Improved molecular constants and empirical corrections for the torsional ground state of the CO stretch fundamental of CH3OH

JOURNAL

OF

MOLECULAR

SPECTROSCOPY

85,

282-300 (1981)

Improved Molecular Constants and Empirical Corrections for the Torsional Ground State of the C-O Stretch Fundamental of CH,OHl J. 0. HENNINGSEN Physics Laboratory

I, H.C. @wed

Institute,

University of Copenhagen,

Copenhagen,

Denmark

The C-O stretch fundamental of CH,OH is analyzed on the basis of previously published diode laser spectra and data from optically pumped far-infrared laser emission. Improved values for ZbrZ,, and V, are presented, and I,, and I,, are determined separately. Energy levels are calculated, and empirical corrections tabulated, which show that the levels are heavily perturbed around K = 5. By including these corrections, as well as cubic effects in .I(.! + I), infrared transition energies can be evaluated for K 5 10 and J % 24 with an accuracy approaching the Doppler limit. The improved model is used for performing additional far-infrared laser line assignments. INTRODUCTION

The study of molecular rotation-vibration spectra of relatively simple molecules is a well-established field of physics, which at present is experiencing a surge of renewed interest. Molecules are the basis of various recent technical developments such as generation of laser radiation in the far infrared by optical pumping and laser induced chemistry, and a thorough understanding of such phenomena requires a knowledge about energy level spectra and energy transfer rates, which is more detailed than that offered by the established infrared and far-infrared techniques. At the same time, various new laser based spectroscopic techniques have been developed, and in particular the use of continuously tunable lead salt diode lasers has allowed for a complete mapping of rotation-vibration bands with Doppler-limited resolution. Although such a spectrum in principle yields all possible absorption lines, the interpretation may turn out to be a rather severe problem. The purpose of the present paper is to demonstrate that for a molecule like CH,OH, where the spectrum is complicated by internal rotation, the diode laser spectrum can be much more extensively interpreted if advantage is taken of information provided by optically pumped far-infrared laser emission (Z-3). An absorption line which is accidentally in near coincidence with a CO, laser line, can be pumped, and by measuring the frequency of the subsequently emitted far-infrared laser radiation, a unique fingerprint is obtained which often allows an unambiguous assignment of this particular absorption line. This, in turn, may serve to reveal general patterns in the diode laser spectrum. ’ Work supported and 511-15476.

by the Danish Natural

0022-2852/81/020282-19$02.00/O Copyright

0

1981 by Academic

All rights of reproduction

Press.

Inc.

in any form reserved.

Science

282

Research

Council under Grants 511-10161

C-O

STRETCH

FUNDAMENTAL

OF CH,OH

283

CH,OH is an asymmetric top with an internal degree of freedom, referred to as torsion or hindered internal rotation. The theoretical and experimental study of the rotation-internal rotation spectrum has been advanced in a series of papers by D. M. Dennison and co-workers, leading up to Kwan and Dennison (4) and by Lees and Baker (5). The most important parameters associated with the external rotation are the moments of inertia I,, Zb, and I, about three mutually orthogonal axes through the center of gravity of the molecule. The a-axis is conventionally chosen parallel to the symmetry axis of the CH, group, while b and c are orthogonal to a, with b in the COH-plane. To properly account for the internal rotation, it is further necessary to know the height V3 of the hindering potential barrier, which is supposed to have a sinusoidal dependence on the internal rotation angle, and also to know how I, is shared between Zaz, the moment of inertia of the CH, group, and I,, = Za - Iaz, which is essentially the moment of inertia of the OH group. In the most elaborate model that has been employed so far (5), these parameters are supplemented by a small cross moment of inertia lab, arising from the asymmetry, by rigid rotor centrifugal distortion constants, by a parameter V6 which measures the deviation of the hindering potential from a sinusoid, and by a set of so-called Kirtman constants which account for the effect of centrifugal distortion on the internal rotation. For the vibrational ground state (u = 0), this 20-parameter model represents the energy levels of the torsional ground state (n = 0) in the range K 5 6 and .Z 5 15 to an accuracy of the order of 0.002 cm-‘. The experimental basis is an extensive series of precise microwave measurements up to about 200 GHz (5) and a grating spectrometer investigation of the range 400-900 cm-’ with a resolution of 0.07 cm-‘, performed by Woods and co-workers (6, 7). For Q-band origins involving 0 < n 5 3, the agreement between theory and experiments is of the order of 0.1 cm-‘, and recently a study (8) of the spectral region 80-250 cm-’ indicated agreement to within the experimental resolution of 0.25 cm-l up to II = 5. For the C-O stretch fundamental, the situation is much less satisfactory. It has long been known to have the structure of a simple parallel band (9), but the complexity of the spectrum does not allow resolution of the individual absorption lines by conventional techniques. The most extensive measurements have been carried out by Woods (7) who performed a grating spectrometer study with a resolution of 0.07 cm-‘. The data showed that each P and R branch line was spread out by a Z-independent amount of about 1 cm-‘, and Woods was able to account for this spreading by allowing the hindering barrier V3 to be 19 +- 2 cm-’ higher in the C-O stretch state than in the ground state. However, none of the individual transitions were identified, and since it was not possible to determine I,, and ZaZ, the analysis was performed under the assumption that I, changes in the same way as for the C-F stretch fundamental of CH3F and that all the change is associated with Z,,. Lees (10) studied three rotational transitions which are located in the microwave range. His findings were in agreement with those of Woods and, in addition, his data indicated a somewhat larger interaction between external and internal rotation than for the vibrational ground state. However, even Lees’ additional data did not allow separate determination of I,, and Zaz. Recently, two types of experiment have been performed which, although of a

