Offset-locked CO2 waveguide laser study of formic acid: Reassessment of far-infrared laser assignments

JOURNAL OF MOLECULAR SPECTROSCOPY 92, 67-16

(1982)

Offset-Locked CO, Waveguide Laser Study of Formic Acid: Reassessment of Far-Infrared Laser Assignments B. M. LANDSBERG,' D. CROCKER,' AND R. J. BUTCHER Cavendish

Laboratory,

Madingley

Road,

Cambridge

CB3 OHE, United Kingdom

A number of infrared transitions of formic acid were measured to a precision of better than 100 kHz. In the light of these new data, far-infrared laser measurements were reassessed. Available microwave data were also incorporated in deriving new parameters for the vg and vs states, including the Q/Q a-type Coriolis interaction. INTRODUCTION

The us and vg excited states of HCOOH have been studied by microwave spectroscopy (1) and by assignment of accurately measured far-infrared (fir) laser emissions optically pumped with a CO2 laser (2, 3). Each fir emission is related to two characteristic frequencies; first the fir frequency itself, which is a rotational transition in an excited vibrational state, and second the frequency of the vibrationrotation transition v6 = 1 or v8 = 1 which pumps the fir laser. The fir frequencies have been measured by heterodyne techniques with quoted experimental errors as low as 200 kHz (2,4,5) although discrepancies between the measurements of these authors are of the order of a few megahertz. Frequencies of the vibration-rotation pump transitions have been equated to the relevant CO* laser frequencies, which is an imprecise procedure since a difference of more than a Doppler width (about 50 MHz) may occur between the transition and laser line center (6, 7). Previous attempts to fit the fir frequencies (2, 3) have not approached experimental error, and the possibility of strong v6/vg Coriolis resonance has been postulated (3, 10). Further, two new fir emissions in HCOOH assigned to K, = 12 - 11 b-type transitions have recently been reported (I 1) but their frequencies could not be predicted reliably using the existing data. By using saturation techniques resolutions better than 100 kHz may be obtained in infrared spectra near to each CO? laser line. Further, since the absolute CO2 line center frequencies are now established to great precision (8) it is possible to approach microwave accuracy in frequency measurement by using two lasers and a beat counting method (9). We have thus been able to augment the data, which has allowed us to establish unambiguously the presence of strong vg/v8 a-type Coriolis interaction, reject some earlier assignments of fir emissions, and greatly improve on the molecular constants describing the vg and us infrared bands. I Present address: School of Physical and Molecular Bangor, Gwynedd LL57 2UW, United Kingdom. * Present address: LSI Computers Ltd, Copse Road, Kingdom.

61

Sciences, St. Johns,

University Woking,

College Surrey

of North

GU21

Wales,

ISX, United

0022-2852/82/030067-10$02.00/O Copyright Q 1982 by Academic Press, Inc. All rights of reproductionin any form reserved.

68

LANDSBERG,

CROCKER,

AND

BUTCHER

FIG. 1. Survey scans of third derivative spectrum of formic acid using 9R(20) CO2 line. Labeled transitions occur in the v6 band. Pressure 40 mTorr, beam diameter I5 mm, path length 2.7 m. 0, threelevel dip; +, four-level collison-induced dip.

EXPERIMENTAL

DETAILS

The infrared spectrum of formic acid was investigated at sub-Doppler resolution by using a tunable waveguide laser system to obtain Lamb dip saturation spectra.

INFRARED

AND FAR-INFRARED

ASSIGNMENTS

IN HCOOH

69

+

I

FIG. 2. See Fig. 1.

