Phase Dependence of Double-Resonance Experiments in Rotational

Letter pubs.acs.org/JPCL

Phase Dependence of Double-Resonance Experiments in Rotational Spectroscopy David Schmitz,†,‡ V. Alvin Shubert,†,‡ David Patterson,¶ Anna Krin,†,‡ and Melanie Schnell*,†,‡ †

Max-Planck-Institut für Struktur und Dynamik der Materie, Luruper Chaussee 149, D-22761 Hamburg, Germany Center for Free-Electron Laser Science, Luruper Chaussee 149, D-22761 Hamburg, Germany ¶ Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States ‡

S Supporting Information *

ABSTRACT: We here report on double-resonance experiments using broadband chirped pulse Fourier transform microwave spectroscopy that can facilitate spectral assignment and yield information about weak transitions with high resolution and sensitivity. Using the diastereomers menthone and isomenthone, we investigate the dependence of pumping a radio frequency transition on both the amplitude and phase of the signal from a microwave transition with which it shares a common rotational level. We observe a strong phase change when scanning the radio frequency through molecular resonance. The direction of the phase change depends on the energy level arrangement, that is, if it is progressive or regressive. The experimental results can be simulated using the three-level optical Bloch equations and described with the AC Stark effect, giving rise to an Autler−Townes splitting.

rotational Q-type transitions that follow the selection rule ΔJ = 0. Because the signal strength in FTMW spectroscopy depends directly on the population difference between the two energy levels involved, transitions that occur between rotational energy levels nearby in energy are typically quite weak and thus difficult to detect, even under the cold conditions of a molecular jet. In addition to changes in the amplitude, we report on characteristic phase changes observed in the free-induction decay (FID) for the MW signal transition when scanning the RF through resonance. This phase was not extensively considered in previous experiments. As we will discuss below, the direction of the phase change allows for definitive information not only about which energy levels are connected with each other but also about how they are connected, that is, in a progressive or regressive arrangement (Figure 1). This additional information goes clearly beyond what can be obtained from an amplitude analysis and can be key to facilitating the assignment of complex rotational spectra. The measured phase is typically substantially more stable than the amplitude, which is affected by instabilities of the supersonic jet expansion, for example. Double-resonance experiments in the MW frequency range were already introduced in the early period of impulse FTMW spectroscopy on static gases and have been steadily developed since then. Examples include the study of coherence transfer

M

ajor developments in the technology of high-frequency test and measurement equipment led to the development of a novel spectrometer design by Pate and co-workers based on a broadband microwave (MW) chirp.1 It allows for the recording of large fractions of rotational spectra within a single acquisition. With these new chirped pulse Fourier transform microwave (CP-FTMW) spectrometers, broadband operation over tens of GHz has been demonstrated,2,3 transforming FTMW spectroscopy into a fast, sensitive technique. However, spectral complexity grows rapidly as the molecules get larger. The rotational spectra of medium-sized molecules like the terpenes investigated in the present work can be very rich due to the presence of several conformers, internal dynamics, or hyperfine splitting arising from nuclear quadrupole coupling, for example.4−6 Methods to simplify spectral assignment are thus highly desirable. One approach to overcome this challenge is the development of computerassisted autoassignment programs.7,8 From an experimental point of view, double-resonance experiments can significantly facilitate the analysis of complex high-resolution rotational spectra by identifying the connectivity of energy levels.9−11 For example, for the microwave−radio frequency (MW−RF) double-resonance experiments that we report herein, the amplitudes of any MW transitions that share a common level with the transition selectively excited by the RF pulse will be depleted in the spectrum because the resonant RF pulse influences the signal coherence of the MW transition. Thus, weak transitions, such as those at low frequency, can be observed as a modulation on a connected strong transition.10,12 Such transitions include l-type and K-type doubling splittings that are plentiful in near-symmetric top molecules, as well as © 2015 American Chemical Society

