Laser-microwave two-photon and double resonance spectroscopy of two linear molecules; HCCF and FCN

JOURNAL OF MOLECULAR SPECTROSCOPY 78, 452-468 (1979)

Laser- Microwave Two-Photon and Double Resonance Spectroscopy of Two Linear Molecules; HCCF and FCN

HAROLD JONES

Department of Physical Chemistry, University of Urn, 79 U/m. West Germany

The technique of laser-microwave two-photon spectroscopy has been used to determine the frequencies of a number of transitions in fundamental and hot-bands of the two linear molecules HCCF and FCN. This method has previously only been applied in a systematic way to spectroscopy in NH, and it was the aim of this investigation to determine to what extent this method was applicable to more normal molecular species. The maximum effective tuning range produced with these molecules was -t3.7 GHz with a microwave power density of = 100 mW/cm2 and a laser power density of =40 W/cm2. Transition frequencies were determined with accuracies up to t3 MHz using a Lamb-dip technique. In the case of fluoroacetylene the observation of a number of double resonance signals involving direct /-type doubling transitions allowed determination of /-type doubling constants for the states (un = 1, u4 = 1) and (uB = 1. ci = 1). The P(l2) C’“0, laser line was shown to lie within the Doppler width of the upper /-type doublet R(25) transition of the (I+ + v,) - I+ hot band. In this particular case velocity-tuned multiple photon dips were observed. The dispersive component of double resonance and two-photon Lamb-dip signals was observed to have opposite phase in two different vibrational states. The possible diagnostic value of this observation is discussed.

INTRODUCTION

The first report of systematic infrared spectroscopy being carried out by the technique of laser-microwave two-photon spectroscopy was given by Freund and Oka (1) in their study of the V$ band of ammonia. In this technique one is able to make use of the high stability and reproducibility of CO, laser line frequencies in order to accurately determine infrared transition frequencies. A tunable microwave frequency is effectively added to, or subtracted from, a fixed frequency laser line using the nonlinearity of the molecular absorption process itself. In this way an effective tunable, coherent infrared source may be generated, the useful tuning range of which is determined by the laser and microwave power levels available and by the molecular species under investigation.

It has been shown from this laboratory (2,3) that in the case of ammonia it is possible to produce effective tuning ranges of ? 12 GHz about the CO, laser line frequencies with very low microwave power levels (ca. 20 mW). It has also been shown that provided cells of suitable construction are used (e.g., (4)) even at the extremes of this range transition frequencies can be determined with an accuracy of 215 MHz.

Ammonia is almost uniquely well suited to this type of two-photon spectroscopy, since it possesses a very large number of strong microwave transitions in a con- venient spectral region. The purpose of the work described in this paper was to

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452

TWO-PHOTON SPECTROSCOPY OF HCCF AND FCN 453

determine to what extent this relatively new spectroscopic technique could be applied to more normal molecular species than ammonia. For this purpose the two linear molecules, HCCF and FCN, were selected. These two molecules both have intense infrared absorption bands in the 10 pm region, both possess strong microwave absorptions, and precise infrared and microwave data were available in both cases. Stark laser spectroscopy studies of the Ye band (C-F stretch) and associated hot bands of both molecules (5, 6 ) has been carried out, microwave data on FCN has been given (6), and microwave measurements on HCCF have been carried out in this laboratory (7).

EXPERIMENTAL DETAILS

The apparatus used in this work consisted of a semi-sealed-off CO, laser with an intracavity cell designed to transmit at the microwave frequencies required in the experiment.

The laser employed had a l-m active-length discharge tube of 8-mm diameter, was operated at -2o”C, and was capable of using normal COP, 13C02, or C?*O, as lasant. The cells used were a wide-band waveguide cell described previously (4) for frequencies above 7 GHz and a coaxial cell for the low frequency microwave measurements. This latter cell consisted of a 40-cm length of stainless steel tube of 28 mm inside diameter, with a stainless steel rod 12 mm in diameter mounted at its center. The ends of both the tube and the rod were tapered down and connected directly to a 3.7-mm diameter semirigid coaxial cable (DC-18 GHz). Vacuum seal was achieved by use of epoxy cement between the outer sheath of the cable and the cover of the cell and reliance on the longitudinal gas-tightness of the cable itself. The dimensions were chosen so as to produce a coaxial cell with characteristics similar to a 50 R transmission line. This cell proved to be suitable for measurements up to 1.5 GHz.

A 6-mm diameter free aperture, for passage of the laser beam through the cell, was produced by boring a hole in each tapered end section of the cell. Brewster windows were fitted over the holes so that the plane of polarization of the laser light was perpendicular to the microwave field within the cell.

Microwave power was passed through the cell and was absorbed by a suitable termination. Signals were observed by frequency modulating the microwave power at a frequency of 60 kHz and observing the changes in the laser output so produced using a Pb-Sn-Te infrared detector and a phase detector.