Details of this apparatus are given in (9). The central components are two stable boron nitride waveguide lasers and a computer-driven difference frequency counter and offset lock. One laser is locked to the Lamb dip in the 4.3~pm fluorescence from a CO2 cell, thereby providing an absolute frequency reference (8). The other is operated at a total pressure up to 0.3 atm and can be tuned over its gain profile of a few hundred megahertz, the exact range depending on which line is in operation. The frequency difference between the two lasers is counted as the beat from a

70

LANDSBERG,

CROCKER,

AND

BUTCHER

copper-doped germanium detector at 4°K. A microprocessor runs the system and third derivative saturation spectra can be obtained at linewidths down to 150 kHz by tuning the second laser. For strong absorptions, the second laser can be locked to the absorption and an accuracy better than +50 kHz is obtained counting the laser beat directly. On weaker absorptions locking is not possible and the second laser is then scanned continuously, giving an accuracy of f250 kHz. The absorption cell was 2.7 m long, cell beam diameter 15 mm and gas pressures of about 10 mTorr were employed. Time of flight through the beam, pressure broadening, and wavefront curvature contribute to the resolution attainable. The cell also had facilities for crude Stark modulation. ANALYSIS

The data used for the least-squares fitting consisted of the microwave data for the Q = 1 and o8 = 1 states (I), measurements of the fir laser emissions (2, 3) and the laser offset measurements as obtained in this work. As the frequencies

ll

b

in the vs band. FIG. 3. Effect of electric field on the 22,~ - 2214.p and 301,29 - 302,28 transitions Formic acid pressure 40 mTorr, beam diameter 15 mm, path length 2.7 m. 98(38) CO1 line: approximate electric fields (a) 0, (b) 35 V/cm, (c) 65 V/cm, (d) 350 V/cm. 0, Offset + 15 MHz: markers 5 MHz, increasing to right.

INFRARED

AND

FAR-INFRARED

ASSIGNMENTS

TABLE Microwave

Far-Infrared

and Infrared

J’

71

IN HCOOH

I

Data

for y6 and v8 Bands

J”

K;;

9

2 I 3 2 I 2 0 I 2 3 I 2 I 0

KI;:

of Formic Frequency

Acid Obs.CalC.

Microwave Transitions in v6 (a) 2 I 3 2 I 2 0 I 2 3

I I I 2 I 6 5 4 3 3 2 7

7 2 I4 8 3 9 I 4 IO I7 5 II 2 2 6 7 3 3 2 I 1 2 2 3 3 4 I 3 3 5 4 6 3

I7

3

I5

fs”

:

1:

: I2

f: 14 29 19 32 33 20 21 25 26 39

9 I7 10 4 II

I 5 12 20

I 2 I 0 I I I 0 2 2

I3

8

I

7 7

Far Infrared frequencies

8 3 I5 9 4 IO 0 5 II I8 6 12 I I 7 8 2 2 I 0 2 I 3 4 4 5 0 2 2 4 3 5 2

9775.67 9902.61 12710. IO 14440.89 16501.81 20460.29 22355.24 24745.12 27979.55 30779.43 34624.22 37109.73 43060.29 44679.84 46128.08 59235.47 64570.79 66942.31 67067.26 67189.77 69181.03 69521.84 71760.12 75304.75 76052.48 79902,48 156604.80 156613.78 156646. IO 156716.76 156761.75 180939.43 201371.28

0.33 0.28 -0.29 0.14 0.47 -0. I6 0.06 0.54 0.20 -1.09 -0.25 0. I8 0.29 0.37 -0.01 0.36 0.24 0.21 0.48 0.53 -0.03 0.45 -0.23 -0.26 0.81 -0.43 0.59 0.43 0.13 -0.22 0. I8 0.22 0.05

I4 I5 9

381336.90 403721.60 402919.60

-0.08

I2 0 0 I2 12 9

f? I3 28 I8 31 32 I9 20 24

:

:‘8

W%: 88 581930.00 653822.20 671419.50 672335.50 692949.50 693788.50 716155.80 739161 .OO 761607.60 991776.90

3 I7 10 4 II 0 5 I2 20 6 I3

I I 7 8 2 2 2 2 2 2 3 4 5 5 6 6 6 6 6 7 8

I I 0 2 2 0 I 0 0 I 0 6 5 4 3 3 2 7

I6 I7 17

z

1

laser in v6(b)

