CRASY: Mass- or Electron-Correlated Rotational Alignment Spectroscopy

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Science  19 Aug 2011:
Vol. 333, Issue 6045, pp. 1011-1015
DOI: 10.1126/science.1204352


Rotational spectra have traditionally been measured without a concurrent means of differentiating the molecular constituents of the sample. Here, we present an all-optical multipulse experiment that allows the correlated measurement of rotational and mass or photoelectron spectra by combining Fourier transform rotational coherence spectroscopy with resonance-enhanced multiphoton ionization. We demonstrate the power of this method with the determination of ground-state rotational constants and fragmentation channels for 10 different isotopes in a natural carbon disulfide sample. Three of the reported rotational constants were previously inaccessible by conventional spectroscopic techniques.

The information obtained from n independent measurements is, at best, equal to the sum of the information content in the individual measurements, that is, scales linearly with n. This is a rather unfavorable scaling law relative to the experimental effort. If n correlated properties are investigated simultaneously, the information content scales as the product of the information from individual measurements, that is, scales exponentially with n, because the spectroscopic axis is now replaced with an n-dimensional spectroscopic space spanned by the axes of the individual measurements. The experimental implementation of correlated measurements and the analysis of unwieldy quantities of multidimensional data are considerable technological challenges but are facilitated by a careful choice of correlated properties.

As demonstrated by Ernst and co-workers in the field of nuclear magnetic resonance (NMR) spectroscopy, the correlated measurement of n-dimensional spectroscopic data is most efficiently performed in the time domain with the use of Fourier transform (FT) methods [e.g., correlation spectroscopy (COSY) (1, 2)]. The large amount of information emanating from correlation spectroscopy and related techniques allowed the disentanglement of overlapping signals and coupling constants in convoluted spectra and culminated in the analysis of macromolecular structure by NMR (3, 4).

Optical spectroscopy based on femtosecond lasers is routinely used to carry out time-domain experiments on rotational, vibrational, and electronic degrees of freedom. But the correlated measurement of observables akin to COSY has only been pursued in the field of condensed phase vibrational and electronic spectroscopy (5, 6). Here, we describe such an approach for the correlated measurement of ground-state rotational structure and pump-probe ionization spectra in correlated rotational alignment spectroscopy (CRASY). With this method, we assign rotational spectra to a number of naturally occurring carbon disulfide (CS2) isotopes that hitherto eluded experimental measurement.

The measurement of rotational spectra in the time domain requires the excitation of a coherent superposition of rotational states (rotational wave packet). With rotational periods of typical chromophores in the range of a few to hundreds of picoseconds, such an excitation can be generated by direct absorption of radiowaves or by short optical pulses. In FT microwave spectroscopy (7) and related broadband spectroscopy techniques, a cold molecular jet is excited with radiowaves, and the induced polarization is recorded to yield rotational spectra with extraordinary contrast and resolution. Recent examples highlight the power of this approach through the determination of cluster structures in weakly bonded clusters (8), the investigation of isomerization kinetics (9), the detailed characterization of biomolecular structures (10), and the rapid analysis of complex molecular mixtures (11, 12).

When vibrational or electronic states are excited with short and polarized laser pulses, a rotational wave packet may be formed in the excited state. In rotational coherence spectroscopy (RCS), Felker and many others monitored the evolution of such wave packets to characterize the excited state structure of mostly aromatic molecules and clusters (13, 14). A rotational wave packet can also be created in the ground state by coherent Raman excitation, an approach used for RCS spectroscopy (1517) or to achieve field-free (“nonadiabatic”) alignment of molecular samples (18, 19). We used this last approach as a first step in CRASY experiments and probed the rotational wave packet by electronic excitation and subsequent ionization.