Over the range of 8 to 50 GHz, microwave power in the range of 5 to 30 mW was supplied by a Marconi Model 6600A sweeper with various plug-ins. For the measurements where more microwave power was required, such as by the Lamb-dip observations and for measurements at frequencies above 50 GHz, OKI 4OV10, 5OVl 1, and 6OV12 klystrons were used. Measurements with the coaxial cell over the range 5 to 15 GHz were carried out using a Varian T.W.T power amplifier with output power in the watt range. Laser power densities of typically 10 to 50 W/cm* were used.

The sample of FCN was produced by passing commercial cyanuric fluoride over a white-hot platinum spiral and collecting the products of pyrolysis in a trap. Flu- oroacetylene was prepared according to the method of Viehe and Franchimont (8).

454 HAROLD JONES

THEORY

The situation encountered in this type of two-photon spectroscopy consists of a molecular three-level system, with a microwave transition q2 c q, and an infrared transition q\Ir3 + qz. The fixed frequency laser, with frequency vl, is off- resonant with the infrared transition by an amount Au and the microwave fre-

quency, v,, is tuned so that @iv, ? +IVJ is equal to the energy interval E, - E,. The transition moment for the ensuing two-photon transition is

M 3ct1 = 0 (~pE,12)(2111”~,13)/2~A~,

where pP and p, are the permanent and vibrational dipole moments and E, and E, are the microwave and laser field strengths, respectively. Consequently, since for any particular molecule pP and pV are fixed, the maximum value of Au for which a two-photon transition may be observed is given by the experimental values ofE, and El, i.e., high microwave and laser powers favor observation of two- photon signals. In practice high laser power densities can be easily produced by placing the gas to be studied within the laser cavity. The production of high microwave powers over the wide range of frequencies required for a systematic study tends to be a considerably more expensive and difficult task. Fortunately the intracavity arrangement brings with it such high sensitivity that frequently only milliwatt power levels are required for the observation of two-photon transitions.

The infrared transition frequencies of a parallel band of a linear molecule are given by

vm = v + (B' + B")m + (B' -B" -D' + D")d

- 2(D’ + D")wz3 - (D' - D")m4

where m = (J + 1) for the R branch and m = (--J) for the P branch. In the case of the hot bands of the type (v, + v3) - v, the transitions are split symmetrically about the frequencies given by the above expression into two f-type components.

The rotational transitions of a linear molecule are given by

V .I = 2BJJ + 1) - 40~5 + l)“,

where B, and D, are the rotational and distortion constants of the vibrational state concerned, respectively. Since for the molecules considered here B, = 10 GHz it is clear that rotational transition frequencies of these molecules rise very quickly with increasing J and soon exceed the frequency capabilities of the generally available primary microwave sources.

In the case of a vibrational state involving a singly excited degenerate bending mode each rotational level is split into a doublet corresponding to the two possible values of the quantum number I of + 1 or - 1. Transitions between these levels, so-called direct I-type doubling transitions, are allowed and have frequencies,

v, = q’“‘J(J + 1) - q(~‘.P(, + 1)’ - q’*‘.P(J + 1)”

where q lo) is the l-type doubling constant and the other q’s are the higher order correction terms. In the case of these transitions since q’“’ is of the order of 15 MHz all transitions up to J = 30 lie below 20 GHz, well within the normally used part of the microwave spectrum.


OBSERVATIONS

Using the data available from Stark laser spectroscopy and microwave work various combinations of laser lines and molecular transitions were selected which were likely to give rise to two-photon signals in an accessible microwave region. In the case of the I+ fundamental and the hot band (2v, + Ye) - 2vs, where V, is a degenerate bending mode, the highest available microwave frequency of 63 GHz restricted measurement to transitions with a maximum value J = 3. In the case of the hot bands of the type (us + V& - Y, a much larger range of J could be investigated, at low-J making use of rotational transitions and at high-J via the direct l-type doubling transitions.

(a) Fluoroacetylene

The results obtained for fluoroacetylene are summarized in Table I. Two transitions of the va band, the P(1) and R(3) transitions, happened to fall close to two PO, laser lines. In the case of the P( 1) transition, where Au = - 1.140 GHz, the three two-photon signals shown diagramatically in Fig. 1 were observed at the frequencies shown in Table I. These Doppler limited signals were observed using about 20-mW microwave power and 200-mTorr pressure of HCCF. In the case of the signal near 40 GHz a strong two-photon signal and an off-resonant double resonance signal at the frequency of the ground state J = 2 -+ 1 transition using 500 mW of microwave radiation but no Lamb-dip signal was observed. With the R(3) transition a weak two-photon was observed using the 200-mW power available at 54 GHz. This latter measurement seems to set the maximum value of Au in the case of fluoroacetylene at about 4 GHz unless much higher power levels than those used here are available. This point is further illustrated by the fact that two-

TABLE I

Two-Photon Transitions in Fluoroacetylene

ri:2. 25 **:i " t

S.3036 n.02n: (l,l,?)*!n,l,r) Q(25)

:6,+-q, '7.3013 Y.9225 ,, 1075.0b52a

i;aser = 1 brn band Of c 16” -1

~2 IsseT; Band = :,"!,"","5)-(~3,"","5:; u = upper, P = lower;