2’5 26 30 30 32

I I2 0 0 I2 I2 9 9 6

;: 32 33 34 44

12 25 29 29 31

-

From reference

(

I

(b)

From reference

(

2,3

(c)

This

I

)

emissions

of

CO2 laser

weight

) weight

work

Frequencies FIR

3 12

3’; 31 32 33 43

(a)

(d)

3

1 0.1

weight

1

weight

0.0001

giving

-E -A.$: 0:43 0.71 I .26 -0.71 -1.34 0.82 -0. I2 2.65 I .64 0.72

72

LANDSBERG,

CROCKER,

TABLE

AND BUTCHER

I-Continued

Frequency Infrared in v,(c)

absorptions 40 26 44 29 21 34 33 33 33 33 32 22 6 6 25 30 18 26 19 18 22 30 18

Microwave in v,(a)

I2 I2 6 I2 3 9 0 0 I I I2 2 4 4 5

I 8 5 4 4 14 I 3

28 14 39 I7 I8 26 33 33 33 33 20 20 2 3 21 30 10 22 15 15 8 29 I6

40 26 45 28 22 35 34 34 34 34 33 23 7 7 25 31 17 27 19 I8 23 30 IV

I3 13 6 13 4 9 I 0 1 0 12 3 5 5 6 0 9 5 5 5 I4 2 3

27 13 40 I6 IV 27 34 34 34 34 21 21 3 2 20 31 9 23 14 I4 9 28 I7

7 2 8 3 15 9 16 1 4 10 17 5 II 2 6 2 27 7 13 3 3 2 1

9 3 10 4 I8 II I9 0 5 12 20 6 I3 I 7 I 31 8 I5 2 2 2 2

2 1 2 I 3 2 3 0 I 2 3 I 2 I I 0 4 I 2 1 0 2 2

8 3 9 4 I6 10 17 0 5 II 18 6 12 I 7 I 28 8 I4 2 2 I 0

31437987.38 31491501.85 32004016.13 32134182.90 32176205.84 32296749.46 32335224.28 32335361.87 32335393.84 32335531.50 32373175.86 32373291.04 32373315.20 32373315.20 32373323.78 32410006.60 32410192.38 32481918.04 32516370.92 32516403.01 32647442.52 32647451.80 32678207.36

0.04 -1.07 -0.01 1.67 0.86 -0.11 -0.02 -0.02 0.06 0.13 -0.78 -0.23 0.13 0.29 0.32 -0.10 0.53 0.46 -2.66 -1.28 0.05 -.3l 2.25

transitions 9 3 IO 4 18 II 19 1 5

Ii

2 I 2 I 3 2 3 0

I

20

2 3

6 13 2 7 2 31 8 15 3 3 3 3

2 I I 0 4 I 2 I 0 2 2

1

9150.96 9488.35 13527.44 15811.60 15987. I9 19181.19 21484.59 22421.26 23710.06 26255.47 28299. I6 33178.02 34859.7 I 43261.12 44203.24 44813.55 52935.17 56766.34 56936.16 64873.28 67148.63 67264.89 67379.01

0.18 0.17 0. I5 0.27 0. IV -0.67 -0.21 0.03 -0.18 -0.09 0.22 0.01 0.24 0.09 0.37 -0.04 0.00 0.06 -0.29 -0.06 0.33 0.57 0.24

reported by various authors disagree by a few megahertz as mentioned earlier, they are taken to be less reliable than the microwave and offset locked laser data and were given a weight of 0.1 in the fit. Some CO, laser lines give rise to fir emissions but unambiguous assignments could not be found. These were included in the fit by assuming the pumping transition to be of the same frequency as the CO* laser line within a Doppler width (about 50 MHz), and given a weight of 0.0001. The

INFRARED

AND FAR-INFRARED

ASSIGNMENTS

IN HCOOH

73

TABLE I-Continued J’

“i

KI-

J”

“I;

K’d

Frequency

Obs.CZAC.