Received: March 9, 2015 Accepted: April 3, 2015 Published: April 3, 2015 1493

DOI: 10.1021/acs.jpclett.5b00494 J. Phys. Chem. Lett. 2015, 6, 1493−1498

Letter

The Journal of Physical Chemistry Letters

Figure 1. Schematics of energy level configurations for MW−RF double-resonance experiments: (a) progressive arrangement, (b) regressive arrangement with the RF transition ω0,bc connecting the upper two energy levels (Λ-type), and (c) regressive arrangement with the RF transition connecting the lower two energy levels (V-type). The initial MW transition is called the signal transition, while the RF transition is denoted as the pump transition. ω0,ab = Eb − Ea and ω0,bc = Ec − Eb are the resonance frequencies, while ωab and ωbc are the frequencies that are actually employed in the experiment. The MW signal pulse is used to prepare ab coherence, and ωbc is scanned through ω0,bc from negative to positive detunings.

and the development of assignment aids (see, for example, refs 9, 10, and 13−15). However, the time required to check the many possible double resonances prevented the technique from becoming a routine application in MW spectroscopy. This restriction is now removed. Due to the drastically reduced time requirements for wide frequency coverage in the MW domain, CP-FTMW spectroscopy is particularly attractive for advanced double-resonance and two-dimensional (2D) spectroscopy schemes.11,16 In principle, the chirp technique can be combined with almost any frequency region of the electromagnetic spectrum. Infrared−MW (IR−MW) double-resonance experiments were used to study the kinetics of conformational isomerizations.17 Recently, we developed a MW three-wave mixing scheme, which can be understood as a polarizationdependent double-resonance experiment, to differentiate between the two enantiomers of chiral molecules exploiting enantiomer-dependent signal phases,18−21 and other groups are currently following.22 Powerful arbitrary waveform generators can generate MW excitation sequences of great complexity so that, ultimately, the development of a full-bandwidth 2D CPFTMW technique can provide all of the spectral connectivity information in a single measurement. Such experiments can be very useful in facilitating or even enabling the analysis of the spectra of larger molecules or mixtures. In many ways, the situation is analogous to NMR analysis of complex samples, where 2D techniques are now routinely used to deconvolve overlapping spectra. The MW−RF double-resonance experiments are performed with the same Hamburg COMPACT broadband rotational spectrometer23 that is modified to perform enantiomeric differentiation with MW three-wave mixing.20 This modified spectrometer operates in the 2−6 GHz MW and 50−550 MHz RF ranges. Molecules are seeded into a neon carrier gas (3 bar) by heating (110 °C) and introduced into the interaction region of the spectrometer via pulsed supersonic expansions. Menthone and isomenthone (Sigma-Aldrich, 97% purity, mixture of isomers) are used without further purification. Figure 2 shows a scheme of the interaction zone of the apparatus and a timeline for the experiments. The MW signal pulse (a chirp spanning 2−6 GHz in 1 μs) and the RF pump pulse (single-frequency with 5 μs duration) are generated on two channels of the same arbitrary waveform generator to ensure phase stability (Figure 2b).20 These pulse durations, of the RF pulse in particular, allow us to both see a sizable effect on the phase behavior (see below) as well as to have a sufficiently strong FID signal strength at the time that we can

Figure 2. Scheme of the experimental setup and timeline. (a) The interaction zone of the molecular sample supersonically expanded from the top with the MW signal and RF pump pulses. For introducing RF radiation, two electrodes are integrated into the setup. The polarization directions of the MW excitation and the RF pump pulses are perpendicular with respect to each other. (b) Schematic timeline (not to scale) for the MW−RF double-resonance experiments, illustrating the duration τMW of the broadband MW excitation pulse and τRF of the RF pump pulse. Both pulses are generated from the same source, starting at the same time (tRF0) and with the same phase. However, due to different pathways taken by the RF and MW pulses, the MW pulse arrives slightly later in the interaction region than the RF pulse (about 13.1 ns). t0 indicates when the FID starts, and tr gives the time when broadband FID recording starts with respect to the excitation pulses.

