Spectra of the CH stretch overtone bands. The wave number scale is relative to the values of ␯ 0 , 13 455, 11 000, 8445, 5745 and 2940 cm Ϫ 1 , respectively ͑ a ͒ – ͑ e ͒ . The dashed lines serve as a guide to the eye to follow the positions of the ␯ a and ␯ b overtone bands at each overtone level. The triangles under trace ͑ d ͒ indicate band positions predicted in Ref. 32. 

Contexts in source publication

Context 1

... assignments, the most intense line of each band is chosen as the band center, ̃ . Depending on the form of the band, this may introduce an error of about 10 to 15 cm Ϫ 1 relative to the true band center. 2,4 The observed wave numbers and assignments are listed in Table I. Figure 4 shows Birge–Sponer plots for the families n ␯ 1 ϩ ␯ 6 , n ␯ 1 ϩ ␯ 8 and n ␯ 1 ϩ ␯ 6 ϩ ␯ 8 , including the band centers from this work along with those from Fang et al. 18 The Birge–Sponer plot for the family n ␯ 1 is included for comparison. 13 The band at 12 939 cm Ϫ 1 ͑ Fig. 3 and Table I ͒ is likely to be 3 ␯ 1 ϩ ␯ 6 ϩ ␯ 8 but is shifted 90 cm Ϫ 1 to higher wave number from its expected position and therefore is not included in the Birge–Sponer regression. If this assignment is in correct, it implies that this band is affected by a strong perturbation. The slopes and intercepts of the Birge–Sponer plots in Fig. 4 are similar. Small differences can arise from the de- termination of the band-center and from cross-anharmonicity between the different vibrational modes. Our confidence in the vibrational assignments is based on these Birge–Sponer plots together with the band contour considerations outlined below. The combination bands involving the ␯ 6 vibration are spread over a wide spectral range and have contours that are markedly different from other bands. This is most clearly visible for the ␯ ϩ ␯ , 2 ␯ ϩ ␯ , and ␯ ϩ ␯ ϩ ␯ bands Figs. 2 c , 2 b , and 3 c , which have the highest signal-to- noise ratio. In each of these bands, several of the subbands are shifted 50 to 160 cm Ϫ 1 to higher wave number from the apparent band center. One such subband, expanded in the inset of Fig. 2 ͑ b ͒ , has the clear P and R branches expected for a K ϭ 0 ← 0 subband. The simplicity of its structure sug- gests that this feature is not an entire band in itself, since at the jet temperature of 5 to 10 K, 2 an entire vibrational band would have a dozen or more subbands arising from K Љ ϭϪ 1, 0, 1 and A and E symmetries. It is more likely to be a subband of 2 ␯ 1 ϩ ␯ 6 . The spread out structure of the ␯ 6 combination bands can be explained by analogy with the ␯ 6 fundamental. Rota- tionally resolved spectra of the ␯ 6 fundamental of both 12 CH 3 OH ͑ Ref. 28 ͒ and 13 CH 3 OH ͑ Ref. 29 ͒ reveal an excep- tionally large torsional tunneling splitting ͑ about 24 cm Ϫ 1 for the COH bend upper state as compared to 9.1 cm Ϫ 1 for the ground state ͒ , and this causes the subbands origins to be more widely spread. 29 Lees et al. 28 found that torsionally excited states of the methyl rocks ( ␯ 7 and ␯ 11 ) and of the CO stretch ( ␯ 8 ) fall in the same region as the ␯ 6 fundamental. The strong mixing among these bands results in intensity transfer to the torsional combination bands, which are more spread out than the fundamentals. For the CH stretching overtone bands, we use the local mode labels, ␯ a and ␯ b , employed by Fang et al. for assignment of their photoacoustic spectra. 18 The ‘‘unique’’ CH stretch, ␯ a , refers to a local vibration of the CH bond anti to the OH bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure ...