2 1 3 4 23 5 3 6 6 5

6T913.59

I 51047.84 55363. I9 56716.76 57059.98 57092.64 57161.54 57202. I7 181331.74 185059.83

0.06 0.28 0.05 -0.03 0.00 -0.15 -0.06 -0.29 -0.07 0.00 -0.04 0.18 -0.01 -0.06 -0.12 -0.17

Microwave in v8 (a)

transitions 2

I

1

3 3 4 28 5 5

I

I

2 2 3 24 4

I

4

1

7

0

7

2 5 4 3 3 2

6 2 4 5 4 6

I

7

2 2 3 4 27 5 4 6 6 6 6 6 6 6 7 7

II 30

4 4

8 26

11 30

4 4

8 26

7

7

8 8 Far infrared frequencies

I I 4

0

I 0 0 5 0

1 I 0 2 5 4 3 3 2

I

69617.42

70382.42 73772.86 77128.40 78167.17 15926.25

I

3 4 3 5 6

10 29

4 4

7 25

247075.80 685316.60

0.06 -0.04

12 30

3 3

10 28

31159508.30 31491437.40

-11.07 II.07

laser in v8(b)

Infrared absorptions in v8 (d)

rotational constants of the ground state were constrained to those of Ref. (Z2). Considering the very high values of J and K, used in their fit, this constraint should not be a serious source of error in the calculation of the infrared transition frequencies. The preliminary analysis employed the Hamiltonian of Watson (13) up to sextic centrifugal distortion terms for both upper and ground states using a type I’ representation. It became apparent that certain of the assignments of Refs. (2, 3) were false for the v6 = 1 state; the basis for this decision was mainly the large differences between the 9-pm observed and calculated frequencies. These false assignments are the 447 765.0-MHz emission pumped by the 9-pm R(30) CO* laser previously assigned to the 20s - 198 transition (2, 3) and the 516 538.7-MHz line pumped by the 9R(22) CO1 laser previously assigned to the 235,19 - 225,18 transition (I) or the 235.18 - 225,17 transition (3). Neither of these emissions, nor any of the emissions previously unassigned, could be assigned to a transition in the vg or us manifold, and therefore are believed to arise from optical pumping of excited vibrational states. After removal of these transitions the resulting fit of the vg state was improved, but still did not approach the level of experimental error. Addition of octic centrifugal distortion terms to the Hamiltonian did not significantly improve the situation. In particular, a most remarkable feature occurred in the quartet of tran-

74

LANDSBERG,

CROCKER, TABLE

AND BUTCHER II

Formic Acid Molecular Parameters of v6 and vg Ground

State(a)

77512.2310 12055.1045 10416.1145 9.9894 - 86.250 1702.29 1.94920 42.600 0.00928

0.0 -10.26 119.5 0.006035 0.0 12.55

%s=l[fbJk3) 1+(vg/ug) t 1

(a)

From

(b)

Constrained

“6 =

I

33122629.0 77600. I 12oe3.17l99 10352.0459 10.2447 - 89.313 1774.2 2.0429 48.96 0.0164 - 0.759 -25-67 30.2 0. 0125 0.0 0.0

V8 = (10) (18) (59) (68)

1

30982554

(41)

76977.5 12001.623 10419.643

(76)

9.763 -69.9 1260. 1.820 23.0

(87) (13) (56) (27)

II:; (17) (34) (16) (31) (18) (28)

(32)

0.0

( b)

(57) (84)

0.0 0.0

( b) ( b)

(38) (29) ( b)

0.0 0.0 0.0

( b)

0.0

( ( ( (

2AQ ca = 23292 68 68

(80)

b) b) b) b)