J. 0. HENNINGSEN

284

quite different nature, both supply additional information about the C-O stretch fundamental. In the first, medium and high power CO, lasers are used for optical pumping of CH,OH with subsequent FIR laser emission. Many pump transitions and emitting transitions have been assigned, providing information about C-O stretch levels with Doppler-limited resolution (II -14). In the second, the much less powerful, but continuously tunable PbSnSe lasers have been used for an extensive investigation of the fundamental C-O stretch band between 1027 and 1068 cm-’ by absorption spectroscopy (15, 16). In the present paper we shall review all of the available information and show that it allows determination of I,, and Za2, and also leads to a more precise value for Vs. The revised parameters allow a more extensive interpretation of the diode laser spectrum, and in support of Stark laser data (17) it is shown that the C-O stretch band has a pronounced anomaly around K = 5. The anomaly is quantified in terms of empirical corrections, and tables are given from which transition frequencies in the torsional ground state up to K = 9 and .Z = 24 can be calculated with an accuracy of about 0.003 cm-‘. Transition frequencies calculated from the tables are compared with results from Doppler-free spectroscopy (Z8), and, finally, the tables are used for performing some additional assignments of previously observed FIR laser lines (14, 19 -23). ENERGY LEVELS

A particular state is characterized by the quantum numbers (~TK,J)~, where .Z measures the angular momentum, K its projection on the u-axis, IZ and 7 label the internal rotation or torsional levels, and a indicates the vibrational state. In a condensed notation the energy may be written as E(nTK,J)”

= Ezib + B”(nTK)J(J

+ 1) - D”(n7K)J2(.Z + 1)2

- Z+Yn7JW3(J + 1)3 + W”(n&)

+ (asym. split).

In the following, we shall suppress the vibrational superscript The coefficients of Eq. (1) are given by (5) B(nrK)

= ; (R + C) + F,( 1 - cos 37) + G,(P$)

wherever

= D.,., - d(mK),

W(mK)

= ; V3(1 - cos 3~) + F(P;)

possible.

+ L,K(P,) - D.,&’

D(mK)

(1)

+ b(mK),

(2) (3)

+

1

A - ; (B + C) K2 + AE(n7K),

(4)

while the H(n7K) term is added to get a better representation of the energies at high J. y is the angle of internal rotation, and the bracketed quantities are internal rotation expectation values. B, C, F, and A are related to the moments of inertia of the molecule according to lb

B=

fi (5)

IgG’

C-O STRETCH FUNDAMENTAL

285

OF CH,OH

TABLE I Experimental

Basis and Results for vvib in Units of cm-’

ref

measured 1transition

IlTK

EI1 (I-ITK) firom exp.

Uvib (nrK) from exn.

"vib :this work)

”

010

1033.899

0.79783

1029.594

1029.593

020

1033.708

0.79812

1030.070

1030.086

0.002

011

1034.372

0.79785

1030.098

1030.089

0.005

1033.536

0.79812

1030.072

1030.085

0.001

1033.908

0.79793

1030.068

1030.082

-0.002

-0.491

R(J) 021 J<24 -

15.1 031 012

1034.301

0.79787

1030.120

1030.085

0.001

022

1033.434

0.79817

1030.087

1030.080

-0.004

032

1034.107

0.79782

1030.083

1030.081

-0.003

11

010

R(lO)

1033.894

0.79794

1029.589

1029.588

-0.496

11

034

PC261

1034.524

0.79727

1030.279

1030.185

0.101

11,l

027

Q(16)

1034.246

0.79844

1030.311

1030.042

-0.042

11.1

018

Q(l6)

1033.755

0.79791

1030.497

1030.097

0.013

11.1

0210

R(26)

1034.793

0.79753

1030.641

1029.978

-0.106

13

039

R(29)

1034.492

0.79746

1030.774

1030.170

0.086

17

025

I?(8)/P(9)

1033.824

0.80090

1030.245

1030.131

0.047

17

016

1033.739

0.80013

1030.305

1030.046

-0.038

Q(lOl -

=

=

Note. Horizontal line separates low-K diode laser data and far-infrared laser data extending to high K.

c==,

(6)

c

F=

I,I,

- I&

I,lI,,Ib A=

- I&b

I, + z,Ib

n -7 h

-

Ib I;b

--. -

1%

(7) h

Ib

(8) +

z;b

1 h

The terms with F,, G,, and L, are interaction terms which account for J-dependent centrifugal effects on the internal rotation. D JK and D.,., are the usual centrifugal stretching constants while b(nrK) and d(n~K) represent contributions from the asymmetry. These terms are calculated by second-order perturbation theory, starting from a symmetric-top representation. The hrst two terms of W(mK) are the expectation values of the internal, rotation potential and kinetic energy, while AE(n7K) lumps together all residual J-independent contributions originating from the K4 centrifugal stretching term, the departure of the hindering potential from a sinusoid, the seven Kirtman terms which measure J-independent centrifugal effects, and the asymmetry.

