Infrared–microwave double resonance spectroscopy of DCCCHO using the 3.51 μmHe–Xe laserMichio Takami and Masao Suzuki Citation: The Journal of Chemical Physics 72, 4089 (1980); doi: 10.1063/1.439637 View online: http://dx.doi.org/10.1063/1.439637 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/72/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Infrared–microwave double resonance spectroscopy of the ν3 band of BF3 using a tunable diode laser J. Chem. Phys. 84, 6027 (1986); 10.1063/1.450792 Infraredmicrowave double resonance spectroscopy of the ν3 band of 1 1BF3 using a tunable diode laser J. Chem. Phys. 83, 1444 (1985); 10.1063/1.449429 Infrared–microwave double resonance spectroscopy of the antisymmetric amino wagging band of hydrazine inthe 10 μm region J. Chem. Phys. 78, 1039 (1983); 10.1063/1.444904 Infraredmicrowave double resonance of NH3 using a tunable diode laser Appl. Phys. Lett. 34, 682 (1979); 10.1063/1.90644 OBSERVATION OF AN ENHANCED LAMB DIP WITH A PURE Xe GAIN CELL INSIDE A 3.51μ He–Xe LASER Appl. Phys. Lett. 17, 120 (1970); 10.1063/1.1653330

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Infrared-microwave double resonance spectroscopy of DCCCHO using the 3.51 JLm He-Xe laser

Michio Takami

Microwave Physics Laboratory. The Institute of Physical and Chemical Research. Wako. Saitama 351. Japan

Masao Suzuki

Department of Electronic Engineering. Tokyo Institute of Polytechnic. Iyama 1583. Atsugi 243-02. Japan (Received 18 October 1979; accepted 20 December 1979)

Microwave spectrum of propynal-d,. DCCCHO, was investigated in the V2 = 1 excited state by an infrared-microwave double resonance method. The 3.51 11m He-Xe laser was magnetically tuned over ± 0.1 cm -, and used as an infrared radiation source. Eighteen pure rotational transitions in the excited state were observed and assigned. The observed spectrum was found to be badly perturbed by other vibrational states. In addition to the transitions within the V2 = 1 state, ten microwave transitions from the V2 = I to other vibrational states were observed. These intervibrational microwave transitions were discussed in relation to vibrational quasicontinuum states of polyatomic molecules.

I. INTRODUCTION

In the past several years we have applied infrared­microwave double resonance to microwave spectroscopy of simple organic molecules in their CH stretching vi­brational states. Microwave transitions have been ob­served so far in the excited states of HDCO, 1,2 CH4,3.4 HCOOH,5 and HCCCHO,6.7 using Zeeman-tuned 3.51 ).Lm He -Xe and 3.39 ).Lm He -Ne lasers. Since there has essentially been no spectroscopic measurement of excited molecules around 3000 cm -I with the resolution of better than 100 MHz, it is of great interest to inves­tigate the microwave spectrum of polyatomic molecules in such excited states with the resolving power of the order of 100 kHz.

The most remarkable feature of the microwave spec­trum observed in the CH stretching vibrational states was the existence of many perturbations. In HDCO the observed three a-type Q-branch transitions of the VI = 1 state could not be fitted to an ordinary nonperturbed semirigid rotor model. 2 The 19 microwave transitions observed in the V2 = 1 state of HCOOH showed remark­able systematic deviations when the eight rotational con­stants were determined by a least-squares fit. 5 In HCCCHO, where 22 microwave transitions were ob­served in the 1'2 = 1 state, the low -J lines showed small but clear systematic deviations which was explained by higher-order Coriolis interactions. 7 The high-J lines of this molecule showed large frequency irregularity.

It is well known that the vibrational state density of a polyatomic molecule increases very rapidly as the in­ternal energy of the molecule increases, or as the num­ber of its normal modes increases.s In HCCCHO, the Vibrational state denSity is already about 1.7 states per cm -I around the 112 = 1 state. Since propynal belongs to the C. point group, all of the vibrational states can, as far as the selection rules by molecular symmetry are concerned, perturb the 1'2 = 1 state by higher-order Coriolis or Fermi-type (anharmonic) interactions. Al­though most of the vibrational states near the 112 = 1 state are the combination states which consist of many vibra­tional quanta, it is not surprising that the 112 = 1 state of

HCCCHO is perturbed simultaneously by several differ­ent vibrational states in the accuracy of microwave spectroscopy.

In this work, we investigated the microwave spectrum of propynal-dl (DCCCHO) in the 1J 2 = 1 state using the 3.51 ).Lm He -Xe laser. Eighteen pure rotational transi­tions in the excited state were observed and assigned. The observed microwave spectrum was so badly per­turbed that no reliable rotational constants could be de­termined. During this measurement, several very strong microwave transitions were observed which could not be explained as the transitions within the ground state or the 1'2 = 1 rotational manifold. Careful examina­tions of these signals revealed that they were the inter­vibrational microwave transitions from the v 2 = 1 to other nearby vibrational states which were enhanced by vibra­tion-rotation interactions. 9 Ten microwave transitions from the 1'2 = 1 to at least six such other rotational-vi­brational states were confirmed. Some of the perturb­ing states were found to have the effective coupling con­stants lO of only a few hundred megahertz.

