Anal. Chem. 2005, 77, 5467-5473
Peak Separation and Sorting by Coherent 2D Resonance Raman Spectroscopy Peter C. Chen* and Candace C. Joyner
Chemistry Department, Spelman College, 350 Spelman Lane, Atlanta, Georgia 30314
The ability to separate and sort peaks is explored using a new coherent two-dimensional form of resonance Raman spectroscopy. This experimental technique distributes normally congested rotational-vibrational peaks along a series of curved lines according to vibrational sequence, rotational quantum number, and selection rule. Each line consists of rotational-vibrational peaks that have the same vibrational sequence and the same value for ∆J, distributed in order by rotational quantum number. For diatomic molecules, these lines originate from points where they initially travel in opposite or orthogonal directions in two-dimensional space, which helps facilitate the separation between lines. Simulations and experimental results on C2 in a flame confirm the ability to separate and sort these normally congested rotationalvibrational peaks. This method appears to provide a solution to the long-standing problems of spectral congestion and disorder in gas-phase electronic spectra. The electronic spectra of gas-phase molecules are potentially rich but often notoriously difficult-to-analyze sources of information on molecular structure and behavior. These spectra typically contain thousands of peaks from transitions between the many rotational-vibrational levels of the ground and excited electronic states. The peaks originate from multiple pathways corresponding to spectroscopic selection rules, different modes of vibration, and isotopes. Peaks from different pathways often overlap with one another, resulting in severe spectral congestion and the appearance of disorder. In conventional spectroscopy, the congestion can cause the peaks to form unresolved bands unless performed under conditions for high-resolution spectroscopy. Even if individual peaks are resolved, the assignment of such peaks can be difficult because peaks from one process occupy the same spectral space as peaks from other processes. Effects such as perturbations can cause peak frequencies to deviate from their theoretical position, further complicating the ability to sort through the congestion. Consequently, the gas-phase UV-visible spectra for the vast majority of molecules have never been completely analyzed. Recently, two-dimensional (2D) spectroscopy has gained attention as an effective approach for improving spectral resolution and addressing the issue of spectral congestion by dispersing information (peaks) along a second dimension.1 Among these 2D * To whom correspondence should be addressed. E-mail: spelman.edu. Fax: 404-270-5752. 10.1021/ac0504215 CCC: $30.25 Published on Web 08/04/2005
pchen@
© 2005 American Chemical Society
Figure 1. Simple simulated 2D plot (left) and energy level diagram (right) for C2DRR spectroscopy. The simple simulated plot shows the location of off-diagonal cross-peaks between a vibration in the ground electronic state (level b) and a coupled vibration in the excited electronic state (level d). For the energy level diagram, the thick arrows indicate broadband light and the thin arrow (for ω3) indicates narrowband light. Level c is a (nonresonant) virtual level.
techniques are a number of new coherent 2D spectroscopic techniques that can use electronic or vibrational coupling to resolve overlapping peaks.2-5 Information not available from conventional one-dimensional (1D) techniques can be extracted from the location, amplitude, shape, and behavior of cross-peaks that appear in the off-diagonal region of the 2D spectra (see Figure 1). In 1991, Suter et al.6 published a paper showing cross-peaks due to atomic sublevel coherences in sodium vapor. In 1993, Tanimura and Mukamel7 proposed using 2D femtosecond spectroscopy to study dephasing mechanisms in liquids. Afterward, Jonas and co-workers published work on 2D Fourier transform electronic spectroscopy as an analogue to 2D NMR spectroscopy,8 a well-established and powerful technique based upon spin coupling. Other groups have used coherent 2D spectroscopy to develop alternative approaches such as phase cycling9 instead of (1) Noda, I. Vib. Spectrosc. 2004, 36, 143-165. (2) Wright, J. C. Int. Rev. Phys. Chem. 2002, 21, 185-255. (3) Jonas, D. M. Annu. Rev. Phys. Chem. 2003, 54, 425-463. (4) Mukamel, S. Annu. Rev. Phys. Chem. 2000, 51, 691-729. (5) Cho, M. Adv. Multi-Photon Proc. Spectrosc. 1999, 12, 229-300. (6) Suter, D.; Klepel, H.; Mlynek, J. Phys. Rev. Lett. 1991, 67, 2001-2004. (7) Tanimura, Y.; Mukamel, S. J. Chem. Phys. 1993, 99, 9496-9511. (8) Hybl, J. D.; Albrecht, A. W.; Gallagher Faeder, S. M.; Jonas, D. M. Chem. Phys. Lett. 1998, 297, 307-313. (9) Tian, P.; Keusters, D.; Suzaki, Y.; Warren, W. S. Science 2003, 300, 15531555.
