high resolution fourier transform spectroscopy of the overtone co stretch band of methanol-d3

Spectrochimica Acta Part A 54 (1998) 1901–1908

High resolution Fourier transform spectroscopy of the overtoneC�O stretch band of methanol-D3

Subhasis Maiti a, Indranath Mukhopadhyay b,*a Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064, India

b Laser Programme, Centre for Ad6anced Technology, Indore 452 013, India

Received 1 December 1997; received in revised form 25 March 1998; accepted 30 March 1998

Abstract

In this work, high resolution Fourier transform infra-red (IR) spectrum corresponding to the weak overtone C�Ostretch band of methanol-D3 (CD3OH) has been recorded at a resolution of 0.004 cm−1, in the range 1882–2012cm−1. The spectrum has the typical appearance of a DK=0 spectrum of a near symmetric molecule and shows verycomplicated fine structure due the torsion–rotation–vibration interaction. It has been possible to identify eightdifferent R- and P-sub-branch combinations spanning a K value of 4. The assignments have been confirmed fromcombination relations using R- and P-branch transitions having the same upper level and accurately measuredmicrowave (MW) and millimeterwave (MMW) transitions in the ground vibrational state. Using the assignedtransitions a set of molecular parameters has been obtained for the second excited C�O stretch state of CD3OH.© 1998 Elsevier Science B.V. All rights reserved.

Keywords: Methanol; Deuterium substitution; Torsion; Infrared; Fourier transform; Anharmonicity; Hamiltonian

1. Introduction

The high resolution spectroscopy of overtonebands of polyatomic molecules is one of today’sfields of research interest [1–3]. The main reasonbehind this interest is to be able to investigatemolecular dynamics such as intramolecular vibra-tional energy redistribution (IVR). The under-standing of the IVR dynamics is particularlyinteresting at chemically significant energies, ac-cessing regions of the potential energy surface

where large amplitude, anharmonic coupling ef-fects are very efficient and may encounter highbarrier chemical transformations. Spectroscopicaccess to high energy states of the stretchingvibration through overtone bands allows the in-vestigation of the energy flow from these anhar-monic modes to other vibrational modes of themolecule. These are of significant importance forthe understanding of energy distribution processtaking place in an optically pumped molecularlasers.

Since the initial observation of far-infrared(FIR) laser emission from normal CH3OH in 1970[4] this molecule and its other isotopic species

* Corresponding author. Tel.: +91 731 488431; fax: +91731 481416/8430; e-mail: [email protected]

1386-1425/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved.

PII S 1 3 8 6 - 1 4 2 5 ( 9 8 ) 0 0 1 4 8 - 6

S. Maiti, I. Mukhopadhyay / Spectrochimica Acta Part A 54 (1998) 1901–19081902

have been exploited as prolific sources of opticallypumped FIR laser. Among the isotopic deriva-tives, methanol-D3 (CD3OH) is the second only tothe parent CH3OH species [5–15] in richness ofFIR emission, due primarily to the excellent over-lap between the C�O stretch vibrational band andthe 10-mm bands of the CO2 laser. Although manyof the FIR laser lines have been assigned todefinite quantum states mainly in the first excitedC�O stretch state, majority of them remain to beidentified. These unassigned FIR lines may arisefrom transitions in other vibrational states whichmay become accessible to the strong CO2 laserbands through hot or combination bands.

This paper reports assignments of a-type transi-tions corresponding to the overtone C�O stretchband spectrum recorder at a resolution of 0.004cm−1. It has been possible to identify eight differ-ent R- and P-sub-branch combinations spanninga K value of 4. The assignments have been confi-rmed from combination relations using R- andP-branch transitions having the same upper leveland accurately measured microwave (MW) andmillimeterwave (MMW) transitions in the groundvibrational state. Using the assigned transitions aset of molecular parameters has been obtained forthe second excited C�O stretch state of CD3OH.The results will be useful for the discovery of FIRlaser lines from the second excited C�O stretchstate of methanol-D3, optically pumped by a CO2

laser through hot band or by a CO laser pumpedthrough a direct overtone transition.