Recently, much attention is focused on the nature of vibrational quasicontinuum states in relation to infrared multiphoton processes. 11 In DCCCHO the vibrational state density around the V2 = 1 level is about 2.4 states per cm- I , A crude estimate shows that, with the pres­ent sensitivity of measurement, about 0.5 intervibra­tional microwave transitions are to be observed on av­erage for each vibration-rotation line of the v2 band. This value, as well as the experimental result, shows that even in such a simple molecule as DCCCHO, the fundamental CH stretching vibrational state is no longer a pure normal mode of Vibration but it is strongly cou­pled with its dense background vibrational states.

The vibrational quasicontinuum states have been in­vestigated so far in the time domain with a TEA CO2

laser l2 or in the frequency domain with a tunable dye laser.13 The present experiment shows that the double resonance technique can be used to investigate the nature of higher-order vibration-rotation interactions which are important for interpretation of infrared multi photon pro-

J. Chern. Phys. 72(7), 1 Apr. 1980 0021·9606f80/074089·10$01.00 © 1980 American Institute of Physics 4089

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4090 M. Takami and M. Suzuki: Spectroscopy of DCCCHO

cesses in a vibrational quasicontinuum state. One of the advantages of using double resonance is that an intervi­brational microwave transition to a weakly perturbing vibrational state can be observed by using a strong mi­crowave field with the resolution of homogeneous line­width. In a higher energy state of propynal or in heavier molecules, a larger number of intervibrational micro­wave transitions can be observed, from which useful informations on the nature of higher-order vibration­rotation interactions may be obtained.

II. PRINCIPLE OF DOUBLE RESONANCE SPECTROSCOPY

There are two detection methods for microwave spec­troscopy of vibrationally excited molecules by double res­onance, i. e., microwave detection and optical detection. In the present work the latter method is used; the double resonance effect is observed by a variation of infrared absorption caused by microwave pumping. This detec­tion method has a higher sensitivity and therefore it is more advantageous when a laser with low output power such as a Zeeman-tuned rare gas laser is used.

Let us consider a three-level system shown in Fig. l(a). Observation of the microwave transition 3 - 2 by optically detected double resonance is based on the principle that, when the vibration-rotation transition 2 - 1 is saturated by a laser, simultaneous saturation of the microwave transition 3 - 2 increases the infrared absorption. 1 In such a molecule as propynal, two mi­crowave transitions are frequently allowed in series from the upper state of the vibration-rotation line as shown in Fig. 1(b). In this case a triple resonance method is used for observation of the second microwave transition by saturating the infrared and two microwave transitions simultaneously. This type of triple resonance has been used in excited state spectroscopy of formic aCid,s propynal,7 and allylamine. a This technique is useful for observing a greater number of microwave transi­tions in excited states when the laser frequency tuna­bility is poor. We call the microwave radiation which saturates the 3 - 2 transition the pumping microwave radiation and the other (4 - 3) the signal microwave radi­ation for convenience.

The triple resonance effect can also be observed in the four-level system shown in Fig. 1(c). In this type of triple resonance, the interference effect on the 3 - 2 -1 double resonance signal when the 4 - 2 transition is saturated is observed. This saturation causes two ef­fects: one is the decrease of the double resonance sig­nal, and the other is the shift of the peak by a micro­wave Stark effect when the pumping microwave frequen­cy is slightly detuned. These effects are useful for con­firming that two microwave transitions share the upper level of the vibration-rotation transition. The laUer effect can be used to find whether levels 3 and 4 are on the same side of level 2 or opposite. This type of triple resonance is extensively used in the present work to in­vestigate the intervibrational microwave transitions. This technique has also been used by Jones independent­ly for a similar purpose. 14

In general, the line shape of these triple resonance

3 MW

2

IR (o)

1

4 4

3 MW

3 TMW

MW MW

2 2

IR IR

1 1 (b) (c)

FIG. 1. (a) Three level system. (b) Four level system for triple resonance. Two microwave transitions are allowed in series. (c) Another four level system for triple resonance. Two microwave transitions share the upper level of the infrared transition.

signals depends critically upon experimental conditions. A theory of IR-MW-MW triple resonance has been de­veloped as will be discussed elsewhere. 15

III. EXPERIMENTAL PROCEDURE

The 3.51 /lm He-Xe laser of 60 cm effective dis­charge length was placed in a solenoid and Zeeman tuned over ±3 GHz. Under an axial magnetic field, the laser oscillated in two Zeeman components. One of the cir­cularly polarized components was selected by a quarter­wave plate and polarizer. The selected infrared radia­tion was detected with an InSb photoconductor.

Three different kinds of DCCCHO spectra were ob­served, infrared absorption, infrared Stark, and double resonance. The infrared absorption spectrum was ob­served with a 1 -m-long cell at room temperature. The Stark spectrum was observed either with a square wave Stark field at 5 kHz or with a dc field modulated by a small amplitude 100 kHz sinusoidal field. The Stark cell consisted of 40 cm long chromium-coated glass plates separated by O. 5-mm-thick Teflon spacers.

Experimental details of infrared-microwave double resonance were reported previously. 5.7 The double res­onance signals were observed in a frequency range from 1 MHz to 80 GHz. The pressure of DCCCHO was kept at about 1 mTorr, the optimum pressure for observation of the double resonance signal. The microwave frequency was modulated by a 10 kHz square wave and scanned. In the triple resonance experiment, another microwave source for the microwave pumping, whose frequency was fixed at the resonant frequency of the 3 - 2 transi­tion, was connected to the cell. For observation of weaker signals, the double resonance cell was cooled by dry ice. Accuracy of the frequency measurement ranged from a few tens of kilohertz to a few megahertz depending upon the signal intensity.

