Fourier transform spectroscopy of the CO-stretching band of O-18 methanol

Journal of Molecular Spectroscopy 256 (2009) 91–98

Contents lists available at ScienceDirect

Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms

Fourier transform spectroscopy of the CO-stretching band of O-18 methanol R.M. Lees a,*, Reba-Jean Murphy b, Giovanni Moruzzi c, Adriana Predoi-Cross b, Li-Hong Xu a, D.R.T. Appadoo d, B. Billinghurst d, R.R.J. Goulding e, Saibei Zhao a a

Centre for Laser, Atomic and Molecular Sciences (CLAMS) and Department of Physics, University of New Brunswick, P.O. Box 5050, Fredericton and Saint John, NB, Canada E2L 4L5 Department of Physics and Astronomy, 4401 University Drive, University of Lethbridge, Lethbridge, Alta., Canada T1K 3M4 c Dipartimento di Fisica ‘‘Enrico Fermi” dell’Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy d Canadian Light Source, 101 Perimeter Road, University of Saskatchewan, Saskatoon, Sask., Canada S7N 0X4 e Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, Nfld, Canada A1B 3X7 b

a r t i c l e

i n f o

Article history: Received 17 December 2008 In revised form 10 February 2009 Available online 24 February 2009 Keywords: Methanol CH318OH Infrared spectra Fourier transform spectra CO-stretching mode Internal rotation Rotation–torsion–vibration energies Ritz analysis Perturbations

a b s t r a c t The high-resolution Fourier transform spectrum of the m8 CO-stretching band of CH318OH between 900 and 1100 cm1 has been recorded at the Canadian Light Source (CLS) synchrotron facility in Saskatoon, and the majority of the torsion–rotation structure has been analyzed. For the mt = 0 torsional ground state, subbands have been identified for K values from 0 to 11 for A and E torsional symmetries up to J values typically well over 30. For mt = 1, A and E subbands have been assigned up to K = 7, and several mt = 2 subbands have also been identified. Upper-state term values determined from the assigned transitions using the Ritz program have been fitted to J(J + 1) power-series expansions to obtain substate origins and sets of state-specific parameters giving a compact representation of the substate J-dependence. The mt = 0 subband origins have been fitted to effective molecular constants for the excited CO-stretching state and a torsional barrier of 377.49(32) cm1 is found, representing a 0.89% increase over the ground-state value. The vibrational energy for the CO-stretch state was found to be 1007.49(7) cm1. A number of subbandwide and J-localized perturbations have been seen in the spectrum, arising both from anharmonic and Coriolis interactions, and several of the interacting states have been identified. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction In this work, we have analyzed high-resolution infrared spectra of CH318OH recorded on the Fourier transform spectrometer at the Far-Infrared Beamline at the Canadian Light Source (CLS) in Saskatoon, in order to assign and characterize the complex torsion–rotation structure of the m8 CO-stretching infrared band centred near 1007 cm1. The m8 band is one of the strongest vibrational bands for methanol, and previous studies for other isotopic species ([1–7], for example, and references cited therein) have revealed numerous interesting features of the CO-stretching mode and its interactions with other vibrational states. The closest state to m8 is the m7 in-plane CH3-rocking mode, which can couple to the CAO stretch via a variety of Coriolis resonances. The m7 band for CH318OH was explored in an earlier investigation [8]. The far-infrared spectrum has also been analyzed in detail [9,10], with global fitting of the energy manifold in the ground vibrational state up to the mt = 2 second excited state of the torsional ladder [10]. The current study of CH318OH falls within our collaborative research programs at the CLS synchrotron facility to determine energy level structures of methanol isotopologues as accurately as possible in * Corresponding author. Fax: +1 506 648 5948. E-mail address: [email protected] (R.M. Lees). 0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2009.02.015

the international effort to compile reliable laboratory databases for major interstellar molecules in support of the Herschel Space Observatory and the ALMA telescope array.

2. Experimental details The CO-stretching band of CH318OH falls in the 900–1100 cm1 region and was recorded at room temperature at the Far-Infrared Beamline at CLS using the Bruker IFS 125HR Fourier Transform Spectrometer (FTS). A globar source, KBr beamsplitter, and an MCT detector were employed in the measurements, and a multipass White-type cell with a base length of 2 m [11] was used to attain a path length of 48.15 m. The primary spectrum for our present analysis was taken at a pressure of 1.4 mTorr, measured on a Baratron capacitance manometer with full-scale range of 10 torr. Nineteen double-pass scans were co-added to achieve a good signal to noise ratio at a resolution of 0.00096 cm1 (the inverse of the optical path difference). A second spectrum was recorded from 500–1950 cm1 at the same path and resolution at a higher pressure of 62 mTorr with 70 scans co-added. The CO-stretching band is strongly saturated in this spectrum, which was aimed at later extension to higher quantum number of the analysis of the much weaker m7 in-plane CH3-rocking band centred at 1073 cm1 [8].

