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Radio frequency-microwave double resonance as a tool in the analysis of microwave spectra
JOURNALOF MOLKULARSPECTROSCOPY 37, 445-463 (1971)
Radio
Frequency-Microwave Double Resonance as a Tool in the Analysis of Microwave Spectra’ F. J. WODARCZ~K~ AND E. B. WILSON
Department
of Chemistry,
Harvard
[Jniversity,
Cambridge,
Massachusetts
02138
The pract,ical application of radio frequency-microwave double resonance as a spectroscopic technique in the analysis of microwave spectra has been investigated. Application of a high-power amplitude-modulated radio-frequency field to a gaseous sample in a waveguide cell provides a means of detecting microwave transitions, analogous to the situation in microwavemicrowave double resonance. The sensitivity of the technique compares favorably wit,h that of Stark modulation. Near-symmetric top molecules with allowed K-type doublet transitions are especially amenable to the technique. Accidental near degeneracies of dipole-connected rotational levels in asymmetric top molecules are also useful. A description of a radio frequency-microwave double resonance spectrometer is given together with a discussion of the special problems associated with radio frequency circuits. Applications of the technique are discussed with examples. INTRODUCTION
For several years two-photon absorpt)ion processes have proven to be a useful tool in the analysis of the microwave rotational spectra of polyatomic molecules (1-7). In this double resonance technique, a sample of gas in a waveguide cell is irradiated simultaneously with two radiation fields, one a strong saturating field near resonance between two electric-dipole connected energy levels of the gas, and t,he other a much weaker field with its frequency near another dipoleallowed transition, which is used to monitor the effect of the st)rong perturbation. If the two transitions are chosen to have an energy level in common (Fig. l), the shape of the observed signal is modified in a characteristic manner. Instead of using Stark modulation to det’ect the modified microwave absorption, the modulation is applied to t,he strong (“pump”) radio frequency source as squarewave, on-off modulat’ion. Then no microwave signal frequencies are seen except those sharing an energy level with the pump t,ransition. To dat’e, double resonance work in microwave spectjroscopy has been restricted 1This research was supported in part by a grant extended to Harvard University by the National Science Foundation, GP14012X. 2 National Science Foundation Predoctoral Fellow, 1966-71. 445
WODARCZYK
446
AND
WILSON
--E .
d
0°P2 EC
EQ FIG. 1. Energy-level arrangement of a three-level double resonance system
mostly to the use of pump and signal frequencies in the micro\vave region (MMDR) . Autler and Townes (8) first demonstrated two-photon absorption with one radio frequency and one microwave source. They saturat’ed the radio frequency E-type doublet,, J = 1 transition at 12.73 MHz in OCS and observed the effect on the lineshapes of the J = 2 +- 1 l-type doublet in t,he microwave region. Later Shimoda (9) saturated t,his microwave transition and observed t’he radio frequency transition in bot’h emission and absorption, depending on the microwave transition pumped. It is the purpose of t,his paper to describe the successful application of t,he Autler-Townes technique of radio frequency-microwave double resonance (RFMDR) to asymmetric top spectra. A brief qualitative review of t,he thcoretical considerations will first be presented followed by a descript,ion of the radio frequency-microwave spectrometer used. Finally, examples of applications of the technique will be given, mainly to the assignment of transitions in complex spectra. I. THEORETICAL
CONSIDERATIONS
The theory of double resonance has been discussed by many aut,hors. In t,his section we will present a qualitative picture of the pert#inent effects of a saturating field on the lineshape of a connected signal absorption. A. The Three-Level
System
Three-level double resonance (Fig. 1) involves the simultaneous irradiat,ion of a gas sample with two linearly polarized fields, one a skongly pert,urbing pump field E, = Epo sin W& and the other a weaker signal radiation E, = E,3osin WJ, where Epo >> E,‘. The frequencies of the two radiation fields, wP and (~1~ , are each near resonance with the dipole-allowed transitions at frequencies wi’ and G”,
RF-MICROWAVE
DOUBLE
RESONANCE
447
respectively, which share a common energy level. Javan has worked out a t8heory which explains the signal line shape of the three-level case in terms of the quantity Y==
PP
EPO
(1)
in which p, is the dipole moment matrix element for the transition The effect of the saturating field Ep is to split the signal absorption ponents whose frequencies are
being pumped. into two com-
WI = wso & 6 - y
(?a)
w2 = wso f
6 + y,
(2b)
6 = (w,” -
w,)/2
where we have defined (3)
and y = (2 + 1y /2)1’2.
(4)
Here the choice of the upper or lower sign on 6 depends on the relative order of the energy levels. For convenience the upper sign will be used in this discussion, but analogous arguments hold in eit’her case. When wP is sufficiently far from resonance so that 6’ >> / y 12,then Wl E OS0
(5n)
and w2 e
wso + WPO-
WP
7
(5b)
i.e., one of the components, the “main line,” is close to t,he zero-field frequency, while the other smaller line, the “creeper,” is displaced from resonance about as far as the pump frequency is from it,s resonant frequency, but in the opposibe direction. As wP is brought closer wPo, the creeper increases in size and moves towards the main line, which in turn decreases and moves away from wso until, form a symmetrical doublet. displaced + 1y 1 when wP = wPo,the two components the main line and creeper and -1 y 1 about wso. As wP is swept past resonance, exchange roles, the new main line increasing in size and approaching as” while t,he new creeper decreases and moves away from it. B. The Four-Level System Very often in radio frequency-microwave double resonance, a situation arises in which four energy levels are involved in the double resonance process. For example, consider t.he energy level situat.ion of Fig. 2, in which the transitions indicated by arrows are the only ones allowed. Here w”,, and w”,? are in the radio frequency region, while C& and wi2 are microwave frequencies. Such an arrangement describes the energy level pattern for K-type doublets in near symmetric
44s
WODARCZYK
AND WILSON
A
FIG. 2. Arrangement
of the energy levels in a four-level
EC
double resonance
system
top molecules, or I-type doublets in linear molecules. If the two radio frequent> splittings are not too different in value, so that (w”,, - ~:~)/2a 5 15 MHz, then there is a range of frequencies over which the pump radiation can be considered t.o be near the resonances of bot8h transitions. It should be emphasized here that the 15 MHz upper limit on the frequency difference is purely arbitrary, and intended only to give a rough value below which the four-level phenomenon should be clearly discernible. When wP is very close to resonance with eit,her w”,, or w!& , the three-level sit,uation qualitatively holds, and a creeper and main line straddle both microwave frequencies & and & , since both these transit’ions have energy levels in common with the affected pump t.ransition. The energy levels are so arranged that the two main lines or the two creepers occur “facing each other” in the frequency region between US, and otp. However, when the pump frequency is between the two resonant radio frequencies (u”,, < wP < wi2), a unique situation arises. As wP is swept above the a”,, resonance, the two creepers move towards each other in the region bet.ween t,he zero field absorptions until, at a frequency
the two merge into a single absorption. But as wP is swept above this point and nearer to wit, this single absorption again splits into two creepers, which approach the zero-field positions as wp nears the w”,‘zresonance. This phenomenon is useful for measuring the two resonant radio frequency values in cases in which a direct measurement by three-level techniques is not possible. A more exact formula for wPi at resonance is derived in the Appendix, and the procedure for measuring frequencies using this method is outlined there.
The theoretical considerations presented so far are valid provided 1y l/co, and / y I/w: << 1 and interference terms with frequencies such as wP + OJ~ are not
RF-MICROWAVE
DOUBLE
449
RESONANCE
important. Autler and Townes (8) show that for transitions in the radio frequency region, the interference terms which Javan was able t,o neglect in his derivation of the three level case do become important, since 1y 1, which is typically of the order of 1 MHz, may not be negligible compared with the radio frequency wP . The interference terms modify the expression for y in Eq. (4) so that (7) formula y = / y I. Yet, For wP = w,‘, this expression reduces to the three-level even in this approximation, the interference terms modify t,he intensities of the two components so that the ratio of their intensities at pump resonance is (1 + ] y 1/2~0,‘)~. However, for pump frequencies in the microwave region, 1y 1becomes negligible compared with oP , and the expressions for the frequencies of the components as well as those of the relative intensities reduce to those given by Javan (10). To higher order in the quantity 1y I/u:, Eq. (7) is modified further such that, when wP = w,‘, the components are split by an amount
(8) while the frequency
at which the two components
are equally
intense
becomes
(9) Again,if I Y Ilap’ is reader is referred these points.