J. Chem. Phys .. Vol. 72, No.7, 1 April 1980

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M. Takami and M. Suzuki: Spectroscopy of DCCCHO 4091

Infrared-radiofrequency double resonance was car­ried out with a 1-m-long parallel plate cell with a 2.3 mm electrode spacing. The radiofrequency field was amplitude modulated by 10 kHz square waves. Infrared­microwave-radiofrequency triple resonance was per­formed using another parallel plate cell of 80 cm effec­tive length. The electrodes of 6 cm width and 4 mm spacing worked as a transmission line for microwave radiation and as electrodes to apply a radiofrequency field. In all the double and triple resonance experi­ments, the cell was placed in the laser cavity.

IV. INFRARED ABSORPTION SPECTRUM AND ASSIGNMENT

Figure 2 shows the infrared absorption spectrum of the lJ2 perpendicular band of DCCCHO observed with the 3.51 J.lm He-Xe laser. The upper trace is the output of the laser, and the lower the absorption spectrum at 0.8 Torr of DCCCHO in the 1-m-long cell at room tem­perature. The resolution is limited by the Doppler line­width of DCCCHO, which is about 70 MHz in half-width at half-maximum. In addition to several strong absorp­tion lines, the spectrum is accompanied by a near-con­tinuum absorption, probably consisting of dense hot band absorption lines.

The "'z fundamental frequencies of DCCCHO were de­termined to be 2858.6 cm-1 by Brand et aZ. 18 Since the available molecular constants in the V z = 1 state of DCCCHO were not accurate enough to assign the infrared absorption spectrum observed in the present work, Stark effects of the infrared absorption lines were stud­ied. Figure 3(a) shows an example of the Stark spec­trum observed with a dc Stark field modulated by a 100 kHz sinusoidal field. Figure 3(b) shows another spec­trum observed with a 0 to 2 kV jcm square wave field at

0'> .-t .-t N

0 N oN d

0< d ~

<!) ~ N N

N

"-

'" 0 00 .-t

'" <:> .-t

<:> .-t

i i • • i •

-3 -2 -1 012 36Hz

L 2850.639 cM-l

FIG. 2. Infrared absorption spectrum of DCCCHO. Upper trace is the output of the laser. The lower trace shows the absorption spectrum with 0.8 Torr DCCCHO in a 1-m-long cell at room temperature.

LlM=O

ac --------------~----------~---

- 2 kV/em

de , 21 kV/em

22

, 23

24 (0)

25

26

I I I I -3 -2 -1 ° 1 2 3 GHz

L-2850,639cm-1

~~ .:IM:!.1

2 kVlcm square ( b) wave

I I I I i i ,,,, -3 -2 -1 0 1 2 3 GHz

FIG. 3. Infrared Stark spectrum of DCCCHO. The top trace shows the absorption spectrum. (a) Stark spectrum with a de field modulated by a 100 kHz sinusoidal field. Two lines which show a typical second order Stark shift are seen. (b) Stark spectrum observed with a 2 kV/cm square wave field at 5 kHz. The peaks in the trace arise from the infrared absorption lines which show the first-order Stark effect.

5 kHz. Since propynal is a slightly asymmetric top molecule, many vibration-rotation lines. show the first­order Stark effect arising from nearly degenerate K­type doublets. The peaks in Fig. 3(b) correspond to such lines in the lJz fundamental and hot bands.

The vibration-rotation lines which show the second­order Stark effect are shown in Fig. 3(a). Two strong infrared absorption lines are found to show a typical second order Stark shift as is clear ly seen in the figure. From their Stark coefficients and the frequency differ­ence at zero electric field, they were aSSigned tenta­tively to be the 191• 19(1J2) - 192• 18( g) and the 20 1•20(lJ 2)

- 202• 19( g) transitions. These assignments were con­firmed by infrared-microwave double resonance in which microwave transitions coupled to the vibration-rotation lines in the ground vibrational state were saturated. Since the molecular constants of DCCCHO in the ground state had been determined accurately, 17 we could con­firm the assignments by this method without ambiguity.

Once one or two vibration-rotation lines were as­Signed, it was rather easy to extend the assignment to

J. Chem. Phys., Vol. 72, No.7, 1 April 1980

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4092 M. Takami and M. Suzuki: Spectroscopy of DCCCHO

TABLE I. IR-MW double resonance of DCCCHO: ground state.