286

J. 0. HENNINGSEN TABLE II Parameters Used for Vibrational Ground State and C-O Stretch State

CH30H

CH30H

ground state ($5)

-

Evjtb 'b

0

CH30H

C-O stretch (1,

C-O stretch (this work)

1030.036

1030.084(3)

34.003856

34.3495

34.2828(26)

35.7288

35.6380(26)

Ic

35.306262

I al

-0.1079

I a.

1.2504

t 1.2504

t 1.2523(e)

Ia:

5.3331

5.3486

5.3334(e)

373.21

392.2

"3

392.35(30)

-0.52

"6 DKI

0.38~10-~ -0.48~10-~

kl

-18.41~10-~

k2

-53.73x10-4

k3

-85.50~10-~

k4

137.07x10-4

k5

67.85~10-~

k6

0

k7 F" G"

I -2.389~10-~

.6.546~10-~

-1.168x10-4

-1.168x1o-4

-1.67~10-~

-2.26~10

L" DJP; DJ;r -

I

-2.389~10-~

-6

9.54x10-6 1.6345~10-~

i-

-

Note. Calculations performed as in Ref. (4). Moments of inertia are in units of kg m’ x 10” and may be converted to amu.A* by dividing the number in the table by 1.660531. Other parameters are in cm-‘. V, of the center column has been adapted to the ground-state barrier of (4).

DATA ANALYSIS

The key to a determination of Zal and I,, are the two constants A and F. Since lab is small, A = l/(Zal + Z,,)(fi/47r) is related to the total moment of inertia about the a-axis while F 5 (l/la1 + l/Z&(h/47r) is related to the reduced moment of inertia of the OH group. Both enter in W(n7K) only. The experimental data are summarized in Table I, except for the diode laser spectra which are found in (15,26). To determine the coefficient A - (l/2)@ + C), it is necessary to reduce the measured frequencies to .Z = 0. To do this for the diode laser data, we express the equation for the R(J) absorption frequency in

C-O STRETCH FUNDAMENTAL

287

OF CH,OH

TABLE III Measured and Calculated Q-Band Coefficients in cm-’ for the 012 + 021 Transition vib state

90

91

92

93

94

measured

(1,

v=o

0.83218

-0.9813x10-4

3.7059x10-6

-0.3536x10-'

-1.634.10-11

measured

Cg,

v=l

1.59831

-2.1955x10-4

3.012~10-~

-1.564x10-9

-1.301.10-11

calculated

v=o

0.83237

-O.9716x1O-4

3.7184x10-6

calculated

v=1

1.5980

-3.6053x10-4

3.0814x10-6

Note. Calculations are based on Table II, columns 1 and 3.

the form v(J+J

+ 1) - 2B”(J + 1) + 4D”(J + 1)3 + 6H”(J + 1)5

= v,,,(n&)

+ 6B(J + l)(J + 2) - SD(J + 1)3(J + 2)3 - 6H(J + 1)3(J + 2)3,

(9)

where V,,(nrK)

E V,ib + W’(~TK) - WO(nrK),

6B = Bl(rmK) - BO(mK), SD = D’(mK)

- P(n7K),

6H = H’(WK)

-

H’(nTK)

(10) (11)

(12)

and where only the leading term involving Ho has been retained. We shall later explicitly consider the cubic energy term, but for the time being we assume H”(n7K) = Hl(rz~K) = 0. The remaining u = 0 terms on the lefthand side of Eq. (9) are calculated with parameters from (4, 5) as summarized in the first column of Table II, and the resulting left-hand side is plotted as a function of (J + l)(J + 2). For all (~TK) considered in (15, I6) the plot is perfectly linear up to J = 10, indicating that in this range at least, 6D is unimportant. The resulting v,ib(nrK) as given by the zero intercepts, and B’(PzTK) as given by the slopes in conjunction with Eq. (1 l), are quoted in columns 4 and 5 of Table I. For the remaining cases the reduction to J = 0 is less trivial. The reason for this is that only high J information is available, and effects from the cubic terms in (J + l)(J + 2), as well as from perturbations, may be important. On the other hand, the data from (15, 16) are not sufficient, since they involve low K only and do not determine the coefficient of the K2 term with the required accuracy. To identify the safest procedure we consider the Q-branch expansion u&J) = In qnJ”(J + 1)” for the 012 + 021 transition, which is the only case that has been studied for both u = 0 (24) and v = 1 (IO). The experimental expansion coefficients are quoted in Table III, and compared with calculated values. In the calculation for u = 1 we have anticipated the results of the present paper and used the last column of Table II, but the conclusions would be the same if the middle column were used. We note that the magnitude of q1 and q3 increase significantly when the C-O stretch is excited, and that for the C-O stretch, the experimentally

288

J. 0. HENNINGSEN

at 'ii

103.6029

ii

-Rs

(10)

