr). Calibration of the spectra was again checked against internal H 2 O standards [17]. Relative to the earlier NRC recording, the peaks in the 0.25 mbar spectrum were somewhat sharper and stronger with a better signal/noise (S/N) ratio, hence the final wave numbers were taken from this spectrum with an uncertainty estimated at ± cm 1 for unblended lines. 3. Subband assignments and power-series expansions In the initial phase of this work, a substantial number of series of related lines with uniform spacing were identified in the spectrum, corresponding to R or Q subbranches of a particular vibrational band. The second differences of the lines in each series were positive, with the Q subbranches shading to higher frequency, indicating an increase in the B-value consistent with a bending vibration. We employed a computer spreadsheet for each series to monitor the trends and allow convenient extrapolation with increasing J. Then, with use of accurate ground-state energies [18,19] and educated guesses about the rotational quantum numbers, we were able to link R and Q subbranch partners through groundstate combination differences and establish the full torsion rotation labelling of the lower states of the subbands. Here, we will adopt the common E(nτK, J ) v T S notation for a vibration torsion rotation energy level, in which n is the torsional quantum number, τ is Dennison s energy curve index [20] related to the torsional symmetry, K is the quantum number for the a-component of the overall rotational angular momentum J, v labels the vibrational state, and T S is the A, E 1,orE 2 torsional symmetry [21]. For

5 Lees et al. 439 Table 2. Substate J = 0 origins and effective B-values from J(J+1) power-series least-squares fit to term values of a CH 3 - bending mode of CH 3 OH. a Substate J = 0 origin Beff bend Fit (nτk)t S (cm) 1 (cm) 1 S.D. b (012) E (5) (10) 0.41 (013) A (7) (2) 1.40 (013) A (6) (2) 1.25 (034) A (13) (9) 0.56 (034) A (29) (19) 1.40 (024) E (16) (10) 0.96 (014) E (13) (10) 0.40 (025) A ± (14) (5) 0.89 (015) E (6) (3) 0.43 (035) E (36) (15) 1.55 (016) A ± (10) (3) 0.67 (036) E (60) (24) 1.89 (026) E (48) (17) 2.47 (037) A ± (27) (7) 1.58 (027) E (67) (29) 0.53 (017) E (19) (6) 0.45 (028) A ± (19) (3) 1.38 (018) E (382) (129) 2.23 (038) E (19) (5) 0.52 (019) A ± (7) (22) 1.22 (039) E (14) (26) c (029) E (6) (11) c (0310) A ± (73) (15) 1.03 (0210) E (69) (13) 0.82 (0211) A ± (163) (28) 1.62 (0112) A ± (131) (22) 0.68 (116) A ± (17) (8) 0.27 a Upper substate term values were determined from K (K 1) CH 3 -bending subbands and fitted to series expansions in powers of J(J + 1) up to the 6th order. Parameter uncertainties shown in parentheses are 1σ standard deviations in the last digit. b Overall unitless standard deviation of the weighted least-squares fit to the CH 3 -bending substate term values. c Initial levels and certain localized levels at higher J are perturbed, hence term values are not well represented as a power series. those states of A torsional symmetry that have resolved asymmetry splitting, a superscript + or is added to K to indicate the specific doublet component. In this work, we are concerned principally with ach 3 -bending vibrational state, which we will denote as v = bend. The CO-stretching state is denoted as v = co, and the ground state asv=gr. Using the above approach, we have so far identified 24 bending subbands for the n = 0 torsional ground state and one tentatively for the n = 1 excited state. All of the assigned CH 3 -bending subbands correspond to K =+1 perpendicular transitions on the basis of their subbranch starting J -values and relative intensity patterns. Approximate extrapolated J = 0 subband origins are given in Table 1 to illustrate their locations, which are quite widely distributed across the spectrum as expected for K = 1 transitions. We note that although the associated K = 1 subband wave numbers can be accurately