IR transition

Line MW transition

position Transition

Frequency (GHz)a "2 g Transition (MHz)

-2.59 25 3,23-244,20 244,20-244,21 11. 47

-1. 92 201,20-202,19 202,18-202,19 6975.05

21 1,20-202,19 25846.62

-1. 88 253,22-244,21 244,20-244,21 11. 44

-0.87 112,10-10 3,7 10 3,7-10 3,8 3.67

-0.09 112,9-10 3,8 10 3,7-10 3,8 3.66

0.23 200,20-21 1,21 21 1,20-21 1,21 65648.10

202,18-21 1,,1 46776.57

1. 15 191,19-192,18 192,17-192,18 3733.90

20 1,19- 192,18 14434.90

1. 43 27 1,27-280,28 272,25 -280"s 50389.21

2.60 21,2-32,1 32,1-22,0 25932.10

aAdd 85460.00 GHz (2850.639 cm -1).

other lines. From the Fortrat diagram around the laser frequency, vibration-rotation lines were assigned one after another based upon their Stark behavior. The as­signments were confirmed by double resonance. The result is shown in Fig. 2 and Table I. The ground state niicrowave lines used for confirmation of the assign­ments by double resnance are also shown in Table I. The frequencies of the vi bra tion-rotation lines were measured from the axial mode spacing of the laser out­put and from the frequency of the 3.51 j..Lm He-Xe laser line at zero magnetic field measured by Jennings et al. 18

V. MICROWAVE SPECTRUM IN THE V2 = 1 STATE

Microwave transitions in the excited state were searched for based upon the corresponding transition frequencies in the ground state. All of the lines were observed within ± 2 GHz from the corresponding ground state transition frequencies although the observed spec­trum showed large frequency irregularities. This shows that the effective rotational constants in the excited state are not very much different from those of the ground state, and therefore, the perturbations causing the fre­quency irregularity are of local nature. The observed transition frequencies are shown in Table II.

The greatest perturbations are found in the low-J lines. The K -1 = 0 levels are almost free from irregular energy shift. However, the energy differences between the K -1 = 0 and 1 states are about 1 GHz less than the corresponding values in the ground state. Furthermore, the 21 and 31 K -type splittings are about 7ci'!o of those of the ground state. Since the other K -1 = 1 K -type s plittings observed in the high-J lines are not very much different from the ground state splittings, we conclude that the low -J K -1 = 1 states are perturbed locally. The energy level diagram of those states is shown in Fig. 4.

Several models were considered to explain the fre-

000

322

HE-XE LASER

2850.725 eM-1

FIG. 4. Energy level diagram of DCCCHO in the v2 = 1 state: J::s 4. The arrows show microwave transitions observed by double and triple resonance methods. The energy level shown with broken line is a rotational-vibrational state which does not belong to the v2 = 1 state.

quency anomaly observed in the low-J lines based upon higher-order Coriolis interactions. However, none was successful if only one perturbing state was assumed. The spectrum could be explained only by assuming that the low-J states were perturbed simultaneously by more

TABLE II. Microwave transitions in the v2 = 1 state.

Vobs-Vca.lc a

Transition "obs (MHz) (MHz) Methodb

2 1,1- 21,2 654.86 -209.80 d

2 1,2- 11,1 17230.48 231. 36 d

2 1,2 -10,1 78127.52 -1207.97 d

2 1,2 -30,3 34948.67 -1174.95 d

31,3- 21,2 25835.37 337.39 d

3 1,2- 21,1 26531. 06 168.46

30,3 -20,2 25906.18 - 19. 91

4 1,4 -31,3 34380.62 384.61

40,4 - 30,3 34536.94 -26.35 t

112,10 -121,11 71841. 22 -734.60 d

121,11- 121,12 22349.39 -107.53 t

19 1,18 - 191,19 55394.45 873.80 d

192•17 - 20 1,20 50883.30 -551.17 d

20 1,19- 201,20 60776.76 565.90 d

25 3,23 - 262•24 75326.26c 1534.04 d

262,24 - 262,25 19824.99c 843.34 t

262,24 - 27 1•27 29018.75c -577.18 d

253,22 -- 25 3,23 745.7 -48.6 d

aFrequencies calculated from the constants in Table III.

bd: measurement by double resonance, t: measure-ment by triple resonance.

cThe assignment is somewhat uncertain. See Sec. VI.

J. Chem. Phys., Vol. 72, No.7, 1 April 1980

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M. Takami andM. Suzuki: Spectroscopy of DCCCHO 4093

TABLE III. Rotational constants and band origin of DCCCHO.

A B C

v2=1 (MHz)

66811(302)a 4466(26) 4178(26)

0.0015919b

- 0.139214b

9.4328b

0.0002885b

0.03069b

V2 = 2857.888 ± 0.001 cm-!

aStandard deviation.

Ground state (MHz)

66778.016 4463.8489 4177.7950

0.0015919 -0.139214

9.4328 0.0002885 0.03069

bFixed at the ground state constants in Ref. 17.

than one nearby vibrational state. Since the number of observed low-J lines (Js, 4) was too small, it was not possible to characterize the perturbing states from the observed spectrum.

From the observed transition frequencies shown in Table IT, the three rotational constants in the excited state were determined assuming the ground state cen­trifugal distortion constants. The agreement between the observed and calculated frequencies is quite poor. When eight parameters including five centrifugal distor­tion constants were adjusted, the root mean square of the fit decreased from 756 to 321 MHz. However, the centrifugal distortion constants showed quite abnormal values and therefore the result was disregarded. Table ITI shows the rotational constants in the ground and the excited states, and the band origin of the 112 vibration. It is interesting that, in spite of large standard devia­tions, the rotational constants in the excited state are very close to those of the ground state. This suggests that the frequency irregularity observed in the v2 = 1 microwave spectrum is more or less stochastic.