1071.6636 -RsW 1074.6465

0

-F'S (36) 1031.4774

c:

16

FIG. 1. Optically pumped far-infrared laser data involving combination loops. Wavenumbers in cm-‘.

determined q1 does not agree with the calculated value. On the other hand, q2 and q4 change only moderately, and the experimentally determined q2 is in good agreement with the calculated value, both for the vibrational ground state and for the C-O stretch. Since q1 = B(012) - B(021)andq2 = -0(012) + 0(021), we therefore infer that D’(n7K) may be calculated with sufficient accuracy, whereas B’(n7K) must be determined experimentally. When pumping a level J, the frequency of the subsequently emitted far infrared radiation of the (MK, J --, J - 1) transition is given by v_,_+_~= 2JB’(nrK)

- 4J3D1(n7K)

- 6J5H1(n7K),

(13)

where again only the leading term with H’ is retained. Neglecting the J5-term, this equation is then used for determining B ‘( n7K) with D ‘( ~TK) calculated from the parameters of Table II. To check the consistency of this procedure and get a quantitative estimate for the uncertainty, we consider Fig. 1, which summarizes the experimental data for pumping with P,(36), R,( 14) and R,( 10) (11-13,25). It is seen that B ‘(039) can actually be evaluated in several independent ways. Using the two (0210) --, (039) emission lines together with Eq. (13), we get B’(039) = 0.79746 cm-‘. Using the loop involving both R,( 14) and R,( 10) with calculated ground-state level separations (given in brackets in the figure), we hnd B’(039) = 0.79716 cm-‘, and, finally, the (039, 30 + 29) line yields B’(039) = 0.79725 cm-‘. The deviation translates into an uncertainty of the order of 0.2 cm-’ for V,r,(O39), and a similar check performed for B’(OlQ leads to an uncertainty in yvib(018) of about 0.05 cm-‘. If the uncertainty can be associated with the neglected J5-terms, the H coefficients for such K-values must be 50.3 X 10Vgcm-‘. This conclusion will be verified a posteriori by the further analysis of the diode laser spectra.

C-O STRETCH FUNDAMENTAL

I

I

0

OF CH,OH

289

I

so

100 K2+

FIG. 2. Vibrational frequencies vvlbdetermined from data for different K. Internal rotation contributions are subtracted on the basis of Woods’ parameters.

Having reduced the transition frequencies to J = 0 with results as given in column 4 of Table I, we next evaluate WO(mK) from the parameters of Table II, column 1, and W’(nrK) from those of column 2, which reflect Woods’ assumptions with VA adapted to conform with Kwan and Dennison’s choice for Vi (4). The resulting values for Yvibas derived from Eq. (10) are quoted in column 5 of Table I and plotted as a function of K2 in Fig. 2. Disregarding (OlO), to which we shall return later, the points exhibit a reasonably linear behavior. However, the nonzero slope, which originates from the K2 term of Eq. (4), indicates that [A - (1/2)(B + C)]’ is not given correctly by Woods’ parameters. According to Fig. 2 the required value is about 0.006 cm-’ higher, and anticipating the result of an iterative procedure, we find 1

A

-

;

(B + C)

I

= 3.4499 cm-l.

To extract A’ we further need to know (l/2)@ + C)’ which, according to Eq. (2), is the dominant term in the rotational constant B’(n7K). In order to identify the contribution from the interaction constants, we consider the eight values of B’(n7K) which are deduced from the data of (15). LA, DiK, and b’ contribute by insignificant amounts and are chosen equal to the u = 0 values. A least-squares determination of the remaining three parameters (l/2)@ + C)‘, F& and GA leads to unreasonable results when compared with those for u = 0. If instead we assume various values for G: and determine (l/2)(8 + C)’ and Ft, by a least-squares procedure, we fmd the relationship shown in Fig. 3, and the quality of the fit turns out to be essentially independent of our choice for GA. Although we therefore cannot uniquely determine F: and GA, it is clear that F: is significantly larger than F,O,and if we follow Lees (10) and assume a GA = -5 MHz, we find the values

290

J. 0. HENNINGSEN

-----

1

+

I

assumed -G:

/ / 0.798

-G,(MHzl-

FIG. 3. Least squares determination

of Fk and (1/2)(B + C)’ as a function of assumed Ct..

Gh = -5 MHz = - 1.668 x 10m4cm, F; = -196.3 MHz = -6.546

x lop3 cm-‘,

i (B + C)l = 24013.7 MHz = 0.801011 cm-‘, which are comparable to those deduced by Lees on the basis of a single Q-band transition (10). From the K = 1, 2, and 3 A-state splittings (16) and from (10) we take B - C = 0.03104 cm-‘, and using the v = 0 value for IA*, we now know I:, Zj. and ZA = z;, + z;,. It remains to determine Vvib, Vi and F’ by a least-squares fit to v,ib(fiTK). Since the uncertainty of the r+ib(nrK) derived from the diode laser data is at least an order of magnitude smaller than for the v,,(nrK) derived from the optical pumping data, we again use the data based on (16) only-excluding (010). The final set of parameters is listed in column 3 of Table II, and the V,ib as determined from this set in column 7 of Table I. The average value (Y,ib), based on the data from (15)-excluding (OlO)-is (vvib > = 1030.084 2 0.003 cm-‘,