Context 2

... CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , and ␯ . To characterize the band positions in the overtone region, we carried out a least squares fit of the transition wave numbers in Table I to the anharmonic expression in Eq. ͑ 1 ͒ . Where the data are available, the band centers in Table I are derived from rotationally assigned high-resolution spectra. These band centers, ␯ , which represent the energy difference between the J ϭ 0 levels of the upper and lower states, are not equal to the band origins that result from fitting high resolution data to a torsion-rotation Hamiltonian. The latter would be the difference between the minima of the one- dimensional effective torsional potentials for the upper and lower states, and they differ from our measured ␯ by the change in torsional zero-point energy upon vibrational excitation ͑ a difference of 9 to 24 cm Ϫ 1 for the bands ␯ 1 to 3 ␯ 1 ). 2,20 We have chosen to use the band centers ␯ in our fits because the data are available for more bands. For the many bands without detailed rotational assignments, each ␯ tabulated in Table I is approximated as the wave number of the absorption maximum in the band profile. Our fit differs from that of H ̈ nninen and Halonen 32 in several respects. Most importantly, their fit uses dozens of fixed parameters derived from ab initio calculations, whereas ours is strictly empirical. A full understanding of the methanol spectra will certainly require an effective synthesis of theory and experiment, but the ...

Context 3

... bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , and ␯ . To characterize the band positions in the overtone region, we carried out a least squares fit of the transition wave numbers in Table I to the anharmonic expression in Eq. ͑ 1 ͒ . Where the data are available, the band centers in Table I are derived from rotationally assigned high-resolution spectra. These band centers, ␯ , which represent the energy difference between the J ϭ 0 levels of the upper and lower states, are not equal to the band origins that result from fitting high resolution data to a torsion-rotation Hamiltonian. The latter would be the difference between the minima of the one- dimensional effective torsional potentials for the upper and lower states, and they differ from our measured ␯ by the change in torsional zero-point energy upon vibrational excitation ͑ a difference of 9 to 24 cm Ϫ 1 for the bands ␯ 1 to 3 ␯ 1 ). 2,20 We have chosen to use the band centers ␯ in our fits because the data are available for more bands. For the many bands without detailed rotational assignments, each ␯ tabulated in Table I is approximated as the wave number of the absorption maximum in the band profile. Our fit differs from that of H ̈ nninen and Halonen 32 in ...