9 r + O.O"OI cn , b = + 0.0005 cm -1) _

456 HAROLD JONES

J STATE

(0,0,1,0,0)

4GHz

FIG. 1. Schematic of the three two-photon transitions observed with the P(30) C’“0, laser line.

photon transitions involving theR(2) transition, which is about 3.2 GHz away from the P(28) PO, laser line, were not observed, presumably because the 60-mW power available at the required frequency was insufficient. Using the two transition frequencies which can be derived from these measurements and the microwave data of the ground and (vg = 1) excited state one arrives at a value for the band center of yg of v0 = 1061.4452 t 0.0005 cm-‘. This is identical with the value obtained by Tanaka et al. (5) in their Stark laser work.

As may be seen from Table I the upper frequency f-type component of the R(18) and P(16) transitions of the hot band (vQ + us) - ug both lie approximately 100 MHz from two C’*O, laser lines. Under these circumstances using several watts of microwave power at the appropriate frequencies the two-photon transitions were saturated and inverse Lamb-dip signals were easily observed with gas pressures in the region of 100 mTorr. In each case two-photon transitions as indicated in Fig. 2 were observed. The high accuracy obtainable in the Lamb-dip measurements is indicated by the extra significant figure in the value of Av in Tables I and III. In the case of the R(18) transition the two independently determined values of Av agree to within 1 MHz. The slightly worse agreement in the case of the P(16) transition was probably due to the weakness of the Lamb-dip signal at 4.8130 GHz which was caused by a considerable drop in the power levels available below 5 GHz.

In addition to the two-photon signals observed with these two infrared transitions, strong off-resonant double resonance signals were observed near the frequencies of the I-type doubling transitions involving the levels of the infrared transition concerned. However, even more interestingly, even in this case where the laser line lay outside the Doppler width of the infrared transition, sufficient population transfer was produced by the off-resonant pumping to allow further l-type transitions to be observed as collisionally induced double resonance signals. The frequencies at which signals were observed together with their assign- ments are shown in Table II. The constants describing the l-type doubling in the (Q = 1) state have already been determined (7) from microwave measurements and in the present work we obtain the frequencies of six I-type transitions in the state (us = 1, us = 1). Analysis of the data showed, however, that the transitions


J=19

J=18

FIG. 2. Schematic of the two two-photon transitions involving direct /-type doubling transitions which were observed with the P( 10) C’“02 laser line.

involving the levels of the infrared transition could not be use to determine the I-type doubling constants, since they exhibited quite a large frequency shift produced by the high-frequency Stark effect. This shift, which was primarily due to the effects of the off-resonant laser field, was determined to be 2.1 MHz in the case of the R(l8) transition, i.e., the lower state J = 18 transition was measured 2.1 MHz higher than the 6612.20 MHz measured in microwave spectroscopy and the upper state J = 19 transition was measured 2.1 MHz lower than the frequency calculated from a fit including only the collisionally induced double resonance signals of the (us = 1, uj = 1) state. Thus it would appear that, at least to first order, a correction to the value of Av of this magnitude would lead to a more accurate result, i.e., Au = 96 MHz. This correction term is not of great significance in this work since the uncertainty in the laser frequency was considered to be &3 MHz, but it illustrates one source of difficulty if the accuracy of measurement with this method is to be significantly increased. The constants determined by a least squares fit of the four collisionally induced double resonance signals of the (us = 1, v5 = 1) state are shown in Table II. The transition frequencies calculable from these measurements are shown in Table I.

The signals observed using the P(12) C’xO, laser line and scanning the microwave region 8.2 to 10.0 GHz are shown in Fig. 3. The observed signals were easily assigned as three I-type doubling transitions in each of the states (vq = 1) and (ug = 1, uq = l), with J as shown in this figure. The origin of these signals can easily be understood by consideration of Fig. 4. The laser line lies within the Doppler width of the R(25) upper frequency l-type doublet of the (Q + ivq) - uq hot band. Two very strong double resonance signals were observed, one at J = 25 in the lower state the other at J = 26 in the upper state. The effects of the population transfer produced by the laser pumping was then transmitted to other

458 HAROLD JONES

TABLE II

Direct /-Type Doubling Transitions in Fluoroacetylene

(l,O,l) state (O,O,l) state

EJ y (MHZ) " (MHZ)

P(38) 15 4705.00'

16 5329.68 5152.16'

P(10) 18 6699.80 6614.54*

19 74111.26"

20 8225.94

21 9047.08

q(O) = 19.6115(9)

Q (1) : 6.26(23)x10-5

(l,l,O) state (O,l,O) state

Laser P v (MHZ) u (MHZ) ~-

P(12) 22 6692.75

23 7299.95 24 7933.32 7684.66

25 8592.96 8324.34"

26 9278.70" 8989.26

27 9990.82 g68o.16

28 10729.20 10396.16

29 11493.50

q(o)_ 13.2573(14)

q(l)= 7.00(41)x10~~ q(2)= 1.93(29)x10

l : Directly pumped transitions,

Laser = C1802 Laser.

state = (v3,vq,v5)

rotational levels by collisional transitions indicated in Fig. 4 by broken arrows. Collisionally induced double resonance signals were observed in a number of transitions lying energetically above and below the levels directly pumped by the laser. The mechanism indicated in Fig. 4 is a cascade in which each transition obeys dipole selection rules. This is generally [e.g., (9, IO)] considered to be the mechanism of primary importance in such collisional transfer.