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phase matching, and to explore other applications such as the study of electronic coupling in dimers.10 Coherent 2D vibrational spectroscopy, based upon vibrational coupling, has been used to study vibrational anharmonicities (to separate contributions from overtones and combination bands),11 to study and distinguish between conformational changes,12 to study solvent-solute interaction,13 to determine the angles between transition dipoles,14 and to use vibrational coupling to resolve peaks that are unresolved in conventional vibrational spectroscopy. Techniques used to produce coherent 2D vibrational spectra include the DOVE technique15 developed by the Wright group, 2D IR technique16 developed in Hochstrasser’s group, and a six-wave mixing approach developed by Tokmakoff and coworkers.17 In this paper, we introduce coherent two-dimensional resonance Raman (C2DRR) spectroscopy as a new spectroscopic technique that can explore and use the coupling among rotational, vibrational, and electronic motions in molecules. Figure 1 illustrates how this C2DRR approach can be used to produce a cross-peak between a lower state vibration at frequency ωba and a coupled higher electronic state at frequency ωda. The spectral resolution of this 2D technique is sufficiently high to resolve rotational structure in the region of the cross-peaks. Therefore, the observation, location, and structure of the cross-peaks are sensitive to factors such as the electronic, vibrational, and rotational spectroscopic constants, the sequence of vibrational transitions, the values of rotational quantum numbers, and various selection rules. Furthermore, this technique appears to have the ability to separate, resolve, and sort peaks in a way that should be useful for addressing the long-standing problem of congestion and disorder in electronic gas-phase spectroscopy. THEORY AND SIMULATIONS Resonance Raman spectroscopy is an attractive technique because the Raman effect provides a rapid, in situ, universal method for fingerprinting molecules that can simultaneously probe electronic, vibrational, and rotational information. Coherent forms of spectroscopy provide several advantages over incoherent counterparts, including (1) the generation of an intense signal in the form of a coherent beam, (2) spatial resolution defined by the overlap of three beams, (3) the ability to distinguish between stray and coherent light by blocking beams, and (4) the use of spatial filtering through phase-matching rather than frequency filtering to remove light from the input beams. The use of a multiplex coherent Raman approach provides the additional benefits of high speed and noise reduction.18 (10) Prall, B. S.; Parkinson, D. Y.; Fleming, G. R.; Yang, M.; Ishikawa, N. J. Chem. Phys. 2004, 120, 2537-2540. (11) Zanni, M. T.; Ge, N.-H.; Kim, Y. S.; Hochstrasser, R. M. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11265-11270. (12) Woutersen, S.; Mu, Y.; Stock, G.; Hamm, P. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11254-11258. (13) Demirdoven, N.; Khalil, M.; Tokmakoff, A. Phys. Rev. Lett. 2002, 89, 237401/ 1-237401/4. (14) Zanni, M. T.; Gnanakaran, S.; Stenger, J.; Hochstrasser, R. M. J. Phys. Chem. 2001, 105, 6520-6535. (15) Zhao, W.; Wright, J. C. J. Am. Chem. Soc. 1999, 121, 10994-10998. (16) Hamm, P.; Lim, M.; DeGrado, W. F.; Hochstrasser, R. M. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 2036-2041. (17) Golonzka, O.; Demirdoven, N.; Khalil, M.; Tokmakoff, A. J. Chem. Phys. 2000, 113, 9893-9896.
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The nonlinear polarization responsible for generating a coherent Raman signal can be described by the third term in the expansion
P ) χ(1)E + χ(2)EE + χ(3)EEE + ...
(1)
where E is the electric field generated by one or more input beams of light. The third-order nonlinear susceptibility χ(3) can be described by
χ(3) ∝
∑µ
acµcbµbdµda/∆ca∆ba∆da
(2)
where µxy is the transition dipole moment between levels x and y; the resonant denominators take the form ∆levels ) ωlevels - ωlasers - iΓlevels, and the summation is over all states. In the case of the C2DRR process shown in Figure 1, (b) represents a rotationalvibrational level in the lower electronic state and (d) is a rotational-vibrational level in the upper electronic state. The energies for the upper and lower states of a simple diatomic molecule are commonly described by
E ) Te + G(v) + F(J)
(3)
where
G(v) ) ωe(v + 1/2) - ωe xe(v + 1/2)2 + ωe ye(v + 1/2)3 + ... (4a) F(J) ) Bv J(J + 1) - Dv J2(J + 1)2 + ...