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... geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , and ␯ . To characterize the band positions in the overtone region, we carried out a least squares fit of the transition wave numbers in Table I to the anharmonic expression in Eq. ͑ 1 ͒ . Where the data are available, the band centers in Table I are derived from rotationally assigned high-resolution spectra. These band centers, ␯ , which represent the energy difference between the J ϭ 0 levels of the upper and lower states, are not equal to the band origins that result from fitting high resolution data to a torsion-rotation Hamiltonian. The latter would be the difference between the minima of the one- dimensional effective torsional potentials for the upper and lower states, and they differ from our measured ␯ by the change in torsional zero-point energy upon vibrational excitation ͑ a difference of 9 to 24 cm Ϫ 1 for the bands ␯ 1 to 3 ␯ 1 ). 2,20 We have chosen to use the band centers ␯ in our fits because the data are available for more bands. For the many bands without detailed rotational assignments, each ␯ tabulated in Table I is approximated as the wave number of the absorption maximum in the band profile. Our fit differs from that of H ̈ nninen and Halonen 32 in several respects. Most importantly, their fit uses dozens of fixed parameters derived from ab initio calculations, whereas ours is strictly empirical. A full understanding of the methanol spectra will certainly require an effective synthesis of theory and experiment, but the purpose of our present fit is just to characterize the experimental data. Second, we have included CH overtone data in the range v CH ϭ 3 – 7. Finally, the experimental wave numbers for ␯ 1 , ␯ 2 , and ␯ 9 on which the two fits are based differ by as much as 10 cm Ϫ 1 because of differences in the way torsional tunneling and torsional zero point energy are handled. Neither fit includes the torsional tunneling dynamics explicitly. A total of 36 bands were included in the fit, yielding a root mean square deviation of 12 cm Ϫ 1 . The resulting spectroscopic parameters, shown in Table II, include the har- monic frequencies ␻ 0 i of the six relevant vibrational modes and their anharmonicities x ii and x i j . The OH and CH stretch parameters are in agreement with those of Fang et al. , 18 except that the confidence intervals are reduced and the CH anharmonicities are a little larger in magnitude. The difference between x and x is now significant and it is evident visually as the divergence of the slope lines in Fig. 7. This difference implies that the torsion-vibration coupling parameter ␮ increases with CH stretch excitation. The parameters involving the CO stretch and COH bend are poorly determined because of the uncertainty in the band origins and the low level of excitation of these modes in the observed combination bands. We have measured the infrared spectrum of methanol from 5000 to 14 000 cm Ϫ 1 using the IRLAPS technique and have assigned most of the observed bands. The spectrum is dominated by the OH stretch overtones and combination bands involving the OH stretch, CO stretch, and COH bend. The band positions were fit to a simple expression involving the low order anharmonicity constants. All of OH stretch combination bands show sharp rotational structure, which remains unassigned for many of the bands. In contrast, the CH overtone bands are weaker, often structureless, and fewer combinations with other modes are evident in the spectrum. It appears that the observed CH overtones undergo faster IVR than nearby OH stretch combinations. We thank the E ́ cole Polytechnique F ́d ́ rale de Lausanne and the Fond National Suisse through Grant No. 21- 67070.01 for their generous support of this work, as well as support from the United States Department of Energy under Grant No. ...

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... bands, which are more spread out than the fundamentals. For the CH stretching overtone bands, we use the local mode labels, ␯ a and ␯ b , employed by Fang et al. for assignment of their photoacoustic spectra. 18 The ‘‘unique’’ CH stretch, ␯ a , refers to a local vibration of the CH bond anti to the OH bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , and ␯ . To characterize the band positions in the overtone region, we carried out a least squares fit of the transition wave numbers in Table I to the anharmonic expression in Eq. ͑ 1 ͒ . Where the data are available, the band centers in Table I are derived from rotationally assigned high-resolution spectra. These band centers, ␯ , which represent the energy difference between the J ϭ 0 levels of the upper and lower states, are not equal to the band origins that result from fitting high resolution data to a torsion-rotation Hamiltonian. The latter would be the difference between the minima of the one- dimensional effective torsional potentials for the upper and lower states, and they differ from our measured ␯ by the change in torsional zero-point energy upon vibrational excitation ͑ a difference of 9 to 24 cm Ϫ 1 for the bands ␯ 1 to 3 ␯ 1 ). 2,20 We have chosen ...

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... splitting ͑ about 24 cm Ϫ 1 for the COH bend upper state as compared to 9.1 cm Ϫ 1 for the ground state ͒ , and this causes the subbands origins to be more widely spread. 29 Lees et al. 28 found that torsionally excited states of the methyl rocks ( ␯ 7 and ␯ 11 ) and of the CO stretch ( ␯ 8 ) fall in the same region as the ␯ 6 fundamental. The strong mixing among these bands results in intensity transfer to the torsional combination bands, which are more spread out than the fundamentals. For the CH stretching overtone bands, we use the local mode labels, ␯ a and ␯ b , employed by Fang et al. for assignment of their photoacoustic spectra. 18 The ‘‘unique’’ CH stretch, ␯ a , refers to a local vibration of the CH bond anti to the OH bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , and ␯ . To characterize the band positions in the overtone region, we carried out a least squares fit of the transition wave numbers in Table I to the anharmonic expression in Eq. ͑ 1 ͒ . Where the data are available, the band centers in Table I are derived from rotationally assigned high-resolution spectra. These band centers, ␯ , which represent the energy difference between the J ϭ 0 levels of the upper and lower states, are not equal to ...