92

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

can run on all Unix-like platforms, including Linux and Mac OS X. The present version offers the option of editing the list of transitions between two chosen level sequences (by level sequence we mean a sequence of levels sharing all quantum numbers other than J), or the list of all transitions originating from a single chosen level sequence. In both cases, transitions already assigned can be changed, and new transitions can be added to the list. When checking an assigned transition, or looking for an unidentified transition, the spectral region of interest and the peaklist can both be displayed on the computer monitor. If a line is missing from the peaklist because of line blending, the blended profile in the spectral region of interest can be analysed by a line-fitting routine in real time, and the new peaks inserted into the peaklist and/or into the assignment list. An example is shown from the R(5) spectral multiplet in Fig. 2, in which the two members of the close K = 2A asymmetry doublet are nicely extracted from an overlapped profile with nearly equal intensities, as expected. Furthermore, the program can output PostScript or TeX files containing tables and plots. With the combined use of the Loomis–Wood plots, the subband spreadsheets and the Ritz analysis, we have been able to assign all of the CH318OH m8 subbands from K = 0 to 11 for the mt = 0 torsional ground state for both A and E torsional symmetries up to J values typically well above 30. For the mt = 1 first excited torsional state, we have A and E assignments up to K = 7 plus the 8A and 9A subbands, while for the mt = 2 second excited torsional state we so far have 8 assigned subbands ranging from K = 0 to 5. (The status of our current information on the spectral structure within the ground and CO-stretch vibrational states is reported in the supplementary information in graphic form as charts summarizing the known rotation–torsion–vibration (R–T–V) substates along with the identified subband links which connect them. Boxes in the charts give the J-independent origin energies of the substates together with the ranges of J for which the term values are currently known.) Most of the substates are accessed by several different

3. Subband assignments, Ritz analysis and R–T–V term values In order to initiate the classification of the spectral lines into related subbranches, the Loomis–Wood approach was very useful in which spectral segments differing by approximately 2B are plotted above each other. As illustrated in Fig. 1, related transitions differing just in J-number for many of the series then lie on smooth near-vertical curves that can be clearly picked out. When the wavenumbers for a given series were tabulated in a spreadsheet difference table, educated guesses about the J values could be made from the magnitudes of the first differences, leading in turn to an informed guess about the K value from the starting J value of the series. Since accurate ground-state combination differences were available from the analyses of the far-infrared spectrum of CH318OH [9,10], corresponding R and P subbranches could be unmistakably linked and the A or E torsional symmetry and torsional quantum number mt established to give the full subband assignment. However, the CO-stretching band has a dense structure and exhibits severe overlapping, as seen in Fig. 1, so that assignments can be difficult and uncertain when different line series slowly merge and cross over with increasing J. Here, the Ritz approach [12] was an important tool in the analysis in helping to extend and confirm the subband identifications. The Ritz program was developed for assigning the spectra of molecules having non-stringent selection rules, so that many transitions accessing a given energy level are allowed and are all present in the measured spectra. Assignments involving that level can then be checked by a variety of combination difference loops of microwave, far-infrared and infrared transitions, giving powerful confirmation of the analysis. The Ritz analysis method has the advantage of not requiring a precise Hamiltonian, and provides accurate term values for the torsion–rotation levels in both ground and CO-stretch states. The program has recently been ported to the X-Window system, so that it

3A v t =1

995.05

993.35

995.10

993.40

-1 E v t =1 991.65

996.80

996.75

996.70

991.70

0A v t =2 996.85

995.20

995.15

993.45

0A 1A 991.75

996.90

993.50

995.25

993.55

-3 E

991.80

996.95

991.85

995.30

993.60

993.65

1A 991.95

992.00

+

-1 E 992.05

997.20

995.50

995.45

993.75

993.70

997.15

997.10

995.40

995.35

0 E -2 E 991.90

997.05

997.00

993.80

4A 992.10

997.25

995.55

993.85

7A 992.15

997.30

995.60

993.90

6E 992.20

995.65

993.95

0A v t =1 992.25

Fig. 1. Sample Loomis–Wood plot for the m8 CO-stretching band of CH318OH, showing the P(7) to P(10) mt = 0 multiplets from top to bottom with the K = 0A transitions vertically aligned. Successive lines in the different subbranches are connected by solid blue lines, and a sample of the subbranches are labeled with the K value and torsional symmetry. Several subbranches of the mt = 1 (dashed red lines) and mt = 2 (dash-dot pink lines) excited torsional states are also shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

93

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

Fig. 2. Example of profile fitting using the graphic tools available in the Ritz program. Identified lines are members of the mt = 0 CO-stretching J = 6 assignments (a) K = 1A+, (b) K = 2A, (c) K = 2A+, (d) K = 3E, (e) unassigned.

subbands, so that an individual energy level is determined simultaneously by a number of independent transitions, leading to very accurate and reliable R–T–V term values.

