Mass-correlated rotational Raman spectra with highresolution, broad bandwidth, and absolutefrequency accuracyChristian Schrotera, Jong Chan Lee ( )a, and Thomas Schultza,1

aDepartment of Chemistry, Ulsan National Institute of Science and Technology, Eonyang-eup, Ulju-gun, Ulsan, 44919, Republic of Korea

Edited by Philip H. Bucksbaum, Stanford University, Menlo Park, CA, and approved March 30, 2018 (received for review December 17, 2017)

We present mass-correlated rotational alignment spectroscopy,based on the optical excitation of a coherent rotational quan-tum wave and the observation of temporal wave interferences ina mass spectrometer. Combined electronic and opto-mechanicaldelays increased the observation time and energy resolution byan order of magnitude compared with preceding time-domainmeasurements. Rotational transition frequencies were referencedto an external clock for accurate absolute frequency measure-ments. Rotational Raman spectra for six naturally occurringcarbon disulfide isotopologues were resolved with 3 MHz res-olution over a spectral range of 500 GHz. Rotational constantswere determined with single-kilohertz accuracy, competitive withstate-of-the-art frequency domain measurements.

multidimensional spectroscopy | correlated measurement | rotationalalignment | Raman spectroscopy | high-resolution spectroscopy

Correlated spectroscopy combines the information content ofmultiple spectroscopic measurements into a single multidi-

mensional dataset. It is therefore uniquely suited for the analysisof heterogeneous signals, where a single experiment cannotresolve or assign all signal contributions. Correlated rotationalalignment spectroscopy (CRASY) correlates gas-phase rota-tional Raman spectra with observables from short-pulse laserspectroscopy. Our initial mass-CRASY experiments resolvedisotopic heterogeneities and determined isotope-specific rota-tional constants and fragmentation channels in carbon disulfide(CS2) and butadiene (1, 2). Here, we describe two developmentsthat greatly enhance the power of CRASY: (i) a method toobtain high-resolution rotational spectra from CRASY experi-ments and (ii) a method to reference rotational frequencies toan external clock for highly accurate spectroscopic frequencydetermination.

CRASY is based on time-domain rotational Raman spec-troscopy and requires the excitation of a coherent super-position of rotational states and the subsequent observationof the wave packet formed by this state superposition. Firstrelated experiments were performed by Heritage et al. (3),who observed the transient birefringence caused by an evolv-ing rotational wave packet in carbon disulfide. Felker (4) andcoworkers developed a number of experimental schemes underthe label rotational coherence spectroscopy (RCS). RCS wasused to analyze the rotational structure of molecules andclusters with small or no dipoles (5–9). The highest resolu-tion RCS experiments scanned opto-mechanical delays up to2 m (10, 11) and observed rotational wave packets over atime range ∆t ≤ 6 ns. The spectroscopic resolution is limitedby the Heisenberg energy uncertainty (Fourier limit), ∆E ≥~/(2 ·∆t), corresponding to less than 100 MHz in the RCSexperiments.

The spectroscopic resolution improves proportionally to theobservation time range ∆t . Order-of-magnitude extensions ofopto-mechanical delays, however, are impractical: Even the bestcommercial Fourier-transform spectrometers reach only a rangeof about 10 m [e.g., 11.7 m for the Bruker ETH-SLS 2009 FTIR

spectrometer prototype at the Swiss Synchrotron Light Source(12)]. This limitation is overcome in the present work: We usediscrete electronic delays to select a laser pulse from a sta-ble laser oscillator pulse train, adding discrete nanosecond tomillisecond delays with negligible timing uncertainty.

Spectroscopic accuracy does not necessarily scale with res-olution but requires a reliable calibration. In the frequencydomain, the inception of frequency comb spectroscopy allowedfor referencing spectroscopic frequencies directly to a clock(13, 14). The resulting improvement of spectroscopic accu-racy had a great impact in the fields of atomic spectroscopy,molecular spectroscopy, and metrology (15). Here, we createa time-domain equivalent to frequency comb spectroscopy byreferencing rotational Raman frequencies to an external clock.