Context 7

... to 10 K, 2 an entire vibrational band would have a dozen or more subbands arising from K Љ ϭϪ 1, 0, 1 and A and E symmetries. It is more likely to be a subband of 2 ␯ 1 ϩ ␯ 6 . The spread out structure of the ␯ 6 combination bands can be explained by analogy with the ␯ 6 fundamental. Rota- tionally resolved spectra of the ␯ 6 fundamental of both 12 CH 3 OH ͑ Ref. 28 ͒ and 13 CH 3 OH ͑ Ref. 29 ͒ reveal an excep- tionally large torsional tunneling splitting ͑ about 24 cm Ϫ 1 for the COH bend upper state as compared to 9.1 cm Ϫ 1 for the ground state ͒ , and this causes the subbands origins to be more widely spread. 29 Lees et al. 28 found that torsionally excited states of the methyl rocks ( ␯ 7 and ␯ 11 ) and of the CO stretch ( ␯ 8 ) fall in the same region as the ␯ 6 fundamental. The strong mixing among these bands results in intensity transfer to the torsional combination bands, which are more spread out than the fundamentals. For the CH stretching overtone bands, we use the local mode labels, ␯ a and ␯ b , employed by Fang et al. for assignment of their photoacoustic spectra. 18 The ‘‘unique’’ CH stretch, ␯ a , refers to a local vibration of the CH bond anti to the OH bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , ...

Context 8

... P and R branches expected for a K ϭ 0 ← 0 subband. The simplicity of its structure sug- gests that this feature is not an entire band in itself, since at the jet temperature of 5 to 10 K, 2 an entire vibrational band would have a dozen or more subbands arising from K Љ ϭϪ 1, 0, 1 and A and E symmetries. It is more likely to be a subband of 2 ␯ 1 ϩ ␯ 6 . The spread out structure of the ␯ 6 combination bands can be explained by analogy with the ␯ 6 fundamental. Rota- tionally resolved spectra of the ␯ 6 fundamental of both 12 CH 3 OH ͑ Ref. 28 ͒ and 13 CH 3 OH ͑ Ref. 29 ͒ reveal an excep- tionally large torsional tunneling splitting ͑ about 24 cm Ϫ 1 for the COH bend upper state as compared to 9.1 cm Ϫ 1 for the ground state ͒ , and this causes the subbands origins to be more widely spread. 29 Lees et al. 28 found that torsionally excited states of the methyl rocks ( ␯ 7 and ␯ 11 ) and of the CO stretch ( ␯ 8 ) fall in the same region as the ␯ 6 fundamental. The strong mixing among these bands results in intensity transfer to the torsional combination bands, which are more spread out than the fundamentals. For the CH stretching overtone bands, we use the local mode labels, ␯ a and ␯ b , employed by Fang et al. for assignment of their photoacoustic spectra. 18 The ‘‘unique’’ CH stretch, ␯ a , refers to a local vibration of the CH bond anti to the OH bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental ...