negligible, these formulas reduce to those of Javan (10). The to the paper of Autler and Townes (8) for a full discussion of
II. EXPERIMENTAL
In this section we will describe the two experimental arrangements used in t,he RFMDR spectrometer. In both cases the strong radio frequency pump used as the perturbing field is amplitude modulated with a square wave, so that it is “on” for one half of the modulation cycle and “off” for the other half. The effect of the field is monitored with the microwave absorption signal using the usual microwave detectlion system, which involves an amplifier tuned to t,he modulation frequency. In this way, only the effects of the pump radiat,ion on the molecules in the cell are detected, and the unmodulated absorptions of the molecule are not observed. The spectrum is thus cleared of all signals but the ones sought after. A. Arrangement Using cn RFMDR
Waveguide Cell
A convenient way to introduce a radio frequency trometer is to apply it between walls and septum
field into a microwave specof a Stark waveguide cell, a
4.50
WODARCZYK
AND WILSO?rT
met,hod used by Autler and Townes (8) and by Shimoda (9) in their earlier experiments. But there are t’echnical draw-backs with such an arrangement. One difficulty is that voltage variations in the rf field along the Stark septum can arise if the length of the septum from input to end is greater t,han about one quarter of the rf wavelength. Another disadvantage is that. the capacitive reactance presented by the cell decreases lvit,h increasing frequency according to the formula XC = (WC)-l. Since Stark cell capacities are generally in the range 500-1000 pf, at radio frequencies above 50 MHz, e.g., the source works into an impedance of less than 7 CLSince it is difficult to maintain the desired voltages at such low load impedances with most available radio frequency sources, a way has to be fourld around this difficulty. Autler and Townes overcame t.hese difficultIirs by using a cell with a septum whose effective length nas considerably short,er than ;L quarter wavelength of t,he highest, frequency t.hey were to work at. They also included the capacitance of t’he waveguide as part, of a series tuned circuit which, n-hen adjusted to resonat)e at t’he output frequency of their oscillator, increased the impedance of the load by a factor equal t’o the Q of the resonant circuit. Still, the first solution involves a decrease in sensitivit>y of the spectrometer over that obt#ained wit#h a longer cell, while the second has the disadvant,age of recluirin,g tuning at, each radio frequency, making searches with the pump radiation slow and t,edious. We have used an arrangement which overcomes these two difhculties wit.hout sacrificing the convenience of being able to use the waveguide cell for normal Stark spect’roscopy as well as radio frequency-microwave work. A waveguide cell with Stark septum can be t,hought of as a section of unterminated transmission line with characteristic impedance 2” . Use of a cell whose septum is terminated with a pure resist’ive load equal to ZO and matched t.o t#hr rf source by suitable impedance transformers eliminates the standing wave problem, the voltage st,aying constant with frequency wit,hin the specifications of the apparatus and circuits used. Such a cell has been constructed and used successfully for both RF’MDR and normal Stark spectroscopy. Figure 3 shows the schematic diagram of the RFMDR system. The cell consist,s of a 3.3-m copper X-band waveguide into which is insert)ed a copper septum ?4z in. t’hick. The septum is held in the center of the waveguide parallel to the broad face by teflon strips, as in a normal St,ark cell, and it’ is tapered at, both ends to minimize reflections of the microwaves. Hermetically sealed connectors capable of withstanding high voltages are attached to the sept.um at both ends by means of a wire threaded into a small hole tapped into each t,apered edge of the septum, and the wire connection is insulated with t,eflon tubing to prot’ect the system from voltage breakdown in high Stark fields. The flexibility of t#his connection allows for normal creeping of t’he septum as a result of temperature variat,ions and shrinkage of the teflon supporting strips. For normal Stark spectroscopy the square wave generator is connected at, one end of the
RF-MICROWAVE
KLYSTRON POWER SUPPLY
SWEEP _ CIRCUIT
DOUBLE
451
PHASE SENSITIVE DETECTOR
OSCILLOSCOPE.
-
500
RESONANCE
SQUARE WAVE GENERATOR
PREAMPLIFIER
CABLE 20 = 25 n
SEPTUM KLYSTRON
DETECTOR
xFMFl= IMPEDANCE TRANSFORMER
FIG. 3. Schematic trometer.
diagram
of the radio frequency-microwave
double
resonance
spec-
cell while the other end is capped to prevent radiation and possible damage due to inadvertent shorting of the connector. For RFMDR, the rf source is connected at one end, while the other is terminated with a pure resistive load of 25 ohms, corresponding t.o t.he characteristic impedance of the cell. This impedance was estimated from the cell capacitance and lengt’h (11) and confirmed by Time Domain Reflect’ometry. TDR also indicates that reflections in the rf circuit due to the connect.ions t.o the septum are small. The radio frequency generator is a Hewlett-Packard 606B oscillator whose output is amplitude modulat,ed using a HP 10534A double balanced mixer. The modulation is provided by a HP 311A square wave generator synchronized t’o the stable crystal oscillat’or reference circuit of the Stark generator, which circuit also provides the reference signal for t>he phase sensitive det’ector. The amplitudemodulated radio frequency signal from t.he double balanced mixer is amplified by one or two wideband amplifiers (Instruments for Indust#ry, Inc., Model 500, and Spencer-Kennedy Laboratories, Inc. Model 20PD) which are matched to the circuit by toroidal impedance transformers. The impedance transformers used are either commercial (SKL 200-34) or laboratory Would, using ferrite cores which work over the frequency ranges covered by the RF oscillator. Radio frequency fields of t,he order of 3-10 V/cm are used in t,he experiments and are found to be sufficient even for molecules like 1-butene with relatively small dipole moments. In normal operation, the pump frequency remains fixed while the signal klystron is swept. The sweep and detection circuits are the ones used for normal Stark spectroscopy.
WODARCZYK
452
AND
WILSON
IIII~III1IIIII1,I,1IIIII~IIIIIII,,’II,IIIIIY,I
38490
,,,,,,,,,,,,
38480
38470
38460
38450
I,,,,‘,,
38440
l,,,,,,
38430
4,
38420
FIG. 4. Spectra of ethyl formate from the HP 84OOC microwave spectrometer: (a) Stark spectrum of region taken at 50 V, (b) RFMDR spectrum of the same region with pump frequency at 6.5 MHz.
B. Arrangement
Using a Convewtional Waveguide
Cell
Very often it is possible to use a conventional, single connector Stark cell for RFMDR work. In such a case, the following conditions should be fulfilled: (1) the radio frequencies used are of sufficiently long wavelength that, voltage variations along the length of the cell are not critical, and (2 j the impedance that the cell presents to the source does not overtax its current-delivering capabilities.
RF-MICROWAVE
DOUBLE
RESONANCE
453
These conditions are satisfied fairly often, and much work has been done in our laboratory wit.h unterminated waveguide cells. In this case, the experimental arrangement is similar to the one described above except that the cell is not t,erminabed and matching transformers are not used at the cell connection. RIWDR experiment’s have also been successfully conducted using a commercial Hewlett-Packard 8400C microwave spectrometer. In this case, t’he amplitude modulation voltage is supplied by an S-V square wave from the calibration output of the Stark modulator. This square wave is imposed on the radio frequency through t,he external modulat,ion capability of the 606B oscillat.or, and t,he resulting amplitude-modulated rf is amplified and t,hen applied t’o the two Stark septa by means of a tee adapter. The phase adjustment of t,he phase sensitive detector is optimized on a known double resonance signal. Figure 4 shows examples of both Stark and double resonance spectra taken on t’his instrument. Notice that the RFllIDR spectrum is virt’ually free of the interfering lines which occur even at, the 50 volt St,ark modulation used in making the Stark spectrum. Since the radio frequency field is fully amplitude modulated, so that it is “on” and ‘r~ff” in opposite halves of t,he modulation cycle, the double resonance signal has one polarity and the zero-field absorption the opposit,e polarity. C. Intemity
Considerations
In our experimental arrangement the radio frequency field is applied parallel to the polarization of the microwave radiation, so that only the rotational states with the same projection quantum number M are connected. Thus, for a Por R-branch transition, all the 2J + 1 111 components are affected by the radiation field, while for a Q-branch, only 2J components are affected, the M = 0 component having zero transition moment. If the radio frequency transition being pumped is a Q-branch (as with K-type or Z-type doublet,s) and the observing transition is also a Q-branch, then a fully modulated RFMDR zero-field signal is the same size as the fully modulated Stark signal. If, however, the signal absorption is an R-branch transition, a fully modulated RFMDR signal is decreased from the size of the Stark signal by a factor of l-3( J + l)/ (2J + 1)(2J + 3), w h ere J is the rotational quantum number for the transition J + 1 t J, The reader is referred to the paper by Flynn (12) for a more complete discussion of the intensity of double resonance signals. Anot,her important intensity consideration is the range of pump frequencies over which a double resonance signal should be noticeable. Figure 5 shows a plot of the normalized single-double resonance intensity difference (10 - 1,)/I, versus distance from pump resonance, vpo - vp , where I, is the intensity of the zero-field signal at the peak maximum, and Ip is the intensity of the double resonance signal at the same frequency. This plot gives an indication of the strength of the signal seen at the zero-field maximum in the double resonance detection scheme. The calculations were made on an IBM 1620 computer using the Javan
WODARCZYK
454
AND WILSON
1.00
!
0.90I-
0.6C I-Y \ ;i 0.5C
0.40
0.30
0.20
0.10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -I
0
I
VgVp(MHz)
FIG. 5. Plot (I0 - Z,)/IO at vrnaxVS. symbols are defined in the text.