Experimental DesignThe experimental scheme is illustrated in Fig. 1. Helium gas at 10to 20 bar pressure was seeded with small quantities of CS2 andexpanded through a pulsed valve operating at 500 Hz. A 1-mmskimmer, placed at 280-mm distance from the valve, skimmedthe resulting cold molecular beam to a collimation angle of0.10◦. In the spectrometer region of a time-of-flight Wiley–McLaren mass spectrometer (16), an IR laser pulse (alignmentpulse) crossed the molecular beam and created a coherent wavepacket by rotational Raman excitation. The wave packet wasprobed by resonant two-photon ionization with an UV laserpulse (ionization pulse), ionizing CS2 via the 1Σ+

u state. Ionswere detected with a multichannel plate detector, and theirtime-of-flight was measured in a scaler card with 0.5 ns timeresolution.

Significance

Mass-correlated rotational alignment spectroscopy (mass-CRASY) is a laser spectroscopic method for the simultane-ous characterization of molecular composition and rotationalstructure in a heterogeneous (impure) sample. The presentwork extends CRASY by referencing the spectroscopic datavia a stable laser oscillator frequency to an external clock.Data for carbon disulfide provide mass-selected rotationalspectra for multiple isotopologues with significantly improvedspectroscopic accuracy compared to preceding measurements.

Author contributions: T.S. designed research; C.S., J.C.L., and T.S. performed research;C.S., J.C.L., and T.S. analyzed data; and T.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.

Data deposition: Raw experimental data corresponding to Figs. 2–4 and a simpleguide for data analysis have been uploaded to https://figshare.com/articles/CRASY data/5886406 (DOI: 10.6084/m9.figshare.5886406).1 To whom correspondence should be addressed. Email: schultz@unist.ac.kr.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1721756115/-/DCSupplemental.

Published online April 27, 2018.

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Fig. 1. Experimental scheme. Molecules from a cold molecular beam sourcewere excited and ionized by two laser pulses (L1 and L2) in a mass spec-trometer. The time delay ∆t between the laser pulses was adjusted throughan opto-mechanical (OM) and an electronic pulse-selection (PS) delay: Elec-tronic selection of laser oscillator pulses for amplification in amplifier 1 and2 introduced discrete 12.5-ns delays. A frequency counter monitored theoscillator period and characterized the discrete delays with high accuracy. Amechanical delay stage added≤12.5 ns delays to allow continuous scanningfrom femtoseconds to microseconds.

The laser pulses originated from an amplified 796 nm fem-tosecond laser system consisting of a single Ti:sapphire laseroscillator (Coherent Vitara-T, 80 MHz repetition rate) andtwo regenerative amplifiers (Coherent, Libra USP-1K-HE-200,1 kHz repetition rate), synchronized via electronic timing units.Amplified alignment pulses were compressed to 150–1,500 fspulse duration and attenuated to 50–150 mJ pulse energy. Ampli-fied ionization pulses were compressed to bandwidth-limited45 fs pulse duration and were frequency doubled, tripled, andquadrupled with nonlinear beta barium borate crystals to give 0.1to 0.2 µJ pulses at 199 nm. Alignment and ionization pulses werejointly focused with a 75 cm spherical mirror onto the molecularbeam in the active spectrometer region.

The time delay between alignment and ionization pulses wascontrolled by coupling selected oscillator pulses into the regen-erative amplifiers and by an opto-mechanical delay stage asillustrated in Fig. 1. Distinct oscillator pulses were selected forthe alignment and ionization amplifiers. Because both amplifiersreceived their pulses from the same frequency-stable oscillator,this allowed for adding discrete delays of ∆t = 1/(80 MHz) =12.5 ns with negligible timing-jitter. A frequency counter (Aim-TTI TF930) monitored the oscillator repetition rate against aninexpensive GPS-stabilized clock (Leo Bodnar GPSDO). Theoscillator repetition rate was stable with an Allan deviation below10−10, and the accuracy of the frequency measurement was∆ν/ν� 10−8, limited by the counting statistics. The alignmentbeam was routed through a 30 cm opto-mechanical delay stage(Physik Instrumente, MD-531) with a 100 nm internal encoder.The laser beam path was folded 16-fold across the stage toobtain up to 4.8 m (16 ns) adjustable delays with ≥ 5 fs stepsize, covering the delay range between oscillator pulses. Driftsin the oscillator repetition rate were corrected with the opto-mechanical delay.