(4b)
Bv ) Be - Re(v + 1/2) + γe(v + 1/2)2 + ...
(4c)
Dv ) De + βe(v + 1/2) + ...
(4d)
The off-diagonal region of the 2D spectrum should be dominated by cross-peaks from levels that are coupled through the resonance Raman effect; strongly coupled transitions that obey the relevant selection rules may enhance wave mixing between the input and output fields, resulting in the appearance of these off-diagonal peaks. Raman selection rules based upon the rigid rotor and harmonic oscillator models dictate that ∆J ) 0, (2 for rotations and that ∆v ) (1 between vibrations in the same electronic state. Selection rules such as those for nuclear spin statistics can cause alternations in the peak intensity for neighboring processes. If the spectral resolution is sufficiently high, effects from spin-orbit coupling and λ-type doubling may also be observed. Figure 2 shows three simulated plots of different off-diagonal cross-peak regions that could be observed using C2DRR spectroscopy. These cross-peak plots were generated by creating a set of energy levels for a model diatomic molecule using eq 3 and then (for simplicity) applying only the rigid rotor and harmonic oscillator selection rules to determine the potentially coupled levels. Several of the curved lines roughly resemble that of a Fortrat parabola,19 a theoretical plot of the rotational quantum number versus energy. The Fortrat parabola is often used when (18) Chen, P. C.; Joyner, C. C.; Patrick, S. T.; Benton, K. F. Anal. Chem. 2002, 74, 1618-1623.
Figure 2. Simulated 2D plots for C2 showing portions of the (a) Mulliken band (Jmax ) 20), (b) Phillips band (Jmax ) 20), (c) Swan band (Jmax ) 40), and (d) Swan band at elevated temperatures (Jmax ) 40). The red points are from ∆J ) 0 transitions, and the blue points are from ∆J ) (2 transitions. The spectroscopic constants used to generate these plots were taken from the NIST website database.23
assigning observed rotational peaks, which is often an early step when analyzing spectra to determine the structure and dynamics of diatomic molecules. In both the case of the Fortrat parabola and that of the simulated 2D spectra, rovibrational peaks from the same vibrational sequence appear on the same curved line, in order according to rotational quantum number (J). In contrast, peaks in conventional spectroscopies that come from different processes are restricted to 1D space and therefore overlap, making them difficult to resolve and identify. By distributing the spectral information over 2D space, as shown in Figure 2, this new technique groups peaks from the same process (along a single curved line) while preserving the peak order (J increases starting from the point where the parabolas intersect). Simulations based upon a model molecule (C2) indicate that a 2D resonance Raman approach should provide an accurate method for identifying (fingerprinting) molecules and studying their structure. The location of the cross-peaks is sensitive to the electronic and vibrational constants, and the shape of the curved lines is sensitive to the rotational constants. For example, the relative size of the rotational constant B determines whether the curved lines extend toward longer or shorter wavelengths with increasing J. In Figure 2a, the rotational constants in the upper and lower electronic levels are similar (B′ ) 1.8332 cm-1 and B′′ ) 1.8198 cm-1), and the resulting pattern resembles a cross. The spectroscopic values used in this simulation are those for the Mulliken band of C2. In Figure 2b, the rotational constant for the lower electronic level is greater than that of the upper electronic level, and what is initially a cross evolves into a pair of parabolas (one wide and one narrow) that extend toward longer wavelengths with increasing J. The spectroscopic values used for this simulation (B′ ) 1.613 cm-1 and B′′ ) 1.8198 cm-1) are for the Phillips band of C2. Figure 2c represents the opposite case where B′ > B′′, and the spectroscopic constants (B′ ) 1.7527 cm-1 and B′′ ) 1.6324 (19) Hertzberg, G. Molecular Spectra and Molecular Structure. Vol. 1. Spectra of Diatomic Molecules; D. Van Nostrand Co., Inc.: Princeton, NJ, 1950; p 48.