where the rms deviation of 0.003 cm-’ is comparable to the experimental uncertainty quoted in (15). The result is close to the value 1030.072 cm-’ deduced from laser Stark spectroscopy on low-K lines in conjunction with calculations based on Woods’ parameters (18). The rms deviation for the vvib determined from the optical pumping data is 0.068 cm-‘, which is consistent with the uncertainty involved in the reduction to .Z = 0. v,ib(OlO) is found from both types of measurements to deviate by -0.491 and -0.496 cm-‘, respectively, corresponding to about 165 standard deviations. Since B’(O10) shows no peculiarity, the entire (010) ladder seems-for reasons unknown-to be displaced downwards. The statistical uncertainties are given in Table II. In addition, lb, I, and I,, are subject to a systematic uncertainty arising from the arbitrary choice of GF.

C-O

STRETCH

FUNDAMENTAL

OF CHSOH

291

Choosing instead the ground-state value, would increase both Zb and I, by about 0.016 x 10m4’kg m2, andI,, by 0.0008 x 10P4’kg m2. The results corresponding to other values of Gh are easily found from Fig. 3 and Eqs. (5)-(8). From Table II it follows that upon vibrational excitation, Za2is essentially unchanged, while I,, experiences a modest relative increase of about 1.5 x 10e3. As a result, even though the last term of A - (l/2)@ + C) accounts for only 20% of the total, it is this term that carries essentially all the effect of the vibration. Our result of 19.35 + 0.30 cm-’ for the increase in barrier height agrees with Woods’ result of 19 ? 2 cm-l. EXTENDED

INTERPRETATION

OF DIODE LASER SPECTRA

In (15), Sattler et al. published their spectra up to R(ll) and identified the K-values of nine different series of lines. Following this, in the later and more extensive version (Z6), they included the spectrum up to R(24) and identified all (OTK)-ladders up to K = 2 plus the asymmetry-split (013). In addition, they made a partial identification of another four ladders with K ranging up to 5. With the improved band parameters at hand, we can now reexamine their spectrum and try to perform a more complete interpretation. Sattler et al. introduced a particularly useful representation of their data. The spectrum was broken up into segments, each covering the range of a certain R(J), and the different segments were arranged such that lines of the (020)-ladder were placed on the same vertical line. In this representation it is in most cases relatively easy to identify lines that correspond to the same (nrK) since, when interconnected, they will lie along smooth curves which tend to be vertical for low .Z. When attempting to identify the quantum numbers appropriate to the various ladders, it must be borne in mind that, according to (Z7), rather severe perturbations may be expected for certain (~TK). The line positions are determined by Eq. (9), and we hrst try to estimate to what extent the perturbation affects the different terms. For v,ib(nTK) the calculated spread caused by the internal rotation is of the order of 1 cm-‘. On the other hand, for all (nrK) included in Table I-excluding (OlO)-the difference between measured and calculated v,ib(nTK) is at most 0.1 cm-‘, corresponding to 10% of the spread. Furthermore, a major part of this difference definitely arises from the reduction to J = 0, which can be performed much more reliably from the diode laser spectra than from the optical pumping data. If we now turn to B’(~TK), the calculated spread is about 3 x 10m4cm-‘, whereas the difference between measured and calculatedB’(n7K) can exceed 2 x lop3 cm-‘. Combining this insight with the conclusions based on Table III, it seems safe to conclude that the perturbation-whatever its source may be-has a much more drastic effect on energy terms involving odd powers of J(J + 1) than on terms involving even powers. Consequently we base the identifications primarily on V,ib(nrK). For those (~TK) where FIR laser action is observed, the B’(n7K) deduced from the emission frequencies provide a check on the assignments which is particularly useful in cases where B’(n7-K) is strongly perturbed. In principle, one might also note that a series with a given K will terminate at J = K. However, this is not a reliable check since the lines get weaker

292

J. 0. HENNINGSEN

FIG. 4. Measured and calculated v,it,(n~K).

as J approaches K, their intensity being proportional to ((J + 1)’ - K2)l (J + 1) (26). For a given series, preliminary values for V,ib(nTK) and B ‘(nrK) are found by using Eq. (9) with estimated values of BO(nrK) and DO(nrK), assuming Ha = 0 and plotting the left-hand side as a function of (J + l)(J + 2). A comparison of v,,,(n~K) with calculations then suggests an identification, and improved values can now be found by using the proper B”(n7K) and DO(nrK). The resulting v,&nrK) are compared with the calculated values in Fig. 4. A problem exists around 1034.55 cm-’ where there is a cluster of nearly coincident band origins. A series of R-lines corresponding to these (nrK) can be identified, but it is difficult to unambiguously assign (~TK) because the lines with lowest J are missing. This may be settled by an analysis of the Q-band where lines with lowest J are the strongest. As previously noted, the (OlO)-ladder is shifted downwards relative to the calculated position by about 0.5 cm-‘. From Fig. 4 it is seen that this behavior is unique, the shift being more than five times larger than for any other (nrK). We are not able to explain this observation. THIRD-ORDER