(v," -
v,,)
2
3
4
5
6
7
8
I
910
for a typical double resonance signal. The
formulas (10) for net power absorbed by the signal transition in a double resonance. The relaxation time was taken as lo-” set, the pump field was 3.75 V/cm, and the matrix element used was that for the J = 1 I-t’ype doublet transition at 12.78 MHz in OCS. These conditions are fairly represent’ative of t,hose encountered in RFMDR. Examination of t.he plot indicat,es t.hat a double resonance signal should be discernible from a few MHz off resonance for even weak signal absorptions. This fact is somet’imes useful in applicat’ions of double resonance. Since tdle response breadth of the radio frequency resonance is considerably more than the pressure-broadened line width, even at very low pressures, we would expect to obt,ain the Doppler width characteristic of the microwave, rather than the radio frequency.
RF-MICROWAVE
DOUBLE
RESONANCE
4.55
In order to see an appreciable change in line shape with the double resonance technique, the pumping radiation must be a strong perturbation on the system. However, care must be exercised that the amplitude of t,he radiation field is not SO large as t’o cause Stark modulation of the signal absorptions. Ton-nes and Merritt (13) have studied the effect of rapidly varying electric fields on microwave transitions, and their results for fields oscillat,ing at, frequencies greater t,han or equal t’o the half-width of a transition are applicable here. If a high frequency electric field is applied t,o a sample, lines which exhibit second order Stark effecbs are shifted to frequency I/~+ Av/~ and are accompanied by satellites at vo + Av/2 f YZV~ with relat,ive intensity J,‘( Av/vp), where Av is t,he second-order Stark shift due to a DC field of the same amplitude and J,( Av/vp) is t,he Bessel function of order ‘~1.First, order lines, on the other hand, are unshifted as a result of the field, but. they have satellit#es spaced every 3v, with relative intensities Jn2( Av/4v,), where Av is the first-order Stark shift expected from the corresponding dc field. It, is thus apparent) t,hat) if the elect’ric field, and hence, Av, is too large, the intensky of the satellites or t,he shift of the second-order lines may be appreciable enough to modulate transitions which are nonresonant w-it’ll the oscillating field. In doubtful cases, the behavior of creepers as a fun&ion of frequency should be enough t,o dist,inguish double resonance signals from Stark-modulat’ed lines. III.
APPLICATIONS
Asymmetric top molecules in general offer t,wo sources for radio frequency transitions: K-type doublet splittings and accidental near degeneracies. The former are plentiful in near symmetric top molecules with nonzero p, dipole moment’ components for near-prolate rotors or kc for near-oblat’e tops. While t’he latter are not so common, they are very useful if the suitable dipole-connected transitions esist . The same active near-degenerate pair of levels required for RP,1IDR will also normally produce a strong, near first-order Stark effect for t,he linked microwave transition. Consequently, candidate microwave lines which might show up with RFAIDR will always be limited to those which appear on Stark modulation at low modulation voltages. Such lines can be tested one by onr. 1lany of t,he benefits accruing to MXIDR as a specbroscopic tool also characterize RFAIDR. A fern examples will illustrate some of the usefulness of t)he technique. ( 1) As shown by Autler and Tonnes, (8) the resonant values of radio frequency transitions can be measured to give an addit’ional piece of information for analysis. This can be accomplished most easily by measuring the radio fre-
WODARCZYK
456
a
AND WILSON
b
w
d FIG. 6. An example of four-level double resonance in the skew 1-butene 42-32 K-type doublets. Here v”,, = 2.04 MHz and Y”,, = 6.10 MHZ. (u) yP = 3.00 MHz, (b) yP = 4.05 MHz, (c) yP = 4.50 MHz, (d) yP = 6.00 MHz.
quency
at which the two double resonance components of a microwave transition are equally intense. It is easily seen from Fig. 5 that t,he ot’her alternat,ive, finding the point, at, which the modulated signal is most, intense, is less certain. If the effect on the intensities of the quantity y/wP ’ is expected to have a measurable components at resonance, Eq. (9) can be used t,o find wPousing an extrapolation procedure as described by Autler and Tonnes (8). The four-level case, which arises often wit>h K-type doublet spectra, provides another means by which resonant frequencies can be measured. As discussed in Section I, there is a pump frequency, wPi at which the two innermost components of t,wo adjacent, microwave double resonance signals merge into a single absorption (Fig, 6b). By measuring this frequency, one can calculate w”,, and w”,, by using Eq. (6) or (A15) derived in the Appendix. The errors in t’he frequencies thus calculated are only slightly larger than those for normal microwave frequency measurements. (2) RFMDR can be used to measure the zero-field frequencies of micro\\-ave transitions. Many times these frequencies cannot be measured accuratel\with
RF-MICROWAVE
DOUBLE
RESONANCE
457
G” 2,110
Illlllllllllll
2,740
IIlI 21150
f1lJI1I*
21760
IIII’l(II
21710
IIII”I/I21780
FIG. 7. A portion of the RFMDR spectrum of I-pentyne, truns 524-423(I) and 5z3-422(II) transitions. The 422-423rf transition is pumped. The labels indicate the different st,ates that these absorptions may be attributed to: G = ground state, T = first excited C-C torsion, M = first excited methyl torsion, B = first excited C=C-C bending motion. The vibrational assignment of the other absorptions in the spectrum has not yet) been made.
Stark modulation because of a badly zero-based square wave, overlapping lines, or doubt as to the identities of several equally likely candidates. With pump frequency on resonance, the double resonance component,s are essentially equally displaced about the zero-field signal, and the frequency of t)he signal transition can be measured. (3) One of the main uses of double resonance is as an aid in searching for specific transitions or in identifying certain observed microwave transitions. Where both the radio frequency and microwave transitions with a common level are known only approximately, a two-dimensional search may be necessary. In certain cases, however, the radio frequency transit,ion may be sufIicient,ly wellknown (considering the breadth of the response curve shown in Fig. 5) so that only the microwave transitsion needs to be searched for. An example is the locat,ion of high-J transitions, which may be considerably shifted from their predicted rigid rot,or values because of centrifugal distortion. The connect8ed radio frequency transition may be so little shifted in absolute value that the radio frequency may be set on the rigid rotor predicted value. In cis-propionaldehyde, t’he 176,12-167,9 and 176,11-167,10transitions were found 110 and 114 MHz off rigid rotor prediction by pumping the 16 1,9-167,10transit’ion, which was only 0.9 MHz from its rigid rotor value. Other high-J transitions were found in the same manner, and all of them fit a semirigid rotor calculation incorporating centrifugal distortion terms. A similar and very powerful use is for assigning vibrationally excited state transitions. The frequencies of the radio frequency transitions oft,en change by only a fraction of MHz wit,h each step of vibrational excitation. Hence, t#he radio frequency can be fixed at the frequency appropriate for the ground state and the microwave frequency varied to find a whole sequence of vibrationally excited transit,ions. Figure 7 shows a portion of the spectjrum of 1-pentyne, in which
458
WODARCZYK
III1
29145
6
AND WILSON
III
7 8 9 50 1 2 3
IIII
4
5 6 7 29158
V(MHz)
FIG. 8. RFMDR signals of 1-pentyne. The larger line is the gauche 532-431transition in the ground state, while the smaller is an excited state gauche 533-432transition. The 432-431transition (v,o = 7.79 MHz in the ground state, 7.94 MHz in the excited state) is pumped at 6.50 MHz.
only the ground and several excited state signals of the 524-$a and 5.~42~ transitions of the tram rotamer are seen. The other lines in t’he region are not modulated, and hence, are not, detected. In this case the pump was kept near resonance with the ground state 4.~423 transition, and absorption signals were recorded up to the fourth torsionally excited state, 119 MHz from the ground state lines. In t’his way, the method provides a means of unambiguously determining weak excited state absorptions in the dense spectra associated with relatively heavy molecules. Even though such a double resonance spectrum is cleared of interfering lines, a question may still exist, as to which of t,wo possible transitions showing double resonance signals (such as K-doublets) a given excit,ed st,at#e should be assigned. This question cm often be answered by taking advantage of the fact, that the creepers and main lines can form distinctive patterns which will be mirror images in the case of four-level systems. Figure S shows two absorptions in 1-pentyne. The larger line is t,he ground state, gauche 532-431 transition. The smaller line, however, is an excited state of t)he other K-doublet transition, the qauch.e &-432 resonance, as it,s mirror-image appearance indicat)es. In applications like t,his, however, one should be cert#ain t)hat the radio frequency pump is below or above the resonant frequencies simultaneously. (4) In 2 ,2-difluorosilacyclobutane (14) the first excited state of t#he ring
RF-MICROWAVE
DOUBLE
RESONANCE
459
puckering vibration is close enough to the ground state that some rotational energy levels of both states are perturbed strongly. RFMDR was useful in assigning transitions which had been shifted from their rigid rotor predictions. For example, the 523-422and 533-432transitions of t.he 2) = 1 stat.e were shifted 92 and 263 MHz, respectively, from the predicted frequencies, and both occurred wit’hin four MHz of each other. The proper assignment was immediately confirmed when the 533-432 showed a double resonance signal with the pumped 431-432radio frequency transition. (5) Martins and Wilson (15) have used the magnitude of the XIMDR splitting to measure the dipole moment of xenon oxytetrafluoride. In the same vein, Azrak (16) has suggested that the failure to observe an RFMDR signal in the 329-3110 transitions of 2-chloroethanol when the K-type doublet 3110.~1-3110.22 was pumped at 3.8 MHz gives an upper limit to the value of jam, the dipole moment component responsible for the radio frequency transition. In his work, he calibrated the rf field by pumping a b-type accidental near degeneracy, the 413-322 at 4 MHz, and observed the double resonance of the connected 3~~3~~ microwave transition. (6) The various M components of a transition have different transition moments, and, hence, different values of 1y (. Thus, it is theoretically possible to resolve the different M components of a double resonance signal (la), since the frequencies of the various components depend on 1 y 1. Oka (7) has resolved the JJ! fine structure of an ethylene oxide transition in high power MMDR studies. Figure 9 shows the M components in an RFMDR signal of ethyl acetylene. This
1 /MI=2 ’
2
FIG. 9. M-component fine structure in a low-pressure RFMDR scan of the ethyl acetylene 3z1-220 microwave transition. The 11741 = 1 and 2 components are resolved. The 2~2~ transition was pumped at 7.50 MHz.