The frequencies at which double resonance signals were observed are shown in Table II. The transitions in the lower state were predictable from microwave data (7), but the eight transitions of the (Q = 1, u4 = 1) state given in Table II represent data which are probably impossible to produce by any other technique. The energy zero of this state is about 1644 cm-’ and the highest J transition measured lies approximately 300 cm-’ above this zero and consequently under normal circumstances the population of these levels is extremely small.

In this case a fit of all eight transitions yielded the constants shown in Table II, with standard deviation shown in parenthesis. Since the laser line lay within the Doppler width of the transition the shift produced by the high-frequency Stark


(o,o,O,l+O) J=25 J-26

a.2

1 (O,O;r,l,O) J=25

J=27

J=27

HC<F ~(12) c”02 Laser

FIG. 3. Double resonance signals produced using the P(l2) C’“0, laser line and scanning the microwave frequency between 8.2 and 10.0 GHz in I00 sec. Time constant = 30 msec, pressure = 80 mTorr. The assignment of the transition is given. Note the assymmetry of the two strong signals corresponding to the directly pumped J = 25 transition of the (u, = I) state and J = 26 transition of the (ua = I, u4 = I) state. The weaker signals are induced by collisional processes.

effect in the frequency of the J = 26 transition was very small. In order to fit the observed frequencies it proved necessary to include terms up to P6. The inclusion of this term reduced the accuracy of the determination of the two lower order constants, but the statistics of fits which excluded P6 terms indicated the require- ment of an extra term. In all other states of HCCF and DCCF so far examined (7) it was found sufficient to include terms up to P4.

From the observed strong double resonance signals it was clear that the laser line lay within the Doppler width of the R(25) transition, but to determine the positioning of the laser line relative to the transition center it was necessary to observe the two-photon Lamb-dip signal. The signals shown in Fig. 5 were observed slightly lower in frequency than the J = 25 lower state transition. Two definite dips were observed and possibly a third broad signal was present at somewhat lower frequency. By varying the laser frequency slightly it was determined that the frequency difference between the narrower signal of Fig. 5 and the center of the J = 25 transition was always two-thirds that of the broader signal. This type of effect has been observed previously by Freund et al. (1 I ) in CH3F, in ammonia by Jones (2) and Amano and Schwendemann (12), and in formaldehyde by Glorieux and Hills (13). The two-photon dip which is required to determine AV is the broader signal at 20.7 MHz in Fig. 5. The narrower signal at 14.0 MHz is an example of a “velocity-tuned multiple-photon dip” (11) and this particular one, which occurs at %Av, was produced by combination of a three-photon laser

460 HAROLD JONES

H-C=C-F

State (O,O,l ,I,01 *j-j-+0

27

26

25

State (0,0,0,1,0)

FIG. 4. Schematic explaining the signals of Fig. 3. The laser line was coincident with the upper R(25) transition and strong double resonance signals were observed in J = 25 of the lower state and ./ = 26 in the upper state. The population disturbance produced by the laser was transferred in a cascade by dipole-allowed collisional transitions, which are indicated by broken arrows. The direct /-type doubling transitions observed as double resonance signals are indicated by the short solid arrows. Note that this diagram is by no means to scale, the energy separation between levels of different J is about I7 cm-’ compared to the /-type splitting which is only about 0.3 cm-‘. The energy of the upper laser level is =I868 cm-‘.

process and an infrared-microwave two-photon process. In NH3 a third dip at 2Av was also observed, but in the present case this dip appeared to be very weak and broad. The I dip was also observed in formaldehyde. The uncertainty over whether this dip was present in HCCF or not is probably due to the fact that Au is larger than in the other cases mentioned here. The processes involved in the production of these dips is extremely complex and very much dependent on the experimental conditions used, but it appears that in this case the %Av dip is considerably narrower than the one at Au and that the dip expected at 2(Av) is very much weaker than the other two. The values of Au determined and the transition frequency calculable from these data are shown in Table I.

