Two-dimensional correlation experiments in microwave Fourier transform spectroscopy

Volume 144, number 2

CHEMICAL PHYSICS LETTERS

19 February 1988

TWO-DIMENSIONAL CORRELATION EXPERIMENTS IN MICROWAVEFOURIER TRANSFORM SPECTROSCOPY B. VOGELSANGER, M. ANDRIST and A. BAUDER Laboratoriumfir Physikalische Chemie, Eidgeniissische Technische Hochschule, CH-8092 Zurich, Switzerland Received 28 October 1987; in final form 7 December 1987

Two-dimensional (2D) correlation techniques were applied to microwave Fourier transform (MWFT) spectroscopy. A threepulse sequence supplied with a phase cycle acting as a double-quantum filter as well as a two-pulse “CO%” sequence were found to be useful for the correlation of connectivities between rotational transitions. Experiments were performed on l-chloro-l-fluoroethene in order to show common energy levels within the 35C1hypertine structure. The relationship to similar NMR techniques is also discussed.

1. Introduction Pulsed microwave Fourier transform (MWFT) spectroscopy is a powerful method for the observation of pure rotational spectra. The improved sensitivity, compared to conventional microwave spectrometers, enables molecules with very small dipole moments to be investigated [ l-31, whereas the higher resolution means that the small splitting of rotational transitions, arising from internal motions [ 41 or from quadrupolar nuclei [ 51, can be resolved. However, whereas in conventional microwave spectroscopy additional information is obtained from Stark or double-resonance effects, which are used as modulation techniques, no such information is available in the standard MWFT experiment. This renders the assignment of the observed MWFT spectra more difficult. Often the correct assignment can only be confirmed by the inner consistency of a large set of measured transition frequencies. Although some MWFT double-resonance experiments have been suggested [ 6-81, only recently have such experiments been applied to assign MWFT spectra [9-l 1] with the help of continuous microwave or radiofrequency pump radiation. The development of additional pulsed double-resonance techniques can be of great help in utilizing the full power of MWFI spectroscopy. In NMR spectroscopy a large variety of two-di180

mensional (2D) experiments have been developed in order to simplify spectra (2D separation of interactions), to correlate transitions of coupled spins (2D correlation spectroscopy) and to study dynamic processes (2D exchange spectroscopy) [ 12,131. Recently such techniques have been transferred to other fields of pulsed Fourier spectroscopy as well. Both 2D correlation and 2D exchange electron spin resonance (ESR) spectra have been reported [ 14,15 1, and in ion cyclotron resonance (ICR) 2D exchange experiments have been carried out [ 161. It was shown that 2D correlation techniques also work in MWFf spectroscopy. Andrews et al. [ If] used continuous microwave signal radiation and applied two pump pulses with a variable delay between them. Stahl et al. [ 81 performed a purely pulsed experiment where the two pump pulses followed an initial signal pulse. In both experiments only a onedimensional Fourier transform was applied to the measured time domain signals. Information from the second dimension, i.e. the pump transition frequency, was calculated from the oscillating signal transition intensity obtained by plotting the observed intensities as a function of the delay between the two pump pulses. These two experiments are similar to heteronuclear correlation spectra in NMR, which explores the connectivities between transitions with significantly differing frequencies [ 12,13,18].

0 009-26 14/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

Volume 144. number 2

CHEMICAL PHYSICS LETTERS

In the present work, the three-pulse MWFT correlation experiment was applied to 1-chloro- 1-flueroethene in order to mark common energy levels within the hyperfine multiplet arising from the 3sCl nucleus. In this way the hyperfine components of the rotational transitions J( K,, &) = 2( 1,2) +- 1( 1,l) and l(l)1 ) t-0( 0,O) were correlated in a 2D spectrum. A O/l 80” phase cycle acting as a multiple-quantum filter helped to simplify the spectra. We also report on the first autocorrelation 2D experiment in MWFT spectroscopy which, in contrast to the experiment above, explores connectivities between close-lying transitions. The two-pulse sequence correlated the components within the hypertine structure of a single rotational transition. The experiment is equivalent to the NMR homonuclear correlation experiment (“COSY”) first described by Jeener [ 13,191.