VI. INTERVIBRATIONAl MICROWAVE TRANSITIONS

During these measurements', several very strong dou­ble resonance signals were observed which could not be assigned as transitions within the v2 = 1 rotational mani­fold. A remarkable case was observed in the search for the rotational transition 25 3•23 - 262•24 in the 112 ex­cited state. Instead of one microwave transition ex­pected from the v2 = 1 rotational energy level structure, three very strong signals were observed with about 400 MHz frequency intervals. All of the three transitions showed intenSity maxima when the laser frequency was resonant to the 253•23(112) - 244•20(g) transition.

The transition to the 262• 24(1)2) state from another ro­vibrational state 271• 27(112) was also searched for. Here again three very strong signals were observed. Since the sum frequencies of the three pairs of transitions agreed within the experimental accuracy of 60 kHz, we concluded that there existed two unidentified rotational­vibrational levels close to the 262•24(112) level as shown by a and b in Fig. 5. Among the three energy levels, the highest one was aSSigned tentatively as 262•24 (1)2) be-

cause ~he transitions to this level were the strongest among the three. This energy level structure was also confirmed by the triple resonance of the type shown in Fig. 1(b).

In the energy level system described above, another transition 262•24(112 ) - 262•25 (112) was searched for by triple resonance. Instead of one rotational tranSition, two signals of nearly equal intensity were observed with about 480 MHz frequency interval. The existence of two closely spaced energy levels was confirmed by triple resonance from each of the three energy levels around 262 •24( 112) as shown in Fig. 5. Since the transitions to the upper level was slightly stronger, this state was as­signed to be 262•25 (1/2). The observed intervibrational microwave transitions are summarized in Table IV with the rotational-vibrational levels not identified with the v2 = 1 state labeled as a, b, c, ....

Other examples of the intervibrational microwave transitions are the signals observed with the 253• 22 (1)2)

- 244•21(g) infrared absorption. Two very strong signals were observed at 74114 and 78058 MHz. They were confirmed to be the transitions from the 253•22 (1/2) state by saturating the 253•22(112)- 253• 23(112 ) transition simulta­neously. The frequency shift by triple resonance indi­cated that both were the transitions from 253•22(112) to higher energy states (see Fig. 5). However, no transi­tion within the v2 = 1 state is expected in this frequency region if we assume that the r~tational energy level structure of the v 2 = 1 state doe!:! not differ largely from the ground state.

r------ d I (3.94) f.r------ e /I 1/

(78) I (74)

f , m.m

2850.552 eM-l

2850.576 eM-l 2850.686 eM-l

FIG. 5. Energy level diagram of DCCCHO in the v2 = 1 state; high...! level. The every levels which belong to other vibra­tional states are shown with broken lines (a-e). The solid line arrows show the observed microwave transitions within the v2 = 1 state, while the broken line arrows show the observed in­tervibrational transitions. Figures in parentheses are energy differences in GHz.

J. Chern. Phys., Vol. 72, No.7, 1 April 1980

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4094 M. Takami and M. Suzuki: Spectroscopy of DCCCHO

TABLE IV. Intervibrational microwave transi­tions.

Transition"

253,23-a

25 3,23-b

a-27 1,27

b-27 1,27

262,24-C

a-262,25

a-c

b-262,25

b-c

d-25 3,22

e-253,22

1-2 1,2

Frequency (MHz)

75734.01 76103.54 28611.02 28241. 52 20305.14 19417.37 19897.35 19047.77 19527.87 78058.22 74114.28 74317.75

Assignment

a: J=26 b: J=26

c: J=25-27

d: 26 3,24 (vI+vd? e: 244,20 (VI + vI2)? I: J=1-3

"a-I are the energy levels which belong to the vibrational states other than V2 = 1. See Figs. 4 and 5.

An intervibrational microwave transition was ob­served also in the levels of low rotational quantum num­ber (see Fig. 4). During the double resonance mea­surement of low-J lines with the infrared transition 21,2(v2)- 32• 1(g), one mysterious line was observed at 74318 MHz. The intensity of this line decreased dras­tically when the 31•3(V2)- 21,2('-'2) or the 21.2(v2)-11.1('-'2) line was saturated. The frequency shift observed by triple resonance indicated that the transition was from the 21•2(1/2) to an unidentified higher energy level. After this line was found, an extensive search for intervibra­tional microwave transitions from 21• 2(v2 ) was carried out. However, no other line was observed. Unfortu­nately the frequency of the infrared transition 21• 2(v2 )

- 32• 1( g) was close to the tuning limit of the laser, where the laser oscillation was noisy and had a smaller output power. Because of these reasons the double resonance signals observed using the 21•2(V2) - 32,I(g) infrared transition had a very poor signal-to-noise ratio. Thus further investigation of this intervibrational microwave transition by triple resonance was abandoned.

For vibrational assignments of these unidentified lev­els, vibrational energy levels near the v 2 = 1 state were calculated from the 12 fundamental vibrational frequen­cies determined by Brand et al. 16 Figure 6 shows the calculated vibrational states up to four vibrational quan­ta where anharmonicity effects are neglected. The den­sity of all vibrational states is about 2.4 states per cm -I. Among the vibrational states with two vibrational quanta, the vI +V I2 state lies only 4.4 cm-I below the V2 = 1 state and therefore should provide relatively large perturbations to the microwave spectrum. Since VI + Vl2

has a" symmetry while V2 has a', these states can per­turb each other through a- and b-type CorioUs interac­tions.