A further point about the signals observed with this laser line can be immediately seen by consideration of Fig. 3. The two .very strong signals are very asymmetric, and more interestingly, the asymmetry appears to be of opposite sign in the lower state signal than in the upper state signal. An identical effect was also observed in the off-resonant double resonance signals observed with the P( 10) C’*O, laser line. In addition to the obvious asymmetry in Fig. 3, the Lamb-


20.7 MHz * _

14.0 MHz l ( I

HCCF P(12) C’*02 Laser

FIG. 5. The inverse Lamb-dip signal observed 20.7 and 14.0 MHz below the center of the (Do = 1). J = 25 transition. The broader dip at 20.7 MHz is the normal two-photon dip; the extra dip is a so- called velocity tuned multiple photon dip, in this case at %Av. Signals of very similar appearance, but phase inverted. were observed about the (Q = 1, L’~ = I ), J = 26 transition.

dips of Fig. 5 had opposite phase to those observed 14.0 and 21.0 MHz above the J = 26 upper state double resonance signal. These effects appear at first sight typical of the lineshape distortion problem frequently encountered with the intracavity arrangement, but their possible significance will be discussed later.

(b) Cyanogen Fluoridr

The results obtained for FCN are summarized in Table III. The frequencies of two of the transitions of the vg fundamental were determined with Lamb-dip accuracy (?3 MHz). Using the R(20) line of the normal CO, laser the frequency of the Z?(2) transition was determined. Two-photon signals with this combination of laser line and infrared transition had been observed using an external waveguide cell (14). In the present work Au was determined three times independently with a spread of only 0.5 MHz. The result, Au = 109.5 f 3 MHz, obtained here agrees well with the earlier value of Au = 104 + 15 MHz (14). The frequency of the P(2) transition of the us fundamental was determined by the Lamb-dip measurements shown in Table III.

The determination of the frequencies of these two low-J transitions allowed calculation of the V~ band center as v,, = 1076.4920 + 0.0001 cm-‘, a result which agrees exactly with that obtained from Stark laser spectroscopy (0). These data also allow us to carry out a simple check on the accuracy of our measurements. Since both transitions involve the J = 2 level of the ground state, it follows that the difference in frequency between these two infrared transitions should be the sum of the.! = 2 +- 1 and J = 3 + 2 transitions in the (Q = 1) state. The sum of these frequencies was determined to be 105 107.73 MHz from microwave measurements, which compares to the two-photon result of 105 112.0 ? 6.0 MHz. Since the two results agree to within the expected experimental error it seems that one is justified in claiming an uncertainty of -+3 MHz on the Lamb-dip measurements.

462 HAROLD JONES

TABLE III

Two-Photon Transitions in FCN

Laser Two-Photon Transition

J'CCJ" Y (GHz) bv (GHz) --

R(20)* 3 cc 1 42.1071 -0.1098

3 ++ 3 63.4347 -0.1096

2 *t 2 63.1743 -0.1093

P(l2) 2 +t 2 41.8891 -0.1543

1 ++ 1 42.0624 -0.1543

0 cc 2 (21.150) (-0.129)

R(4) 2 ++ 2 41.444 0.855

1;++ 1; 42.269 0.861

R(26) 22"**21L 9.342 0.259

22a+*21u 10.524 s

R(8) 2 +t 2 42.268 0.061

1 cc 1 42.512 0.070

0 cc 2 21.083 0.053

Infrared Transition

Band cm -1

(0,0,1)+(0,0,0) R(2) lo78.5870a

1 (0,0,1)*(0,0,0) P(2) 1075.0808a

> (0,1,1)+.(0,1,0) R(llp 1087.1436b

(0,1,1)+(0,1,0) R(21)” 1100.6011b

1 (0,2,1)*(0,2,0) P(2) 1089.7430b

(Laser = 9 VIII band of C1'02 laser; l q normal co2 laser; Band = (v~.Y~,Y~)+(Y~,v~,Y~);

s = see text; a = + 0.0001 cm -1 _ , b = + 0.0005 cm-l; u = upper, c = lower)

Two transitions of the hot band (v2 + Ye) - yp were measured with Doppler limited accuracy (+ 15 MHz). The R(1) transition frequency was determined using the J = 2 + 1 rotational transitions and the R(21) transition frequency via the J = 21 and J = 22 I-type doubling transitions. The latter case seems to represent an example of the maximum allowable value of Av for two-photon transitions involving/-type doubling transitions in these molecules. Even with the several watts of microwave power available in the measurements, the signal observed in this case, where Av = 259 MHz, was much weaker than the signal observed using the J = 2 t 1 transition (Av = 860 MHz) and very much lower laser and microwave power levels. All attempts to observe two-photon transitions involving I-type doubling transitions with Av > 300 MHz failed to produce a detectable signal.

Although the signals observed in the case of the R(21) transition were weak, with careful adjustment it proved possible to observe a weak double resonance signal in addition to the two Doppler broadened two-photon signals, the frequencies of which are shown in Table III. This signal at 9082.38 MHz was assigned as the J = 2 1 transition of the ( v2 = 1) state. Reason dictates that a similar signal should also be observable corresponding to the J = 22 transition of the (up = 1, o3 = 1) state. This signal was sought but not observed. As will be seen in the discussion, there is a discrepancy between the observations made here and what might be expected from the Stark laser measurements. Because of the failure to measure the upper state J = 22 transition frequency this discrepancy cannot be completely resolved, but suggestions for its origin will be made. During the search


for this transition a very weak double resonance signal at 9946.37 MHz was observed corresponding to the J = 22 transition of the lower state.