Context 9

... analyzing each family of bands, we expect the Birge– Sponer constants A and B to be close to values reported for the ␯ overtones, 3773.2 and Ϫ 86.3 cm Ϫ 1 , respectively. 13 Figure 2 shows the portions of the IRLAPS spectrum of CH 3 OH containing the families of combination bands, n ␯ 1 ϩ ␯ 6 and n ␯ 1 ϩ ␯ 8 . In this figure, these families are plotted relative to the wave number of the respective n ␯ 1 overtone band in such a way that the bands in a given family appear stacked above one another. The overtone family n ␯ 1 ϩ ␯ 6 ϩ ␯ 8 is similarly shown in Fig. 3. In the absence of detailed rotational assignments, the most intense line of each band is chosen as the band center, ̃ . Depending on the form of the band, this may introduce an error of about 10 to 15 cm Ϫ 1 relative to the true band center. 2,4 The observed wave numbers and assignments are listed in Table I. Figure 4 shows Birge–Sponer plots for the families n ␯ 1 ϩ ␯ 6 , n ␯ 1 ϩ ␯ 8 and n ␯ 1 ϩ ␯ 6 ϩ ␯ 8 , including the band centers from this work along with those from Fang et al. 18 The Birge–Sponer plot for the family n ␯ 1 is included for comparison. 13 The band at 12 939 cm Ϫ 1 ͑ Fig. 3 and Table I ͒ is likely to be 3 ␯ 1 ϩ ␯ 6 ϩ ␯ 8 but is shifted 90 cm Ϫ 1 to higher wave number from its expected position and therefore is not included in the Birge–Sponer regression. If this assignment is in correct, it implies that this band is affected by a strong perturbation. The slopes and intercepts of the Birge–Sponer plots in Fig. 4 are similar. Small differences can arise from the de- termination of the band-center and from cross-anharmonicity between the different vibrational modes. Our confidence in the vibrational assignments is based on these Birge–Sponer plots together with the band contour considerations outlined below. The combination bands involving the ␯ 6 vibration are spread over a wide spectral range and have contours that are markedly different from other bands. This is most clearly visible for the ␯ ϩ ␯ , 2 ␯ ϩ ␯ , and ␯ ϩ ␯ ϩ ␯ bands Figs. 2 c , 2 b , and 3 c , which have the highest signal-to- noise ratio. In each of these bands, several of the subbands are shifted 50 to 160 cm Ϫ 1 to higher wave number from the apparent band center. One such subband, expanded in the inset of Fig. 2 ͑ b ͒ , has the clear P and R branches expected for a K ϭ 0 ← 0 subband. The simplicity of its structure sug- gests that this feature is not an entire band in itself, since at the jet temperature of 5 to 10 K, 2 an entire vibrational band would have a dozen or more subbands arising from K Љ ϭϪ 1, 0, 1 and A and E symmetries. It is more likely to be a subband of 2 ␯ 1 ϩ ␯ 6 . The spread out structure of the ␯ 6 combination bands can be explained by analogy with the ␯ 6 fundamental. Rota- tionally resolved spectra of the ␯ 6 fundamental of both 12 CH 3 OH ͑ Ref. 28 ͒ and 13 CH 3 OH ͑ Ref. 29 ͒ reveal an excep- tionally large torsional tunneling splitting ͑ about 24 cm Ϫ 1 for the COH bend upper state as compared to 9.1 cm Ϫ 1 for the ground state ͒ , and this causes the subbands origins to be more widely spread. 29 Lees et al. 28 found that torsionally excited states of the methyl rocks ( ␯ 7 and ␯ 11 ) and of the CO stretch ( ␯ 8 ) fall in the same region as the ␯ 6 fundamental. The strong mixing among these bands results in intensity transfer to the torsional combination bands, which are more spread out than the fundamentals. For the CH stretching overtone bands, we use the local mode labels, ␯ a and ␯ b , employed by Fang et al. for assignment of their photoacoustic spectra. 18 The ‘‘unique’’ CH stretch, ␯ a , refers to a local vibration of the CH bond anti to the OH bond. The stretches of the other two ‘‘nonunique’’ CH bonds ͑ gauche to the OH bond ͒ are equivalent and des- ignated ␯ b . We label the three corresponding CH bonds as a , b , and b Ј . Figure 5 shows a stack of CH stretch overtone spectra up to v CH ϭ 5. IRLAPS spectra of the higher CH overtones were too weak to be measured. Because the ␯ a fundamental occurs at higher wave number than ␯ b and the anharmonicities are similar, the splitting between the overtones of these two local modes increases linearly with v CH , reaching 570 cm Ϫ 1 at 7 ␯ CH . 18 The ␯ a overtones are consistently weaker than those of ␯ b , in part because there is only one anti -CH bond as opposed to two in the gauche position. In the region of v CH у 3, the onset of local mode behav- ior causes the overtone spectra to be relatively simple. The single-bond anharmonicity ( x aa Ϸ x bb Ϸ Ϫ 60 cm Ϫ 1 ) causes the local mode overtones ͑ e.g., 5 ␯ b ) to become isolated from the nearest local-local combinations ͑ e.g., 4 ␯ b ϩ ␯ b ). The spacing becomes much larger than the local-local coupling 42.1 cm so that the local mode overtones are not significantly mixed with the local-local combinations. More- over, in the bond dipole model only the local mode overtones carry oscillator strength, which simplifies the spectrum to a single feature for each bond at each overtone level. Finally, the increasing separation of the ␯ and ␯ overtone bands where becomes too 2933.48 great cm for them is the to frequency be significantly of the mixed three equiva- by the lent local-local CH local coupling modes ͑␭͒ in , the allowing G molecular the higher symmetry ␯ a and group. ␯ b over- In tones to be treated separately. Although each of these simpli- fications is an approximation, together they provide a reasonable description of the assigned CH stretch features in the v CH ϭ 3 – 7 region. In the CH stretch fundamental region ͓ Fig. 5 ͑ e ͔͒ , the local-local coupling is dominant and results in three normal vibrations. The situation is further complicated by rapid torsional tunneling, which interchanges the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ...