For large alignment-ionization delays, a motorized mirrormount adjusted the position of the alignment laser on the

molecular beam to correct for the molecular beam velocity of1,100 m/s. A (91.6± 0.4)◦ angle between molecular beam andlaser beams caused a small Doppler shift of (1.0± 0.26) · 10−7.Doppler broadening was negligible due to the small collimationangle of our skimmed molecular beam.

A chopper wheel (Thorlabs MC2000) was used to alternatinglymeasure alignment–ionization signal and ionization-only (refer-ence) signal. The temporal signal modulations (ratio of signal toreference) in selected mass channels were Fourier transformedto obtain rotational Raman spectra. A detailed description of thedata analysis protocol for each figure is given in SI Appendix.

The laboratory was temperature and humidity controlledto (21± 0.5)◦C and (45± 10)% relative humidity Care wastaken to avoid oscillatory temperature or humidity fluctua-tions. During high-resolution measurements, the temperatureon the laser table was stable within ±0.05◦C, and we usedthe National Institute of Standards and Technology shop-floorequation to approximate the air refractive index with a relativeaccuracy below 10−7 (17). Delay stage encoder positions werecalibrated against a temperature-insensitive optical encoder[Sony Laserscale BL57-RE, thermal expansion coefficient of0.7 · 10−6 m/(m·K)] and by measuring laser cross-correlationsignals displaced by one oscillator pulse jump (12.5 ns).

ResultsFig. 2 illustrates the correlated measurement of mass and rota-tional Raman spectra. The photoionization mass spectrum ofCS2 showed multiple ion signals due to the presence of isotopo-logues, sample impurities, and molecular fragmentation pro-cesses. Mass spectra were collected after inducing a rotationallycoherent wave packet with the alignment laser pulse. The rota-tional coherence affected the orientation of transition dipoles forthe resonant two-photon ionization process and thereby createdpronounced delay-dependent signal modulations, as shown forthe main 12C32S2 isotopologue at mass 76 u. A Fourier analy-sis of the delay trace revealed the amplitudes and phases for allrotational transition frequencies that were encoded in the wavepacket. The plotted power spectrum is equivalent to a Ramanspectrum measured in the frequency domain.

The spectroscopic bandwidth of 500 GHz was sufficient toobtain the complete rotational spectra for our cold molecularbeam. The resolution for each rotational line in Fig. 2 was closeto 60 MHz full width at half maximum (FWHM) and was nearthe Fourier limit for the scanned delay range. A greater resolu-tion can only be achieved by scanning a longer delay range, butthe collection of mass spectra for a large number of alignment–ionization delays was time-consuming and created exceedinglylarge datasets. We therefore used random sparse sampling toaccelerate long delay scans—that is, measuring data only for arandomly selected subset of delays along an extended time axis.

Fig. 3 compares rotational Raman spectra for the main12C32S2 isotopologue with full and sparse sampling. For the fullysampled scan, we measured mass spectra over a delay range of15,325 ps with 1 ps delay steps, integrating signals over 3,000laser shots for each mass spectrum (51 h data acquisition time).For the sparsely sampled scan, we measured 17,110 mass spectraover a delay range of 312.832 ns with random delay steps in mul-tiples of 1 ps, integrating signals over 1,000 laser shots for eachmass spectrum (19 h data acquisition time). Signal modulationsat the main isotopologue mass 76 u were Fourier-transformed toobtain the displayed frequency spectra.

The FWHM resolution in the sparse data were 2.9 MHz, afactor 20 better than in the fully sampled scan and close to theFourier limit. The increased resolution came at the cost of noise:The noise floor in the sparse data were 30-fold higher than in thefully sampled dataset. Part of the noise difference was due to alower ion count rate and the shorter signal integration period inthe sparse scan.