The frequency of one transition in the hot band (2~~ + vg) - 25 was determined using the R(8) PO, laser line. The signals observed in theJ = 2 +-- 1 region are shown in Fig. 6. Four strong signals were observed, two off-resonant double resonance signals and two broader two-photon signals. In this case Av = 60 MHz and this gave rise to the very strong signals observed here using a microwave power level of only 5 mW. When it is remembered that 2v2 in FCN lies at approximately 900 cm-’ the sensitivity of this intracavity method is clearly demonstrated. The frequency determined for the P(2) transition of this hot band was in very good agreement with the Stark laser results (6).

DISCUSSION

The purpose of this investigation was to determine how well this two-photon technique could be applied to determining the infrared spectrum of two simple linear molecules. The answer to this question can be given immediately by consideration of Tables I and III. Clearly these molecules are not as suited to this technique as was ammonia. The number of transitions determined in each band considered was relatively small, usually two in each case, but it is also clear that

FIG. 6. The signals produced using the R(8) C’“0, laser line, 80-mTorr FCN and 5-mW microwave

radiation in the range 42.0 to 42.7 GHz. The two sharper features are off-resonant double resonant signals and the two broader features are Doppler broadened two-photon signals. The infrared transition

involved in the P(2) transition of the hot band (2~5 + ~~~1 - 2~~. The two lower frequency signals

belong to the upper state which has energy of = 1975 cm-‘. Time constant = 30 msec. AV = 60 MHz.

464 HAROLD JONES

the accuracy of the results obtained makes them of considerable value. In particular the determination of relatively high-1 transitions in the hot band produces not only confirmation of the Stark laser results but also complementary information.

The Stark laser spectroscopy studies were generally restricted to very low-J transitions. In the case of v3 fundamentals and the hot band (2~ + Q) - v3 of FCN this is also true of the present work. Consequently these measurements can do no more than check on the data from Stark laser spectroscopy studies. Since both techniques are relatively new the excellent agreement achieved in all cases is very comforting. Constants determined in this work which differ from those in Refs. (5-7) are summarized in Table IV.

In the case of the hot bands (v, + vg) - v3 our measurements allow us to test the exactness of the frequency predictions from the Stark laser at relatively high J and to determine the correction terms (if any) required.

In the Stark laser work on HCCF (5) the constants of the (v3 + Q) - vs hot band were calculated using microwave data (7) and measurements on M-components of a single infrared transition (J = 2 +- 1) and on an upper state microwave transition. It was assumed that the upper state distortion constant was the same as that of the lower state.

The present work has shown that these constants reproduce the spectrum of this band adequately up to at 1eastJ = 18 and probably higher. For example, from constants available prior to this work we calculate the center frequency of the R( 18) transition to be 1076.5566 cm-’ compared to the 1076.5567 cm-l determined in the present measurements. The agreement for the P(16) transition is equally good. This measurement confirms that the assumption made (5) that D’ = D” is a very good approximation.

The I-type doubling constants of the state (u3 = 1, zlj = 1) and (v, = 1, u4 = 1)

TABLE IV

Constants of HCCF and FCN Determined in this Work

HCCF

(“3=1, VqZlj q(O) = li.2573(19) MHz

g(l) T 7.00(91)x10-5 MHZ

q(?) _ 1.33(29)x10 -8

?,HZ

Cv3.1, v,=l) q(o) = 13.6115(9) MHZ ,

q(1) _ 6.26(23)x10-~ MHZ

D" = 3.55x10-5 MHz*

PC’:

(u2:l, "3=1) o(l) = 2.7X10 -4

MHZ*

D" = 5.1x10-4 MHZ'

l = see text


Table II are considerably more accurate than those determined previously (5) but are within the error limits given for these constants.

In the present work we were able to determine the frequency of a single transition in the ( vs + vq) - vq band of HCCF. However, comparisons with calculations similar to those carried out for the (vs + Q,) - vj band reveal a discrepancy of approximately 50 MHz between the calculated center of the R(25) transition and that determinable from these results. Since low-J transitions were measured in the Stark laser work it seems likely that their values of v,, and B’ are relatively good. The source of this discrepancy would appear to be mainly due to the assumption made previously that D' = D". At this high-1 the fourth term in (D' - D")m4 in the frequency expression makes appreciable contributions for very small changes of distortion constant with rotational state. If we assume this discrepancy to entirely originate from this source we estimate a value of (D' - D") = - 1.0 x lop4 MHz, which produces the required adjustment of -45 MHz for m = 26. The problem with this calculation is that since we only have one high-J measurement the effects of the quoted (5) uncertainties in B' cannot be taken into account and the value obtained here for (D' - D") must be considered to be only approxi- mate. However, the observed change in the magnitude of the q”’ I-type doubling constant (which is a distortion term) between the states (~1~ = 1) and (v.? = 1. z)~ = 1) lends support for the indication that D, is different in these two states.