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... the identity of the a , b , and b Ј CH bonds. The torsion-rotation structure of the CH fundamentals has been assigned at high resolution 4,5,30 to yield the three normal mode frequencies, ␯ 3 ϭ 2844.69, ␯ 9 ϭ 2956.91, and ␯ 2 ϭ 2998.77 cm Ϫ 1 . 4 The internal coordinate Hamiltonian of Wang and Perry, 4 which includes the CH local-local coupling and the lowest order torsion-vibration coupling, successfully reproduces the three fundamental frequencies and corresponding torsional tunneling splittings. Although the CH fundamentals appear in the spectrum as three normal modes, it is possible to use the Wang–Perry Hamiltonian to derive theoretical fundamental transition frequencies for the local modes, ␯ a and ␯ b . With the torsional angle frozen at the equilibrium geometry and neglecting the local-local coupling between the CH bonds, their Hamiltonian matrix reduces to H ˆ ϭ ͩ ␻ ϩ 0 3 ␮ ␻ Ϫ 0 2 3 ␮ 0 0 ͪ , ͑ 4 ͒ 0 0 3 where 2933.48 cm is the frequency of the three equivalent CH local modes in the G molecular symmetry group. In Eq. 4 , we have kept the torsion-vibration coupling parameter, ␮ ϭ 12.4 cm Ϫ 1 , which gives rise to the frequency difference between ␯ a and ␯ b . From Eq. ͑ 4 ͒ we determine the fundamental frequencies of ␯ a and ␯ b to be 2970.68 and 2914.88 cm Ϫ 1 , respectively. Note that these derived values are approximate, because the treatment of Wang and Perry neglects the interactions of the CH stretches with the six HCH bend overtones and combinations that fall in this region. The 2 ␯ CH bands ͓ Fig. 5 ͑ d ͔͒ fall in the transition region between the normal mode and local mode limits and are therefore more complicated than either the fundamental or the higher overtones. In Fig. 5 ͑ d ͒ , features appear at the expected positions of the local mode bands 2 ␯ a and 2 ␯ b as well as in the general region of the local-local combinations. Local-local combinations with reasonable intensity have been observed in 2 ␯ CH spectra of other molecules. 31 More- over, there are 18 CH bending combinations of the form ␯ CH ϩ 2 ␯ bend that will interact with and borrow intensity from the six possible 2 ␯ CH bands. As expected, Fig. 5 ͑ d ͒ shows many bands and a complicated structure throughout the extended 2 ␯ CH region. H ̈ nninen and Halonen 32 have employed ab initio calculations to determine the Fermi and Darling–Dennison resonance coupling constants for methanol. These constants, together with a fit to a set of experimental band centers, enabled them to calculate the 24 tran- sition frequencies and wave functions in the 2 CH region. As shown in Fig. 5 ͑ d ͒ , their calculated transition frequencies for the eight bands with the highest percentage of CH stretch character show a good qualitative correspondence with the observed spectrum. In the 3 ␯ CH to 5 ␯ CH region, some of the CH overtone bands are overlapped by OH overtone and combination bands. In Fig. 5 ͑ a ͒ , only the 5 ␯ b band at 13 295 cm Ϫ 1 is distinguishable, because 5 ␯ a is obscured by the much stron- ger 4 ␯ 1 band. The unstructured contour of the 3 ␯ a band ͓ Figs. 5 ͑ c ͒ and 2 ͑ b ͔͒ at 8544 cm Ϫ 1 is overlapped by the nearby 2 ␯ 1 ϩ ␯ 6 combination band. In Fig. 5 ͑ b ͒ , the sharp rotational lines of the OH stretch combinations, 3 ␯ 1 ϩ ␯ 12 and 3 ␯ 1 ϩ 2 ␯ 