6 440 Can J. Phys Vol. 79, 2001 Table 3. Molecular parameters (in cm 1 )forach 3 - bending mode and the ground vibrational state of CH 3 OH. Ground Parameter CH 3 -bend state E v + a a B eff (A B) eff a C K a a a a a ρ b a E A splitting c ωv d a Varied in the Fourier fit to the CH 3 -bending substate origins. b Dimensionless parameter; ρ I a2 /I a (See ref. 21). c E A energy separation between E and A substates for K = 0. Value for the CH 3 -bend is derived from (3) using the fitted Fourier parameters. Ground-state value is from results in refs. 18 and 19. d Vibrational band origin, calculated as ω v = {(E v + a0 v) agr 0 }, where agr 0 is the ground-state torsional zero-point energy. predicted from ground-state combination differences, the K = 1 P-subbranches are barely visible in the spectrum and are very much weaker than the K =+1 R-subbranches. This intensity anomaly is quite puzzling. Next, we determined upper-state term values by adding the appropriate ground-state energies as tabulated by Moruzzi et al. [18] to the subband IR wave numbers. We then calculated hypothetical J = 0 origins and effective B-values for the upper CH 3 -bending substates by least-squares fitting the term values to series expansions in powers of J(J + 1), E(nτK, J ) bend = W bend + B bend eff J(J + 1) D bend J 2 (J + 1) 2 + H bend J 3 (J + 1) (1) where the substate origin W bend, effective B-value Beff bend, and higher order expansion coefficients D bend, H bend... are all phenomenological parameters dependent on the particular (nτk) bend CH 3 - bending substate. In the fits, term values were weighted by the inverse squares of the corresponding IR wave-number accuracies, estimated as ± cm 1 for well-resolved lines and ±0.002 cm 1 for blended lines. Several subbands displayed J -localized perturbations, hence the perturbed lines were zero-weighted. In Table 2, we present the J = 0 substate origins and effective B-values obtained in the fitting, with standard deviations in parentheses. The A + and A term values were fitted separately for the (013) and (034) substates, but the A ± origins and B-values agree to within their uncertainties as they should. The typical representative value of Beff bend is 0.82 cm 1. The fact that this is higher than the ground-state value of cm 1 is indicative of a bending mode. The overall standard deviations of the fits given in the last column of Table 2 are reasonably close to the expected statistical value of 1.0 except for the K = 9 E 1 and E 2 substates. For the latter, there appear to be significant perturbations to the initial lines of the K = 9 8 E 1 and E 2 subbands as well as localized resonances at higher J, causing problems for the power-series model. The higher order parameters D, H, were generally

7 Lees et al. 441 not statistically well-determined and have limited physical significance, so are not included in Table 2. Fuller details of the subband wave numbers, upper state term values, and series expansion coefficients are available from one of us (RML) on request. 4. K-reduced energy pattern and fit to Fourier model The power-series fitting to (1) effectively removes the J -rotational dependence of the bending substate energies. In order then to separate out the K-rotational dependence and isolate the torsional energy pattern in the excited vibrational state, a useful approach is to plot K-reduced energy τ-curves [1,3,9,20]. The rotational contribution (A B)K 2, where (A B)is the effective K-rotational constant, is subtracted from the substate origins and the resulting K-reduced energies are plotted against K for given values of τ. When this was done for the data of Table 2, using the ground-state value of 3.45 cm 1 for (A B), the resulting τ-curves had some residual quadratic K 2 variation due to the vibrational change in rotational constants, but also appeared to have a significant linear shift with K, analogous to that observed for the CH-stretching modes [3,9]. Therefore, we tried fitting the CH 3 -bending origins to a model including both linear and quadratic K-dependence, W(nτK) bend = (A B) bend K 2 + CK bend K + Ebend v + E tor (nτk) bend (2) where CK bend is a constant, Ebend v is the purely vibrational energy, and the E tor (nτk) bend are the torsional energies. In the usual model, the K-reduced torsion vibration energies should fall on τ-curves with period 3 in the variable (1 ρ)k, where ρ is a scale factor approximately equal to the ratio I a2 /I a between the axial moments of inertia of the methyl group and the whole molecule, respectively [1,20,21]. The curve for τ = 2 is shifted by 1 unit along the (1 ρ)k axis relative to τ = 1, and the curve for τ = 3 is shifted by +1 unit. Thus, the K-reduced energies can be compactly represented as a Fourier cosine series [1,9] with use of a symmetry index σ : W(nτK) bend (A B) bend K 2 CK bend K = Ebend v + E tor (nτk) bend = E bend v + a bend 0 + a bend 1 cos { [(1 ρ)k σ ] 2π 3 } { + a2 bend cos [(1 ρ)k σ ] 4π 3 } (3) where a0 bend is the torsional zero-point energy and σ equals 0, 1, or +1 for τ = 1, 2, and 3, respectively. This model appeared to work quite well previously for the inverted torsional curves of the ν 11 