In order to determine the J-independent origins of the substate level sequences, which are sensitive to the torsional barrier height and molecular structural parameters, we have fitted the R–T–V term values to Taylor-series expansions in powers of J(J + 1) of the form:

ð1Þ

where r is the A or E torsional symmetry. The lower order a0, a1 and a2 coefficients represent, respectively, the substate J-independent origins, the effective B-values, and effective centrifugal distortion parameters, while the higher order terms have less well-defined physical significance but are important in reproducing the experimental transition wavenumbers to close to the measurement uncertainty. In Tables 1 and 2, we present just the a0, a1 and a2 coefficients for the assigned A and E substates, but have included the full set of fitted coefficients in the supplementary material for reference. As well, for those substates of A symmetry with K > 0 for which the asymmetry doubling has been resolved, we have fitted the splittings to the expression

Dðm; mt ; K; JÞ ¼ ½S þ TJðJ þ 1Þ þ UJ2 ðJ þ 1Þ2 þ VJ 3 ðJ þ 1Þ3 þ . . . ðJ þ KÞ!=ðJ  KÞ!

(1) and (2) serve as a compact representation of the CO-stretch energy level manifold to quite good accuracy. As an illustration of this, Table 1 Lowest order Taylor-series expansion coefficients for energy levels in states of A symmetry of the CO-stretch mode in CH318OH. Higher order terms are tabulated in the supplementary material.

4. Taylor-series fitting and substate origins

Eðm; mt ; KÞr ¼ a0 þ a1 JðJ þ 1Þ þ a2 J2 ðJ þ 1Þ2 þ a3 J 3 ðJ þ 1Þ3 þ . . .

5 spectral multiplet with

ð2Þ

and give the S and T splitting coefficients in Table 3 with fuller expansions in the supplementary material. The expansions of Eqs.

mt

K

a0

a1

a2  106

0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2

0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 2 3 4 5

1007.95096(17) 1018.07914(16) 1034.0760(17) 1043.0006(27) 1064.51704(63) 1104.35922(20) 1143.61472(17) 1179.76644(20) 1233.02131(28) 1300.79556(67) 1363.01990(91) 1428.4660(27) 1297.75304(16) 1232.235920(87) 1214.43480(13) 1280.65579(19) 1339.42693(32) 1299.93549(45) 1332.7101(14) 1441.54441(59) 1482.74887(47) 1484.67626(49) 1617.97633(29) 1464.91063(12) 1434.2756(56) 1611.67827(17)

0.7648171(29) 0.7648673(18) 0.764910(20) 0.764784(49) 0.7646505(70) 0.7646420(14) 0.7645774(11) 0.7642948(12) 0.7640000(18) 0.7644220(70) 0.7641679(97) 0.764509(31) 0.7624068(89) 0.76268520(80) 0.7625070(11) 0.7628997(17) 0.7629264(83) 0.7623028(71) 0.760361(44) 0.7632885(94) 0.7621881(35) 0.7618119(51) 0.7608430(24) 0.7617741(11) 0.76276(11) 0.7609459(14)

4.419(12) 2.8568(51) 1.493(60) 1.31(27) 0.935(21) 1.4365(23) 1.7421(17) 1.6799(19) 1.4136(29) 1.081(23) 1.124(33) 2.34(12) 4.70(14) 2.2000(16) 1.9098(23) 1.0767(37) 2.011(64) 1.588(31) 9.03(47) 1.454(45) 1.9592(70) 1.778(16) 1.3973(35) 1.4083(19) 8.55(77) 1.4256(23)

94

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

Table 2 Lowest order Taylor-series expansion coefficients for energy levels in states of E symmetry of the CO-stretch mode in CH318OH. Higher order terms are tabulated in the supplementary material.

mt

K

a0

a1

a2  106

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2

11 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 5 2 3

1429.05378(59) 1281.63144(70) 1224.64487(28) 1181.20998(31) 1131.32375(72) 1085.92014(54) 1060.71073(70) 1042.64596(11) 1017.21018(39) 1003.23145(22) 1008.06342(28) 1013.53034(19) 1014.81740(30) 1032.59407(30) 1065.99927(20) 1094.38322(40) 1124.72465(78) 1174.08795(34) 1233.7238(46) 1285.86520(95) 1346.2321(20) 1426.7319(14) 1362.80077(33) 1341.91168(33) 1374.95869(30) 1278.64328(53) 1222.40396(12) 1251.82074(31) 1281.43964(16) 1206.40095(18) 1200.28372(22) 1273.06956(25) 1286.75221(36) 1251.00014(36) 1295.87734(41) 1405.08513(65) 1402.74287(25) 1438.92284(94) 1407.49797(35) 1429.79008(26)