2. Experimental A commercial sample of 1-chloro- l-fluoroethene (Fluorochem Ltd.) was used for all measurements without further purification. The rotational spectrum of this compound was reported in ref. [20]. For all experiments, an Ekkers-Flygare-type MWFT spectrometer [ 2 1] working in the 8- 18 GHz range was used. The 6 m long waveguide sample cell contained the sample gas at a pressure of 1.3 Pa (10 mTorr) and a temperature of - 70°C. Pump and signal radiation were generated by phase-stabilized microwave tubes. Microwave pulses of 10 to 80 ns duration were produced by fast PIN-diode switches, driven by a home-built memory type sequence generator. This unit is equipped with seven individual programmable sequence channels, each of which contains a 4k x 16 bit memory. A resolution of 10 ns in generating pulses was reached by a serial memory readout at a rate of 100 MHz. As described in detail later, some pulses were phase alternated by a O/180 ’ biphase modulator in coherence with the addition or subtraction of the detected signal. Both signal and pump radiation were combined by a coaxial power combiner. After amplification by a travelling-wave tube amplifier up to 10 W, the pulses entered the sample cell. The sensitive detection system was protected by two PIN switches, which were closed dur-

19 February 1988

ing the pulses. After each sequence, the weak transient signals emitted by the sample molecules were down converted with a superheterodyne detection scheme in two steps to frequencies between 0 and 50 MHz. These emission signals, corresponding to the time domain tz, were then digitized with a 3-bit A/D converter at a rate of 100 MHz for 5 12 channels. Each individual pulse sequence was repeated 1O6times at a rate of 50 kHz in order to improve the signal-tonoise ratio. The signals were accumulated digitally in a 16-bit 5 12 channel averager and were then stored in a LSI-1 l/73 data processor. The above procedure was repeated 256 times incrementing the evolution time t, in ‘10 ns steps. In the two-pulse autocorrelation spectra only one frequency is needed. For these experiments the pump radiation system up to the power combiner was removed. Finally, 256~ 512 data points were collected and transferred to a VAX 750 minicomputer and processed using adjusted FTNMR-software. After a real Fourier transform along t2 the resulting complex data were treated by a complex Fourier transform along t,, followed by calculation of the magnitude spectra. Thus a 2D frequency domain MWFT spectrum with 50 MHz bandwidth in both dimensions was obtained containing 128 x 256 points.

3. 2D double-quantum correlation spectroscopy Generally 2D experiments can be divided into four consecutive intervals, denoted the preparation, evolution, mixing and detection periods. The features of the experiment are explained assuming a threelevel system a-b-c, corresponding to the J(K,,K,)=O(O,O)-l(l,l)-2(1,2) energylevelsin lchloro- 1-fluoroethene, neglecting the hyperfine structure (cf. fig. 1). For the three-pulse sequence of fig. 2a the preparation period covers the first two pulses. The initial signal pulse of frequency w$, acts on the system in thermal equilibrium and generates a single-quantum coherence &&,b.If there is a common energy level between signal and pump transition, the following pump pulse of frequency og, transfers the coherence c&b into double-quantum coherence w,,. During the evolution period t, the double-quantum coherence experiences free precession 181

Volume 144, number 2

CHEMICAL PHYSICS LETTERS F

J (Ka,K,)

112 2(1,2)

iv

v

vi

I

712 312

1

512

vii

312

512 I/2 i

iii

ii

312

WW)

Fig. 1. Energy level diagram of 1-chloro-1-fluoroethene. All three hypertine components of the l(l,l) +O(O,O) as well as the four components of the 2( 1,2) + 1 (1 , 1) rotational transition which appear in the range of our 2D spectra are marked.

with the sum of the off-resonance frequencies of signal and pump transition Aw,=ACQ,+AO~~ (in a rotating frame). This means that the phase of the double-quantum coherence rotates with frequency Ao,, which determines the frequencies in the co, domain. The second pump pulse (mixing period) transfers the double-quantum coherence back into observable single-quantum coherence m&. Since this transfer depends directly on the phase of the double-

signal

I I phase:

a b

O!Y1800 00

0’

OYi800

t1

I

t2

00

add/sub

0”

add/sub

+

Fig. 2. Pulse sequence for the 2D double-quantum correlation experiment. Two different phase cycles were used: (a) Phase inversion of the signal pulse only in coherence with addition or subtraction of the transient decay. (b) The phase of the signal pulse remained constant, but the relative phases between the two pump pulses alternated by O/180’ in coherence with transient signal addition or subtraction.