out-ofplane rocking mode [1] as well as the CH stretches (See Fig. 1 of ref. 9). Accordingly, we set up a simple Excel spreadsheet analysis for the bending substate origins with one column for the observed origins from Table 2, one for those calculated from (2) and (3) using trial values for the molecular constants (Ev bend + a0 bend ), (A B) bend, CK bend, abend 1, a2 bend, and ρ, and a third for the (obs calc) differences. Then, we determined the optimum values for the constants by using the Excel Solver function to minimize the sum of the squares of the (obs calc) residuals. The resulting parameters are shown in Table 3 along with ground state values for comparison. The quality of the Fourier representation is displayed in Fig. 2, in which the plotted points are the K-reduced energies W(nτK) bend (A B) bend K 2 CK bend K obtained using the fitted values of (A B) bend and CK bend from Table 3, and the continuous τ-curves are the torsion vibration energies drawn from the Fourier series in (3) using the Table 3 coefficients. Clearly, there are major discrepancies for this vibrational mode between the plotted points and the Fourier τ-curves, with a distinctly anomalous and apparently nonuniform periodicity for the former. Thus, substantial modelling problems still need to be solved and extrapolation to the K = 0 origin of the τ-curves to determine the E A splitting is highly uncertain. Nevertheless, the curves do appear to be inverted relative to the usual model, consistent with prediction for the asymmetric CH 3 -bending modes [13]. Accordingly, the K = 0 E A splitting obtained from our parameters in Table 3 is negative, with a magnitude slightly less than that of the

8 442 Can J. Phys Vol. 79, 2001 Fig. 2. K-reduced substate origin energies (plotted points) and fitted Fourier τ-curves (continuous lines) for n = 0 substates of a CH 3 -bending mode of CH 3 OH. The τ-curves are inverted compared to the n = 0 picture for the conventional one-dimensional torsional Hamiltonian. ground state. We note that a more rigorous least-squares analysis for the parameters is possible, but did not feel it was warranted at this stage with the large uncertainties in the modelling. The vibrational band origin for the bending mode is given according to the above model by ω bend = (Ev bend + a0 bend ) a gr 0, where agr 0 is the ground-state torsional zero-point energy obtained from the reported J = K = 0 term values [18]. Our result of cm 1 from Table 3 is very close to the value of cm 1 calculated for the ν 4 asymmetric bend in the recent ab initio study of Miani et al. [22]. 5. Localized perturbations in the spectrum Several of the CH 3 -bending subbands show J -localized perturbations, which generally arise from level-crossing resonances with substates of other vibrational modes. So far, we have information on the interacting partner states for two of these resonances. In the first system, illustrated in the J - reduced energy diagram of Fig. 3, the (012) bend E 1 substate levels cross those of a state labelled as (n12) v E 1, which is the upper state for a relatively strong parallel K = 0 subband observed in the spectrum with its origin at cm 1. We can firmly identify the lower level of the subband from combination differences as (112) o E 1 in the ground vibrational state, but the vibration torsion identity of the upper (n12) v E 1 level has not yet been established. It lies about 63 cm 1 above the (212) co E 1 CO-stretching state [18], and the subband wave-number second differences are similar to those seen for CH 3 -rocking and OH-bending subbands [1,2], indicating similar B-values. From the location of this (n12) v E 1 substate in the overall energy manifold and its rotational B-value, it is likely associated with either n = 2 torsionally excited CH 3 rocking or n = 1 OH-bending modes. A puzzling aspect of the system is that the perturbation seems significantly larger for the (n12) v E 1 than for the (012) bend E 1 substate, particularly for J = 9, hinting that there may be other levels involved whose presence has not yet been detected. There do appear to be extra perturbation-induced lines in the spectrum connecting to the J = 10 upper levels, but the relative intensities are inconsistent and the presence of J = 10 mixing and intensity borrowing is not yet unambiguously established. The J = 10 perturbations are of the order of 0.3 cm 1 for the (012, 10) bend E 1 level and +0.4 cm 1 for the (n12, 10) v E 1 level, indicating a sizeable anharmonic interaction between the two vibrational modes.