460
WODARCZYK
AND
WILSON
experiment was carried out at low pressure and the normal rf saturating field strength used in the other studies. For this trace, the 220-221transition was pumped at 7.50 MHz while the 321-220microwave signal was observed. The j M / = 1 and 2 components can be seen in the double resonance signals, as expected for a Q-branch pump, R-branch signal combination. Similarly, three components have been resolved in the 423-322 and 422-321 microwave transitions of this molecule when the 321-322t’ransition was pumped at 34.68 MHz. This result suggests t(hat such a resolution of component8s might provide an added piece of information t)o help in assigning the spectrum of a molecule. CONCLUDING
REMARKS
We have at,tempt.ed to show the usefulness of radio frequency-microwave double resonance in a variet.y of applicat.ions. Although t,here are limitations on the transitions in the microwave region which are connected to nearly degenerate levels, most near-symmetric top molecules offer a number of radio frequency transitions which are useful for double resonance applications. The experimemal arrangement involved is simpler and less costly than that of the corresponding microwave-microwave double resonance spectrometer, and there are no difficulties wit,h the pump radiation affecting t’he microwave detectors. The examples we have given are illust,rat,ive of the possible applications and are by no means t,he only ones accessible t.o the spect.roscopist. APPENDIX In this Appendix we will derive the formula for the pump frequency up’ at which the two double resonance creepers of a four-level system merge. Autler and Townes (8) have derived expressions for t,he time-dependent wave functions of a t’wo-level syst,em subjected to a st’rong radio frequency field. These wave functions are expressed as a linear combination of the two unperturbed states +, and #b :
*d(t) The Schroedinger
eyuat,ion &
= Ta(Wa
for this system
+ Il!5(t)lC/bf
(,A11
is then
dqadt) ___ = (Ho - p.E cos ~+,t)q~b(f). at
Autler and Tonnes stant coefficient,s
expanded
and solved t)he Schroedinger
T, and Tt, as sunls of exponential
equation
for this system.
terms with con-
RF-MICROWAVE
DOUBLE
461
RESONANCE
If a weak microwave radiation field is applied to the sample along with the pump, the microwave field may be resonant with the energy difference between one of the components of the mixed state qab and a third state #’ so that a microwave photon is absorbed. The intensity of the absorpt,ion will be proportional to 1A, 1’or 1B, 1’with frequency El/h + X, - nnwP , where X, is a quantity defined by Autler and Townes. In this sense, the authors point out, one can speak of a spectrum associated with the mixed states. The four level system can be thought of as a pair of such two-level systems provided the signal radiation is weak and of high enough frequency so that~ perturbation terms involving it may be neglected compared with those due to the radio frequency field. If one considers the case in which the microwave radiation is resonant between a component of the mixed st’ate \k,b and one of Q,d , the mixed &ate derived from t,he second two-level system, the resulting spectrum is the one associated with the four-level double resonance system. From Eq. (16) of Autler and Townes’ paper (8)) the frequencies of the most intense microwave absorptions of this system can be calculat,ed. For example, t.he frequency of a photon resonant with the energy difference bet,ween the components A0 of the lower mixed state and C-1 of the upper state is WI = x, -
Wp .
Xd -
(A4)
In terms of the frequencies and energy levels of Fig. 2, t’his equation the case u”,, < wP < U”,Z,
w1 = [- >$(c& - w,) - y1 - E&l
- &i’( &
becomes
for
- w,) - ~2 - &@I (A3
-
wp =
->i(&
+
$2)
+
(Ed -
&)/‘A
-
where y1 = [(wil - up)‘/4 + I yl 1211’2, I YI I = / pLpl/ Ii’,“/%, similarly defined. From Fig. 2 it is evident thatj (& so
E,)/fi
-
= w:, + w”,, = co”,,+
w:2
~1 + ~2, and ~2 and y2 are
,
(A6)
that Wl =
Rearranging
0 W,? -
which, when substituted
-
into (A7), Wl =
)k(&
Wo,l) -
cd",,=
cd:2 -
71 +
(A71
72.
&,
(ASI
gives +
&1
it can be shown that other photons wz = >i(&
and
-
(A6) , we have 0 up2
Similarly,
!2(&
+ &)
-
r1+
72.
will be absorbed +
Yl -
Ys
C-49)
at (AlO)
WODARCZYK
462
AND
W ILSOX
These are the frequencies of the creepers and main lines in a double signal, valid t,o first order in the quantities 1y j/u, and / y l/q,“. The frequency wPz at which t’he t’wo creepers merge occurs n-hen
resonance
(Al’)‘)
Yl = Ys,
for then Wl = w:! = f/i(& Substitution
of (4), t)he lowest order expression (C& -
qy
( x1:3 1
+ 22).
+ 4 / y1 1” = (cd”,, -
for y, into (AU)
yields
Wpi)? + 4 / yz /?,
(A141
which, when solved for wPi, becomes
The second term in this expression can very often be neglected, wit811 wpl = f&l + &,,
so that we arc left iAl6)
which is just Eq. (6) of Section II. experimentally by measuring The values of w”,, and w”,~ can be det,ermined tin’, wi1, and wi, and solving (As) and either (ills) or (AlB) simultaneously. An expression for wP’ to higher order can be obtained by subst#ituting expressions for the y’s as given by Eq. (7) of Section II int,o (Al?) and solving for wPi. Then this expression, together with (,A8), cm be used to find a”,, and w”,, . ,4CKNOWLEDC:MENTd were carried out in these laboratories by Dr. John Rigden and hy Mr. Carey Rosenthal. The authors would like to t.hank Dr. J. S. Muenter for discussions concerning the development of the radio frequenry techniques described. We would also like to acknowledge the help of Dr. 1~. C;. Ford and Messrs. G. Pisiello and F. Lewandowski in the construct,ion of the RFMDR waveguide cell. We are indebted to Dr. J. Furtkhouser of t,he Arthur 1). Little Company for making available t,he commercial microwave spectrometer used in some of t,he studies.
Prelinlinary
RECEIVED:
experiments on RFMDR
September
15, 1970 REFERENCES
1. A. BITTAOLIA, A. GOZZINI, AND E. POL~CO, Suwo Cirnento 14, 1076 (1959). 2. T. Y.UIM.I AND K. SHIMODA,J. Phys. Sot. Jap. 16,1668 (1960). 3. J. MESSELYN .ZND 1~. WEKTHEIMER, Corn@. Rend. 268, 4473 (1964). 4. A. P. Cox, G. W. FLYNN, .IND E. B. WILSON, JR., J. Chem. Phys. 42, 3094 (1965). 5. B. MXKE, J. MESSELYN, .LNDR. WERTHEIMER, .I. Phys. (Paris) 27, 579 (1966). 6. R. C. WOODS, III, A. M. RONN, AND E. B. WILSON. JIL, Rev. Sci. Zn.strum. 37, 927 (1966). Y. T. OKA, Can. J. Phys. 47, 2343 (1969). 8. S. H. AGTLER ND C. 1%.TOIVNES, Phys. Rev. 100, 703 (1955).
RF-MICROWAVE
DOUBLE
RESONANCE
463
9. K. SHIMODA, J. Phya. Sot. Jap. 14,954 (1959). 10. A. JAVAN, Phys. Rev. 107, 1579 (1957). 11. For this calculation we have used the free-space formula COZO = eovo , where Co is the capacitance per unit length, ZO is t,he characteristic impedance, eo = 8.85 X lo+ f/m, and ~0 G 377 a. We are grateful to Dr. A. E. Sanderson for pointing out this formula t,o us and to Mr. Lang Hedrick for suggesting the use of TDR. fu”. G. W. FLYNN, J. Mol. Speclrosr. 28, 1 (1968). 13. C. H. TONNES .%NDF. R. MERRITT, Phys. Rev. 72, 1266 (1947). 14. R. G. FORD, private communication. 15. J. F. MARTINS AND E. B. WILSON, JR., J. Mol. Spectrosc. 26, 410 (1968). 16. R. G. AZRX, Ph.D. Thesis, Harvard University, Cambridge, Mass., 1969.