start recording the signal (tr in Figure 2). Both pulses are amplified using a 300 W traveling-wave tube amplifier specified in the 2.5−7.5 GHz range and a 100 W solid-state amplifier operating at 50−550 MHz, respectively, before they are coupled into the spectrometer chamber. The MW pulse is broadcast into the chamber via a horn antenna and temporally overlapped with the first 1 μs of the RF pulse. Coupling the RF pulse to a set of stainless steel electrodes creates a RF field in the interaction region between the broadcast and receiving horns. The horns are arranged colinearly, and the MW and RF 1494


Letter


Figure 3. MW−RF double-resonance experiments for two conformers of menthone (left and right columns). The simulations are based on the three-level optical Bloch equations. First row: Energy levels involved in the double-resonance experiments for (a) conformer A and (d) conformer B as well as molecular structures. Second row: Illustration of the amplitude dependences observed for the FID at the respective MW signal transition frequency, that is, the 212← 101 b-type transitions of the two menthone conformers, as a function of the RF pump frequency. The RF transition 211 ← 212 is predicted at 323.81 MHz for conformer A (b) and at 394.20 MHz for conformer B (e) from the experimentally determined rotational constants (see text). The amplitudes are normalized. Third row: Phase dependence of the FID at MW signal transition frequencies on the RF pump frequencies for (c) conformer A and (f) conformer B, illustrating the striking change at RF resonance. Both the amplitude and the phase dependence are extracted from the same experimental data.

fields are linearly polarized perpendicular to each other, which is not needed for these experiments but for our MW three-wave mixing experiments, for which the setup was originally designed. A macroscopic polarization is created when the molecules are resonant with a frequency within the MW signal chirp. Up to 20 μs of the FID of this polarization is recorded. In the doubleresonance experiments, the RF pump frequency is varied in 20 kHz steps to pass through the resonance of a RF transition connected to a respective MW signal transition. For each RF pump frequency step, 5000 acquisitions are averaged. The phases and amplitudes are evaluated for the FIDs at the relevant MW signal frequencies of interest. The experimental results for double-resonance experiments on the two menthone conformers A and B are presented in Figure 3, along with a scheme of the molecular structures and the energy levels involved that follow a progressive arrangement. (The rotational constants, as determined in a previous broadband rotational spectroscopy investigation, are A = 1953.43379(43) MHz, B = 694.51551(19) MHz, and C = 586.57758(19) MHz for conformer A and A = 2021.98637(36) MHz, B = 693.53686(16), and C = 562.13636(16) MHz for conformer B.8) The two conformers differ in the orientation of the isopropyl group with respect to the cyclohexanone ring,

resulting in different rotational spectra. We here concentrate on the (J + 1)K′a,K′c ← JKa,Kc = 212 ← 101 rotational transition as the MW signal transition (b-type) for both conformers of menthone (located at 3713.17 MHz for conformer A and at 3708.40 MHz for conformer B). The amplitudes for these MW signal transitions are significantly influenced by the RF pump frequency. Clear amplitude minima are obtained when the RF pump becomes resonant with the 211 ← 212 transition for menthone (at 323.81 MHz for conformer A and at 394.20 MHz for conformer B). Generally, a MW chirp covering the MW signal frequency ωab converts population difference between the rotational energy levels |a⟩ and |b⟩ into polarization (abcoherence), similar to one-dimensional MW spectroscopy.24 When the RF pump frequency is at or close to resonance (ωRF ≈ ω0,bc; see Figure 1), the RF pump transfers abcoherence to ac-coherence, resulting in a significant decrease in signal intensity for the b ← a transition. This transfer is reduced for larger detunings, in agreement with our results. It is intriguing to look at the double-resonance experiments in another way. In Figure 3c and f, we show the phase behavior as a function of the RF. Its detuning can be defined as ΔRF = ωRF − ω0,bc. Strong changes of about π radians or more are observed for the phase of the FID of the signal transition with inflection points at ΔRF = 0, that is, when the RF pump pulse is 1495