9 Lees et al. 443 Fig. 3. J -reduced energies showing a level-crossing resonance between the (012) bend E 1 CH 3 -bending substate of CH 3 OH and an (n12) v E 1 interaction partner. The term values of the latter are established from a K = 0 subband originating from the (112) o E 1 substate of the ground vibrational state. The J -reduced energies are equal to the term values minus 0.8J(J + 1), where 0.8 cm 1 is the approximate B-value. Fig. 4. J -reduced energies showing the level crossing between the (014) bend E 2 CH 3 -bending and (214) co E 2 CO-stretching substates of CH 3 OH. The J - reduced energies are equal to the term values minus 0.803J(J + 1). The second resonance has the (014) bend E 2 bending substate interacting with the (214) co E 2 torsionally excited substate of the CO-stretching mode, and is shown in Fig. 4. The assignment of the parallel K = 0 (214) co E 2 subband was reported relatively recently [23]. Its lower level is established from ground-state combination differences, while the upper state energy and rotational B-value fit well with those for other known n = 2 CO-stretching subbands. The (214) co E 2 subband wave-number second differences are strongly perturbed above J = 10, in a pattern complementary to that for the (014) (023) bend E 2 subband. For both of the interacting partner states, our assignments currently extend just up to the level-crossing point, which is extrapolated to occur between J = 18 and 19. Thus, the difference of cm 1 between the perturbed energies of the two states at J = 18 will be close to the separation of the curves at the crossing point, equal to twice the interaction matrix element. This gives W int 0.72 cm 1 as the estimated magnitude of this torsion-mediated anharmonic coupling. 6. Identity of the observed CH 3 -bending mode Of the three CH 3 -bending fundamentals, the ν 5 A symmetric (umbrella) bend is expected to be a parallel band and is reported to lie near 1455 cm 1 [5]. The two asymmetric bending fundamentals, ν 4 (A ) and ν 10 (A ), are both expected to be perpendicular bands with ν 4 predicted to lie near 1474 cm 1 [5]. There are some differences in earlier reported predictions for ν 10, ranging from about 1472 cm 1 [5] down to 1460 cm 1 [10]. However, a very recent high level ab initio study by Miani et al. [22] employing

10 444 Can J. Phys Vol. 79, 2001 Fig. 5. Energy level and transition scheme showing CH 3 OH IR transition wave numbers and ground-state K- doublet splittings (in cm 1 ) establishing the transition ordering and J = 21 doublet splitting of cm 1 for the (013) bend A substate. The A± ordering for the upper levels shown on the left is inverted relative to the K = 3 ground-state doublets, and would correspond to b-type IR selection rules consistent with an A ν 4 upper state. The A± ordering on the right would correspond to c-type selection rules, consistent with an A ν 10 upper state. an anharmonic force field and including Fermi intermode coupling has given the best current predictions of , , and cm 1 for the ν 4, ν 5, and ν 10 modes, respectively. Our observed subbands are located towards the high side of the broad absorption in the CH 3 -bending region shown at low resolution in Fig. 1. Above about 1525 cm 1, the spectrum is very well-resolved, and almost all of the significant lines have been assigned to our bending mode. There appears to be little possibility that another perpendicular fundamental could lie at higher wave number. In the lower regions, Fig. 1 shows a hole in the absorption just above 1440 cm 1, with a sudden spike and jump in absorption at about 1450 cm 1. At high resolution, the spectrum is indeed very quiet from cm 1, but at cm 1 there is a sudden onset of a congested Q branch shading to higher wave number, giving the abrupt rise in absorption seen in Fig. 1. The first few lines in this Q branch are strong and well-resolved, with the intensity pattern of a parallel K = 0 subbranch, and we have assigned them as K = 7A for n = 0 by identifying the associated R and P subbranches, which are much weaker. It seems definite that this Q branch belongs to the ν 5 symmetric bend from its frequency and parallel character, although we have not so far been able to identify further individual ν 5 subbands. The spectrum remains extremely crowded moving up through about 1490 cm 1, and then gradually thins out with more isolated and well-defined line series. This would be consistent with a ν 10 perpendicular band lying hidden in the 1466 cm 1 region, as ν 10 is expected to be a weak c-type fundamental. So far, however, our progress in assigning the spectral structure in the cm 1 region has been limited, due to the high line density. Overall, we believe that (i) the relatively complete assignment of all significant spectral features towards the high side of the bending absorption region and (ii) the very close agreement between the predicted ν 4 band origin of cm 1 [22] and our value of cm 1 from the Fourier fit to the substate origins, both strongly favour the identification of our observed band as the ν 4 A asymmetric bending fundamental.