MHZ

(12) to

0.0

sitions on the o-pm R(20) line assigned to L)6= O;34Ka6.34 - 2)6= 1;33~~.,~~ Figs. 1 and 2. The energy difference between the +, = 1;330,33and 33,,33 levels was always predicted 10 MHz larger than observed, as has already been reported (9). Although formic acid is a near-symmetric prolate top, at very high J and very low K, the molecule behaves like a near-symmetric oblate top, since the rotational axis is essentially perpendicular to the molecular plane, and levels denoted by the same KC quantum number tend to lie closer together with increasing J and decreasing K,. For J = 33 and KC = 33, the splitting is predicted to be only about 180 MHz in the v6 = 1 state, and furthermore should vary much more slowly with the rotational constants than the frequencies of most other observed transitions. Thus some form of perturbation must be considered to explain this discrepancy. The only vibrationally excited states near or below the v6 manifold are v7, us, and 5. The v7 and u9 energies are too low, and the 2v7, 2v9, and u7 + u9 energies too high, to be able to give a significant resonance with v6. A Y6/@ Coriolis interaction must therefore be considered. Evidence for an interaction of this kind has already been published (IO), although the microwave spectrum of the v6 and v8 excited states shows no corresponding obvious perturbation (1). As v6 is an in-plane vibration and vg an out-of-plane vibration, the resulting interaction may be u-type and/or b-type. Invoking a finite b-type interaction decreased the quality of the fit

INFRARED

AND

FAR-INFRARED

ASSIGNMENTS

IN HCOOH

75

and made the lo-MHz discrepancy even more anomalous. However, introduction of an a-type interaction resolved the situation. The rather large value of the Coriolis coupling parameter 2AQ,&, of well over 20 GHz not only explained the lo-MHz discrepancy in the J = 33 quartet of transitions, but also brought the observed and calculated frequencies of the fir emissions and the 9-pm offset-locked measurements near to experimental uncertainty. ,The effect of this perturbation was not seen in the microwave spectrum of the v.Jug states (I) since, up to K, = 5, it merely changes the value of the effective A rotational constant. One problem met during the assignment of the offset-locked laser measurements was discriminating between two frequencies which are close together and of similar intensity. On the 9-pm R(38) laser line, for example, two strong absorptions were observed at +19.6 and at +10.3 MHz. These must be assigned to the u6 ZZ1;30,,2s - v6 = O;302,2stransitions which gives rise to an fir emission and the v6 = 0;23,49 transition, but the two ways of assigning these lines u6 = 1;22,4,8 gave equally good fits. The problem was resolved by application of a small electric field to show that only the absorption of an offset of +10.3 MHz has a very fast Stark effect and therefore must be assigned to the K, = 14 transition (Fig. 3). A large number of offset locked laser measurements were also made in the vs region of the spectrum, but, although several plausible fits have been obtained, no one is completely convincing. It did become apparent, however, that the fir transition at 561 748.6 MHz pumped by 9P( 16) cannot be assigned to 25, - 24, (3). Indeed, there is no plausible assignment in the vg or vs manifold and the emission must arise from a vibrationally excited state. The fir laser at 516 170.8 MHz, pumped by 9P(38), could be equally well assigned to U, = 1;23,, - 22i2 as in Ref. (I) or 23r3 - 22,3. In either case, the fir and infrared frequencies fit well if the sextic, H,, is allowed to vary. The resulting values of HK are respectively +2 kHz and -2 kHz; the magnitude being more than 20 times greater than the ground state. Due to the large values for HK and the ambiguity of the assignment this line was also not included in the fit. The fir laser v)6= 1;l 88 - 178 may be pumped via a quite strong absorption on 9R(24), offset + 122.97 MHz. All fits using this assignment, however, led to significant discrepancies (lo-20 MHz) in parts of the fit. Our suspicion is that the &,/va b-type Coriolis coupling is coming into play, but because of the quantity of computing involved we have not pursued this part of the TABLE Predictions

of Far-Infrared

Transitions

Assigned

Transition (in v = I state) 6

in

III

(I 1) which Have Not Been Accurately Predicted frequency (MHZ)