12 , which have been assigned and fit to a torsion-rotation Hamiltonian, 2 are superimposed on the broad, featureless 4 ␯ b band at 10 820 cm Ϫ 1 . The 4 ␯ a band, which is centered at 11 181 cm Ϫ 1 , is free from overlapping bands but is much weaker than 4 ␯ b . To confirm the assignments in the 4 ␯ CH region, we present the corresponding spectrum of CH 3 OD and compare it with CH 3 OH in Fig. 6. As expected, the sharp lines of the OH stretch combinations are absent from the CH 3 OD spectrum, while the CH stretch bands occur in nearly the same position for the two isoto- pomers. Figure 7 shows Birge–Sponer plots for the ␯ a and ␯ b CH stretch overtones. The residuals of the fits are well within the band contours of the assigned spectral features, consis- tent with our simplified treatment of the v CH ϭ 3 – 7 overtone region and our approximate derivation of ␯ a and ␯ b local mode frequencies from the CH fundamentals. A more realis- tic model of the CH overtone bands would include couplings between the local CH stretch modes ͑ i.e., local-local coupling ͒ as well as stretch-bend and stretch-torsion coupling. The application of such a detailed stretch-bend model re- quires additional constraints, either from experiment or from ab initio theory. 32 The smooth contours and lack of obvious torsion- rotation structure in the 3 ␯ CH , 4 ␯ CH , and 5 ␯ CH bands are likely the result of rapid IVR, and our observed band profiles place limits on the initial IVR rates. Even though torsion- rotation structure will contribute to the band profiles, the overall width of the CH overtone bands defines an upper bound to the IVR rate. For example, the best Lorentzian fit to the 3 ␯ b band in Fig. 5 ͑ c ͒ gives a FWHM of 50 cm Ϫ 1 , which would correspond to a decay time of 100 fs if this band were coherently excited. At the other limit, a lower bound to the IVR rate is determined by the minimum coupling width needed to smooth out the torsion-rotation structure that is seen in other bands. By comparing the 3 ␯ b band with the structured 2 ␯ 1 ϩ ␯ 8 band, we estimate that a coupling width of at least 5 cm Ϫ 1 would be required to produce a smooth contour, corresponding to an IVR lifetime of 1 ps. These estimates of IVR lifetimes serve to highlight the qualitative difference in the hypothetical dynamics subsequent to coher- ent excitation of the OH stretch combinations and the CH overtones. For example, the narrowest features in the 2 ␯ 1 ϩ ␯ 8 band ͓ Fig. 5 ͑ c ͔͒ are 0.1 cm Ϫ 1 wide, corresponding to a nominal IVR lifetime of ϳ 50 ps. More confident estimates of these methanol IVR lifetimes will have to await double resonance experiments that eliminate inhomogeneous spectral structure. Figure 8 shows the spectral region containing the binary combinations of the CH stretches with the OH stretch. We assign the ␯ 1 ϩ ␯ 3 , ␯ 1 ϩ ␯ 9 , and ␯ 1 ϩ ␯ 2 bands based on the their coincidence with the sum frequencies calculated from the rotationally assigned fundamental spectra. 5,21,30 Since the time that the spectrum of Fig. 8 was recorded, the ␯ ϩ ␯ band has been recorded at high resolution using CW cavity ringdown spectroscopy and analyzed in detail. 