0.7639189(28) 0.7636189(70) 0.7641194(11) 0.7643686(26) 0.7644550(83) 0.7645265(63) 0.7647069(45) 0.7648932(15) 0.764823(18) 0.7647886(72) 0.764992(12) 0.7648200(44) 0.764909(13) 0.7647313(34) 0.7647965(14) 0.7646451(47) 0.764432(10) 0.7642624(12) 0.762175(99) 0.7637125(83) 0.762642(26) 0.763885(13) 0.7620930(29) 0.7622439(29) 0.7633381(51) 0.762640(16) 0.7624585(12) 0.7643487(70) 0.7634905(35) 0.7625999(30) 0.7625742(29) 0.7631874(36) 0.7630321(87) 0.7624128(62) 0.7622901(62) 0.764071(12) 0.7620929(29) 0.761524(27) 0.761640(11) 0.7615400(42)

1.7414(28) 1.206(21) 1.73028(84) 1.6223(57) 1.260(27) 1.144(20) 1.6167(69) 1.5467(56) 2.04(24) 5.791(66) 11.09(14) 0.251(26) 1.50(17) 0.172(10) 1.4928(22) 1.800(15) 1.577(42) 1.42250(88) 7.31(79) 1.428(20) 0.78(12) 1.665(36) 3.1261(67) 1.8096(64) 0.368(23) 1.44(14) 1.8746(28) 1.323(42) 1.053(20) 1.925(12) 1.9545(97) 1.254(13) 4.524(59) 1.922(30) 1.597(24) 1.783(64) 1.8619(91) 1.06(24) 1.418(90) 1.485(16)

Figs. 3 and 4 show the deviations between the experimental term values and those calculated from Eq. (1) for the K = 1A levels for mt = 0 and 1, respectively. In the two deviation plots, the A+ states are represented by squares and the A states by triangles. 5. Spectral perturbations and vibrational interactions As with the other methanol isotopologues [1–7,13], several of the CH318OH m8 CO-stretching subbands show evidence of perturbations due to intermode interactions, most notably with excited torsional levels of the ground state or with the m7 in-plane CH3rocking mode [8]. The perturbations can either extend over an entire substate or be strongly localized due to a sharp level-crossing

Table 3 Asymmetry doubling coefficients for states of A symmetry of the CO-stretch mode of CH318OH. Higher order terms are tabulated in the supplementary material.

mt 0 0 0 0 1 1 1

K 1 2 3 4 1 2 4

S

T 02

1.29355(37)  10 2.649(28)  1006 3.62(41)  1010 5.65(26)  1014 1.3439(11)  1003 1.9812(100)  1007 1.400(93)  1013

1.32(20)  1007 1.43(52)  1010 6.09(76)  1013 7.0(19)  1018 3.88(26)  1008 7.93(93)  1012 2.37(20)  1016

resonance. An interesting aspect of this coupling is the effect of ‘‘isotopic tuning” since the CO-stretch is lowered significantly by isotopic substitution on either the C or the O atom whereas the ground state torsion and the CH3-rock are relatively unaffected. Thus, different substates come into resonance as the origin of the CO-stretch band shifts down from approximately 1034 cm1 for the parent normal CH3OH to 1018 cm1 for 13CH3OH and then to 1007 cm1 for CH318OH. The first class of interactions, due to coupling of the CO-stretch with the mt = 3 and mt = 4 ground-state torsional levels [14], is of the Fermi or anharmonic type in which DK = 0 resonances produce shifts in the energies of entire substates. In Fig. 5, we show the torsion–vibration energies plotted as a function of K in the form of Dennison’s oscillating s-curves [5,15]. (The index s = 1, 2 or 3 is an alternative label for the torsional symmetry given by (|K| + s)mod3 = 1 for A levels, 2 for E(K 6 0) and 3 for E(K P 0) levels.) Where the mt = 3 and mt = 4 ground vibrational s-curves cross the CO-stretch curves, anharmonic resonances will occur if two levels of the same s in different states are nearly degenerate [14]. The closest such degeneracies are highlighted by circles in Fig. 5, and account for distinct irregularities in analogous s-curve plots of the subband origins against K shown in Fig. 6. In Fig. 6a, the shifts of the (mt,s,K) = (0,1,0)A and (0,3,5)E levels seen previously for the normal and C-13 species [1,4,5,14] are still present for CH318OH, and the strong perturbation anticipated for the (0,2,10)E substate [4] is indeed observed. For mt = 1 in Fig. 6b, the downward shift expected for the (1,3,7)A origin is seen and the isotopic tuning has now brought the (1,3,2)E and (4,3,2)E levels into near-coincidence so that there are two hybridized K = 2E subbands in the spectrum separated by about 4 cm1. The intensities of the hybridized 2E subbands are fairly similar, indicating that the mixing of the two states is almost complete. We can obtain an approximate measure of the interaction constant W from the information in Fig. 6b if we make the assumption that the unperturbed position of the (1,3,2)E level is halfway between the (1,3,1)A and (1,3,3)E levels. The upward perturbation d would then be equal to 1.48 cm1 while the perturbed separation DE between the (1,3,2)E and (4,3,2)E levels is 3.90 cm1, corresponding to a deperturbed separation DE0 of 0.94 cm1. Treating the interaction as a simple 2  2 resonance, we then obtain the interaction constant and the |b/a| eigenfunction mixing ratio as [5]