Among the six unidentified levels (a-f in Table IV), d and e levels may be assigned to be 263•24(v l + v 12 ) and 244 ,20(V1 + V12 ) respectively, which are coupled to the v2 = 1 state by an a-type Coriolis interaction. The cal­culated transition frequencies to these levels are about 0.5 cm -I higher than the observed ones. However, these

'discrepancies can be explained by an anharmonicity ef­fect and experimental errors in the fundamental vibra-

tional frequencies. The observed energy difference of these two levels is 3.94 GHz, while the corresponding energy difference in the ground state is 5.56 GHz. These assignments are also favored by the fact that these levels are relatively isolated from the liz = 1 rota­tional-vibrational levels with J = 24-26 and therefore have relatively large coupling energies. If these as­signments are correct, however, two other intervibra­tional transitions, 263•23(V I + 1/12)- 253•23(v2 ) and 244•21(v l +V I2)-253,Z3(v2), will be observed. So far the attempt to observe these transitions is not successful. There­fore, the assignments have not been confirmed yet al­though the energy differences of these levels strongly support the assignments.

One of the possible assignments of level f is that it is 11•0(vx) coupled with 1I ,I(v2) by an a-type CorioUs inter­action. This assignment is consistent with the experi­mental fact that no other intervibrational tranSition has been observed in the frequency range below 74 GHz. Another possible assignment of levelfis 32•Z(!/1 j-v 1?)

coupled with the v2 state by a- and/or b-type Coriolis interaction. The assignment of level f might be con­firmed by triple resonance if the sensitivity of measure­ment can be increased.

It is clear from the selection rules for electric dipole transitions that the rotational quantum number of levels a and b is 26 and that these levels are coupled with 262 •24(v2 ). When two rotational-vibrational levels are

CM-l

2950

2900

2850

2800

2750

2V5

FIG. 6. Calculated vibrational states near the v2 = 1 state. The vibrational states up to four vibrational quanta are shown. The total state density is about 2.4 states per em-I,

J. Chern. Phys., Vol. 72, No.7, 1 April 1980

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M. Takami and M. Suzuki: Spectroscopy of DCCCHO 4095

TABLE V. Hot band signals.

IR frequency"- MW frequency (GHz) (MHz)

-2.55 72674.51 -2.41 72451. 55 -1.92 60564.27 -1. 88 76852.58 -1. 84 73649.66 -1.48 29794.66 -1. 01 77643.51 -0.87 74873.13 -0.65 46656.51

0.14 28522 28559

1. 40 28925.02 29831. 90

1. 43 29761 1. 53 29950.80

IR frequency (GHz)

2.00 2.50 2.53

2.56

2.60

2.62

2.65

aAdd 85460.00 GHz (2850.639 em-I).

MW frequency (MHz)

60929.44 43278.92 43919.35 76261. 62 29160.93 65508.66 66504.27 71849.26 42182.73 43620 47263 35065.98 75226.10 30269.53

perturbing each other, the effective coupling energy is equal to or smaller than the energy difference of the perturbed levels. Because levels a and b are only 0.37 and 0.78 GHz from the 262,24(v2) level, respectively, these two levels have very small coupling energies, and are observed because they accidentally lie very close to the 262,24(v2) level. As for level c, it is not clear whether it is coupled with the 262,a5(Va) level. So far we have no vibrational assignments for these levels.

VII. HOT BAND SIGNALS

In addition to the intervibrational microwave transi­tions, many weaker double resonance signals were ob­served accidentally during the search for the v2 funda­mental signals. They were found to be the signals as­sociated with hot band infrared transitions because the signal intensities became maximum at the laser fre­quencies slightly different from the va fundamental ab­sorption lines. Because the Doppler width of the vibra­tion-rotation lines is about 70 MHz (HWHM), the hot band lines which are within ± 100 MHz of the va funda­mentals might give rise to signals during the search for the va fundamental signals. This observation shows that the density of the hot band lines is very high in the ob­served frequency region. Table V lists the observed hot band Signals. If the hot band signals are searched for systematically over the whole tuning range of the laser, it is likely that more than ten times as many lines will be observed.

Propynal-d1 has two low-lying bending vibrational modes v9 (195.6 cm- i ) and V 12 (248.5 cm-1). Since ex­cited levels of these modes have high populations at room temperature, quite strong double resonance sig­nals should be observed associated with the hot band lines from these two fundamentals and their overtone and combination states. Unfortunately, the rotational spectrum of DCCCHO in these excited states have not been analyzed yet. If the molecular constants in these vibrational states are determined, assignment of some of the hot band signals should be possible.

VIII. DISCUSSION

The large frequency irregularity observed in the va = 1 microwave spectrum of DCCCHO raises a serious ques­tion whether it is meaningful to analyze microwave spec­trum of a medium- or large-sized molecule in such a high energy state with the purpose of accurately deter­mining molecular constants. If the perturbations are weak and stochastic, at least three effective rotational constants will be determined with a reasonable accuracy from the observed spectrum. When the spectrum is badly perturbed by many vibrational states, however, an accurate determination of various molecular con­stants will not be feasible even if a large number of ob­served lines are available.

On the other hand, the badly perturbed spectrum in­cluding intervibrational microwave transitions will pro­Vide somewhat different kinds of information. For ex­ample, the linewidth of the microwave transitions ob­served in the present work is about 100 to 200 kHz (HWHM) for either ground or excited state lines when the microwave power is suffiCiently reduced to avoid saturation broadening. Since some of the rotational­Vibrational levels investigated in the present work are the mixed states of several different vibrational modes, we can confirm experimentally that a collisionless in­tramolecular vibrational relaxation does not exist when a single molecular eigenstate is excited by a laser.