EFFECTS

The deviation from linearity in (J + l)(J + 2) reflects the contributions to Eq. (9) from 8D, Ho, and SH. Guided by the results quoted in Table III, we assume

C-O STRETCH FUNDAMENTAL 0.2 -^ k u E

I

I

OF CH,OH

293

I

(nTK).(OlB) H=~I23.10-~cm-'

& L O.lz &

--I

(J+l)'(J +213

FIG. 5. Third-order

contribution

to the energy of C-O stretch levels for (mK)

= (018).

that 6D may be calculated, and that Ho < H’, so that we may take Ho = 0 and 6H = H’. In a majority of cases the deviation is indeed linear in (J + 1)3(J + 2)3 up to the highest J, indicating that these assumptions are reasonable. As an example, we show in Fig. 5 the plot for (n7K) = (018), which only exhibits an apparent local perturbation around J = 15. The results for H’(n7K) agree with expectations. The third-order contributions are expected to be largest for small K where the separation between adjacent levels of the same internal rotation symmetry is smallest. This is particularly notable for (012) and (021) which are separated by only 1.598 cm-‘. The measured H’ correspond to a (0 12) + (021) Q-branch expansion coefficient q3 = -H’(012) + H’(021) = -0.77 x 10mgcm-l. This compares reasonably well with the q3 of -1.564 x 10Pg cm-‘, quoted in Table III, which is determined from microwave spectroscopy (IO). The discrepancy presumably reflects the fact that for these (m-K),the assumption Ho = 0 is not justified. Also, the q4 coefficient of Table III indicates that a fourth-order energy term is needed. EMPIRICAL

CORRECTIONS

TO W’(n7K) AND B’(mK)

Table V contains a summary of the results obtained by using Eq. (9) for a threeparameter least-squares fit of vvib(nTK), 6B and 6H, taking Ho = 0 and 6D = D, - Do. W”, B”, and Do are calculated from Table II, column 1, and listed in Table IV. W’, B l, and D’ are calculated from Table II, column 3, and the experimentally determined energies and rotational constants are expressed as W' + AW andB’ + AB. With the exception of four cases, marked with an asterisk in Table V, the rms deviation for all (m-K)is about 0.002 cm-‘, and introducing an adjustable 6D or a fourth-order term in J(J + 1) did not improve the fits. Thus, the rms deviation represents the statistical uncertainty of the measured frequencies, in good agreement with the estimate ~0.004 cm-’ of Ref. (15). For (012), (014), (024), and (032), the measured R(J) frequencies deviate in a systematic way from the predictions of the three-parameter fit, indicating violation of some of the assumptions. While an adjustable 6D did not lead to a significant improvement, the rms deviation for these (m-K)could be reduced from 0.005 to 0.002 cm-’ by introducing in Eq. (1) a fourth-order term -L’J4(J + 1)4 with Lo = L'. The result of the four-

294

J. 0. HENNINGSEN TABLE IV Calculated Energies and Coefficients for the Vibrational Ground State IITK

-1 WO(cm ) I

011 012 013 014 015 016 017 018 019 0110

121.915 131.851 143.435 162.587 189.072 222.553 262.618 308.841 360.901 418.699 482.396

b.806772 0.806768 0.806761 0.806724 0.806684 0.806628 0.806550 0.806443 0.806302 0.806126 0.805920

020 021 022 023 024 025 026 027 028 029 0210

137.097 142.602 154.163 171.559 194.697 223.820 259.319 301.615 351.077 407.975 472.479

0.806865 0.806858 0.806861 0.806815 0.806733 0.806622 0.806489 0.806341 0.806183 0.806020 0.805855

030 031 032 033 034 035 036 037 038 039 0310

137.097 138.080 145.975 161.136 183.818 214.174 252.264 298.057 351.430 412.166 479.949

0.806865 0.806831 0.806763 0.806696 0.806620 0.806536

010

4.91 6.45 -3.03 1.13 1.66 1.80 1.81 1.78 1.72 1.67 1.64

12.86 3.15 -2.83 -0.15 0.77 1.25

parameter fit is given in Table VI. It is seen that H’ has increased significantly and is balanced by an L’ of opposite sign. This suggests that the model should be regarded merely as an interpolation scheme. When combined with asymmetry splittings, Tables IV, and V or VI reproduce the experimental frequencies with a maximum uncertainty of about 0.003 cm-‘. K - 5 PERTURBATION

An unexpected finding in (17) was the presence of a perturbation having a strong effect on the series (025) and (016), and leading to a splitting of the former. Figs. 6 and 7, which show the empirical corrections A W and AB, clearly support this conclusion, since both tend to diverge at intermediate K for all three T. Transitions to the upper components of the (025) levels have been identified in the diode laser spectrum up to J = 19 and to the lower components up to J = 24, the latter being

C-O STRETCH FUNDAMENTAL

OF CH,OH

295

TABLE V Calculated Energies and Coefficients for the C-O Stretch State, Supplemented Corrections Accounting for Interaction with Unidentified States Wlbn-1)

IVTK

010 011 012* 013, 014* 015 016 017 018 019 0110

B(cm -1 x10-5,/ &nl-1x10-6)

AW(cm-') B1bn-l)