11 Lees et al. 445 In principle, one other clue is available from our spectrum, but paradoxically it points more towards the opposite vibrational assignment, i.e., the ν 10 A asymmetric bend! For the (013) bend (022) bend A subband, the K-doubling is resolved, allowing the A± transition selection rules to be checked for b-type or c-type character. In Fig. 5, we show the energy level and transition diagram for the R- and Q-subbranch lines accessing the J = 21 K-doublet levels of the (013) bend upper state. To satisfy the combination relations among the IR transition wave numbers and the known ground-state K-doublet splittings [18,19] given in Fig. 5, the IR transitions must follow the specific pattern shown, with good agreement between the two independent combination difference results of and cm 1 for the upper doublet splitting. Note that the latter is significantly larger than the corresponding groundstate J = 21 splitting of cm 1 [18]. Now, if the A± ordering for the (013) bend upper state were the same as the ground state, as shown on the right-hand side of Fig. 5 with the A + level below A for K = 3, then the IR transitions would follow c-type selection rules. This would imply A symmetry for the upper state, making it the ν 10 asymmetric bend. However, asymmetry splittings are very sensitive to vibrational interactions [24] and have been found to be anomalous in a number of cases. The (013) bend (022) bend A subband in fact displays a localized perturbation around J = 14, so there is at least one unidentified state in the vicinity. Thus, we believe the picture on the left-hand side of Fig. 5 is more likely, with inverted (013) bend K-doubling and b-type IR selection rules consistent with the A symmetry of the ν 4 upper state. In future, we hope that identification of additional line series observed in the spectrum but not yet assigned will shed further light on the K-doubling and vibrational identity questions. Further data on the transition patterns for K-doublets would be particularly useful, hence we are actively seeking assignments of low-k Asubbands in the spectrum with resolved asymmetry splittings. 7. Discussion and conclusions In this work, we have recorded the Fourier transform spectrum of CH 3 OH at high resolution in the CH 3 -bending region from cm 1 and have identified 25 K = 1 subbands of a perpendicular vibrational fundamental, which we believe to be the ν 4 (A ) asymmetric bending mode. The torsion rotation assignments of the lower levels of the subbands are firmly established through ground-state combination differences, allowing determination of the upper state term values by addition of known ground-state energies [18,19] to the experimental IR transition wave numbers. These term values have been fitted for each substate to series expansions in powers of J(J+1) to find the J -independent substate origins and effective B-values. The substate origins have then been fitted to a model incorporating both linear and quadratic K-dependent terms and a Fourier expansion of the torsional energies, in order to examine the torsional pattern and determine the vibrational band origin. There are several interesting and sometimes anomalous aspects to this vibrational band of CH 3 OH. First of all, the K-reduced torsion vibration energy curves appear to be inverted compared to the customary one-dimensional model, with the E energy below A for K = 0. However, such inversion has also been reported for the ν 2 and ν 9 CH-stretching modes [3,9] and the ν 11 outof-plane CH 3 rock [1], and may well be a universal phenomenon for certain excited vibrational states of torsional molecules. Secondly, only K =+1 subbands have significant intensity in the spectrum. Although we can predict the K = 1 subband wave numbers accurately through combination differences, the lines are surprisingly weak. Thirdly, the substate origins show a substantial linear shift with K, with a value of cm 1 for the shift coefficient C K comparable to that seen for the ν 9 band [9], suggesting quite strong Coriolis effects.