Because molecular collisions reduce the lifetime of rotational states, high-resolution rotational spectroscopy is best performed with isolated molecules in the collision-free environment of a molecular beam vacuum spectrometer. Microwave spectroscopy established rotational dephasing times in the range of 10 to 100 μs for unskimmed molecular beams (20), four orders of magnitude slower than the observation times relevant for our experiment. The dephasing times were dominated by Doppler broadening effects, which play no role in our impulsive measurement scheme. Hence, the physical limit for rotational resolution in CRASY is in the kHz regime or below. The vacuum conditions are also perfectly suited for the efficient detection of electrons and ions on which our detection scheme relies.

The experimental principle is depicted in Fig. 1 (21). We seeded a liquid sample of CS2 in 30 to 60 bar of helium and expanded the mixture through a pulsed valve into a vacuum spectrometer. The resulting cold molecular beam was skimmed and crossed the ionization region of an electron and mass spectrometer. There, a rotational wave packet was induced via an 800-nm, 1.5-ps nonadiabatic alignment pulse. The evolution of the wave packet was probed via two-photon ionization with a 200-nm, 100-fs ionization pulse. The 200-nm wavelength induces the two-photon ionization of CS2 via a resonant electronic state. The resultant molecular ions were mass-analyzed in a Wiley-McLaren time-of-flight mass spectrometer, and the kinetic energy of the emitted electrons was determined in a magnetic-bottle electron spectrometer (22).

Fig. 1

CRASY experimental scheme. A freely rotating ensemble of molecules in a cold molecular beam (A) is exposed to a strong, linearly polarized alignment laser pulse (B). Thus, the ensemble is subjected to a torsional potential because of the anisotropy of molecular polarizability. After the pulse, the molecules rotate coherently with a new angular momentum L (C), and we observe states of alignment (D) and anti-alignment (E) as a function of time. The coherent rotational motion is probed by delayed photoexcitation and ionization with a second laser pulse. Because of the transient alignment of transition dipoles, the signal intensity is modulated with the delay time.

The alignment pulse generates a rotational wave packet via a Raman excitation process. Such an excitation is feasible if the molecule can be anisotropically polarized, as is the case in CS2 along the axis of the linear molecule. The excitation process is an impulsive event; that is, all molecules simultaneously receive an angular momentum kick toward the polarization axis of the exciting laser. As a result, the molecules rotate coherently within the reference frame of the laboratory, and a transient alignment of the molecules is observed. Because the transition dipoles for electronic excitation are fixed in the molecular frame, we can interrogate the rotational wave packet by electronic excitation with a probe laser pulse. If the polarization of the probe pulse is parallel to the transition dipoles, the excitation probability is large. However, if the probe polarization is perpendicular to the transition dipoles, the excitation probability is zero. Therefore, a corresponding signal will show a temporal modulation, which contains all the eigenfrequencies of the coherently excited rotational states. We probed the wave packet for a sequence of evolution times by resonant two-photon ionization via an electronically excited state. Thus, we observed the signal modulation in the amplitudes of ion signals in a mass spectrometer or in the amplitudes of electron signals in an electron spectrometer. The FT of the temporally modulated signal in each ion mass channel or for each electron energy gives a correlated mass-rotational (mass-CRASY) or photoelectron-rotational (electron-CRASY) spectrum. Similar CRASY experiments should be possible by using any optical probe pulse that drives a transition with a well-defined excitation dipole in the molecular frame; for example, any rotational, vibrational, or electronic transition.

In practice, the observation window of the time domain signal is limited by the scan range of an electronic or optical delay. We used an optomechanical delay with folded beam geometry and a 300-mm traveling range (corresponding to 2-ns delay range), which limits the resolution in our experiment to 500 MHz. This resolution is sufficient to resolve isotopic, isomeric, and even tautomeric structure in many chromophores and can be easily improved by extending the delay range. Comparison of our spectroscopic results with literature values for the most abundant CS2 isotope (17) indicate an absolute positioning error of less than 100 μm over the 300-mm length of the delay stage.

The mass spectrum of a CS2 sample shows multiple signals in the range of 76 to 82 atomic mass units (amu) because of the presence of 12C, 13C, 32S, 33S, 34S, and 36S isotopes (Fig. 2). For each isotope signal, we observed a time-dependent signal modulation because of coherent rotational alignment. A FT of the time-domain traces yields rotational Raman spectra containing the frequency components for all rotational states forming the coherent wave packet. To minimize artifacts in the FT process, we used a Hamming window and zero padding as common in NMR data analysis (23).