j W j¼ ½dðd þ DE0 Þ1=2 ¼ 1:89 cm1

ð3Þ

j b=a j¼ d= j W j¼ 0:78

ð4Þ

The value of W is in agreement with that found previously for the same levels of the C-13 species, while the mixing ratio has increased significantly from the C-13 value of 0.57 [5] in accordance with the closer degeneracy. The major feature in Fig. 6 that is not explained by Fig. 5 is the sizeable downward shift of the (1,3,6)E level. The behaviour of this substate represents an intriguing and still unsolved mystery. For the C-13 species the (1,3,6)E subband was never identified [5] while for normal CH3OH the energy of the assigned (1,3,6)E substate is anomalously high and this state is believed to be hybridized [16,17]. The perturbing partner state has not been conclusively identified, but because the (1,3,6)E level lies near the top of the s-curve, it will be close to the OH-bending state [5] which may be the source of the interaction. A second class of strong substate-wide perturbations arises from DK = 1 CO-stretch/CH3-rock Coriolis coupling of m8 K levels with m7 (K  1) levels [18]. This coupling has previously been investigated for the normal and C-13 isotopomers [3–5,13], and we now have evidence of such coupling for the O-18 species as well. Again the effect of isotopic tuning comes into play. If one examines the C-13 energy structure shown in Fig. 3 of [13] and lowers the

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

95

Fig. 3. Differences between the experimental term values and those calculated from Eq. (1) for the K = 1A levels for mt = 0. The A+ states are represented by squares and A states by triangles.

Fig. 4. Differences between the experimental term values and those calculated from Eq. (1) for the K = 1A levels for mt = 1. The A+ states are represented by squares and A states by triangles.

CO-stretch manifold by an additional 11 cm1, one sees that the lower-K resonances will be detuned and the onset of m8(K)/ m7(K  1) near-coincidence will shift upwards to around K = 9 for the O-18 CO-stretch. An indicator of strong Coriolis resonance is a marked J-dependence of the second differences [3–5,13], and

we see this clearly for the K = 9A, 10A and 11A subbands. For example, the second differences for the K = 9A subband, normally equal approximately to 2(B0  B00 ), evolve from 0.016 cm1 at low J up to +0.010 cm1 by J = 30. To treat this coupling quantitatively, one requires information on the levels of the perturbing CH3-rock-

96

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

1008.0

1500

τ=1

vt = 1 co

1300

vt = 4 gd

Subband Origin (cm-1)

1400

1007.0 1006.5

τ= 2

1006.0 1005.5 1005.0

(b) vt = 1

1004.5 1004.0

τ= 3

[ ]

1003.5

1200 1003.0 0

vt = 0 co

1

2

3

4

5

6

7

8

9

10

K

1100

1008.8

0

1

2

3

4

5

6

7

8

9

10 11

K Fig. 5. Torsion–vibration energies for assigned mt = 0 and mt = 1 CO-stretching substates of CH318OH plotted as s-curves, with s = 1, 2 and 3 energies shown, respectively, as open circles, filled (red) circles and filled (blue) triangles. The mt = 3 and mt = 4 curves for the vibrational ground-state are also shown, crossing the COstretching curves at sharp angles. The small splitting of 0.32 cm1 that separates the mt = 3 and mt = 4 states just above the mt = 0 CO-stretch state is not visible on the scale of the diagram. The principal near-degeneracies (highlighted by circles) near crossing points of the CO-stretch curves with ground-state curves of the same s give rise to significant anharmonic perturbations in the spectrum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