Letter


Figure 4. MW−RF double-resonance experiments for two different energy level combinations (left and right column) of isomenthone. The simulations are based on the three-level optical Bloch equations. First row: Energy level schemes visualizing the connectivity of energy levels and the two double-resonance schemes, progressive (a) and regressive (Λ-type) (d), as well as the molecular structure for (+)-isomenthone. For (−)-isomenthone, the arrangement at both stereogenic centers would be inverted. Second row: Illustration of the amplitude dependence observed for the FID at the respective MW signal transition frequency, that is, the 404← 313 b-type transition at 5316.79 MHz (b) and the 414← 303 b-type transition at 6070.63 MHz (e), as a function of the RF pump frequency. The RF transition 414 ← 404 connects the two b-type transitions. Third row: Phase dependence of the FID at MW signal transition frequencies on the RF pump frequency, illustrating the strong change close to RF resonance that is opposite for the two different energy level combinations (progressive (c) and regressive (f)).

−(π/2) to +(π/2) (Figure 4c), as also observed for menthone (Figure 3). For the regressive scheme, the phase change is opposite (Figure 4f). The same behavior is observed for double-resonance measurements on 4-carvomenthenol that are summarized in the Supporting Information. For 4-carvomenthenol, we investigated both V- and Λ-type regressive arrangements that are found to follow the same phase behavior, as also predicted by the dressed state picture and by our simulations (vide infra). To further illuminate the amplitude and phase dependences, we performed simulations utilizing the optical Bloch equations for a three-level system (see also the Supporting Information). The optical Bloch equations for a three-level system can be obtained in a straightforward way within the density matrix formalism.9,13,16,25 The results are included in Figures 3 and 4 and show a very good agreement with the experimental results. A more physical explanation of the observed behavior can be provided with the help of the AC Stark effect, that is, the interaction of a polar molecule with a time-dependent, external electromagnetic field ,field = , 0 cos(ωt ) and the corresponding Stark energy EStark = −μ,field . Note that the energy level

resonant with the molecular transition. The data are extracted from the same measurements as the amplitude dependence shown in Figure 3b and e. Of note here is the significantly better signal-to-noise ratio for the phase dependence than that for the amplitude dependence. The inflection point of the phase gives direct access to precisely determining these lowfrequency transition frequencies. In addition, it provides information about how the relevant energy levels are arranged, that is, progressively or regressively. This observation is further illustrated by the experimental results obtained for isomenthone, which is the diastereomer of menthone (Figure 4). All measurements were performed on the lowest-energy conformer of isomenthone (with rotational constants A = 1535.27577(48) MHz, B = 812.92526(33) MHz, and C = 671.43466(33) MHz8) schematically displayed in Figure 4 using the same RF pump transition (the (J + 1)Ka′,Kc′ ← JKa,Kc = 414 ← 404 transition at 304.26 MHz) but two different signal transitions (404 ← 313 at 5316.79 MHz (progressive scheme 1, Figure 4a) and 414 ← 303 at 6070.63 MHz (regressive, Λ-type scheme 2, Figure 4d)). For the progressive scheme (left column), the phase changes from approximately 1496


Letter


Figure 5. Dressed state formalism describing the interaction of the RF pump field ℏωbc with the molecular energy levels |b⟩ and |c⟩ in a progressive scheme, for (a) blue and (b) red detuning of the RF field with respect to molecular resonance. The unperturbed states |c,N⟩ and |b,N−1⟩, dressed with N and N − 1 photons, respectively (given on the left-hand side), are transformed into two dressed states, |1⟩ and |2⟩, due to the interaction with the RF field and with each other (given on the right-hand side). For blue detuning (a), the unperturbed |b,N⟩ state is higher in energy than the |c,N− 1⟩. This situation is reversed for red detuning (b).