132.281 136.135 147.651 166.696 193.043 226.375 266.311 312.467 364.559 422.500 486.436

-0.495 0.004 0.010 0.022 0.051 0.062 0.000 0.024 -0.001 -0.032 -0.042

0.797808

5.22 7.09 -2.88 1.07 1.62 1.77 1.79 1.76 1.72 1.67 1.64

11.4 -6.1 -6.3 -10.2 -26.2 -51.7 174.0 50.1 32.8 29.1 19.6

0.797813 0.797827 0.797844 0.797863 0.797873 0.797857 0.797794 0.797666 0.797470 0.797216

by Empirical

H l(cm-1x10-9)

1 -0.14 -0.50 1.55 0.30 -0.46 -0.11 -1.57 a:22 0.23 0.35 0.25

-

I

020 021 022, 023 024* 025a, 026 027 028 029 0210

I

140.719 146.053 157.536 174.922 198.182 227.513 263.264 305.819 355.521 412.625 477.295

0.000 0.001 -0.002 -0.008 -0.028 0.058 -0.072 -0.034 -0.009 0.030 0.129

0.798126 0.798181 0.798219 0.798177 0.798067 0.797902 0.797703 0.797491 0.797279 0.797078 0.796891

12.75 0.14 1.54 1.55 1.48 1.44 1.44 1.47 1.53 1.62 1.74

6.6 -8.5 -4.6 -24.1 -46.2 275.2 184.0 96.6 66.7 46.2 32.5

-0.55 0.78 0.30 0.37 -0.31 -0.20 -1.19 -0.07 0.12 0.18 1 -

I

030 O3hv 032* 033 034 035 036 037 038 039 0310

I

I

140.719 141.906 150.001 165.337 188.156 218.607 256.747 302.544 355.880 416.544 484.237

0.000 -0.002 -0.008 0.000 0.026 0.102 0.036 -0.016 0.015 0.018 0.045

0.798126 0.798029 0.797898 0.797781 0.797671 0.797572 0.797483 0.797403 0.797329 0.797255

0.797172

I

6.6 -6.3 1.5 -13.2 -24.3 -49.4 -77.4 87.5 32.8 20.8 17.5

I

I

12.75 3.24 -2.75 -0.12 0.78 1.25 1.53 1.70 1.80 1.85 1.87

I

-0.55 0.12 0.00 0.15 0.08 1.06 -0.30 -0.01 -3.40 0.11

generally somewhat stronger. The data entered in Table V refer to the average frequency of transitions to the two split levels of a given J, and should be supplemented by Fig. 8 when evaluating the actual level positions. RESULTS FROM DOPPLER-FREE

SPECTROSCOPY

Bedwell et al. (18) performed saturated absorption spectroscopy on CH,OH, using two CO2 lines known to lead to FIR laser emission, P,(34) and P,(36). With P,(34) they were able to Stark tune into coincidence four different Q-band transitions, belonging to the torsional ground state. The lines were assigned by comparing with frequencies calculated from Woods’ model. This leads to correct conclu-

Parameters

-0.022

+

8)

1033.489

1033.4880

(015,8

Lines

-1 xl0

-2.15

1.48

1.62

-2.88

D'(cm

Pump

-6)

Higher-Order

-1.95

-1.34

2.13

5.31

H'(cm -1 x10 -9)

Asymmetry

Shifts

Based

-

28.31

41.11

353.3

243.3

48.17

48.8

207.6

205

48.71

22.13

205.3

61.01

451.9

(cm-L)

163.9

~ -

leasured

e:m.freq.

IT

on Calculated

Fnl.

(015,8)

(015,8)

(016,6)

(016,6)

(024,lO)

(024,7)

(024.8) +

i

(025",5) (025',5)

+

+

-f 13)

-t (033,9)

(025l,14

(025',14)-(034,13)

assigned em. (IITK,J)

trans.

Frequencies

41.021

28.263

48.628

48.007

48.747

22.286

61.132

ca1c. em.froq. (cm-l)

10.3

5.1

-14.0

-20.8

Ll(Crn-1 x10-12)

rr VII

-5)

Large

ca1c. nleasured pump freq . e?m.wavel. (cm-L) (Pm)

Laser

TABLE

-7.8

-52.9

1048.662

025,13)+(025',14)

assigned pump trans. (IITK,J)

of Far-Infrared

0.797898

1048.6608

pump freq. (cm-l)

Assignment

-0.002

0.798067

-13.7

0.797863

xl0

9.0

-1

0.797827

0.041

VI

with Particularly

0.001

AB(cm

(MK)

B'(cm -l)

for Four

Aw(cm -l)

I-

Interpolation

TABLE

C-O STRETCH FUNDAMENTAL

^

OF CH,OH

297

0.1

E 0 % x=1

-0.1

ti

7

E

m M

0.1

0

22

0

TZ2

-0.1

7

^

5 1

0.1

0

0

z=3 -0.1 0

5

10

K-

FIG. 6. Empirical corrections identified states around K = 5.

to internal rotation energy w’(n~K),

showing interaction

with un-

sions for three K = 1 transitions since Woods’ model gives good results at small K. The fourth transition, however, at a measured frequency of 1033.492 cm-‘, must be reassigned from Q(O26,6) to &(016,6), since Table V for these two transitions predicts 1033.667 and 1033.489 cm-l. In the following section it will be shown that this change is supported by FIR laser emission data obtained in the presence of a Stark field (21-23). LASER LINE ASSIGNMENTS

Three FIR emission lines pumped by P,(17) (24) have previously been assigned on the basis of information provided by the diode laser spectrum (27). Based on

0

5

10

K-

FIG. 7. Empirical corrections to the effective rotational with unidentified states around K = 5.

constant II’(

showing interaction

J. 0. HENNINGSEN

298

I

OO

I 5

I 15

IO

FIG. 8. Reduced level splitting for (~TK) = (025) determined optical pumping data (17).