ing state, but this is not yet available. We hope in the future with our higher pressure spectrum to be able to assign m7 subbands up to higher K and carry out an analysis of the Coriolis coupling. The last class of perturbations involves J-localized level-crossing resonances due to accidental degeneracies between interacting substates. In the previous study of the m7 CH3-rocking band for CH318OH [8], a local resonance between the m8 K = 6E and m7 K = 4E levels was observed and characterized, and the familiar methanol resonance in the ground vibrational state between the 9A mt = 0 and 5A mt = 1 levels has been analyzed as well [8,19]. Here, we have observed several further local resonances, again occurring at different points in the energy manifold due to the isotopic tuning. In the mt = 0 torsional state, the K = 8E subband shows a small resonance with an unidentified partner between J0 = 17 and 18 giving a perturbation of 0.0032 cm1 for J0 = 17. The K = 3A+ subband exhibits a level-crossing between J0 = 27 and 28 with a maximum perturbation d(27) of approximately 0.025 cm1. In this case, the interaction is with the K = 0A+ mt = 4 level of the ground vibrational state, according to the approximate energy level picture shown in Fig. 7. At present, we have accurate Ritz energy term values for the K = 0A+ mt = 4 levels only up to J = 12. However, the K = 0A+ mt = 3 substate lies just below, and the energy difference is only 0.704 cm1 at J = 12 with a rather slow J-dependence. Thus, we have extrapolated the mt = 4 curve by simply adding 0.704 cm1 to the mt = 3 Ritz term values, and believe this should be good to within about 0.01 cm1 except at the level-crossing point. Note that the perturbation only affects the A+ members of the K = 3A doublets, since the selection rule for coupling in which Dmt = even requires that the +/– symmetry be preserved in the interaction. Since the opposite is true for coupling with odd Dmt, we might ex-

Subband Origin (cm-1)

1000

1008.7 1008.6

(a) vt = 0

1008.5 1008.4

τ=1

1008.3

τ=2

1008.2 1008.1

τ=3

1008.0 1007.9 0

1

2

3

4

5

6

7

8

9

10

11

12

K Fig. 6. Origins of CO-stretching subbands of CH318OH in the (a) mt = 0 and (b) mt = 1 states, plotted as s-curves. Irregularities in the curves are due to anharmonic resonances with mt = 3 and mt = 4 ground-state levels. In (b), the (mt, s, K) = (1,3,2)E CO-stretch level is strongly hybridized with the corresponding (4,3,2)E level of the ground state, and subbands to both states are seen in the spectrum.

pect the K = 3A levels to interact with the K = 0A+ mt = 3 groundstate levels at higher J. As seen in Fig. 7, this should occur near J = 37 in a rather broad crossing, but unfortunately that is just

1043.5 1043.0 -1

vt = 3 gd

J -Reduced Energy (cm )

-1

Torsion-Vibration Energy (cm )

1007.5

A-

K = 3A vt = 0 co

1042.5

A+

1042.0 1041.5

K = 0A vt = 4 gd

1041.0 1040.5 1040.0

K = 0A vt = 3 gd

1039.5 1039.0 1038.5 0

5

10

15

20

25

30

35

40

J Value Fig. 7. Energy level diagram showing the level-crossing resonance between the K = 3A+ mt = 0 CO-stretch and K = 0A+ mt = 4 ground-state levels, and the probable resonance at higher J between the K = 3A mt = 0 CO-stretch and K = 0A+ mt = 3 ground substates.

97

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

where we lose track of the K = 3A m8 subband in the spectrum, probably due to the onset of the resonance. There are five mt = 1 subbands that show local perturbations. The 0E subband has a crossing between J0 = 21 and 22 with d(22) = 0.0063 cm1 and another between J0 = 28 and 29 with d(29) = 0.043 cm1. The 1E subband has a crossing between J0 = 12 and 13 with d(12) = 0.0053 cm1, and the 5E subband shows a resonance around J0 = 24 (just as we lose it in the spectrum) which may be with the 8E state of the m11 out-of-plane CH3-rocking mode. Also, the 6A m11 substate is the likely partner in a resonance between J0 = 21 and 22 for the 3A subband with d(22) = 0.0030 cm1. Lastly, the 5A subband shows a crossing between J0 = 27 and 28 with d(28) = 0.019 cm1. At present, we do not have enough information about the possible interacting partner states in the above resonances to attempt to analyse the perturbations quantitatively. However, we hope in the future with our new spectra to extend our understanding of the CH3-rocking and OH-bending modes to permit more detailed investigation and determination of the interaction constants.

6. Effective molecular parameters for the mt = 0 CO-stretching state The question of simultaneous determination of the torsional barrier parameters and the vibrational energy for an excited state of methanol is a difficult one. The situation was discussed for the C-13 species in [5] and a number of different fits to varying data and parameter sets were compared. There are two main problems, the first being that the molecular energies can be varied either by adjusting the vibrational energy or by adjusting the barrier height, so that these parameters tend to be highly correlated. In principle, the correlation can be broken by fitting to data from several torsional states, but then the second problem emerges in that the excited torsional states lie in the same region as other vibrational states and are significantly perturbed. In particular, the levels at the tops of the mt = 1 s-curves in Fig. 5 lie just underneath the mt = 0 OH-bending state and are perturbed downwards, significantly modifying the amplitude of the s-curves and altering any effective barrier parameter derived from those data. The situation is even worse for the mt = 2 substates, since they lie in a region of