arrangements involved in the MW−RF double-resonance experiments perfectly resemble the conditions for the Autler− Townes effect.26,27 The RF pump field interacts with the twolevel system comprised of the levels |b⟩ and |c⟩, which we then probe on a transition to a third level |a⟩ (Figure 5). For the AC Stark effect of the |b⟩, |c⟩ two-level system, the magnitude of the detuning of the interacting RF field from molecular resonance determines the strength of the interaction, while its sign determines the direction of the energy shift of the respective energy levels, that is, if they gain or lose Stark energy with increasing electric field strengths. Schematics for the red- and blue-detuned case within the dressed state picture are depicted in Figure 5 for the progressive scheme. The states |b⟩ and |c⟩ are dressed with photons of the RF field of frequency ωbc. The unperturbed |b⟩ state dressed with N photons is described as the |b,N⟩ state. It interacts with the unperturbed |c,N−1⟩ state, that is, |c⟩ dressed with N − 1 photons. They are separated by the detuning ΔRF in the unperturbed case (left-hand part of Figure 5a and b). For blue detuning (a), the |b,N⟩ is higher in energy than the |c,N−1⟩ state. As a consequence, the |b,N⟩ will be shifted toward higher energies for the dressed state |1⟩ (right-hand side), while the |c,N−1⟩ will be shifted toward the lower-energy state |2⟩. The situation is reversed for the red-detuned case (Figure 5b). When probing these shifts by a transition to the third level |a⟩ with ℏω0,ab, which is far detuned from the dressing field, the Autler−Townes splitting appears (because both dressed levels also contain the |b,N⟩ state), |a,N⟩ ↔ |1⟩ with frequency ω0,ab + (Ω − ΔRF)/2 and |a,N⟩ ↔ |2⟩ with frequency ω0,ab − (Ω + ΔRF)/2. The difference between the two transitions equals the generalized Rabi frequency Ω = (Ω′2 + Δ2RF)1/2, where Ω′ is the Rabi frequency Ω′ = μ,field/ℏ. The intensities of the two components of the Autler−Townes splitting differ, as indicated by the thickness of the undulating lines in Figure 5 and better visualized in Figure 3 of the Supporting Information. The simulations revealed an intensity ratio of

Ic , N − 1 Ib , N

⎡1 ⎛ Ω′ ⎞⎤ = tan 2⎢ ·arctan⎜ − ⎟⎥ ⎢⎣ 2 ⎝ ΔRF ⎠⎥⎦

(1)

for the Autler−Townes doublet, which can also be derived within the dressed state picture.27 In our case, the transition between the dressed state evolving from the unperturbed state |b,N⟩ (dressed state |1⟩ or |2⟩ for blue- or red-detuned light, respectively) and |a,N⟩ is always stronger in intensity. In our experimental setup, we cannot observe the Autler− Townes splitting directly because our CP-FTMW spectrometer is constructed to record the FID of weak molecular signals. The sensitive electronic components would be destroyed or at least saturated by any attempt to observe the molecular response during the RF pulse. However, the Autler−Townes splitting is mapped onto the phase of the MW probe signal in the following manner. The MW chirp converts population difference to ab-coherence and ac-coherence. The ab-coherence evolves during the longer RF pulse at a superposition of the Autler−Townes doublet frequencies. Depending on the detuning, the amplitudes and frequencies of the doublet vary, which is mapped onto the phase of the ab-transition in the field-free case. In Figure 2 of the Supporting Information, simulations are presented for varying RF field strengths. As expected, the amplitude dependence and the phase shift become less pronounced with decreasing field strengths. Furthermore, with increasing electric field strength, the Autler−Townes doublet becomes more pronounced. The above discussion concentrates on the progressive case (Figure 1a). For the regressive Λ case, the influence of the AC Stark coupling of the |b,N⟩ and |c,N−1⟩ states is just reversed (see Figure 1b), which results in the opposite phase shift observed for isomenthone (Figure 4). In summary, we used a CP-FTMW spectrometer to investigate the amplitude and phase dependences of MW−RF double-resonance experiments. The experimental results allow us to precisely determine the frequencies of weak transitions using the intensity available on a connected strong transition. 1497