2. Experimental aspects

The sample of CD3OH was supplied by MSDIsotopes of Canada with quoted purity of 99.8%and was used without further purification. TheFourier transform spectrum of the sample wasrecorded on the BOMEM DA3.002 at the Univer-sity of British Columbia in the frequency range1882–2012 cm−1. The maximum path differenceemployed with the instrument was 2.5 m to obtaina resolution of 0.004 cm−1. A glober source anda HgCdTe (MCT) detector cooled with liquid-N2

were used. The multiple reflection cell having abase length of 0.375 m was set to a total absorp-

tion path of 15.75 m. The sample was kept atroom temperature and a pressure of 500 mtorrwas maintained within the cell throughout theexperiment. The final interferogram was obtainedfrom 164 coadded scans, each of which took �4min. A multiplicative calibration correction factorof 1.000001635 was invoked, which was deter-mined from the measurements of the overtonespectra of the parent species [16,17] recorded dur-ing the same time and the precise double reso-nance measurement of some of the lines by Xu etal. [18]. The estimated precision in wavenumbermeasurement for clean unblended lines is of theorder of 0.0005 cm−1.

3. Torsion–rotation Hamiltonian

The Hamiltonian model employed in this workuses an internal axis method (IAM), where thecoupling between torsion and overall rotation isremoved to zeroth order by transforming to theinternal axis system in which the methyl top andthe OH framework have equal and opposite tor-sional angular momentum [19]. Higher order in-teraction terms are then included as first orderperturbations to the zeroth order Hamiltonian.Basis functions for the zeroth order Hamiltonianare taken as eigenfunctions of a symmetric rotorwith free internal rotation.

The torsional Hamiltonian can be written as

HT=FPg2+V3(1−cos 3g)/2 (1)

Where F is a reduced rotational constant and V3

is the internal rotational barrier height and g isthe torsional angle. The Hamiltonian correspond-ing to rotation can be divined into two parts, viz.the symmetric rotor and asymmetric rotor compo-nents. When interaction between torsion and rota-tion is considered the Hamiltonian becomes verycomplicated.

To surmount the difficulties of the Hamiltonianmodel, an alternative procedure was first utilizedby Pickett et al. [20]. In this model the energyvalues for combined vibration, overall rotationand torsion for a given state can be expressed asa series in powers of J(J+1) as follows:

S. Maiti, I. Mukhopadhyay / Spectrochimica Acta Part A 54 (1998) 1901–1908 1903

E(ntK, J)

=Evib+W(ntK)+B(ntK) J(J+1)

−D(ntK) [J(J+1)]2

+H(ntK) [J(J+1)]3+ ···

+ (asymmetry splitting term) (2)

where Evib denotes the pure vibrational termwhich is zero for the ground vibrational state,W(ntK) represents the J-independent energy foroverall and internal rotation, t represents thetorsional symmetry of the level and takes onvalues 1, 2 or 3, n denotes the torsional state andK is the projection of overall rotational angularmomentum J along the symmetry axis of themethyl top. The asymmetry splitting term arisesbecause of asymmetry effects observable for the Aspecies as discussed later.

The J-independent expansion coefficientW(ntK) in Eq. (2) can be written in terms of themolecular parameters

W(ntK)=F�Pg2�+ (1/2) V3�1−cos 3g�

+ [A− (B+C)/2]K2

+ (1/2) V6�1−cos 6g�−DKKK4+k1K3�Pg�+k2K2�Pg

2�+k3K�Pg3�

+k4�Pg4�

+k5K2�1−cos 3g�+k6K�Pg�

+k7�Pg2(1−cos 3g)�+dw(ntK) (3)

The relationship between the J-dependent coeffi-cients and the molecular structural parameterscan be found in Ref. [21]. The bracketed quanti-ties are internal rotation expectation values. Pg isthe torsional angular momentum operator whereg is the torsional angle and is V6 is the barriershape parameter. The parameters in the righthand side of Eq. (3), are the so called b-typeparameters and dw(ntK) represent effects ofasymmetry and are very small. The (ntK) nota-tion is related to the alternative notation of sym-metry species according to the following:

76541 32t+K 8

E2 E1 A E2 E1 E2ATs A

and so on cyclically (4)

It is to be noted that for K=0 there remains nodistinction between E1 and E2 species.