Radio
Frequency-Microwave Double Resonance as a Tool in the Analysis of Microwave Spectra’ F. J. WODARCZ~K~ AND E. B. WILSON
Department
of Chemistry,
Harvard
[Jniversity,
Cambridge,
Massachusetts
02138
The pract,ical application of radio frequency-microwave double resonance as a spectroscopic technique in the analysis of microwave spectra has been investigated. Application of a high-power amplitude-modulated radio-frequency field to a gaseous sample in a waveguide cell provides a means of detecting microwave transitions, analogous to the situation in microwavemicrowave double resonance. The sensitivity of the technique compares favorably wit,h that of Stark modulation. Near-symmetric top molecules with allowed K-type doublet transitions are especially amenable to the technique. Accidental near degeneracies of dipole-connected rotational levels in asymmetric top molecules are also useful. A description of a radio frequency-microwave double resonance spectrometer is given together with a discussion of the special problems associated with radio frequency circuits. Applications of the technique are discussed with examples. INTRODUCTION
For several years two-photon absorpt)ion processes have proven to be a useful tool in the analysis of the microwave rotational spectra of polyatomic molecules (1-7). In this double resonance technique, a sample of gas in a waveguide cell is irradiated simultaneously with two radiation fields, one a strong saturating field near resonance between two electric-dipole connected energy levels of the gas, and t,he other a much weaker field with its frequency near another dipoleallowed transition, which is used to monitor the effect of the st)rong perturbation. If the two transitions are chosen to have an energy level in common (Fig. l), the shape of the observed signal is modified in a characteristic manner. Instead of using Stark modulation to det’ect the modified microwave absorption, the modulation is applied to t,he strong (“pump”) radio frequency source as squarewave, on-off modulat’ion. Then no microwave signal frequencies are seen except those sharing an energy level with the pump t,ransition. To dat’e, double resonance work in microwave spectjroscopy has been restricted 1This research was supported in part by a grant extended to Harvard University by the National Science Foundation, GP14012X. 2 National Science Foundation Predoctoral Fellow, 1966-71. 445
WODARCZYK
446
AND
WILSON
--E .
d
0°P2 EC
EQ FIG. 1. Energy-level arrangement of a three-level double resonance system
mostly to the use of pump and signal frequencies in the micro\vave region (MMDR) . Autler and Townes (8) first demonstrated two-photon absorption with one radio frequency and one microwave source. They saturat’ed the radio frequency E-type doublet,, J = 1 transition at 12.73 MHz in OCS and observed the effect on the lineshapes of the J = 2 +- 1 l-type doublet in t,he microwave region. Later Shimoda (9) saturated t,his microwave transition and observed t’he radio frequency transition in bot’h emission and absorption, depending on the microwave transition pumped. It is the purpose of t,his paper to describe the successful application of t,he Autler-Townes technique of radio frequency-microwave double resonance (RFMDR) to asymmetric top spectra. A brief qualitative review of t,he thcoretical considerations will first be presented followed by a descript,ion of the radio frequency-microwave spectrometer used. Finally, examples of applications of the technique will be given, mainly to the assignment of transitions in complex spectra. I. THEORETICAL
CONSIDERATIONS
The theory of double resonance has been discussed by many aut,hors. In t,his section we will present a qualitative picture of the pert#inent effects of a saturating field on the lineshape of a connected signal absorption. A. The Three-Level
System
Three-level double resonance (Fig. 1) involves the simultaneous irradiat,ion of a gas sample with two linearly polarized fields, one a skongly pert,urbing pump field E, = Epo sin W& and the other a weaker signal radiation E, = E,3osin WJ, where Epo >> E,‘. The frequencies of the two radiation fields, wP and (~1~ , are each near resonance with the dipole-allowed transitions at frequencies wi’ and G”,
RF-MICROWAVE
DOUBLE
RESONANCE
447
respectively, which share a common energy level. Javan has worked out a t8heory which explains the signal line shape of the three-level case in terms of the quantity Y==
PP
EPO
(1)
in which p, is the dipole moment matrix element for the transition The effect of the saturating field Ep is to split the signal absorption ponents whose frequencies are
being pumped. into two com-
WI = wso & 6 - y
(?a)
w2 = wso f
6 + y,
(2b)
6 = (w,” -
w,)/2
where we have defined (3)
and y = (2 + 1y /2)1’2.
(4)
Here the choice of the upper or lower sign on 6 depends on the relative order of the energy levels. For convenience the upper sign will be used in this discussion, but analogous arguments hold in eit’her case. When wP is sufficiently far from resonance so that 6’ >> / y 12,then Wl E OS0
(5n)
and w2 e
wso + WPO-
WP
7
(5b)
i.e., one of the components, the “main line,” is close to t,he zero-field frequency, while the other smaller line, the “creeper,” is displaced from resonance about as far as the pump frequency is from it,s resonant frequency, but in the opposibe direction. As wP is brought closer wPo, the creeper increases in size and moves towards the main line, which in turn decreases and moves away from wso until, form a symmetrical doublet. displaced + 1y 1 when wP = wPo,the two components the main line and creeper and -1 y 1 about wso. As wP is swept past resonance, exchange roles, the new main line increasing in size and approaching as” while t,he new creeper decreases and moves away from it. B. The Four-Level System Very often in radio frequency-microwave double resonance, a situation arises in which four energy levels are involved in the double resonance process. For example, consider t.he energy level situat.ion of Fig. 2, in which the transitions indicated by arrows are the only ones allowed. Here w”,, and w”,? are in the radio frequency region, while C& and wi2 are microwave frequencies. Such an arrangement describes the energy level pattern for K-type doublets in near symmetric
44s
WODARCZYK
AND WILSON
A
FIG. 2. Arrangement
of the energy levels in a four-level
EC
double resonance
system
top molecules, or I-type doublets in linear molecules. If the two radio frequent> splittings are not too different in value, so that (w”,, - ~:~)/2a 5 15 MHz, then there is a range of frequencies over which the pump radiation can be considered t.o be near the resonances of bot8h transitions. It should be emphasized here that the 15 MHz upper limit on the frequency difference is purely arbitrary, and intended only to give a rough value below which the four-level phenomenon should be clearly discernible. When wP is very close to resonance with eit,her w”,, or w!& , the three-level sit,uation qualitatively holds, and a creeper and main line straddle both microwave frequencies & and & , since both these transit’ions have energy levels in common with the affected pump t.ransition. The energy levels are so arranged that the two main lines or the two creepers occur “facing each other” in the frequency region between US, and otp. However, when the pump frequency is between the two resonant radio frequencies (u”,, < wP < wi2), a unique situation arises. As wP is swept above the a”,, resonance, the two creepers move towards each other in the region bet.ween t,he zero field absorptions until, at a frequency
the two merge into a single absorption. But as wP is swept above this point and nearer to wit, this single absorption again splits into two creepers, which approach the zero-field positions as wp nears the w”,‘zresonance. This phenomenon is useful for measuring the two resonant radio frequency values in cases in which a direct measurement by three-level techniques is not possible. A more exact formula for wPi at resonance is derived in the Appendix, and the procedure for measuring frequencies using this method is outlined there.
The theoretical considerations presented so far are valid provided 1y l/co, and / y I/w: << 1 and interference terms with frequencies such as wP + OJ~ are not
RF-MICROWAVE
DOUBLE
449
RESONANCE
important. Autler and Townes (8) show that for transitions in the radio frequency region, the interference terms which Javan was able t,o neglect in his derivation of the three level case do become important, since 1y 1, which is typically of the order of 1 MHz, may not be negligible compared with the radio frequency wP . The interference terms modify the expression for y in Eq. (4) so that (7) formula y = / y I. Yet, For wP = w,‘, this expression reduces to the three-level even in this approximation, the interference terms modify t,he intensities of the two components so that the ratio of their intensities at pump resonance is (1 + ] y 1/2~0,‘)~. However, for pump frequencies in the microwave region, 1y 1becomes negligible compared with oP , and the expressions for the frequencies of the components as well as those of the relative intensities reduce to those given by Javan (10). To higher order in the quantity 1y I/u:, Eq. (7) is modified further such that, when wP = w,‘, the components are split by an amount
(8) while the frequency
at which the two components
are equally
intense
becomes
(9) Again,if I Y Ilap’ is reader is referred these points.