Letter


Autofit, an automated fitting tool for broadband rotational spectra, and applications to 1-hexanal. J. Mol. Spectrosc. 2015, 312, 13−21. (8) Schmitz, D.; Shubert, V. A.; Betz, T.; Schnell, M. Exploring the conformational landscape of menthol, menthone, and isomenthone: A microwave study. Front. Chem. 2015, 3, 15. (9) Vogelsanger, B.; Bauder, A. Two-dimensional microwave Fourier transform spectroscopy. J. Chem. Phys. 1990, 92, 4101−4114. (10) Wodarczyk, F.; Wilson, E. Radio frequency-microwave double resonance as a tool in the analysis of microwave spectra. J. Mol. Spectrosc. 1971, 37, 445−463. (11) Shipman, S. T., Pate, B. H. New techniques in microwave spectroscopy. In Handbook of High-Resolution Spectrosocpy; Quack, M., Merkt, F., Eds.; Wiley: New York, 2011; Vol. 36, pp 801−827. (12) Jäger, W.; Haekel, J.; Andresen, U.; Mäder, H. Two-dimensional Fourier transform spectroscopy in the microwave-radiofrequency range. Mol. Phys. 1989, 68, 1287−1309. (13) Vogelsanger, B.; Andrist, M.; Bauder, A. Two-dimensional correlation experiments in microwave Fourier transform spectroscopy. Chem. Phys. Lett. 1988, 144, 180−186. (14) Wötzel, U.; Stahl, W.; Mäder, H. The influence of an offresonant pump radiation in Fourier transform microwave spectroscopy. Can. J. Phys. 1997, 75, 821−830. (15) Oka, T. High-power microwave double-resonance experiments. Can. J. Phys. 1969, 47, 2343−2350. (16) Wilcox, D. S.; Hotopp, K. M.; Dian, B. C. Two-Dimensional chirped-pulse Fourier transform microwave spectroscopy. J. Phys. Chem. A 2011, 115, 8895−8905. (17) Dian, B. C.; Brown, G. G.; Douglass, K. O.; Pate, B. H. Measuring picosecond isomerization kinetics via broadband microwave spectroscopy. Science 2008, 320, 924−928. (18) Patteron, D.; Schnell, M.; Doyle, J. M. Enantiomer-specific detection of chiral molecules via microwave spectroscopy. Nature 2013, 497, 475−477. (19) Patterson, D.; Doyle, J. M. Sensitive chiral analysis via microwave three-wave mixing. Phys. Rev. Lett. 2013, 111, 023008. (20) Shubert, V. A.; Schmitz, D.; Patterson, D.; Doyle, J. M.; Schnell, M. Enantiomer identification in mixtures of chiral molecules with broadband microwave spectroscopy. Angew. Chem., Int. Ed. 2014, 53, 1152−1155. (21) Shubert, V. A.; Schmitz, D.; Schnell, M. Enantiomer-sensitive spectroscopy and mixture analysis of chiral molecules containing two stereogenic centers: Microwave three-wave mixing of menthone. J. Mol. Spectrosc. 2014, 300, 31−36. (22) Lobsiger, S.; Perez, C.; Evangelisti, L.; Lehmann, K. K.; Pate, B. H. Molecular structure and chirality detection by Fourier transform microwave spectroscopy. J. Phys. Chem. Lett. 2015, 6, 196−200. (23) Schmitz, D.; Shubert, V. A.; Betz, T.; Schnell, M. Multiresonance effects within a single chirp in broadband rotational spectroscopy: The rapid adiabatic passage regime for benzonitrile. J. Mol. Spectrosc. 2012, 280, 77−84. (24) McGurk, J.; Schmalz, T.; Flygare, W. Fast passage in rotational spectroscopy: Theory and experiment. J. Chem. Phys. 1974, 60, 4181− 4189. (25) Grabow, J.-U. Fourier transform microwave spectroscopy measurement and instrumentation. In Handbook of High-Resolution Spectroscopy; Quack, M., Merkt, F., Eds.; John Wiley & Sons, Ltd: New York, 2011. (26) Autler, S.; Townes, C. Stark effect in rapidly varying fields. Phys. Rev. 1955, 100, 703−722. (27) Cohen-Tannoudji, C.; Dupont-Roc, J.; Grynberg, G. Atom− Photon Interactions: Basic Processes and Applications, 1st ed.; WileyVCH: New York, 1988.