cm-1) are for the C2 Swan band. The result shown in Figure 2d is similar to that of Figure 2c, except that the sample temperature is assumed to be sufficiently high to initially populate and permit transitions from levels above the lowest vibrational level. The relationship (B′ > B′′) still applies for the resulting additional transitions, so all of the “hot” parabolas also extend toward shorter wavelengths. Other spectroscopic constants such as the centrifugal distortion constant De affect the ends of the parabolas (where J is large) while terms such as the vibration-rotation interaction term Re (and higher order terms that are multiplied by v) affect the shape similarity among related parabolas such as those shown in Figure 2d. In Figure 2d, the separation between the parabolas depends on the difference between the vibrational frequencies of the upper electronic state and those of the lower electronic state; a large difference between ωe′ and ωe′′ can cause a large separation between the parabolas. The consistency of this separation (with increasing v) depends on the similarity between the anharmonicity of vibrations in the upper electronic state and the anharmonicity of vibrations in the lower electronic state. In the Swan band of C2, the vibrational (ωe′′ ) 1641 cm-1) and vibronic (ωe′ ) 1788 cm-1) frequencies are somewhat similar, making the parabolas sufficiently close to produce the observed fingerprint-like pattern. The anharmonicity constants are ωexe′′ ) 11.67 cm-1 and ωexe′ ) 16.440 cm-1, and the difference is sufficiently large to cause an observed inconsistency in the spacing between the parabolas. The simulations indicate that this technique can sort peaks according to vibrational sequence, rotational selection rule, and rotational quantum number. The fingerprint-like patterns in Figure 2d consist of wide parabolas that are each paired with a nearby narrow parabola. All of the points in a given parabola pair originate from the same vibrational sequence. For example, the upper-rightmost pair (the same parabolas shown in Figure 2c) originate from the sequence v ) 0′′ f 1′′ f 1′ f 0′′, while the points that comprise the second highest pair all follow the sequence v ) 1′′ f 2′′ f 2′ f 1′′. The remaining parabolas follow the same trend. Furthermore, the points that comprise each wide parabola follow the rotational selection rule ∆J ) (2, and the points in the narrow parabolas are due to ∆J ) 0 rotational transitions. The corresponding rigid rotor Raman selection rule can be satisfied in four different ways since each photon can add or subtract one unit of angular momentum. Table 1 lists these four possible pathways and shows whether the corresponding interaction involving ω3 and ω4 is a P-type (J′ - J′′ ) -1) or R-type (J′ - J′′ ) +1). The ability to resolve curved lines is assisted by the fact that the pathways create spatially separated branches starting from the point where the parabolas intersect. The values for the quantum number J increase along each curved line as one travels along a branch and away from these points of intersection. The last two columns in Table 1 are the calculated approximate rotational energy components for ω3 and ω4 as a function of J (within a given parabola, the vibrational and electronic energies remain constant). These results assume that the rotational constant D is negligible compared to B, and they also neglect higher order corrections such as the vibration-rotation interaction term. The results indicate that the energy changes in a relatively systematic way as J increases. The systematic behavior within a branch of parabola causes the peaks to remain in order by Analytical Chemistry, Vol. 77, No. 17, September 1, 2005
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Table 1a ∆J -2 0 0 +2
ω3 R R P P
ω4
ω3 rotational component
ω4 rotational component
P R P R
-2B′′ + (3B′′ - B′)J + (B′ 2B′+ (3B′ - B′′)J + (B′ - B′′)J2 -(B′ + B′′)J + (B′ - B′′)J2 2B′ - 6B′′ + (3B′ - 5B′′)J + (B′ - B′′)J2
-(B′+B′′)J + (B′ - B′′)J2 2B′ + (3B′ - B′′)J + (B′ - B′′)J2 -(B′ + B′′)J + (B′ - B′′)J2 2B′ + (3B′ - B′′)J + (B′ - B′′)J2
B′′)J2
a The molecule’s rotational quantum number J can evolve along four possible pathways due to interactions with ω3 and ω4. Each of these four pathways (shown here) is responsible for generating one of the four branches that comprise two paired parabolas.