12 446 Can J. Phys Vol. 79, 2001 Fourth is the large apparent change from the ground state in the K-scaling factor ρ fitted to the τ-curves, as seen in Table 3, along with the nonuniform period of oscillation of the K-reduced torsion vibration energies seen in Fig. 2. While the CH 3 -bending motion is certainly expected to have some impact on the effective axial moments of inertia determining ρ, a change of the magnitude shown in Table 3 seems unrealistic. Thus, these anomalies in the torsional A E energy ordering, the ρ value and the energy periodicity reinforce the need to reexamine the torsion vibration Hamiltonian from the beginning in terms of a coupled torsion vibration basis. Both the location of our vibrational band at the upper edge of the CH 3 -bending absorption region in Fig. 1 and the increase of effective B-value with vibrational excitation are consistent with this being the ν 4 (A ) asymmetric CH 3 -bending mode. Our band origin of cm 1, although rather uncertain due to questions about the model, matches well with the best reported calculation of cm 1 for the ν 4 mode [22]. Although the transition pattern for the K = 3A bending levels would imply c-type (A ) IR selection rules if the K-doublet A± ordering were the same as the ground state, indicating an alternative vibrational assignment as the ν 10 (A ) mode, we believe it more likely that the K = 3A bending doublets are inverted. However, more definitive experimental evidence is needed. There are still numerous unassigned subbranch line series in the spectrum, and we are actively seeking to identify transitions of the other asymmetric CH 3 -bending partner as well as further subbands of the ν 5 symmetric bend to fill out the vibration torsion rotation energy map and resolve the CH 3 -bending assignment question definitively in the near future. Acknowledgements Financial support to RML and LHX from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. We thank Pam Chu of NIST for furnishing the low-resolution spectrum of CH 3 OH, and J.T. Hougen of NIST for valuable discussions and continuing interest in this project. References 1. R.M. Lees and L.-H. Xu. Phys. Rev. Lett. 84, 3815 (2000). 2. R.M. Lees, L.-H. Xu, and J.W.C. Johns. In The 53rd International Symposium on Molecular Spectroscopy. Columbus, Ohio. June Paper FA L.-H. Xu, X. Wang, T.J. Cronin, D.S. Perry, G.T. Fraser, and A.S. Pine. J. Mol. Spectrosc. 185, 158 (1997). 4. R.H. Hunt, W.N. Shelton, F.A. Flaherty, and W.B. Cook. J. Mol. Spectrosc. 192, 277 (1998). 5. A. Serrallach, R. Meyer, and Hs. H. Günthard. J. Mol. Spectrosc. 52, 94 (1974). 6. F.C. Cruz, A. Scalabrin, D. Pereira, P.A.M. Velazquez, Y. Hase, and F. Strumia. J. Mol. Spectrosc. 156, 22 (1992). 7. R.M. Lees and L.-H. Xu. J. Mol. Spectrosc. 196, 220 (1999). 8. L.-H. Xu and R.M. Lees. J. Opt. Soc. Am. B, 11, 155 (1994). 9. X. Wang and D.S. Perry. J. Chem. Phys. 109, (1998). 10. L. Halonen. J. Chem. Phys. 106, 7931 (1997). 11. V. Hänninen, M. Horn, and L. Halonen. J. Chem. Phys. 111, 3018 (1999). 12. M. Quack and M. Willeke. J. Chem. Phys. 110, (1999). 13. L.-H. Xu. J. Chem. Phys. 113, 3980 (2000). 14. L.-H. Xu, M. Abbouti Temsamani, X. Wang, Y. Ma, A. Chirokolava, T.J. Cronin, and D.S. Perry. In The 55th International Symposium on Molecular Spectroscopy. Columbus, Ohio. June, Paper RB T.Y. Brooke, K. Sellgren, and T.R. Geballe. Astrophys. J. 517, 883 (1999). 16. M.J. Mumma, M.A. DiSanti, N. Dello Russo, K. Magee-Sauer, and T.W. Rettig. Astrophys. J. Lett. 531, L155 (2000). 17. G. Guelachvili and K.N. Rao. Handbook of infrared standards. Academic Press, San Diego

13 Lees et al G. Moruzzi, B.P. Winnewisser, M. Winnewisser, I. Mukhopadhyay, and F. Strumia. Microwave, infrared, and laser transitions of methanol: Atlas of assigned lines from 0 to 1258 cm 1. CRC Press, Fla L.-H. Xu and J.T. Hougen. J. Mol. Spectrosc. 173, 540 (1995). 20. D.G. Burkhard and D.M. Dennison. J. Mol. Spectrosc. 3, 209 (1959). 21. R.M. Lees and J.G. Baker. J. Chem. Phys. 48, 5299 (1968). 22. A. Miani, V. Hänninen, M. Horn, and L. Halonen. Mol. Phys. 98, 1737 (2000). 23. R.M. Lees and L.-H. Xu. In The 54th International Symposium on Molecular Spectroscopy. Columbus, Ohio. June Paper TF R.M. Lees. Phys. Rev. Lett. 75, 3645 (1995).

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