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Fig. 2. CRASY data for carbon disulfide. (Top) The mass spectrum showssignals for multiple CS2 isotopes (76 to 82 u) and their fragments. A grayline shows the same spectrum with 10-fold enlarged ordinate and verticaloffset. Signals from sample impurities are marked with *. (Center) The mass-selected 76 u, 12C32S2 isotopologue signal shows delay-dependent signalmodulation due to rotational coherence. The Inset with 100-fold enlargedabscissa shows the wave packet evolution over a 50 ps period. (Bottom) AFourier analysis of the delay trace resolves the isotope-selective rotationalRaman spectrum.

Fig. 4 shows the rotational band assignment for several CS2

isotopologues in the sparse dataset. Line positions were fitted(cf. SI Appendix) to obtain rotational constants, which are sum-marized in Table 1. For the main isotopologue, we assigned ninelines to the vibrational ground state 1Σg and determined a rota-tional constant of B = 3.271 517 0(±7) GHz. [Errors are given as1σ standard deviation in the last digit(s).] The distortion constantof D = 355(±3) Hz was determined with rather low precisionbecause only low rotational states were observed.

We also resolved 11 weak lines for the first vibrationallyexcited state of the doubly degenerate bending mode Πu .The latter showed a rovibrational splitting (l -type splitting) byq(J (J + 1)) into levels with e and f symmetry (18). The rota-tional constant for this state was B = 3.277 901(±10) GHz witha distortion constant of D = 367(±68) Hz and an l -type splittingconstant of qv = 2,327(±10) kHz.

In the mass channel 77 u, we assigned 5 and 7 lines forthe vibrational ground states of the 13C32S2 and 33S12C32Sisotopologues. The fitted rotational constants (cf. Table 1)

showed a significantly higher uncertainty due to the low isotopeabundance of 13C (1.1%) and 33S (0.75%) (19). In the masschannel 78 u, we assigned 15 lines for the vibrational groundstate of the 34S12C32S isotopologue (8.5% abundance). In masschannel 79 u, six lines for the 34S13C32S isotopologue (0.09%abundance) could be assigned based on their close proximity tothe lines of the 34S12C32S isotopologue. Six lines emerged abovethe sampling noise in mass channel 80 u and could be assignedto the 34S12C34S isotopologue (0.18% abundance).

Discussion and OutlookWe should discuss two fundamental claims of this paper in somedetail: (i) Presented broadband rotational Raman spectra offerorder-of-magnitude improved resolution compared with preced-ing time-domain measurements. (ii) The measurements repre-sent a time-domain equivalent to frequency comb spectroscopyand yield absolute-frequency spectra.

The spectroscopic resolution of previous time-domain rota-tional Raman spectra was limited by the available opto-me-chanical delay stages. The longest available delays were in therange of a few nanoseconds, based on ≤ 2 m mechanical trans-lation stages (10, 11). We overcame this limit with the elec-tronic selection of oscillator pulses from a stable laser oscillator,thereby adding discrete 12.5-ns delay increments to an opto-mechanical delay. The resulting delays are only limited by thelaser repetition rate but can still be sampled with femtosecondstep sizes. To acquire spectroscopic data, we scanned delaysexceeding 300 ns, thereby obtaining a spectroscopic resolutionbelow 3 MHz FWHM, representing a 50-fold improvement overpreceding RCS experiments.

The spectroscopic range in Fourier-transform measurementsis limited according to the Shannon–Nyquist theorem (23) andcannot exceed 1/(2 · tstep size). We used 1-ps steps, and the result-ing spectroscopic range of 500 GHz was sufficient to resolve

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Fig. 3. Rotational Raman spectra for mass 76 u. (Top) Continuous 1-ps sam-pling of a 15.3-ns delay range (total of 1 · 108 ion counts). (Bottom) Randomsparse 1-ps sampling of a 312.8-ns delay range with a similar number of sam-ples (total of 8.5 · 106 ion counts). Insets show data with identical ordinatebut 40-fold and 1,600-fold enlarged abscissa. Please note the logarithmicordinates.