969098

436,38 +

4=6,37

3212

+

32il

1522310

3212

+

3'11

2238564

Measured

76

LANDSBERG,

CROCKER,

AND BUTCHER

analysis. There are, in addition, difficulties due to the inherent weakness of the ugtransition compared with v6 and the abundance of unassigned hot band transitions of vg in the region of vs. A complete set of infrared measurements is given in (14). The result of the least-squares fit to microwave, fir, and infrared data is shown in Table I in which the ground-state parameters are constrained to those in Ref. (12) and the sextics of the v8 = 1 state are constrained to zero. Derived parameters, with standard deviations in parentheses, are given in Table II. We note that our values for vg and v8 are close to, but much better defined than, those given in Refs. (I) and (2). The choice of sextic parameters included in the fit is a reflection of the ranges of quantum numbers sampled in the various spectra. Using our new constants, the frequencies of the new fir lines reported in (I 1). which have been measured to an accuracy of 0.2%, can now be predicted, as shown in Table III. Due to the possibility of small errors in the derivation of the parameters of Table II, it is difficult to estimate the reliability of these predictions, but they should be accurate to a few megahertz. CONCLUSION

By making precise frequency measurements of the 4 band of formic acid, we have been able to establish the presence of a strong vg/v8 u-type Coriolis interaction. By combining our measurements with microwave and far-infrared laser data, improved molecular constants have been obtained and some earlier fir assignments have been disproved. It is clear from this work that the combination of optically pumped fir laser transitions and the corresponding sub-Doppler lo-pm spectra provides a powerful tool for analysis of vibration-rotation interactions. RECEIVED:

June

15,

1981 REFERENCES

I. E. WILLEMOT,D. DANGOISSE,AND J. BELLET,J. Mol. Spectrosc. 77, 16 I- 168 ( 1979). 2. 0. J. BASKAKOV,S. F. DYUBKO, M. V. MOSKIENKO,AND L. D. FESENKO,Soviet J. Quantum Electron. 7, 800-808 (1977). 3. D. DANGOISSE,E. WILLEMOT,A. DELDALLE,AND J. BELLET,Opt. Commun. 28, 11 l-l 16 ( 1979). 4. A. DELDALLE,D. DANGOISSE,J. P. SPLINGARD,AND J. BELLET,Opt. Commun. 22, 333-336 (1977). 5. G. KRAMERAND C. 0. WEISS, Appl. Phys. 10,187-188 (1976). 6. M. S. SHAFIK,B. M. LANDSBERG, D. CROCKER,ANDR. J. BUTCHER,IEEE .I. Quantum Electronics QE-17, 115-116 (1981). 7. G. D. WILLENBERG,V. H~BNER, AND J. HEPPNER,Opt. Commun. 33, 193- 196 (1980). 8. C. FREED,L. C. BRADLEY,AND R. G. O’DONNELL, IEEE J. Quantum Electron. QE-16, 11951206 (1980). 9, D. CROCKERAND R. J. BUTCHER,Infrared Phys. 21, 85-89 (1981). IO. C. HISATSUNEANDJ. HEICKLEN,Canad. J. Speczrosc. 18, 135-142 (1973). Il. B. M. LANDSBERG,Appl. Phys. 23, 345-348 (1980). 12. E. WILLEMOT,D. DANGOISSE,N. MONTANNEUIL,AND J. BELLET,J. Phys. Chem. Ref: Data 9, 59-160 (1980). 13. J. K. G. WATSON, J. Chem. Phys. 46, 1935-1949 (1967). 14. D. CROCKER,“Applications of Carbon Dioxide Waveguide Lasers to Infrared Saturation Spectroscopy,” Ph.D. Thesis, Universityof Cambridge, 1980.