33 In analogy to the spectra in the CH fundamental region, it is likely that the large feature between the ␯ 1 ϩ ␯ 3 and ␯ 1 ϩ ␯ 9 bands is made up of six overlapping combination bands of the form ␯ ϩ 2 ␯ , where the CH bends are ␯ , ␯ , and ␯ . To characterize the band positions in the overtone region, we carried out a least squares fit of the transition wave numbers in Table I to the anharmonic expression in Eq. ͑ 1 ͒ . Where the data are available, the band centers in Table I are derived from rotationally assigned high-resolution spectra. These band centers, ␯ , which represent the energy difference between the J ϭ 0 levels of the upper and lower states, are not equal to the band origins that result from fitting high resolution data to a torsion-rotation Hamiltonian. The latter would be the difference between the minima of the one- dimensional effective torsional potentials for the upper and lower states, and they differ from our measured ␯ by the change in torsional zero-point energy upon vibrational excitation ͑ a difference of 9 to 24 cm Ϫ 1 for the bands ␯ 1 to 3 ␯ 1 ). 2,20 We have chosen to use the band centers ␯ in our fits because the data are available for more bands. For the many bands without detailed rotational assignments, each ␯ tabulated in Table I is approximated as the wave number of the absorption maximum in the band profile. Our fit differs from that of H ̈ nninen and Halonen 32 in several respects. Most importantly, their fit uses dozens of fixed parameters derived from ab initio calculations, whereas ours is strictly empirical. A full understanding of the methanol spectra will certainly require an effective synthesis of theory and experiment, but the purpose of our present fit is just to characterize the experimental data. Second, we have included CH overtone data in the range v CH ϭ 3 – 7. Finally, the experimental wave numbers for ␯ 1 , ␯ 2 , and ␯ 9 on which the two fits are based differ by as much as 10 cm Ϫ 1 because of differences in the way torsional tunneling and torsional zero point energy are handled. Neither fit includes the torsional tunneling dynamics explicitly. A total of 36 bands were included in the fit, yielding a root mean square deviation of 12 cm Ϫ 1 . The resulting spectroscopic parameters, shown in Table II, include the har- monic frequencies ␻ 0 i of the six relevant vibrational modes and their anharmonicities x ii and x i j . The OH and CH stretch parameters are in agreement with those of Fang et al. , 18 except that the confidence intervals are reduced and the CH anharmonicities are a little larger in magnitude. The difference between x and x is now significant and it is evident visually as the divergence of the slope lines in Fig. 7. This difference implies that the torsion-vibration coupling parameter ␮ increases with CH stretch excitation. The parameters involving the CO stretch and COH bend are poorly determined because of the uncertainty in the band origins and the low level of excitation of these modes in the observed combination bands. We have measured the infrared spectrum of methanol from 5000 to 14 000 cm Ϫ 1 using the IRLAPS technique and have assigned most of the observed bands. The spectrum is dominated by the OH stretch overtones and combination bands involving the OH stretch, CO stretch, and COH bend. The band positions were fit to a simple expression involving the low order anharmonicity constants. All of OH stretch combination bands show sharp rotational structure, which remains ...