Fig. 2

Mass-CRASY experimental data. A time-of-flight mass spectrum (top) identifies CS2 isotopes (A to F) and atomic or molecular fragments. u indicates amu. Insets for signals D, E, and F are scaled to show small signal amplitudes. The signal intensities for all CS2 isotopes (bottom left) are modulated as a function of delay time by the coherent rotation of the molecules. FT of the delay traces yields rotational spectra for all isotopes (bottom right). The signal for 81 amu isotopes (F) with an abundance < 2 × 10−5 shows a well-resolved rotational progression and illustrates the sensitivity of our method.

The frequency domain data for the mass channel 76 amu showed a single progression of rotational transitions (bands) for the most abundant isotope, 32S12C32S (Fig. 3A). Raman transition rules for states with frequencies of ωJ = B · J(J + 1) allow ∆J = ±2 transitions. Higher order terms due to centrifugal distortion can be neglected within our experimental precision. Because the molecule is inversion symmetric, only even J states are observed. Hence, a linear fit of band positions to the equation ωJ = B · (4J + 6), (J = 0, 2, 4,...) yields the rotational constant B = 3.2714(2) GHz for this CS2 isotope (numbers in parentheses give the 95% confidence range for the corresponding last digits).

Fig. 3

(A) All 12 rotational bands in the frequency domain spectrum of mass 76 amu (top, bands marked with red dots) are assigned to ωJ = B · (4J + 6) transitions between even rotational states of the symmetric, linear 32S12C32S molecule and allow the determination of a rotational constant B = 3.2714(2) GHz. The negative phases ΘJ and phase-weighted amplitudes rJsinJ) (bottom) of identified bands reflect the delayed alignment relative to the zero in time. (B) The sum ∑rJcos(ωJt + ΘJ) of 12 waves with amplitudes rJ, frequencies ωJ, and phases ΘJ as determined in the rotational spectrum, form a wave packet (red), which reproduces the time domain trace (black). The magnification of areas with quarter and half revivals (insets) shows the excellent agreement of experimental and simulated traces. (C) The frequency domain spectrum for mass channel 79 amu (top) in a measurement with oversaturated detector shows bands corresponding to ωJ = B·(4J + 6) transitions of the linear, asymmetric 32S13C34S (blue dots) and 33S12C34S isotopes (green dots) but also saturation artifacts from the more abundant 32S12C32S isotope (red dots). The phase of the saturation signal and the corresponding phase-weighted amplitude rJsin(ΘJ) (bottom) are inverted and therefore easily distinguished from the true signals. (D) The time-domain data are reproduced with the sum of 43 waves corresponding to band amplitudes and phases for the three isotopes.

The FT permits extraction of the amplitude rJ and relative phase ΘJ for each band in the rotational spectrum. Because the alignment pulse is shorter than the rotational period, the first alignment event occurs with a delay relative to the alignment pulse. In the range of –π to π, a negative phase indicates that the initial rotational motion leads to an increasing signal (alignment of the electronic transition dipoles into the axis of the probe-pulse polarization) and that the electronic transition dipole lies in the axis of largest molecular polarizability, as is the case for CS2 (24). The phase-weighted amplitudes rJsin(ΘJ) allow the simultaneous consideration of signal amplitudes and phases. The amplitudes and phases of the 12 assigned bands were used to reconstruct the time-domain data (Fig. 3B). Enlarged sections of the trace show how the individual waves sum up into a wave packet with pronounced revivals. The revivals correspond exactly to the moments of molecular alignment and offer a high-fidelity reproduction of the experimental trace.