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Fig. 4. Band assignment for CS2 isotopologue spectra. (Top) The spectrumfor the main isotopologue 12C32S2 (76 u) showed one rotational progres-sion for the vibrational ground state (Σg) and two progressions for the firstvibrationally excited bending states (Πe

u and Πfu). (Middle) The spectrum for

mass 77 u showed progressions for the 13C32S2 (13C) and the 33S12C32S (33S)isotopologues. (Bottom) The spectrum for mass 78 u showed one progres-sion for the 34S12C32S (34S) isotopologue. Insets show data with enlargedabscissa.

the complete rotational spectra in our cold molecular beam.The acquisition of correlated broadband, high-resolution dataimposed a serious burden for the data collection and analysis:Already the lower resolution data shown in Fig. 2 required themeasurement of > 15,000 mass spectra for signal and reference

over the course of more than 2 d. Each mass spectrum contained150,000 mass signals, creating signal and reference datasets withapprox. 4.6 · 109 data points.

With random sparse sampling, we greatly reduced the mea-surement time and data quantity. As discussed in the fieldof multidimensional NMR spectroscopy (24, 25), sparse sam-pling led to a modest degradation of the signal-to-noise ratio.Our data acquisition speeds were still severely limited by theused single-ion counting electronics, precluding higher resolu-tion measurements. We expect that future CRASY experiments,based on the detection of larger signals, can collect similar orbetter quality data in a fraction of the measurement time. It isworthwhile to point out that our experiments are not affected byDoppler broadening, which remains below ∆νDb/ν= 6.6 · 10−9

due to the small collimation angle of the molecular beam.The accuracy of CS2 isotopologue rotational constants derived

from our measurements was < 1 kHz for the main isotopologueand a few kilohertz for naturally occurring heavier isotopologues.Through a simple measurement of the laser oscillator frequency,our measured spectroscopic frequencies were referenced with anaccuracy ∆ν/ν� 10−8 to an external clock. Uncertainties due totemperature, air pressure, or humidity affected only the opto-mechanical delay accuracy and created a relative uncertaintyof < 1 · 10−6 for the opto-mechanical (< 12.5 ns) delay. Uponevery oscillator pulse jump, this uncertainty was reset to themuch smaller uncertainty of the oscillator frequency measure-ment. The opto-mechanical delay uncertainty therefore scaledinversely to the number N of oscillator jumps and becamenegligible for large N . Measured frequencies were thereforeabsolute frequency values within the measurement precision.Our rotational constants agreed well with all literature valuesfrom high-resolution rovibrational spectroscopy (see Table 1).Kummli and coworkers (7, 9) reported a significantly differentrotational constant of B = 3.271 549 2 (±18) GHz for the mainCS2 isotopologue ground state, based on RCS spectroscopy.(The striking 18 sigma deviation of this value from ours and lit-erature values may be due to a typographic error: The tabulatedrotational constant in ref. 7 indicates a 10-fold higher standarddeviation than the values claimed in the paper abstract and text.)

Modern chirped-pulse Fourier-transform microwave (FTMW)experiments achieve an instrument resolution and accuracydown to a few kilohertz, with a spectroscopic range exceed-ing 10 GHz (26). Doppler broadening (typically in the 100 kHzrange) reduces the effective resolution, which is neverthelessfar beyond the resolution achieved here. The accuracy of rota-tional constants determined here, however, was comparable tothe 4 kHz frequency precision claimed for FTMW spectroscopy(26). We expect that CRASY experiments will be complemen-tary to FTMW spectroscopy: CRASY explores rotational Raman

Table 1. Observed CS2 isotopologues, isotopologue masses (u), rotational constants (kHz), and centrifugaldistortion constants (Hz)

Rotational constant Beff * Centrifugal distortion Deff

Isotopologue Mass State This work Literature Ref. This work Literature Ref.