182

19 February 1988

quantum coherence at the end of the evolution period, incrementation of tl leads to modulation of the back-transferred single-quantum coherence. Only the co&,coherence is monitored during the detection period t2. A theoretical description of the experiment for the Special case A.o,=O is given in ref. [ 81. A 2D spectrum of 1-chloro-l-fluoroethene with J(K,,Irz)=l(l,l)tO(O,O) signaland2(1,2)+1(1,1) pump transitions is pictured in figs. 3a and 3c. The frequencies of the transitions in w2 can be derived directly from the standard ID spectrum, whereas along o, they correspond to the double-quantum frequencies Aw,,. Therefore, all off-diagonal peaks can be correlated to the corresponding signal and pump transitions by a simple geometrical treatment. These peaks arise from double-quantum coherence during t, and prove connectivities. On the other hand diagonal peaks correspond to single-quantum coherence during t,, due to incomplete transfer of the coherence o&b into coherence oat by the first pump pulse. Because the desired double-quantum pathway cannot be optimized simultaneously for all pump transitions, the signals in the diagonal usually dominate such 2D spectra. However the diagonal peaks can be suppressed by a suitable phase cycle. Instead of cycling the signal pulse (fig. 2a) which only reduces instrumental artefacts, the sequence of fig. 2b inverts the relative phases between the two pump pulses and is combined with addition or subtraction of the detected signal. In this way only signals affected by the pump pulses are accumulated and other unwanted signals are suppressed. The effect of this phase cycle is demonstrated in figs. 3b and 3d, where the diagonal peaks almost disappear in contrast to figs. 3a and 3c. Such phase-cycling procedures which select certain coherence transfer pathways (“multiple-quantum filter”) are well known in NMR [ 22,231, but to our knowledge have not been applied before in MWFT experiments. The spectra in fig. 3 show three double-resonance connections. Only a frequency range of about 15 MHz could be excited by the pump radiation. Further connections within the J(K,, K,) = 2( 1,2) c 1 ( 1,l) e0 (0,O) hyperfine multiplets of 1-chloro- lfluoroethene were found by recording spectra with different pump frequencies.

Volume 144, number 2

19 February 1988

CHEMICAL PHYSICS LETTERS

A,_ 03

I

, I

14153 MHz

I

I

b

Wl 2Tc

.

w,/2lT

-25

-25

MHz

-25

l25

MHz

Fig. 3. 2D double-quantum correlation spectra of I-chloro-1-fluoroethene. Signal pulses of 30 ns duration with a frequency of 14128 MHz and pump pulses of 80 ns duration with a frequency of 15445 MHz were used. Additional information on experimental conditions is given in the text. (a) The contour plot resulting from the phase cycle of fig. 2a. (b) The contour plot obtained for the phase cycle of fig. 2b, which acted as a doublequantum filter. In both 2D spectra w2 corresponds to the signal transition w,,, and w, to the doublequantum coherence ale. Constant pump transition frequencies obe are located on parallels to the diagonal, displaced by the off-resonance frequencies Ao, from the center of the 2D spectrum (Aw~~=Ao~=Aw~,=O). Cross peaks within these spectra indicate double resonance connections. Three connections are marked which correlate the hyperfine components ii and iii of the signal transition 1(1 , 1)-0(0,O) with v, vi and vii of the pump transition 2( 1,2)-l (1,l) sharing a common energy level. The standard 1D MWFT spectra of signal (o.,,) and pump (w,J transitions are also depicted. Connectivities are obtained by crossing the columns of the signal transitions w,,, with parallels to the diagonal corresponding to the pump transitions wbe (c) Stacked plot of (a). (d) Stacked plot of(b).