negligible, these formulas reduce to those of Javan (10). The to the paper of Autler and Townes (8) for a full discussion of
II. EXPERIMENTAL
In this section we will describe the two experimental arrangements used in t,he RFMDR spectrometer. In both cases the strong radio frequency pump used as the perturbing field is amplitude modulated with a square wave, so that it is “on” for one half of the modulation cycle and “off” for the other half. The effect of the field is monitored with the microwave absorption signal using the usual microwave detectlion system, which involves an amplifier tuned to t,he modulation frequency. In this way, only the effects of the pump radiat,ion on the molecules in the cell are detected, and the unmodulated absorptions of the molecule are not observed. The spectrum is thus cleared of all signals but the ones sought after. A. Arrangement Using cn RFMDR
Waveguide Cell
A convenient way to introduce a radio frequency trometer is to apply it between walls and septum
field into a microwave specof a Stark waveguide cell, a
4.50
WODARCZYK
AND WILSO?rT
met,hod used by Autler and Townes (8) and by Shimoda (9) in their earlier experiments. But there are t’echnical draw-backs with such an arrangement. One difficulty is that voltage variations in the rf field along the Stark septum can arise if the length of the septum from input to end is greater t,han about one quarter of the rf wavelength. Another disadvantage is that. the capacitive reactance presented by the cell decreases lvit,h increasing frequency according to the formula XC = (WC)-l. Since Stark cell capacities are generally in the range 500-1000 pf, at radio frequencies above 50 MHz, e.g., the source works into an impedance of less than 7 CLSince it is difficult to maintain the desired voltages at such low load impedances with most available radio frequency sources, a way has to be fourld around this difficulty. Autler and Townes overcame t.hese difficultIirs by using a cell with a septum whose effective length nas considerably short,er than ;L quarter wavelength of t,he highest, frequency t.hey were to work at. They also included the capacitance of t’he waveguide as part, of a series tuned circuit which, n-hen adjusted to resonat)e at t’he output frequency of their oscillator, increased the impedance of the load by a factor equal t’o the Q of the resonant circuit. Still, the first solution involves a decrease in sensitivit>y of the spectrometer over that obt#ained wit#h a longer cell, while the second has the disadvant,age of recluirin,g tuning at, each radio frequency, making searches with the pump radiation slow and t,edious. We have used an arrangement which overcomes these two difhculties wit.hout sacrificing the convenience of being able to use the waveguide cell for normal Stark spect’roscopy as well as radio frequency-microwave work. A waveguide cell with Stark septum can be t,hought of as a section of unterminated transmission line with characteristic impedance 2” . Use of a cell whose septum is terminated with a pure resist’ive load equal to ZO and matched t.o t#hr rf source by suitable impedance transformers eliminates the standing wave problem, the voltage st,aying constant with frequency wit,hin the specifications of the apparatus and circuits used. Such a cell has been constructed and used successfully for both RF’MDR and normal Stark spectroscopy. Figure 3 shows the schematic diagram of the RFMDR system. The cell consist,s of a 3.3-m copper X-band waveguide into which is insert)ed a copper septum ?4z in. t’hick. The septum is held in the center of the waveguide parallel to the broad face by teflon strips, as in a normal St,ark cell, and it’ is tapered at, both ends to minimize reflections of the microwaves. Hermetically sealed connectors capable of withstanding high voltages are attached to the sept.um at both ends by means of a wire threaded into a small hole tapped into each t,apered edge of the septum, and the wire connection is insulated with t,eflon tubing to prot’ect the system from voltage breakdown in high Stark fields. The flexibility of t#his connection allows for normal creeping of t’he septum as a result of temperature variat,ions and shrinkage of the teflon supporting strips. For normal Stark spectroscopy the square wave generator is connected at, one end of the
RF-MICROWAVE
KLYSTRON POWER SUPPLY
SWEEP _ CIRCUIT
DOUBLE
451
PHASE SENSITIVE DETECTOR
OSCILLOSCOPE.
-
500
RESONANCE
SQUARE WAVE GENERATOR
PREAMPLIFIER
CABLE 20 = 25 n
SEPTUM KLYSTRON
DETECTOR
xFMFl= IMPEDANCE TRANSFORMER
FIG. 3. Schematic trometer.
diagram
of the radio frequency-microwave
double
resonance
spec-
cell while the other end is capped to prevent radiation and possible damage due to inadvertent shorting of the connector. For RFMDR, the rf source is connected at one end, while the other is terminated with a pure resistive load of 25 ohms, corresponding t.o t.he characteristic impedance of the cell. This impedance was estimated from the cell capacitance and lengt’h (11) and confirmed by Time Domain Reflect’ometry. TDR also indicates that reflections in the rf circuit due to the connect.ions t.o the septum are small. The radio frequency generator is a Hewlett-Packard 606B oscillator whose output is amplitude modulat,ed using a HP 10534A double balanced mixer. The modulation is provided by a HP 311A square wave generator synchronized t’o the stable crystal oscillat’or reference circuit of the Stark generator, which circuit also provides the reference signal for t>he phase sensitive det’ector. The amplitudemodulated radio frequency signal from t.he double balanced mixer is amplified by one or two wideband amplifiers (Instruments for Indust#ry, Inc., Model 500, and Spencer-Kennedy Laboratories, Inc. Model 20PD) which are matched to the circuit by toroidal impedance transformers. The impedance transformers used are either commercial (SKL 200-34) or laboratory Would, using ferrite cores which work over the frequency ranges covered by the RF oscillator. Radio frequency fields of t,he order of 3-10 V/cm are used in t,he experiments and are found to be sufficient even for molecules like 1-butene with relatively small dipole moments. In normal operation, the pump frequency remains fixed while the signal klystron is swept. The sweep and detection circuits are the ones used for normal Stark spectroscopy.
WODARCZYK
452
AND
WILSON
IIII~III1IIIII1,I,1IIIII~IIIIIII,,’II,IIIIIY,I
38490
,,,,,,,,,,,,
38480
38470
38460
38450
I,,,,‘,,
38440
l,,,,,,
38430
4,
38420
FIG. 4. Spectra of ethyl formate from the HP 84OOC microwave spectrometer: (a) Stark spectrum of region taken at 50 V, (b) RFMDR spectrum of the same region with pump frequency at 6.5 MHz.
B. Arrangement
Using a Convewtional Waveguide
Cell
Very often it is possible to use a conventional, single connector Stark cell for RFMDR work. In such a case, the following conditions should be fulfilled: (1) the radio frequencies used are of sufficiently long wavelength that, voltage variations along the length of the cell are not critical, and (2 j the impedance that the cell presents to the source does not overtax its current-delivering capabilities.
RF-MICROWAVE
DOUBLE
RESONANCE
453
These conditions are satisfied fairly often, and much work has been done in our laboratory wit.h unterminated waveguide cells. In this case, the experimental arrangement is similar to the one described above except that the cell is not t,erminabed and matching transformers are not used at the cell connection. RIWDR experiment’s have also been successfully conducted using a commercial Hewlett-Packard 8400C microwave spectrometer. In this case, t’he amplitude modulation voltage is supplied by an S-V square wave from the calibration output of the Stark modulator. This square wave is imposed on the radio frequency through t,he external modulat,ion capability of the 606B oscillat.or, and t,he resulting amplitude-modulated rf is amplified and t,hen applied t’o the two Stark septa by means of a tee adapter. The phase adjustment of t,he phase sensitive detector is optimized on a known double resonance signal. Figure 4 shows examples of both Stark and double resonance spectra taken on t’his instrument. Notice that the RFllIDR spectrum is virt’ually free of the interfering lines which occur even at, the 50 volt St,ark modulation used in making the Stark spectrum. Since the radio frequency field is fully amplitude modulated, so that it is “on” and ‘r~ff” in opposite halves of t,he modulation cycle, the double resonance signal has one polarity and the zero-field absorption the opposit,e polarity. C. Intemity
Considerations
In our experimental arrangement the radio frequency field is applied parallel to the polarization of the microwave radiation, so that only the rotational states with the same projection quantum number M are connected. Thus, for a Por R-branch transition, all the 2J + 1 111 components are affected by the radiation field, while for a Q-branch, only 2J components are affected, the M = 0 component having zero transition moment. If the radio frequency transition being pumped is a Q-branch (as with K-type or Z-type doublet,s) and the observing transition is also a Q-branch, then a fully modulated RFMDR zero-field signal is the same size as the fully modulated Stark signal. If, however, the signal absorption is an R-branch transition, a fully modulated RFMDR signal is decreased from the size of the Stark signal by a factor of l-3( J + l)/ (2J + 1)(2J + 3), w h ere J is the rotational quantum number for the transition J + 1 t J, The reader is referred to the paper by Flynn (12) for a more complete discussion of the intensity of double resonance signals. Anot,her important intensity consideration is the range of pump frequencies over which a double resonance signal should be noticeable. Figure 5 shows a plot of the normalized single-double resonance intensity difference (10 - 1,)/I, versus distance from pump resonance, vpo - vp , where I, is the intensity of the zero-field signal at the peak maximum, and Ip is the intensity of the double resonance signal at the same frequency. This plot gives an indication of the strength of the signal seen at the zero-field maximum in the double resonance detection scheme. The calculations were made on an IBM 1620 computer using the Javan
WODARCZYK
454
AND WILSON
1.00
!
0.90I-
0.6C I-Y \ ;i 0.5C
0.40
0.30
0.20
0.10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -I
0
I
VgVp(MHz)
FIG. 5. Plot (I0 - Z,)/IO at vrnaxVS. symbols are defined in the text.