4. Assignments

Though the overtone C�O stretch band ofCD3OH has a relatively weak feature in overallspectra of the molecule, it can clearly be resolvedinto a central dense Q branch flanked by R and Pbranch multiplets. The low resolution scan of thespectrum is shown in Fig. 1, which was recordedat a path length og 15.75 m and at a pressure of700 mtorr. At the high resolution the individualJ-multiplets are seen to be resolved into a verycomplicated fine structure due to strong torsion–rotation–vibration interaction in the molecule.This is depicted in Fig. 2, where the R(4) multipleis shown. The assignments of some of the lines areshown. As the R and P branch multiplet structurechanges slowly with J, use has been made of theLoomis–Wood approach [21] in assigning thespectra. In this method the successive multipletsare arranged vertically above one after another sothat the lines of common (ntK) could be shortedout. The spectral lines corresponding to a given(ntK) were arranged vertically in accordance withincreasing J. As expected, it showed a decreasing

Fig. 1. Low resolution spectrum of the overtone C�O stretchspectrum of CD3OH.


Fig. 2. Part of the Fourier transform spectrum of CD3OH showing the R(4) region of the overtone band. Note that the K=0 Eline is shifted to the higher frequency side and the K=0 A shifted further and is not shown in the figure. The line assigned to 1E1

is much stronger than other lines, this indicates that this is a blended line.

D1(J) [=n(J+1)−n(J)] values and an almostequal D2(J) [=D1(J+1)−D1(J)] values. If cen-trifugal and perturbation effects are not consid-ered, we can readily expect that for the P, Q andR branches D2(J):2(B %−B¦) where B % and B¦are the effective rotational constants for upperand lower states, respectively. In the presentwork, D2(J) values started with 0.012 cm−1 andthen showed generally a slow and smooth diver-gence for higher J values. Any discrepancy in theregular trend of D2(J) values naturally indicateslocalized perturbation to the associated energylevels or line blending.

Once such shorting out of the series of transi-tion frequencies belonging to R- and P-brancheshad been done, it was to link R-sub-branch serieswith its P-sub-branch partners and assign theactual (ntK) quantum numbers. Such linking wasdone by trial and error by comparing the [R(J)−P(J+2)] ground state combination differences fortrial subbranch matches against the known values[22,23]. Such eight different series of interlinked Rand P sub-branches were identified up to Jmax=20 and the corresponding (ntK) quantum num-bers were assigned to each series. Table 1represents the transition frequencies belonging toK=0 A and E series.

5. Analysis

The assigned transition frequencies for the IRbranches were then fitted to the phenomenologicalmodel with energy levels expanded as series inpowers of J(J+1) as discussed earlier. In Table 2the state-dependent expansion coefficients are pre-sented, where n0(ntK) represents the J-indepen-dent origins of the different sub-bands. Theparameters B %(ntK), D %(ntK) and H %(ntK) wereseen to be sufficient to reproduce the observedtransition wavenumbers belonging to different se-ries. The overall standard deviations of the fits liebetween s=0.002–0.005 cm−1 which conformsto the experimental accuracy. The quality of theagreement can be verified in Table 1, where thewavenumber residuals for K=0 A and 0 E seriesare almost within the experimental accuracy formost of the lines.

The leading a-type molecular parameters forthe 6 co=2 state were then obtained with a fit ofa-type frequencies calculated from the effectiveconstants of Table 2 to the torsion–rotationHamiltonian model of Lees and Baker [19] asshown in Table 3. The torsional parameters Fv, Gv

and Lv were constrained at the values for the firstexcited C�O stretch state because of the non-


Table 1Transition wavenumbers (in cm−1) for K=0 A and E branches of the overtone C�O stretch (6co=2�0) band of methanol-D3

K=0 A n=0K=0 E n=0

Pobs(J) O–CJ Robs(J) O–C Pobs(J) O–C Robs(J) O–C

0.000362 1967.526621967.14659 0.00611 1960.70810 −0.006051968.77786 0.00058 1959.75782 0.010773 1968.39482 0.00299 1959.39163 −0.00466

0.004201958.41008−0.001834 1969.63101 1970.01296−0.00017 1958.06388 −0.003781971.23236 −0.00619 1957.048255 1970.85582 −0.00235 −0.003701956.73126 0.00310

−0.00250 1955.682656 1972.07322 0.00074 1955.38309 0.00545 1972.44579 −0.002501954.30222−0.000967 −0.003161973.27488 1973.642790.00102 1954.01870 0.00277

0.00145 1952.909658 1974.45983 −0.00233 1952.64679 0.00393 1974.82614 −0.00286−0.001051951.505360.001059 1975.63453 1975.99197−0.00290 1951.25752 −0.00076

1977.14507 0.00277 1950.0866010 −0.000361976.79901 −0.00088 1949.85733 −0.004791948.65371 −0.0003811 0.002421977.95077 1978.281210.00067 1948.45251 −0.00194