This latter point also assumes significance in connection with the measurement of the R(21) transition of the hot band (uq + 03) - L‘~ of FCN. In their Stark laser spectroscopy study of FCN Maki and Freund (6) observed a large number of Stark shifted signals in the (v2 + us) - u2 hot band. However, in their analysis of the data they assumed that the I-type doubling P4 term in the (ZJ* = I, u3 = 1) state to be the same as that determined previously for the (up = 1) state and only the constant q”” = 21.448 MHz was determined. Assuming this value and q”’ = 5.556 x 10-j MHz (the lower state value) one calculates that the upper state J = 22 transition should occur at 10 838.47 MHz. This calculated frequency would mean that in the case of the two-photon signal at 10 524 MHz we have AV = 314 MHz compared to the Av = 259 MHz determined from the lower state transition. Even when allowance is made for the fact that the signals were weak and consequently perhaps the accuracy of measurement is somewhat worse than -+15 MHz, the discrepancy of 55 MHz between Av in the lower state and that in the upper state seems to be unreasonable.

The probable source of error in this calculation is that the assumption made by Maki and Freund, that q”’ is the same in the upper and lower states, is incorrect. With the data obtained in the present work and the microwave work (7) for fluoroacetylene we have one example for and the other against this assumption. In the case of vs, q(l) for the states (us = 1) and (0, = 1, us = 1) are identical, but for the case of v4 the values obtained were q”’ = 2.2 x lo-” and q”’ = 7.0 x lo-” for the states (u4 = 1) and (us = 1, u4 = l), respectively. So clearly it is possible that q”’ changes considerably with state. If we assume that in the upper state in question here, (Q = 1, us = 1). Au is the same as in the lower state we expect the J = 22 transition at 10 783.0 MHz. If we assume the q’O’ of Maki and Freund, this gives rise to a value ofq”’ = 2.7 2 0.7 x 10m4 MHz. This value, which is about

466 HAROLD JONES

five times that observed in the lower state, seems somewhat large, but in view of the rather large uncertainty connected with it and the observed change in q(l) from the (u4 = 1) to (2r3 = 1, v4 = 1) states of fluoroacetylene, probably quite possible.

As in the case of HCCF in the (vg + y4) - vQ band of FCN the Stark laser data are not sufficiently good to predict the high-1 transition frequencies accurately. On the basis of the reasoning given above it appears that (D’ - D”) # 0. A value (D’ - D”) fi 4 x 10T4 MHz seems to be required to reproduce the present measurements, but in the absence of reliable data on the (vz = 1, us = 1) state i-type constants this can only be considered to be a very rough estimation.

The Anomalous Lineshapes

In order to discuss the lineshape problem displayed in Fig. 3 we must first of all consider the mechanisms giving rise to the observed signals. In order to produce a signal, a modulated fluctuation in laser power must be induced by the microwave field and under the conditions used in these experiments this can be produced by two mechanisms. First, the microwave power can cause a change in the absorption intensity of the infrared transition by altering the population of the levels of this transition. Since the absorption process is relevant to this type of signal and since our microwave power is frequency modulated, the observed lineshape is the first derivative of a normal Lorentzian. The collisionally induced signals of Fig. 3 are of this type, since they are produced purely by population changes.

Since the gas is within the laser cavity a second mechanism that will result in laser output fluctuation is that microwave absorption causes a change in the refractive index of the gas and thus comes a slight detuning of the laser cavity. In this case the dispersive lineshape is of relevance (i.e., change in refractive index with frequency) and since this is of derivative form (so-called anomalous dispersion) we expect to observe a signal with second-derivative shape.

It appears that dispersive processes are dominant in the production of the Lamb-dip signals of Fig. 5, an effect which has been frequently observed previously. However, what is more interesting here is that the Lamb-dip signals produced above the ./ = 26 transition of the upper state were of similar appearance to those of Fig. 5, except that they were phase inverted. The two directly pumped signals of Fig. 3 appear to have components from both absorption and dispersion present, but here again it appears that in order to explain these two signals, the dispersive part must be introduced with opposite sign in the two cases.

The theory of the observation of signals with an intracavity cell is extremely complex (e.g., (15, 16)) and the observed lineshape is strongly dependent on the prevailing experimental conditions. However, in this particular case the experimental conditions for the observation of the upper and lower state signals and the associated Lamb-dip signals were to a very good approximation the same. There is apparently no obvious reason from existing theory why a dispersion signal of opposite phase should be observed when microwave transitions in two different vibrational states are irradiated. At this point it should be clearly stated that it seems more likely that this effect is produced by the relative positioning of the energy levels concerned rather than the vibrational state involved. As can be seen from


Figs. 2 and 4 both the P( 10) and P( 12) laser lines induce an increase in microwave absorption in the lower state and a stimulated emission in the upper state I-type doubling transitions. Since very similar effects were observed with these two laser lines, it appears that this is a real effect which occurs at least in HCCF under the conditions used in the measurements with these two lines. Similar effects have also been recently observed in t-f-infrared double resonance experiments on CF,I (2 7) and this indicates that this effect is not something generated by the specific conditions used in the present study.