32S12C32S 76 Σg 3,271,517.0 (0.7) 3,271,516.5 (1.5) 20 355 (3) 352.79 (9) 2076 Πe

u 3,276,738 (9) 3,276,759 (12) 18 347 (58) 359.1 (6) 1876 Πf

u 3,279,064 (7) 3,279,077 (11) 18 386 (38) 360.6 (6) 1832S13C32S 77 Σg 3,271,634.6 (1.3) 3,271,637.8 (0.3) 21 346 (7) 350.76 (2) 2132S12C33S 77 Σg 3,221,849.4 (2.6) 3,221,843 (11) 18 329 (13) 341.3 (1.1) 1832S12C34S 78 Σg 3,175,020.4 (1.2) 3,175,024 (8) 18 318 (6) 332.6 (5) 1832S13C34S 79 Σg 3,175,120 (18) 3,175,115.1 (1.3) 21 318 (95) 332.94 (15) 2134S12C34S 80 Σg 3,079,422 (9) 3,079,377 (27) 18 339 (48) 346 (16) 22

The most precise literature values are given for comparison. Values in parentheses denote the 1σ standard deviation forthe corresponding last digits.*For the vibrationally excited Πu states, Beff differs from B due to the l-type splitting.

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transitions instead of dipole transitions, covers a larger spec-tral range (≥ 10 GHz for chirped-pulse FTMW experiments and500 GHz for our data), and allows correlation to ion masses orother spectroscopic observables.

There are illustrative parallels between the CRASY experi-ment reported here and frequency comb measurements (13, 14,27). Both experiments rely on the discrete emission propertiesof mode-locked laser oscillators. Such oscillators emit a discretepulse train in the time domain and, as expected from the Fouriertheorem, a discrete line spectrum in the frequency domain.Frequency comb spectroscopy exploits the discrete frequencyproperty and compares an interferometric beating pattern to anexternal clock to determine and lock the line frequencies in anactive feedback loop. Spectroscopy with the comb lines measuresabsolute transition frequencies with an accuracy approachingthat of the clock.

High-resolution CRASY exploits the discrete time domainproperty of the oscillator pulse train to observe the beatingpattern between quantum mechanical states. The measurementaccuracy is tied to an external clock through a measurementof the oscillator repetition rate. CRASY does not require afrequency- or phase-locked oscillator but requires merely astable oscillator repetition rate on the time scale of the oscil-lator frequency measurement. Instead of active frequency sta-bilization, oscillator drifts are corrected with an adjustment oftime delays in the opto-mechanical delay line. The resultinglock between clock and measured spectroscopic frequencies isequivalent to that in frequency comb spectroscopy; hence, ourmeasurement is a time-domain equivalent to frequency combspectroscopy.

The inherent value of correlated spectroscopic data aredirectly related to the type and quantity of the collected data: Sig-nals that cannot be resolved along one spectroscopic axis may bedistinguished along another and are therefore easily separated.

The correlation of molecular mass (analyzing molecular com-position) and rotational spectra (analyzing molecular structure)allowed us to separate rotational spectra for 6 (this work) or 10(1) CS2 isotopologues in a single measurement. Signals for smallisotopologues were observed in separate mass channels and weretherefore not obscured by the baseline noise of larger signals.

The correlation of mass and rotational structure, as presentedhere, might become a valuable tool for molecular structure deter-mination and for the analysis of isotope effects. The potential forCRASY spectroscopy, however, goes beyond the data discussedin this manuscript. Future CRASY experiments may correlaterotational spectra with any other spectroscopic observable thatcan be interrogated with ultrafast laser pulses: A coherent rota-tional wave packet will modulate any spectroscopic signal thatis tied to a molecular transition dipole with well-defined orien-tation in the molecular frame. This should be relevant for theanalysis of any heterogeneous sample, where independent spec-troscopic measurements cannot separate signal contributionsfrom individual sample components. The majority of molecu-lar samples are inherently heterogeneous: Natural or synthesizedsamples are rarely of pure structural, isomeric, or isotopic com-position. Traditional spectroscopic experiments excel in the anal-ysis of abundant species and purified compounds. CRASY willfacilitate the characterization of inherently impure samples (e.g.,reactive species, tautomers, or weakly bound molecular clusters).

SI AppendixSI Appendix describes the data analysis protocol for each figureand explains how rotational constants were fitted to the data.

ACKNOWLEDGMENTS. We acknowledge thorough proofreading byDong-Eun Lee. This research was supported by the Basic Science ResearchProgram through the National Research Foundation of Korea (NRF) fundedby the Ministry of Science and Information and Communication TechnologyGrant NRF-2014R1A2A1A11053055.

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