higher state density that is more poorly mapped at present so that one cannot reliably predict where substantial perturbations will occur. Given this somewhat gloomy situation, we have opted in the present paper simply to fit the mt = 0 CO-stretch subband origins to four principal molecular parameters defining the torsion–vibration energies, namely axial moments of inertia Ia1 and Ia2, the barrier height V3 and the vibrational energy Eco. The fit to the subband origins requires a model for the ground-state torsional energies and for this we have adopted the Hamiltonian and parameters from the FIR fit carried out previously [9]. With the subbands affected by Fermi resonance removed from the fit, we obtained a standard deviation of 0.023 cm1 for 28 origins. The results are presented in Table 4 and show a 0.89% increase in effective barrier height V3 from 374.169 cm1 for the ground state to 377.49(32) cm1 for the excited state. We tried a further fit to both mt = 0 and mt = 1 origins with the next V6 Fourier term in the torsional potential included and with the substates closest to the peaks of the s-curves removed in order to reduce the effects of the OH-bend perturbations. A notable feature of this fit was that the (obs–calc) residuals for the omitted substates were indeed large and negative, supporting the idea that these states are repelled downwards by interaction with the OHbending mode just above. As shown in Table 4, however, this fit gave a substantially larger standard deviation of 0.108 cm1, and produced a large negative V6 with a correspondingly large jump in the vibrational energy Eco. These two parameters were highly correlated in the fit, with a correlation coefficient of 0.99, while V3 and V6 themselves had a correlation coefficient of 0.98. Nevertheless, if the V6 term was removed, the fit was seriously degraded, with the standard deviation increasing to 0.334 cm1 and the value of V3 dropping to 370.64 cm1! These rather alarming variations serve to emphasize the ambiguity discussed in [5] that is inherent in torsional fitting problems for excited vibrational states with a limited range of torsional data and the presence of a substantial number of unpredictable perturbations. In terms of the effective rotational constants for the CO-stretch state, we find from comparing the a1 coefficients in Tables 1 and 2 to the Ritz values for the ground state that the B-value is lower by about 0.0084 cm1 for the CO-stretch, as shown in Table 4. As well, we see in Fig. 6 that the mt = 0 subband origins have a distinct up-

Table 4 Molecular constants for the CO-stretching state of CH318OH from least-squares fits to CO-stretch subband originsa. Parameterb

Operator

1

Eco (cm ) V3 (cm1) Ia1 (amu Å2) Ia2 (amu Å2) Ib (amu Å2) Ic (amu Å2) Iab (amu Å2) Beff (cm1) (A  B)eff (cm1) V6 (cm1) DK (105 cm1) k1 (105 cm1) k2 (103 cm1) k3 (103 cm1) k4 (103 cm1) k5 (103 cm1) k6c k7 (103 cm1) S.D.d (cm1) a b c d

h1  cos 3ci>/2

h1  cos 6ci/2 K4 K3hP c i K2hP 2c i KhP 3c i hP 2c i K2h1  cos 3ci K hP 2c ð1  cos 3cÞi

Ground stateb

Fit to mt = 0

Fit to mt = 0,1

0.0 374.169 0.760737 3.21143 21.3759 22.1686 0.1514 0.7745 3.4708 1.273 4.110 5.013 1.881 5.365 8.581 9.720 [0.0] 10.230

1007.490(74) 377.49(32) 0.76117(26) 3.21476(27) 21.6062 22.4163

1016.29(32) 380.75(46) 0.76213(26) 3.21385(41) 21.6062 22.4163

*

0.7661 3.4752 *

*

0.7661 3.4751 23.39(98)

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

0.023

Uncertainties given in parentheses represent one standard error in the last digit. Asterisks indicate parameters fixed at ground-state value. Ground-state Hamiltonian model and parameters are from Ref. [9]. Ia2 is the axial moment of inertia of the CH3 group, and Ia = Ia1 + Ia2. The k6 parameter was fixed to zero to constrain a fundamental redundancy relation [1]. Overall standard deviation of the fit.

*

0.108

98

R.M. Lees et al. / Journal of Molecular Spectroscopy 256 (2009) 91–98

ward trend with K, indicating that the effective (A  B) rotational constant is larger for the CO-stretch state than the ground state. The rise from K = 0 to K = 10 is approximately 0.4 cm1, corresponding to an increase of 0.004 cm1 in (A  B). This agrees with the difference in Table 4 between the CO-stretch and ground state effective (A  B) values of 3.4752 and 3.4708 cm1, respectively.

Acknowledgments R.M.L., A.P.-C. and L.-H. Xu are pleased to acknowledge financial support for this research from the Natural Sciences and Engineering Research Council of Canada (NSERC). The experimental results described in this paper were obtained at the Canadian Light Source, which is supported by NSERC, NRC, CIHR, and the University of Saskatchewan.