Furthermore, they offer promising possibilities for simplifying the assignment of rich high-resolution rotational spectra. A characteristic phase change is observed when the pump frequency is scanned through resonance. This phase change can be attributed to the Autler−Townes effect, that is, we are probing the AC Stark effect induced by the RF field with the MW signal pulse. The Autler−Townes splitting is mapped onto the phase of the MW probe signal, causing the characteristic phase shift. The nature of the splitting changes with the magnitude and sign of the detuning, that is, it depends on the relative arrangement of the energy levels as either progressive or regressive. It can be very well described by simulations exploiting the three-level optical Bloch equations.

■

ASSOCIATED CONTENT

S Supporting Information *

Double-resonance data on 4-carvomenthenol, exploring progressive and regressive V- and Λ-type schemes. The three-level optical Bloch equations are discussed in more detail, and simulation results on the Autler−Townes doublet as well as on the field-strength dependence of the RF-MW double-resonance experiments are given. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work has been supported by the excellence cluster “The Hamburg Centre for Ultrafast Imaging - Structure, Dynamics and Control of Matter at the Atomic Scale” of the Deutsche Forschungsgemeinschaft. M.S. acknowledges funding by the Fonds der Chemischen Industrie via a Dozentenstipendium as well as financial support by the Deutsche Forschungsgemeinschaft.

■

REFERENCES

(1) Brown, G. G.; Dian, B. C.; Douglass, K. O.; Geyer, S. M.; Shipman, S. T.; Pate, B. H. A broadband Fourier transform microwave spectrometer based on chirped pulse excitation. Rev. Sci. Instrum. 2008, 79, 053103. (2) Zaleski, D. P.; Neill, J. L.; Muckle, M. T.; Seifert, N. A.; Carroll, P. B.; Weaver, S. L. W.; Pate, B. H. A Ka-band chirped-pulse Fourier transform microwave spectrometer. J. Mol. Spectrosc. 2012, 280, 68− 76. (3) Steber, A. L.; Harris, B. J.; Neill, J. L.; Pate, B. H. An arbitrary waveform generator based chirped pulse Fourier transform spectrometer operating from 260 to 295 GHz. J. Mol. Spectrosc. 2012, 280, 3−10. (4) Shipman, S. T.; Neill, J. L.; Suenram, R. D.; Muckle, M. T.; Pate, B. H. Structure determination of strawberry aldehyde by broadband microwave spectroscopy: Conformational stabilization by dispersive interactions. J. Phys. Chem. Lett. 2011, 2, 443−448. (5) Betz, T.; Zinn, S.; Schnell, M. The shape of ibuprofen in the gas phase. Phys. Chem. Chem. Phys. 2015, 17, 4538−4541. (6) Shubert, V. A.; Schmitz, D.; Schnell, M. Communication through the phenyl ring: Internal rotation and nuclear quadrupole splitting in p-halotoluenes. Mol. Phys. 2013, 111, 2189−2197. (7) Seifert, N. A.; Finneran, I. A.; Perez, C.; Zaleski, D. P.; Neill, J. L.; Steber, A. L.; Suenram, R. D.; Lesarri, A.; Shipman, S. R.; Pate, B. H. 1498


Phase Dependence of Double-Resonance Experiments in Rotational

Recommend Documents