At the mass of 79 amu, we expected to observe the isotopes 32S13C34S and 33S12C34S with abundances of about 4 × 10−4 (Fig. 3C). However, the signal also showed a progression belonging to the more abundant main isotope. The large signal at the mass of the main isotope (76 amu) reduced the detection efficiency for all ions with longer times of flight (larger masses), leading to a signal modulation with the main isotope frequency but an inverted sign. The phase associated with this saturation artifact is shifted by π; therefore, true signals were easily distinguished from the saturation artifact by plotting the phase-weighted amplitudes. The sulfur isotopes in 32S13C34S and 33S12C34S break the inversion symmetry of the molecule, and we observed transitions for even and odd values of J. We easily distinguish progressions for the two isotopes, and a linear fit of band positions to ωJ = B · (4J + 6), (J = 0, 1, 2,...) yields the ground-state rotational constants of B(32S13C34S) = 3.1746(5) GHz and B(33S12C34S) = 3.1263(5) GHz. Again, the frequencies and phases of the assigned bands allow the reproduction of the time-domain trace (Fig. 3D).

Through the analysis of rotational spectra at all CS2 isotope masses in a sample with natural isotopic distribution, we were able to resolve rotational constants for 10 out of 20 stable CS2 isotopes (Table 1). We found corresponding literature values for only seven of these, mostly derived from measurements on isotopically enriched samples. The extraordinary sensitivity of mass-CRASY experiments is evident in our ability to assign spectra for rare isotopes with abundances in the 10−5 range, which were previously inaccessible to experimental characterization. This sensitivity relies on the fortuitus property of FT spectroscopy, which spreads time-dependent noise across the frequency axis.

Table 1

Table of CS2 isotopes (rare isotope atoms are in bold type), isotope masses (in amu), abundances, and rotational constants (in GHz). Masses and abundances are given according to (26). Calculated density field theory (DFT) frequencies stem from a B3-LYP calculation with 6-311G**++ basis set (27), scaled to the main isotope frequency. We cite the most recent or the most precise literature value for the rotational constant of each isotope.

View this table:

Mass-CRASY data correlate rotational Raman spectra of a neutral ground-state molecule with the masses of ionic products formed by pump-probe ionization. The added value of this correlated information as compared with uncorrelated mass and rotational spectra is best illustrated in a two-dimensional plot of signal intensities versus rotational frequency and ion mass (Fig. 4). It is difficult to distinguish different isotopes with the same nominal mass in a mass spectrum (30); for example, 32S12C33S (76.94 amu) versus 32S13C32S (76.95 amu). It is also difficult to distinguish certain isotopes in the rotational spectrum; for example, 32S12C32S [3.2714(2) GHz] versus 32S13C32S [3.2720(8) GHz]. With the combined mass and frequency information in the mass-CRASY data, the direct assignment of all signals to individual isotopes is easily accomplished (Fig. 4, right inset).

Fig. 4

Two-dimensional representation of a mass-CRASY data set (center). Phase-weighted data show real signals (black spots) and saturation artifacts because of a large 76-amu parent ion signal (red spots). To visualize signal amplitudes spanning many orders of magnitude, we plotted the logarithm of the signal-to-noise ratio in each mass channel (i.e., normalized the noise) and smoothed the data along the mass and frequency axes. Signals can be assigned to single isotopes as illustrated in the inset (right) for 32S12C32S (a), 32S13C32S (b), 32S12C33S (c), 32S12C34S (d), 32S13C34S (e), 33S12C34S (f), 34S12C34S (g), and 34S13C34S (h). Fragmentation in the ionic state leads to the formation of S2 (64 to 68 amu), CS (44 to 48 amu), S (32 to 36 amu), and C (12 to 13 amu). Frequency spectra at fragment masses (top, vertical cuts through the mass-CRASY data) show the rotational Raman frequencies of the parent molecules. Mass spectra at rotational frequencies (left, horizontal cuts through the mass-CRASY data) show fragments stemming from a parent molecule with corresponding rotational frequency. We show data for frequencies of 229.0 GHz (only 32S isotopes in parent and fragments; signals for 76 to 80 amu plotted with inverted amplitude), 209.5 GHz (one 34S isotope), and 190.9 GHz (two 34S isotopes).