7. Conclusions Besides practical application to construction of an extensive laboratory database as a laboratory reference for potential astronomical observations of CH318OH in interstellar and protostellar sources, the present work contributes to the advancement of knowledge regarding current models for the methanol molecular Hamiltonian and energy level structure. The methanol Hamiltonian is affected by strong correlation between certain of the torsion–rotation parameters, so that some of their values must be constrained (usually to zero) in fitting to the observed spectra. Increasing spectroscopic knowledge of a wider range of isotopic species in the far-infrared and infrared regions may increase the number of parameters that can be determined independently, and thus improve our insight into the physics of the molecule. Here, for the CO-stretch band, we have determined preliminary values of the major molecular constants that represent the mt = 0 levels of the first-excited CO-stretching state. Intermode vibrational coupling gives rise to numerous perturbations in the spectrum. Global shifts are seen for several substates due either to anharmonic Fermi-type resonances with ground state mt = 3 and mt = 4 levels or to subband-wide J-dependent DK = 1 Coriolis interactions with levels of the m7 in-plane CH3-rocking mode. A variety of J-localized level-crossing resonances has also been seen involving higher-order Coriolis coupling to several different vibrational modes. To help overcome the problems of dense structure and severe overlapping in the CO-stretching band, the Ritz program was an important tool in the analysis. Assignments could be checked via networks of independent combination difference loops of farinfrared and infrared transitions without requiring a precise Hamiltonian, and accurate Ritz term values were determined for the torsion–rotation levels in both ground and CO-stretch states. These will provide an excellent basis for millimetre and THz studies of the potential astronomical spectrum of this isotopic variant of the notorious methanol ‘‘interstellar weed” molecule.

Appendix A. Supplementary data Supplementary data for this article are available on ScienceDirect (www.sciencedirect.com) and as part of the Ohio State University Molecular Spectroscopy Archives (library.osu.edu/sites/msa/ jmsa_hp.htm). Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jms.2009.02.015. References [1] G. Moruzzi, B.P. Winnewisser, M. Winnewisser, I. Mukhopadhyay, F. Strumia, Microwave, Infrared and Laser Transitions of Methanol: Atlas of Assigned Lines from 0 to 1258 cm1, CRC Press, Boca Raton, FL, 1995. [2] Li-Hong Xu, R.M. Lees, Peng Wang, L.R. Brown, I. Kleiner, J.W.C. Johns, J. Mol. Spectrosc. 228 (2004) 453–470. [3] R.M. Lees, Li-Hong Xu, J.W.C. Johns, B.P. Winnewisser, M. Lock, J. Mol. Spectrosc. 243 (2007) 168–181. [4] I. Mukhopadhyay, R.M. Lees, W. Lewis-Bevan, J.W.C. Johns, J. Chem. Phys. 102 (1995) 6444–6455. [5] R.M. Lees, I. Mukhopadhyay, A. Predoi, W. Lewis-Bevan, J.W.C. Johns, J. Chem. Phys. 105 (1996) 3406–3418. [6] Li-Hong Xu, R.M. Lees, I. Mukhopadhyay, J.W.C. Johns, G. Moruzzi, J. Mol. Spectrosc. 157 (1993) 447–466. [7] M. Mollabashi, R.M. Lees, Li-Hong Xu, J.W.C. Johns, I. Mukhopadhyay, T.J. Lees, Int. J. Infrared Millimeter Waves 21 (2000) 1061–1083. [8] S. Zhao, R.M. Lees, J.W.C. Johns, C.P. Chan, M.C.L. Gerry, J. Mol. Spectrosc. 172 (1995) 153–175. [9] R.M. Lees, R.R.J. Goulding, Saibei Zhao, I. Mukhopadhyay, J.W.C. Johns, Int. J. Infrared Millimeter Waves 15 (1994) 2021–2030. [10] J. Fisher, G. Paciga, Li-Hong Xu, Saibei Zhao, G. Moruzzi, R.M. Lees, J. Mol. Spectrosc. 245 (2007) 7–20. [11] A.R.W. McKellar, D.R.T. Appadoo, J. Mol. Spectrosc. (2008). [12] G. Moruzzi, Li-Hong Xu, R.M. Lees, B.P. Winnewisser, M. Winnewisser, J. Mol. Spectrosc. 167 (1994) 156–175. [13] Adriana Predoi, R.M. Lees, J.W.C. Johns, J. Chem. Phys. 107 (1997) 1765–1778. [14] W.H. Weber, P.D. Maker, J. Mol. Spectrosc. 93 (1982) 131–153. [15] J.S. Koehler, D.M. Dennison, Phys. Rev. 57 (1940) 1006–1021. [16] J.O. Henningsen, Int. J. Infrared Millimeter Waves 7 (1986) 1605–1629. [17] R.M. Lees, Li-Hong Xu, J. Mol. Spectrosc. 196 (1999) 220–234. [18] J.O. Henningsen, J. Mol. Spectrosc. 91 (1982) 430–457. [19] I. Mukhopadhyay, Spectrochim. Acta A 51 (1998) 1895–1899.