If a laser can be tuned over a wide frequency range, and if vibrational aSSignments of the inter vibrational microwave tranSitions are made, it may be possible to determine accurate coupling constants of higher-order Coriolis- and Fermi-type interactions from the observed spectrum. The effective coupling energies of these higher-order interactions are believed to be roughly proportional to K", where K is the Born-Oppenheimer constant19 K2", ErQt/Evlb and n is the number of Vibration­al operators in the perturbation Hamiltonian. When a large number of vibrational quanta are excited, the molecule is in a large amplitude motion. Under such a condition, the higher-order coupling energies will be much greater than the values expected from Born-Op­penheimer expansion because anharmonicity of the mo­lecular motion is very large. This breakdown in the Born-Oppenheimer approximation is very important in the discussion of multiphotonprocesses because the vibration­rotation interactions in Vibrational quasicontinuum states will be mostly of the higher-order type. When the vibra­tional state denSity is very high, it becomes impossible to assign all of the intervibrational microwave transi­tions and therefore the transitions have to be discussed statistically.

From this point of view, it is interesting to calculate how many intervibrational microwave transitions are observed on average for each vibration-rotation line of a molecule in the Born-Oppenheimer approximation, and to compare the resulting number with experiment. First let us consider the energy level diagram shown in Fig. 7, where the rotational-vibrational levels 2 and 3 are coupled with dense background vibrational states. The inter vibrational microwave transitions can be divided into two different groups, shown as I and II in Fig. 7.

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4096 M. Takami and M. Suzuki: Spectroscopy of DCCCHO

-.--- .. ---­.liE ...... ~r----

3 -.....,r--~

z

MW

2 --jr----

IR

FIG. 7. Two different types _-r-- Y of perturbation-allowed transi­

tions. Type-I transition is ob­served via the interaction be­tween levels 3 and z. The

x type-II transition is observed by the perturbation between levels 2 and x when the transi­tion y - x is allowed in the background vibrational states.

The type-I transition is allowed by the interaction between level 3 and one of the background rotational-vibrational levels z. When the y - x transition is allowed in the background state, the type-II transition can be observed by the interaction between levels 2 and x. Since we are interested in the transitions in the vicinity of the 3 - 2 line, we consider only the type-I intervibrational micro­wave transitions in the following.

In general, the intensity of double resonance signal depends upon to the extent that we can saturate the rele­vant microwave transition. If the microwave radiation is sufficiently strong, therefore, all of the intervibra­tiona I microwave transitions within a certain frequency range are observable, in principle, with nearly equal signal intensity. Practically, however, the number of observable transitions is limited by the available micro­wave power, and we need to determine the conditions under which an intervibrational transition can be ob­served by double resonance. Let 6.E the energy differ­ence between levels 3 and z, where the effective coupling energy between these levels is C. When the saturation of the microwave transition z - 2 is small, the signal in­tenSity is proportional to the square of the transition di­pole moment. 20 If we can observe the transition whose intensity is greater than 10-3 of the 3 - 2 transition, the condition will be expressed as (C/6.E)2 > 10-3 , 1. e., an intervibrational microwave transition can be observed when the energy difference I6.E I is smaller than 30 times the effective coupling energy.

In the next step we expand the simplified vibration­rotation Hamiltonian derived by Watson21 in a power series in the normal coordinates and estimate the mag-nitude of effective coupling energy for each term. 22 .

There are two dominant terms in the vibration-rotation interactions, the anharmonic potential V' and the rota­tional resonance term 'EPOl1T8J.i0l8, where POI is the angu­lar momentum operator, 1f 8 is the Coriolis operator, J.l.0l8 is an effective reciprocal inertial tensor, and Viis given by

The effective reciprocal inertial tensor J.iBa is expanded similarly in a power series of the normal coordinates . In the following calculation we assume that the effective coupling energy is proportional to 'C", where n is the number of normal coodinates in the relevant expansion term.

The calculation is carried out for two different kind of molecules, DCCCHO and a hypothetical molecule M which has twice as many of normal modes (24 modes) as DCCCHO, and therefore has a much higher vibration­al state density. In order to simplify the calculation, we assume that M belongs to the C. point group, has the same rotational constants as DCCCHO, and that its 24 fundamental frequencies consist of the 12 vibrational frequencies of DCCCHO and their nearly doubly degen­erate duplicates. We further assume that K=< 1/30, k(3)

is 3 X 105 MHz (10 cm -1) and that the effective coupling constant of the lowest order rotational resonance inter­action (Coriolis interaction) is 3 x 104 MHz (1 cm -1) for both molecules. The last value may be too large for b- and c-type Coriolis interactions in the low -J levels. When J-dependence of these interactions are taken into consideration, however, the value will not be too un­realistic for J'? 20.