1979.40233 0.00189 1947.2086612 0.000881979.08922 0.00029 1947.03653 0.00103−0.00034 1945.7487913 1980.21949 0.00178 1945.60568 −0.00005 1980.50712 0.00070

1944.276870.0000914 0.001691981.34074 1981.600310.00245 1944.16666 0.000761982.67878 −0.00052 1942.7908415 0.001501982.45068 −0.00242 1942.71712 −0.00002

−0.00048 1941.290391983.74502 −0.000640.000220.00020 1939.781131984.80012

1938.25806 −0.001781985.83846 −0.005510.000811936.729800.002781986.88220

1987.90936 0.00094 1935.18962 −0.00018

O–C is the observed-calculated wavenumbers using the expansion parametsers of Table 2.

availability of data for higher torsional states. Toobtain the b-type sub-band origins in the overtoneC�O stretch state (6 co=2), combination loopshave been formed with ground state b-type sub-band origins and a-type origins of the overtoneband. In this manner it was possible to obtain thefollowing three b-type origins (in cm−1) in the6 co=2 state:

K=1�0 E1 : n0=2.445

K=3�2 A : n0=0.479

K=4�3 A : n0=13.999

These three origins have been fitted with theb-type formula with only three parameters viz. Ia1,Ia2 and V3 to be varied. Among the various fitsobtained the best one was with Ia2 fixed at thevalue 6.514209 amu A2 for the 6 co=1 state. Theresulting fit converged with the following valuesfor the other two parameters

Ia1=0.73072 amu A, and V3=387.998 cm−1

Thus the barrier height increases by about 18cm−1 in going from the ground to the overtoneC�O stretch state. In Table 3, the parameters forthe first excited C�O stretch state are also in-cluded for the sake of completeness, the detailedresults of which will appear elsewhere.

We can also calculate the DK=2 matrix ele-ments �K= −1�K= +1� for the A-species withn=0 and the asymmetry splitting parameter forK=1, which is given by

S1=�−1�+1�(B−C)/2 (5)

For the ground state the calculated value of S1 is256.15 MHz, which compared very well with theobserved value of 256.0 MHz. For 6 co=1, thecalculated value for S1 is 307.2 MHz whereas theobserved value is 310.0 MHz and for 6 co=2 thecalculated value is 255.3 MHz for which we haveyet to obtain an observed value.


Table 2State-dependent series expansion parameters (in cm−1) for the C�O stretch overtone band of CD3OHa

n0 B(ntK) D(ntK)×10−6 H(ntK)×10−9(ntK) Ts

2.048.200.6427451963.31763(010) E4.98 3.68(030) A 1963.69434 0.645143

2.894.480.6450571963.69878(021) E1

(022) A 1963.25308 0.6441432.84 1.09(032) E2 1963.12394 0.645486

0.645164 0.82(013) A 1963.154490.645410 0.051963.08825(033) E1

1963.17516 0.645195 0.07(034) A

a Parameters for the ground state were fixed at the values obtained in Refs. [19,22,23]. Ts is the torsional symmetry.

6. Anhamonicity and vibration–rotationinteraction

One of the important findings of the presentstudy is the evaluation of the anharmonicity con-stant for the C�O stretch vibration. We considerthe lowest lying state K=0 A for n=0. TheQ-branch origin of this sub-band for the C�Ostretch fundamental 6 co=1�0 is obtained as985.8237 cm−1 whereas the origin of the samesub-band for the overtone band 6 co=2�1 (Table4) is 1963.7020 cm−1.

Now the vibrational energy for the C�O stretchvibration can be expressed as

Ev=ve(6+1/2)−vexe(6+1/2)2 (6)

where vexe is the anharmonicity constant and 6 isthe vibrational quantum number.

Thus the origin for the fundamental and theovertone band can be written as

n01(6 co=1�0)=ve−2vexe (7)

and

n02(6 co=2�0)=2ve−6vexe (8)

Here we get the anharmonicity constantvexe=n0

1−1/2 n02=3.9727 cm−1 and the vibrational

wavenumber is given by ve=3n01−n0

2=993.7691cm−1.