I

20

from diode laser spectra (16) and

Tables IV and V we are now able to assign seven additional FIR emission lines generated by pumping with the P,(12), P,(B), and P,(34) lines of a regular CO, laser (29-2.3) and by the P,(31) sequence line (14). The relevant data are listed in Table VII and Fig. 9. In all cases the coincidence is predicted to within the lOO-MHz uncertainty of the calculated frequencies. The predicted emission lines agree with observations to within the uncertainty of the wavelength measurements. For P,(31), where the polarization of the emitted radiation has been checked, we further observe agreement with the general rule, which predicts I polarization for the 41.1 l-cm-’ line where AJab, + AJ,, = 0 + (- 1) is odd, and )I polarization for the 28.3 l-cm-’ line where AJabs + AJ,, = 0 + 0 is even (I1 ). The P,(34) lines are only observed in the presence of a Stark field of more than about 1 kV/cm (23), and the splitting of the (025) levels, reported in (17), offers a straightforward interpretation of both lines. It should be noted, however, that the (025) splitting has not been directly verified for J = 5 and 6, and that the Stark effect as reported in (23) seems to favor a Q(O25, 6) assignment for the pump transition. This only allows for identification of one of the emission lines, and also implies a nT;K-034

025

016

FIG. 9. Level diagram showing far-infrared frequencies.

033

024

laser line assignments

015

based on calculated

pump

C-O STRETCH FUNDAMENTAL

OF CH,OH

revision of the P,(lO) pump assignments of (27). More precise quency measurements may resolve this problem.

299 emission fre-

CONCLUSION

The present work serves to illustrate a fruitful interplay between two types of laser based molecular spectroscopy. A complete mapping of the fundamental C-O stretch band of CH30H has previously been provided by diode laser spectroscopy. This has been supplemented by an analysis of the information available from the CO, laser-pumped CH30H laser, which presents a picture, rich in details, of certain selected regions of the energy level spectrum. By combining these results with the theoretical model previously used for the vibrational ground state, improved values have been obtained for the moments of inertia Zb and Z, and the hindering potential barrier V 3, and a separate determination has been made for the hrst time of Zal and I,, for the vibrationally excited molecule. The improved calculations subsequently provide the clue to a more extensive interpretation of the diode laser spectrum, and in this way torsional ground-state R-transitions up to K = 10 have been identified. In support of previous conclusions based on Stark effect studies, the analysis shows that at intermediate K, the levels are strongly perturbed by an interaction whose source is as yet unknown. Its effect has been quantified in terms of empirical corrections to the internal rotation energies, the effective rotational constants, and, for m-K = 025 in terms of a Z-dependent level splitting. At .Z > 15 it has proved necessary to incorporate cubic terms in J(J + 1) in the analysis, and the coefficients of these terms have been tabulated up to K = 10. Using the tables, it is possible to evaluate the frequency of all torsional ground state P, Q, or R transitions from the vibrational ground state to the C-O stretch, up to K = 10and J = 24, with an accuracy of about 0.003 cm-‘. This has been substantiated by the assignment of four additional pump transitions and seven farinfrared emission transitions, which could previously not be accounted for due to insufficient information. Apart from the strong torsional ground-state transitions to the C-O stretch, the spectral region between 1000 and 1100 cm-’ is crowded with numerous weaker lines, some of which clearly originate from transitions between torsionally excited states. Although we can not as yet account in detail for these lines, it seems clear that at least some of the IZ = 1 states in the C-O stretch are better approximated by choosing a hindering barrier which is significantly lower than for n = 0 states. Also, lines are found whose origin is at present completely uncertain, possibly belonging to hot band or combination band transitions (13, 28). When pumped, several of these are known to produce strong far-infrared laser emission, and it is therefore possible that by proceeding along the lines indicated in this paper, an even more line-grained picture can be obtained of the vibrationally excited CH,OH molecule. ACKNOWLEDGMENTS The author wishes to acknowledge J. P. Sattler, T. L. Worchesky, and W. A. Riessler for making their excellent diode laser spectra available prior to publication, and for communicating additional

J. 0. HENNINGSEN

300

unpublished results. Also, thanks are due to Y. Y. Kwan for making her computer program available, and to R. M. Lees, M. Inguscio, F. Strumia, M. Feld, and R. Forber for numerous very iIluminating discussions. RECEIVED:

March 6. 1980 REFERENCES

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Theory Tech. MTT-22,983-988 (1974).

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private

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