In a molecule with the C. symmetry, an a' state cou­ples with another a' state by Fermi-type and c-type Coriolis interactions, and with a" state by a- and b-type Coriolis interactions. The selection rule 6.J = 0 holds strictly for all of the interactions. The b- and c-type Coriolis interactions have the selection rule 6.K -1 = ± 1, and therefore they have twice as great a probability of giving rise to intervibrational microwave transitions as the a -type Coriolis interaction. Since propynal is a slightly asymmetric rotor, we neglect the effect of asymmetry on the selection rules for the per­turbations. We assume that a ' and a" states are distrib­uted with equal state density in the background vibra­tional states although DCCCHO has nine a' and three a II vibrational modes. Further, we consider only intervi­brational microwave transitions whose transition fre­quencies are lower than 75 GHz. With these assump­tions, the average number of observable intervibration­al microwave transitions per vibration-rotation line was calculated for DCCCHO and the hypothetical molecule M. The result is summarized in Table VI. The second line of the Table shows the assumed effective coupling constants of the Fermi type and the rotational resonance interactions between the v2 = 1 and a vibrational,state with no vibrational quanta, where no is given in the first line of the table. The third line shows the calculated average vibrational state density around 2850 cm-1

, and the fourth line the average number of intervibrational microwave transitions expected for each no. The total number of observable intervibrational microwave transitions is about 0.5 for DCCCHO and 6 for the hypothetical mole­cule M. In DCCCHO the calculation is in reasonably good agreement with the experimental result where at most two intervibrational microwave transitions are ob­served for a single vibration-rotation line.

Although the calculation is carried out using very crude approximations, the result shown in Table VI

J, Chern. Phys., Vol. 72, No.7, 1 April 1980

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M. Takami and M. Suzuki: Spectroscopy of DCCCHO 4097

TABLE VI. Calculated number of observable intervibrational microwave transitions.

Number of vibrational quanta in the perturbing state: n. 1

Effective coupling V-coefficients (MHz) };POt7rafJ-0t8 3 X104

Vibrational state DCCCHO 0 density at 2850 cm-I Ma 0 (per cm-I)

Number of observable DCCCHO 0 perturbation allowed Ma 0 transi tions

2 3

3x 105 104

103 30

0.03 0.10 0.13 0.73

0.23 0.27 0.98 1. 93

4

300 1

0.07 10.60

0.02 3.29

5

10 0.03

0.47 7.01

0.00 0.07

Total

2.4 97

0.52 6.27

aHypothetical molecule that has Cs symmetry, has the same rotational constants as DCCCHO, and has 24 fundamental vibrational modes.

shows several interesting qualitative features of inter­vibrational microwave transitions. In DCCCHO, for ex­ample, most of the intervibrational microwave transi­tions arise from the Il.v = 3 and 4 interactions (n. = 2 and 3 in Table VI) which have relatively large coupling en­ergies. As the vibrational state density increases, con­tribution f rom the higher-order interactions becomes more important. Since the higher-order interactions have smaller coupling energies, the intervibrational microwave transitions will tend to cluster around the pure rotational transition 3 - 2 shown in Fig. 7. . For the higher-order interactions, the contribution of the Fermi type interactions to intervibrational microwave transitions is much greater than that of rotational reso­nance interactions.

The microwave transitions between different vibra­tional states are also allowed by nonlinear dependence of an electric dipole moment to normal coordinates. The electric dipole moment of a molecule can be ex­panded in a power series of its normal coordinates as23

The first- and higher-order expansion terms in the above expression allow direct transitions between different vi­brational states. Unfortunately very few experimental data have been reported on the higher-order expansion coefficients. When a molecule is in a low energy state, contributions from direct vibrational transitions will be negligibly small. When a molecule is in a highly ex­cited state and in a large amplitude motion, however, the above expansion is no longer rapidly convergent and the contribution to the intervibrational microwave transi­tion from vibrational dependence of the dipole moment will become important.

The present experimental result shows that the vibra­tional state density around the v2 = 1 state of DCCCHO is not high enough for statistical calculation of the number of intervibrational microwave transitions. In the higher excited state of DCCCHO or in a molecule which has much greater number of vibrational modes, the number of observable intervibrational microwave transitions is large enough to discuss statistically the physical nature of higher-order vibration-rotation interactions. For investigation of higher energy states of molecules, IR-

IR-MW triple resonance should be a useful method in the energy range from 4000 to 5000 cm -1.

IX. SUMMARY

We have investigated the microwave spectrum of DCCCHO in the V2 = 1 state by infrared-microwave double and triple resonance methods. Eighteen microwave tran­sitions observed in the excited state are found to be badly perturbed by other vibrational states. In addition to the pure rotational transitions within the V2 = 1 vibrational state, ten intervibrational microwave transitions from the v2 = 1 to other nearby vibrational states are ob­served. This observation shows that the v2 = 1 state of DCCCHO is no longer a pure state of normal mode but is strongly coupled with its dense background vibrational states. In order to study the nature of intervibrational microwave tranSitions, the average number of the tran­sitions expected for each vibration-rotation line is cal­culated for DCCCHO and a hypothetical molecule M. In the v2 = 1 state of DCCCHO, the calculated number is in reasonably good agreement with the experimental re­sult.

ACKNOWLEDGMENTS

We are grateful to Professor K. Shimoda for critical reading of the manuscript. One of us (M. S.) expresses his gratitude to Professor K. Shimoda and to the mem­bers of Microwave Physics Laboratory of the Institute of PhYSical and Chemical Research for the hospitality.

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coupling energy which includes the J - and K _I-dependent fac-

J. Chem. Phys., Vol. 72, No.7, 1 April 1980

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4098 M. Takami and M. Suzuki: Spectroscopy of DCCCHO

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