4.2D autocorrelation spectroscopy

In contrast to the above double-quantum coher-

ence transfer experiment, the “COW’ two-pulse sequence of fig. 4 correlates singlequantum transitions in both dimensions. In this experiment only a single 183

Volume 144, number 2

CHEMICAL PHYSICS LETTERS

19 February 1988

add/sub

phase: OASO” A

Fig. 4. Pulse sequence for the ZDautocorrelation experiment. Only the first of the two pulses with equal frequency is phase modulated by O/180” in coherence with the addition or subtraction of the detected signal.

microwave frequency is used. The first pulse (preparation period) generates single-quantum coherences in a range covered by the excitation bandwidth of the pulse. The coherence5 precess with their offresonance frequencies during the evolution period t,. After the mixing pulse, the signal is detected during t2. The final calculated 2D spectrum contains three kinds of signals corresponding to different behaviour during the mixing period: (a) The mixing pulse leaves coherences unchanged or only alters their phases. In this case the precession frequencies are equal during t, and t2 and the signals appear in the diagonal w1=02. (b) If two transitions are connected by a common energy level the mixing pulse can interchange the coherences of the two transitions. Thus, coherence which precessed during tl with the off-resonance frequency of one of these two connected transitions rotates during t2 with the off-resonance frequency of the other one, and vice versa. This leads to cross peaks which are located at the cross points of the two frequencies. Diagonal and cross peaks belonging to connected transitions represent the edges of a square in the 2D spectrum. (c) Axial peaks along o I = 0 appear because the mixing pulse also creates new polarisation from remaining population differences during tl. These signals dominated our first autocorrelation spectra, but could be suppressed by phase cycling the preparation pulse alone (cf. fig. 4). A 2D autocorrelation spectrum of l-chloro- 1-fluoroethene containing the J( K,, KC)= 2( 1,2) t 1(1 ,0) transition is depicted in fig. 5. The connectivities of the hyperfine components iv and v as well as vi and vii are indicated by the corresponding cross peaks. The other cross peaks for the connected transitions iv and vi, which are not present in this spectrum, could be found under different experimental con184

I

1

,

3

,

.

I

15418

w*/2Tc

3

I

I

,

15468 MHZ

Fig. 5. Contour plot of a 2D autocorrelation spectrum of l-chloro1-fluoroethene. Two connections within the hyperfine multiplet of the rotational transition 2 (I ,2) c 1(1,1)are indicated by cross peaks. For details see text. The spectrum was recorded using the pulse sequence of tig. 4 with a signal frequency of 15443 MHz and pulse durations of 50 ns.

ditions. In addition to the peaks which are symmetrical to the main diagonal, signals symmetrical to the anti-diagonal also appeared in our spectra. This effect is well known in NMR experiments [ 221, and the two classes arising from mirror image pathways are called “P-type” and “N-type” signals, respectively. However, time proportional phase incrementation or placing the carrier outside the spectrum would disentangle the pathways giving rise to the two types of peaks [22]. We found that in our experiment P- and N-type signals were folded together when the heterodyne detection system was replaced by a homodyne detection. However, since the simultaneous presence of both signal types gives further evidence for the connectivities, we did not suppress this effect in most of the recorded spectra. 5. Discussion In conventional microwave-microwave doubleresonance spectroscopy as well as in continuous

Volume 144, number 2

CHEMICAL PHYSICS LETTERS

pumped MWFT experiments the detection system had to be protected against pump radiation by filters, which required large frequency differences of at least lo-20% between the signal and pump frequency. Pulsed double-resonance experiments remove this restriction by using PIN switches to protect the detection system. These methods have not been applied to solve assignment problems so far. The present work demonstrates the capabilities of pulsed 2D MWFT experiments to correlate rotational transitions. The combination of a phase cycle with the triplepulse sequence of Stahl et al. [ 81 allowed us to optimize the experimental conditions to select only the desired double-quantum coherence. This simplifies the recorded spectra. Signals appear after accumulation only when two connected transitions are affected simultaneously by signal and pump radiation. This method assists greatly in searching for doubleresonance connections in spectral regions which are very crowded or dominated by undesired strong transitions. The autocorrelation experiment directly showed connectivities of rotational transitions with frequencies differing only by a few MHz. Unfortunately for these experiments the diagonal peaks cannot be suppressed by a simple phase cycle. Contrary to the double-quantum spectrum it is difficult to tune the COSY experiment for optimal cross peak intensity by a simple 1D procedure. Whereas the theory for the pulsed experiments is restricted to isolated three-level systems, both 2D double-quantum correlation spectroscopy and 2D autocorrelation spectroscopy were applied here successfully to a multi-level system. Although in this system multiplequantum coherence can be produced by each single pulse, no evidence for higher quantum orders was found in the two experiments. The present work demonstrates that pulsed 2D correlation experiments which are well established in NMR also succeed when applied to MWFT spectroscopy. However, the conditions are more complex than in NMR. Only very small fractions of the microwave spectrum can be excited by a single pulse. The concept of x/2 and n pulses is suspicious considering the different transition moments for each transition in multi-level systems. Different transitions usually experience different pulse excitation