(v," -
v,,)
2
3
4
5
6
7
8
I
910
for a typical double resonance signal. The
formulas (10) for net power absorbed by the signal transition in a double resonance. The relaxation time was taken as lo-” set, the pump field was 3.75 V/cm, and the matrix element used was that for the J = 1 I-t’ype doublet transition at 12.78 MHz in OCS. These conditions are fairly represent’ative of t,hose encountered in RFMDR. Examination of t.he plot indicat,es t.hat a double resonance signal should be discernible from a few MHz off resonance for even weak signal absorptions. This fact is somet’imes useful in applicat’ions of double resonance. Since tdle response breadth of the radio frequency resonance is considerably more than the pressure-broadened line width, even at very low pressures, we would expect to obt,ain the Doppler width characteristic of the microwave, rather than the radio frequency.
RF-MICROWAVE
DOUBLE
RESONANCE
4.55
In order to see an appreciable change in line shape with the double resonance technique, the pumping radiation must be a strong perturbation on the system. However, care must be exercised that the amplitude of t,he radiation field is not SO large as t’o cause Stark modulation of the signal absorptions. Ton-nes and Merritt (13) have studied the effect of rapidly varying electric fields on microwave transitions, and their results for fields oscillat,ing at, frequencies greater t,han or equal t’o the half-width of a transition are applicable here. If a high frequency electric field is applied t,o a sample, lines which exhibit second order Stark effecbs are shifted to frequency I/~+ Av/~ and are accompanied by satellites at vo + Av/2 f YZV~ with relat,ive intensity J,‘( Av/vp), where Av is t,he second-order Stark shift due to a DC field of the same amplitude and J,( Av/vp) is t,he Bessel function of order ‘~1.First, order lines, on the other hand, are unshifted as a result of the field, but. they have satellit#es spaced every 3v, with relative intensities Jn2( Av/4v,), where Av is the first-order Stark shift expected from the corresponding dc field. It, is thus apparent) t,hat) if the elect’ric field, and hence, Av, is too large, the intensky of the satellites or t,he shift of the second-order lines may be appreciable enough to modulate transitions which are nonresonant w-it’ll the oscillating field. In doubtful cases, the behavior of creepers as a fun&ion of frequency should be enough t,o dist,inguish double resonance signals from Stark-modulat’ed lines. III.
APPLICATIONS
Asymmetric top molecules in general offer t,wo sources for radio frequency transitions: K-type doublet splittings and accidental near degeneracies. The former are plentiful in near symmetric top molecules with nonzero p, dipole moment’ components for near-prolate rotors or kc for near-oblat’e tops. While t’he latter are not so common, they are very useful if the suitable dipole-connected transitions esist . The same active near-degenerate pair of levels required for RP,1IDR will also normally produce a strong, near first-order Stark effect for t,he linked microwave transition. Consequently, candidate microwave lines which might show up with RFAIDR will always be limited to those which appear on Stark modulation at low modulation voltages. Such lines can be tested one by onr. 1lany of t,he benefits accruing to MXIDR as a specbroscopic tool also characterize RFAIDR. A fern examples will illustrate some of the usefulness of t)he technique. ( 1) As shown by Autler and Tonnes, (8) the resonant values of radio frequency transitions can be measured to give an addit’ional piece of information for analysis. This can be accomplished most easily by measuring the radio fre-
WODARCZYK
456
a
AND WILSON
b
w
d FIG. 6. An example of four-level double resonance in the skew 1-butene 42-32 K-type doublets. Here v”,, = 2.04 MHz and Y”,, = 6.10 MHZ. (u) yP = 3.00 MHz, (b) yP = 4.05 MHz, (c) yP = 4.50 MHz, (d) yP = 6.00 MHz.
quency
at which the two double resonance components of a microwave transition are equally intense. It is easily seen from Fig. 5 that t,he ot’her alternat,ive, finding the point, at, which the modulated signal is most, intense, is less certain. If the effect on the intensities of the quantity y/wP ’ is expected to have a measurable components at resonance, Eq. (9) can be used t,o find wPousing an extrapolation procedure as described by Autler and Tonnes (8). The four-level case, which arises often wit>h K-type doublet spectra, provides another means by which resonant frequencies can be measured. As discussed in Section I, there is a pump frequency, wPi at which the two innermost components of t,wo adjacent, microwave double resonance signals merge into a single absorption (Fig, 6b). By measuring this frequency, one can calculate w”,, and w”,, by using Eq. (6) or (A15) derived in the Appendix. The errors in t’he frequencies thus calculated are only slightly larger than those for normal microwave frequency measurements. (2) RFMDR can be used to measure the zero-field frequencies of micro\\-ave transitions. Many times these frequencies cannot be measured accuratel\with
RF-MICROWAVE
DOUBLE
RESONANCE
457
G” 2,110
Illlllllllllll
2,740
IIlI 21150
f1lJI1I*
21760
IIII’l(II
21710
IIII”I/I21780
FIG. 7. A portion of the RFMDR spectrum of I-pentyne, truns 524-423(I) and 5z3-422(II) transitions. The 422-423rf transition is pumped. The labels indicate the different st,ates that these absorptions may be attributed to: G = ground state, T = first excited C-C torsion, M = first excited methyl torsion, B = first excited C=C-C bending motion. The vibrational assignment of the other absorptions in the spectrum has not yet) been made.
Stark modulation because of a badly zero-based square wave, overlapping lines, or doubt as to the identities of several equally likely candidates. With pump frequency on resonance, the double resonance component,s are essentially equally displaced about the zero-field signal, and the frequency of t)he signal transition can be measured. (3) One of the main uses of double resonance is as an aid in searching for specific transitions or in identifying certain observed microwave transitions. Where both the radio frequency and microwave transitions with a common level are known only approximately, a two-dimensional search may be necessary. In certain cases, however, the radio frequency transit,ion may be sufIicient,ly wellknown (considering the breadth of the response curve shown in Fig. 5) so that only the microwave transitsion needs to be searched for. An example is the locat,ion of high-J transitions, which may be considerably shifted from their predicted rigid rot,or values because of centrifugal distortion. The connect8ed radio frequency transition may be so little shifted in absolute value that the radio frequency may be set on the rigid rotor predicted value. In cis-propionaldehyde, t’he 176,12-167,9 and 176,11-167,10transitions were found 110 and 114 MHz off rigid rotor prediction by pumping the 16 1,9-167,10transit’ion, which was only 0.9 MHz from its rigid rotor value. Other high-J transitions were found in the same manner, and all of them fit a semirigid rotor calculation incorporating centrifugal distortion terms. A similar and very powerful use is for assigning vibrationally excited state transitions. The frequencies of the radio frequency transitions oft,en change by only a fraction of MHz wit,h each step of vibrational excitation. Hence, t#he radio frequency can be fixed at the frequency appropriate for the ground state and the microwave frequency varied to find a whole sequence of vibrationally excited transit,ions. Figure 7 shows a portion of the spectjrum of 1-pentyne, in which
458
WODARCZYK
III1
29145
6
AND WILSON
III
7 8 9 50 1 2 3
IIII
4
5 6 7 29158
V(MHz)
FIG. 8. RFMDR signals of 1-pentyne. The larger line is the gauche 532-431transition in the ground state, while the smaller is an excited state gauche 533-432transition. The 432-431transition (v,o = 7.79 MHz in the ground state, 7.94 MHz in the excited state) is pumped at 6.50 MHz.
only the ground and several excited state signals of the 524-$a and 5.~42~ transitions of the tram rotamer are seen. The other lines in t’he region are not modulated, and hence, are not, detected. In this case the pump was kept near resonance with the ground state 4.~423 transition, and absorption signals were recorded up to the fourth torsionally excited state, 119 MHz from the ground state lines. In t’his way, the method provides a means of unambiguously determining weak excited state absorptions in the dense spectra associated with relatively heavy molecules. Even though such a double resonance spectrum is cleared of interfering lines, a question may still exist, as to which of t,wo possible transitions showing double resonance signals (such as K-doublets) a given excit,ed st,at#e should be assigned. This question cm often be answered by taking advantage of the fact, that the creepers and main lines can form distinctive patterns which will be mirror images in the case of four-level systems. Figure S shows two absorptions in 1-pentyne. The larger line is t,he ground state, gauche 532-431 transition. The smaller line, however, is an excited state of t)he other K-doublet transition, the qauch.e &-432 resonance, as it,s mirror-image appearance indicat)es. In applications like t,his, however, one should be cert#ain t)hat the radio frequency pump is below or above the resonant frequencies simultaneously. (4) In 2 ,2-difluorosilacyclobutane (14) the first excited state of t#he ring
RF-MICROWAVE
DOUBLE
RESONANCE
459
puckering vibration is close enough to the ground state that some rotational energy levels of both states are perturbed strongly. RFMDR was useful in assigning transitions which had been shifted from their rigid rotor predictions. For example, the 523-422and 533-432transitions of t.he 2) = 1 stat.e were shifted 92 and 263 MHz, respectively, from the predicted frequencies, and both occurred wit’hin four MHz of each other. The proper assignment was immediately confirmed when the 533-432 showed a double resonance signal with the pumped 431-432radio frequency transition. (5) Martins and Wilson (15) have used the magnitude of the XIMDR splitting to measure the dipole moment of xenon oxytetrafluoride. In the same vein, Azrak (16) has suggested that the failure to observe an RFMDR signal in the 329-3110 transitions of 2-chloroethanol when the K-type doublet 3110.~1-3110.22 was pumped at 3.8 MHz gives an upper limit to the value of jam, the dipole moment component responsible for the radio frequency transition. In his work, he calibrated the rf field by pumping a b-type accidental near degeneracy, the 413-322 at 4 MHz, and observed the double resonance of the connected 3~~3~~ microwave transition. (6) The various M components of a transition have different transition moments, and, hence, different values of 1y (. Thus, it is theoretically possible to resolve the different M components of a double resonance signal (la), since the frequencies of the various components depend on 1 y 1. Oka (7) has resolved the JJ! fine structure of an ethylene oxide transition in high power MMDR studies. Figure 9 shows the M components in an RFMDR signal of ethyl acetylene. This
1 /MI=2 ’
2
FIG. 9. M-component fine structure in a low-pressure RFMDR scan of the ethyl acetylene 3z1-220 microwave transition. The 11741 = 1 and 2 components are resolved. The 2~2~ transition was pumped at 7.50 MHz.