In most of the double resonance signals observed in this work, and in the very many double resonance studies carried out in this and other laboratories this effect was not obviously present. This is almost certainly because in most cases the dispersive contribution to the signal was small and/or only one vibrational state could be studied (e.g., NH,) and in general, this effect was not sought. Only recently has the importance of dispersion effects in double resonance experiments been directly investigated (17,18), and clearly work is still needed to characterize this apparently vibrational state dependent phase change. The existence of such an effect would be of considerable practical aid when dealing with double resonance signals of unknown origin, since it would allow at least information over the relative disposition of the energy levels involved to be extracted. Despite its very great advantages the intracavity double resonance arrangement results in a loss of information compared to the less sensitive external cell arrangement (e.g., (19)) since all double resonance signals appear with the same phase no matter what the positioning of the levels concerned. In double resonance investigations involving relatively complex molecules under way in this laboratory at the present time the assignment of the dozens of double resonance signals produced by a single laser line represents a major problem and any aid in dealing with this problem would be welcome indeed.

CONCLUSION

The data which can be extracted from this study which are of direct relevance to this type of two-photon spectroscopy as a technique are as follows. As expected, the maximum value of Av for which two-photon signals could be observed was very much smaller than for ammonia. The maximum value of k3.7 GHz observed in HCCF with a microwave power density of about 100 mW/cmz nevertheless represents an appreciable tuning range. This range compares very favorably with the partially tunable waveguide CO, lasers, which have ranges of only typically 0.2 to 1 GHz, and of course in the present technique the frequency calibration problem associated with such lasers is absent. The effective tuning ranges produced with I-type doubling transitions was, due to the low intensity of these transitions, considerably smaller (+260 MHz) even when power densities in the watt/cm2 range were used. However, as has been demonstrated here this range is frequently sufficient to allow the accurate determination of transitions which happen to fall very close to CO,-laser lines. When it is considered that the number of laser lines available in any given region can be in principle doubled by the use of the so-called sequence band (20) laser lines it is clear that this type of measurement may yield

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a considerable amount of valuable data. The only advantage that two-photon measurements have in this type of molecule, compared to those in NH3, is that Au can be determined several times independently and consequently give a considerable increase in confidence over the value obtained.

It would appear at this place in time that the growth in the importance of the two-photon method as a spectroscopic tool will eventually be curtailed by the technological advances in the tunable laser field. In particular, competition from the diode laser would appear to be of considerable importance. However, it would appear that the accurate results obtainable with this method will still have their importance in the future, if only as a source of calibration lines for a tunable laser spectrometer.

RECEIVED: November 13. 1978

REFERENCES

1. S. M FREUND AND T. OKA, Phys. Rev. A. 13, 2178-2190 (1976). 2. H. JONES, Appl. Phys. 15, 261-264 (1978). 3. H. JONES, J. Mol. Spectrosc. 70, 279-287 (1978). 4. H. JONES, Appl. Phys. 14, 169-173 (1977). 5. T. TANAKA, C. YAMADA, AND E. HIROTA, J. Mol. Spectrosc. 63, 142-151 (1976). 6. A. MAKI AND S. M. FREUND, J. Mol. Spectrosc. 66, 493-499 (1977). 7. H. JONES AND H. D. RUDOLPH, Z. Nnturforsch. A. 34, 340-352 (1978). 8. H. G. VIEHE AND E. FRANCHIMONT. Chem. Ber. 95, 319-327 (1962). 9. T. OKA, Collision-induced transitions between rotational levels, in “Advances in Atomic and

Molecular Physics,” Vol. 9, pp. 127-206, Academic Press, New York, 1973. 10. H. JONES, Laser-microwave double resonance techniques. in “Modern Aspects of Microwave

Spectroscopy” Edit. (C. W. Chantry. Ed.), Chapter 3, Academic Press, New York, to be published.

Il. M. FREIJND, M. RGMHELD, AND T. OKA, Phys. Rev. Lett. 35, 1497-1500 (1975). 12. R. SCHWENDEMAN, Private communication.

13. P. GLORIEUX AND G. W. HILLS, J. Mol. Spectrosc. 70, 459-468 (1978). 14. H. JONES, Z. Naturforsch. A. 31, 1614-1619 (1976). 15. F. SHIMIZU, Phys. Rev. A 10, 950-959 (1974). 16. T. OKA, “Frontiers in Laser Spectroscopy” (Balian et a/., Eds.). pp. 531-569, North Holland,

Amsterdam, 1977. 17. E. ARIMONDO AND T. OKA, to be published. 18. B. MACKE, Appl. Phys. 13, 271-277 (1977). 19. H. JONES AND F. KOHLER, J. Mol. Spectrosc. 58, 125-141 (1975). 20. K. J. SIEMSEN AND B. G. WHITFORD. Opt. Comm. 22, 11-16 (1977).

Laser-microwave two-photon and double resonance spectroscopy of two linear molecules; HCCF and FCN

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Transcript of Laser-microwave two-photon and double resonance spectroscopy of two linear molecules; HCCF and FCN