19 February 1988

angles. Furthermore, the microwave field inhomogeneities along and across the waveguide give rise to uneven polarization within the cell. These effects lead to incomplete coherence transfer and therefore intensities are highly dependent on position, length and power of the applied pulses. We hope that effects from field inhomogeneities and flip angle distributions can be corrected at least partially by the use of composite pulses similar to NMR [24].

Acknowledgement Financial support by the Schweizerischer Nationalfonds (project No. 2.005-0.86) is gratefully acknowledged. We thank Dr. W. Studer for help with the software and Dr. M. Rodler for discussions. We are indebted to Professor R.R. Ernst for permission to use the NMR software and computer. Special thanks go to Mr. C. Radloff for many enlightening discussions and for critically reading the manuscript.

References [ 1] M. Oldani and A. Bauder, Chem. Phys. Letters 108(1984) 7. [2] B. Vogelsanger, M. Oldani and A. Bauder, J. Mol. Spectry. 119 (1986) 214. [3] M. Rodler, M. Oldani, G. Grassi and A. Bauder, J. Chem. Phys. 86 (1987) 5365. [4] G. Bestmann, W. Lalowski and H. Dreizler, Z. Naturforsch. 40a (1985) 271. [51M. Rodler, S. Jans-Btirli, M. Oldani and A. Bauder, Chcm. Phys. Letters 142 (1987) 10. [6] H. Dreizler, E. Fliege, H. Mader and W. Stahl, Z. Naturforsch. 37a (1982) 1266. [7] G. Bestmann and H. Dreizler, Z. Naturforsch. 38a (1983) 452. [8] W. Stahl, E. Fliege and H. Dreizler, Z. Naturforsch. 39a (1984) 858. [9] B. Vogelsanger and A. Bauder, J. Chem. Phys. 87 (1987) to be published. [ 10] B. Vogelsanger, W. Caminati and A. Bauder, Chem. Phys. Letters 141 (1987) 245. [ 111 W. Caminati, B. Vogelsanger and A. Bauder, J. Mol. Spectry., submitted for publication. [ 121 R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of nuclear magnetic resonance in one and two dimensions (Clarendon Press, Oxford, 1987) pp. 283-538. [ 131 W.P. Aue, E. Bartholdi and R.R. Ernst, J. Chem. Phys. 64 (1976) 2229.

185

Volume 144, number 2

CHEMICAL PHYSICS LETTERS

[ 141 P. HBfer, A. Grupp, H. Nebenfuhr and M. Mehring, Chem. Phys. Letters 132 (1986) 279. [ 151J. Gorcester and J.H. Freed, J. Chem. Phys. 85 (1986) 5375. [ 161 P. Pftindler, G. Bodenhausen, J. Rapin, R. Houriet and T. GBumann, Chem. Phys. Letters 138 (1987) 195. [ 171 D.A. Andrews, J.G. Baker, B.G. Blundell and G.C. Petty, J. Mol. Struct. 97 (1983) 271. [ 181A.A. Maudsley and R.R. Ernst, Chem. Phys. Letters 50 (1977) 368.

186

19 February 1988

[ 191 J. Jeener, in: Ampere International Summer School, Basko Polje, Yugoslavia ( 1971) . [20] R.G. Stone and W.H. Flygare, J. Mol. Spectry. 32 (1969) 233. [ 2I] J. Ekkers and W.H. Flygare, Rev. Sci. Instr. 47 (1976) 448. [22] G. Bodenhausen, H. Kogler and R.R. Ernst, J. Magn. Reson. 58 (1984) 370. [23] A.D. Bain, J. Magn. Resort. 56 (1984) 418. [ 241 M.H. Levitt, Progr. NMR Spectry. 18 ( 1986) 6 I,