Using these values we get the dissociation en-ergy D as

D/hc=ve2/4vexe=62147.7 cm−1

This value is of same order of magnitude of thedissociation energy for alkali halides [24]. Forcomparison, we have calculated the correspondingvalues (in cm−1) for the parent species (CH3OH)as,

n01(6 co=1�0)=1033.8966,

n02(6 co=2�0)=2054.8326,

vexe=6.4803, and ve=1046.8572

Thus the dissociation energy in wavenumberunits D/hc=42278.5 cm−1. Hence the dissocia-tion energy for the C�O stretch vibration forCD3OH is higher than that for CH3OH, indicat-ing a stronger C�O bond in CD3OH. It should benoted that in an earlier report on the overtoneband of CH3OH [17] the vibrational energy wasused for the determination of D/hc. In that casethe torsional energy was separated from the J-in-dependent energy, but here the band origins areused. Hence the values of ve and vexe obtained inthis present work represent parameters which canbe measured experimentally and will be moreuseful for the work for higher harmonics. Thecalculated value of the vibrational energy is con-taminated by the internal rotational contributionfrom the excited vibrational state, thus the bandorigins seemed to a better choice.

From the (B+C)/2=Beff values for theground, first and second excited stretch state pre-sented in Table 3 one can obtain the vibration–


Table 3Molecular parameters for the ground, fundamental and second excited C�O stretch states of CD3OH

6=0aUnits 6co=2c6co=1bParameters

MHz 19560.962 19458.897(1673) 19376.52(244)(B+C)/220.21(91) 141.3(340)DJ kHz 28.93

159.4 116.5(802)DJK kHz −390(250)−54.836 78.432d78.432(179)MHzFv

MHz −2.3276 2.841(841) 2.841dGv

0.3158 1.627(404)Lv MHz 1.627d

25.5943525.4699 25.701589amu.A2Ib

26.35798 26.473038Ic amu.A2 26.22830.7307170.76847(1133)0.754621amu.A2Ia1

6.38817 6.51421(2960)Ia2 amu.A2 6.514209370.0637 369.091(375)V3 cm−1 387.998

3.702973.6972263.703029a

0.894525 0.894701r 0.894515

a From Ref. [19,22,23], b From Mollabashi, private communication, c Present work, d Fixed at the 6co=1 state values.a and r are dimentionless parameters defined in Ref [19].

rotation interaction terms ae and ge which aregiven by

B effv =Be−ae(6+1/2)+ge(6+1/2)2 (9)

where Be is the equilibrium Beff value.The following are the values of the above terms

(in MHz) for CD3OH and CH3OH:

CD3OH:Be=19619.4,

ae=121.8 and ge=9.8 and

CH3OH:Be24285.8, ae=91.4 and ge= −61.7

7. Conclusions

In conclusion, assignments and analysis havebeen reported on the high resolution Fourier

transform infrared spectrum corresponding to thevery weak overtone C�O stretch band ofmethanol-D3, recorded at a resolution of 0.004cm−1, in the range 1882–2012 cm−1. The spec-trum shows very complicated fine structure duethe torsion–rotation–vibration interaction. It hasbeen possible to identify eight different R- andP-sub-branch combinations spanning a K value of4. The assignments have been confirmed fromcombination relations using R- and P-branchtransitions having the same upper level and accu-rately measured microwave (MW) and millimetre-wave (MMW) transitions in the groundvibrational state. Using the assigned transitions aset of molecular parameters has been obtained forthe second excited C�O stretch state of CD3OH.In addition, the study of the overtone band al-lowed the anharmonicity and the dissociationconstants for the C�O stretch vibration ofmethanol to be determined. The present resultswill be useful in searching for weak methanolabsorptions for the hot band near CO2 pump linesfor possible FIR emission in the second excitedC�O stretch state. The present work should provevaluable for the study of higher overtone bands inmethanol and other isotopic species for probingthe intramolecular vibrational energy distributionwhich is crucial for the characterization of chemi-cal reactivity.

Table 4Anharmonicity and vibration–rotation interaction constants

(Units)Parameters CD3OH CH3OHa

(MHz)Be 24285.83919619.376(MHz)ae 121.750 91.362(MHz)ge 9.843 −61.687(cm−1)ve 993.7691 1046.8572(cm−1) 6.4803vexe 3.9727

42278.52(cm−1) 62147.72D

a These values are derived form the data of Ref. [19].


Acknowledgements

We are thankful to Professor I. Ozier for theuse of the BOMEM Fourier transform spectrome-ter and to Mr C.P. Chan for the spectral record-ing. S. Maiti is grateful to the Saha InstituteNuclear Physics for financial support and to Pro-fessor R.N. Nandi for encouragement to work inthis line.

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high resolution fourier transform spectroscopy of the overtone co stretch band of methanol-d3

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