460
WODARCZYK
AND
WILSON
experiment was carried out at low pressure and the normal rf saturating field strength used in the other studies. For this trace, the 220-221transition was pumped at 7.50 MHz while the 321-220microwave signal was observed. The j M / = 1 and 2 components can be seen in the double resonance signals, as expected for a Q-branch pump, R-branch signal combination. Similarly, three components have been resolved in the 423-322 and 422-321 microwave transitions of this molecule when the 321-322t’ransition was pumped at 34.68 MHz. This result suggests t(hat such a resolution of component8s might provide an added piece of information t)o help in assigning the spectrum of a molecule. CONCLUDING
REMARKS
We have at,tempt.ed to show the usefulness of radio frequency-microwave double resonance in a variet.y of applicat.ions. Although t,here are limitations on the transitions in the microwave region which are connected to nearly degenerate levels, most near-symmetric top molecules offer a number of radio frequency transitions which are useful for double resonance applications. The experimemal arrangement involved is simpler and less costly than that of the corresponding microwave-microwave double resonance spectrometer, and there are no difficulties wit,h the pump radiation affecting t’he microwave detectors. The examples we have given are illust,rat,ive of the possible applications and are by no means t,he only ones accessible t.o the spect.roscopist. APPENDIX In this Appendix we will derive the formula for the pump frequency up’ at which the two double resonance creepers of a four-level system merge. Autler and Townes (8) have derived expressions for t,he time-dependent wave functions of a t’wo-level syst,em subjected to a st’rong radio frequency field. These wave functions are expressed as a linear combination of the two unperturbed states +, and #b :
*d(t) The Schroedinger
eyuat,ion &
= Ta(Wa
for this system
+ Il!5(t)lC/bf
(,A11
is then
dqadt) ___ = (Ho - p.E cos ~+,t)q~b(f). at
Autler and Tonnes stant coefficient,s
expanded
and solved t)he Schroedinger
T, and Tt, as sunls of exponential
equation
for this system.
terms with con-
RF-MICROWAVE
DOUBLE
461
RESONANCE
If a weak microwave radiation field is applied to the sample along with the pump, the microwave field may be resonant with the energy difference between one of the components of the mixed state qab and a third state #’ so that a microwave photon is absorbed. The intensity of the absorpt,ion will be proportional to 1A, 1’or 1B, 1’with frequency El/h + X, - nnwP , where X, is a quantity defined by Autler and Townes. In this sense, the authors point out, one can speak of a spectrum associated with the mixed states. The four level system can be thought of as a pair of such two-level systems provided the signal radiation is weak and of high enough frequency so that~ perturbation terms involving it may be neglected compared with those due to the radio frequency field. If one considers the case in which the microwave radiation is resonant between a component of the mixed st’ate \k,b and one of Q,d , the mixed &ate derived from t,he second two-level system, the resulting spectrum is the one associated with the four-level double resonance system. From Eq. (16) of Autler and Townes’ paper (8)) the frequencies of the most intense microwave absorptions of this system can be calculat,ed. For example, t.he frequency of a photon resonant with the energy difference bet,ween the components A0 of the lower mixed state and C-1 of the upper state is WI = x, -
Wp .
Xd -
(A4)
In terms of the frequencies and energy levels of Fig. 2, t’his equation the case u”,, < wP < U”,Z,
w1 = [- >$(c& - w,) - y1 - E&l
- &i’( &
becomes
for
- w,) - ~2 - &@I (A3
-
wp =
->i(&
+
$2)
+
(Ed -
&)/‘A
-
where y1 = [(wil - up)‘/4 + I yl 1211’2, I YI I = / pLpl/ Ii’,“/%, similarly defined. From Fig. 2 it is evident thatj (& so
E,)/fi
-
= w:, + w”,, = co”,,+
w:2
~1 + ~2, and ~2 and y2 are
,
(A6)
that Wl =
Rearranging
0 W,? -
which, when substituted
-
into (A7), Wl =
)k(&
Wo,l) -
cd",,=
cd:2 -
71 +
(A71
72.
&,
(ASI
gives +
&1
it can be shown that other photons wz = >i(&
and
-
(A6) , we have 0 up2
Similarly,
!2(&
+ &)
-
r1+
72.
will be absorbed +
Yl -
Ys
C-49)
at (AlO)
WODARCZYK
462
AND
W ILSOX
These are the frequencies of the creepers and main lines in a double signal, valid t,o first order in the quantities 1y j/u, and / y l/q,“. The frequency wPz at which t’he t’wo creepers merge occurs n-hen
resonance
(Al’)‘)
Yl = Ys,
for then Wl = w:! = f/i(& Substitution
of (4), t)he lowest order expression (C& -
qy
( x1:3 1
+ 22).
+ 4 / y1 1” = (cd”,, -
for y, into (AU)
yields
Wpi)? + 4 / yz /?,
(A141
which, when solved for wPi, becomes
The second term in this expression can very often be neglected, wit811 wpl = f&l + &,,
so that we arc left iAl6)
which is just Eq. (6) of Section II. experimentally by measuring The values of w”,, and w”,~ can be det,ermined tin’, wi1, and wi, and solving (As) and either (ills) or (AlB) simultaneously. An expression for wP’ to higher order can be obtained by subst#ituting expressions for the y’s as given by Eq. (7) of Section II int,o (Al?) and solving for wPi. Then this expression, together with (,A8), cm be used to find a”,, and w”,, . ,4CKNOWLEDC:MENTd were carried out in these laboratories by Dr. John Rigden and hy Mr. Carey Rosenthal. The authors would like to t.hank Dr. J. S. Muenter for discussions concerning the development of the radio frequenry techniques described. We would also like to acknowledge the help of Dr. 1~. C;. Ford and Messrs. G. Pisiello and F. Lewandowski in the construct,ion of the RFMDR waveguide cell. We are indebted to Dr. J. Furtkhouser of t,he Arthur 1). Little Company for making available t,he commercial microwave spectrometer used in some of t,he studies.
Prelinlinary
RECEIVED:
experiments on RFMDR
September
15, 1970 REFERENCES
1. A. BITTAOLIA, A. GOZZINI, AND E. POL~CO, Suwo Cirnento 14, 1076 (1959). 2. T. Y.UIM.I AND K. SHIMODA,J. Phys. Sot. Jap. 16,1668 (1960). 3. J. MESSELYN .ZND 1~. WEKTHEIMER, Corn@. Rend. 268, 4473 (1964). 4. A. P. Cox, G. W. FLYNN, .IND E. B. WILSON, JR., J. Chem. Phys. 42, 3094 (1965). 5. B. MXKE, J. MESSELYN, .LNDR. WERTHEIMER, .I. Phys. (Paris) 27, 579 (1966). 6. R. C. WOODS, III, A. M. RONN, AND E. B. WILSON. JIL, Rev. Sci. Zn.strum. 37, 927 (1966). Y. T. OKA, Can. J. Phys. 47, 2343 (1969). 8. S. H. AGTLER ND C. 1%.TOIVNES, Phys. Rev. 100, 703 (1955).
RF-MICROWAVE
DOUBLE
RESONANCE
463
9. K. SHIMODA, J. Phya. Sot. Jap. 14,954 (1959). 10. A. JAVAN, Phys. Rev. 107, 1579 (1957). 11. For this calculation we have used the free-space formula COZO = eovo , where Co is the capacitance per unit length, ZO is t,he characteristic impedance, eo = 8.85 X lo+ f/m, and ~0 G 377 a. We are grateful to Dr. A. E. Sanderson for pointing out this formula t,o us and to Mr. Lang Hedrick for suggesting the use of TDR. fu”. G. W. FLYNN, J. Mol. Speclrosr. 28, 1 (1968). 13. C. H. TONNES .%NDF. R. MERRITT, Phys. Rev. 72, 1266 (1947). 14. R. G. FORD, private communication. 15. J. F. MARTINS AND E. B. WILSON, JR., J. Mol. Spectrosc. 26, 410 (1968). 16. R. G. AZRX, Ph.D. Thesis, Harvard University, Cambridge, Mass., 1969.