Molecular fragmentation is a common process in pump-probe ionization spectroscopy and can seriously impede the interpretation of spectroscopic data. Fragmentation occurs in the excited or ionic state, that is, after the rotational wave packet is probed by the ionization pulse. Hence, the rotational spectra observed at the mass of a molecular or atomic fragment correspond to those of the unfragmented parent molecule and thereby allow the direct assignment of fragment to parent. A horizontal cut through the CRASY data at the frequency of a selected isotope yields a mass spectrum containing the signal of parent and all fragments, as shown for three frequencies on the left of Fig. 4. For CS2, we observe the fragmentation of covalent bonds and the formation of S2, CS, S, and C fragments. The direct characterization of multiple fragmentation pathways in a heterogeneous sample will be of particular importance for the investigation of noncovalently bound clusters, where the interpretation of pump-probe data is hindered by ease of fragmentation [see, e.g., the vast literature on phenol-ammonia clusters as summarized in (31)].

Analogously to the correlation of rotational structure and ion mass with mass-CRASY, electron-CRASY data correlates rotational structure with photoelectron spectra. This allows the measurement of electron spectra with structural selectivity. The combination of electron- and mass-CRASY experiments allows the indirect correlation of mass and electron spectra via rotational frequencies. In appropriate cases, mass- and electron-CRASY experiments could therefore deliver data comparable to that available from femtosecond electron-ion coincidence experiments, which have to be performed with very low signal collection rates and are highly time-consuming (32, 33). In the present study, we observed identical electron spectra for different CS2 isotopes because the isotopic composition has a negligible effect on the electronic structure of the molecule (fig. S7). The bimodal shape of the electron spectrum is due to the presence of a bright 1Σu+ and a dark 1Πg excited state, which interact upon bending of the molecule (34).

The experimental results presented here raise the prospect of numerous spectroscopic experiments on larger and more complex molecules. The only fundamental issue limiting the applicability of CRASY is the requirement of an appreciable anisotropic polarizability (and corresponding rotational Raman cross sections) in the investigated molecules. The same limit applies to nonadabatic alignment experiments, which have been successfully demonstrated for a number of larger chromophores; for example, iodobenzene, dibromothiophene, and difluoroiodobenzene (35, 36). To observe substantial nonadiabatic alignment, the phase relation between the states forming the rotational wave packet must be favorable. This condition does not apply to CRASY, where the mere existence of rotational coherence and the associated temporal signal modulations are sufficient to generate a detectable signal. With the high sensitivity demonstrated here for CRASY, we expect that a large majority of chromophores will be accessible to CRASY experiments.

The information content of rotational spectra is very large, and the interpretation of such spectra is commensurately complicated. The additional spectroscopic axes in CRASY experiments can assist the analysis of rotational spectra in impure samples; for example, by correlated determination of ion masses (in mass-CRASY), ionization potentials (in electron-CRASY), or fluorescence spectra (in fluorescence-CRASY). Together with the recent development of mathematical algorithms for the semiautomated assignment of rotational spectra (37), this technique may generally facilitate the structural characterization of constituents in inherently unstable samples or samples containing inseparable compounds.

Supporting Online Material

Materials and Methods

Figs. S1 to S7


References and Notes

  1. A detailed description of the experimental setup is given in the supporting online material.
  2. Please refer to the supporting online material for a description of the data processing techniques and for enlarged experimental traces (figs. S1 to S6).
  3. Quadrature detection, as is common in NMR (25), could be implemented by alternating the probe pulse polarization between parallel and perpendicular with respect to the pump. This would allow the measurement of absolute phases (and thereby transition dipole orientations).
  4. The distinction of isotopes with the same nominal mass is only possible with very high resolution mass spectrometers, which are capable of resolving the isotopic mass defect.
  5. Acknowledgments: We thank F. Noack for support by providing the laser system in the femtosecond application laboratory of the Max-Born-Institut Berlin. Financial support by the Deutsche Forschungsgemeinschaft through SFB-450 is gratefully acknowledged.
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