Figure 3. Simplified experimental layout of the C2DRR spectrometer.
rotational quantum number. Furthermore, the four branches that constitute a pair of parabolas initially point toward opposite or orthogonal directions from their intersection point. For example, in the simplest case where B′ ≈ B′′ ≡ B, the (x ) ω4, y ) ω3) rotational spacing on the 2D plot would be (-2BJ, +2BJ), (+2BJ, +2BJ), (-2BJ, -2BJ), and (+2BJ, -2BJ) for the four cases (top to bottom) in Table 1. Therefore, the initial directions for curves are opposite or orthogonal. This ordered and opposite behavior helps peaks with the same vibrational sequence and set of ∆J values to remain in order (by J) and separate from other peaks. For the cases where the difference between B′ and B′′ is large, the opposite or orthogonal behavior only occurs for small values of J, but the separation introduced for these small J values helps separate the curved lines when the J’s becomes large. EXPERIMENT Figure 3 shows the experimental layout of the C2DRR spectrometer. A tunable narrowband beam is produced using a commercial OPO (SpectraPhysics MOPO 730 with the frequency doubler option, pumped by an injection-seeded PRO-250 Nd:YAG laser) that can generate pulses of light (bandwidth ∼0.2 cm-1, 5-50 mJ/pulse, pulse duration ∼5 nS, 10 Hz repetition rate) over a continuous range from 220 to 1800 nm (with a few small gaps around 355 and 710 nm). The wide tuning range of this narrow bandwidth source makes it useful for controlling the resonance enhancement effect. The two broadband OPOs, described in ref 18, are each pumped by a 683-nm beam from a hydrogen Raman shifter and tuned to the degeneracy region. The resulting broadband emission covers a continuous range from λ < 1050 nm to λ > 1700 nm with a pulse energy of ∼10 mJ/pulse. The hydrogen Raman shifters are pumped by a frequency-doubled beam from a 10-Hz injection-seeded Spectraphysics GCR-230 Nd:YAG laser. The three beams are then focused and overlapped in the sample using a 1-m focal length lens for the tunable 5470
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narrowband beam and a separate 0.5-m focal length achromatic lens for the two broadband beams. The generated Raman signal emerges in the form of a coherent beam and is spatially separated from the input beams using an iris diaphragm. The beam is collimated using a 0.5-m focal length lens and sent through a BG 40 filter to reduce the risk of accidental damage to the detection system by a stray beam of near-infrared broadband light. A 15-cm focal length lens is used to focus the signal into a 0.5-m Czerny-Turner monochromator (Acton Spectrapro 500i) equipped with a 600 g/mm grating blazed at 500 nm and a gated intensified CCD (Princeton Instruments PI MAX 1024 RB, 1024 × 256, 27 µm/pixel) for multichannel detection. The spectral spacing of this detection system was 0.086 nm/pixel, and the profile of a narrow line source has a fwhm corresponding to 4 pixels (some spectral degradation occurs due to the intensifier), which corresponds to ∼14 cm-1 in the region of the spectrum. The coherent Raman signal contains multiple frequency elements; ω1 and ω2 are sufficiently broad that the combination of ω1 - ω2 interrogates all Raman-active rotational-vibrational frequencies in the lower state from 0 to >3000 cm-1. As the wavelength of ω3 (narrowband OPO) is changed, different vibrational and rotational levels in the electronically excited state are probed for those most strongly coupled to vibrations and rotations in the lower electronic state. 2D spectra are created by stepping the wavelength of the narrowband OPO and recording the resulting sequence of spectra. The spectra are then stacked to show the intensity of the resonantly enhanced Raman signal as a function of input and output wavelengths. The most efficient way to acquire these data involves stepping ω3 without interruption. Therefore, the instrument needs to reject unwanted light over a wide range of input wavelengths without requiring a change in input and output optics. This requirement is accomplished by using the broadly tunable narrowband OPO for the input beam and BOXCARS phasematching, which permits spatial filtering and rejection of elastic scattering from the input beams. An additional advantage of this approach is that one or more of the laser beams can be blocked in order to isolate and then subtract unwanted light generated by other processes (e.g., ambient light or processes that do not depend on all input lasers). BOXCARS phase-matching also allows high spatial resolution because the signal is generated only at the point where the three input lasers intersect. The phasematching angle between the two most widely spaced beams (the two broadband beams) was 2.7°, resulting in a probed volume on the order of 10-5 cm3. The sample was a paraffin oil lamp that burned a mixture of unspecified hydrocarbon fuel in a sooty diffusion flame. Emission
Figure 4. Experimental 2D data shown in the form of a stacked plot. The intensity of the detected light (arbitrary units) is shown as a function of input wavelength λ3 and output wavelength λ4.
spectra of this flame (in the absence of laser beams) were taken using a 1.25-m Czerny-Turner monochromator (SPEX 1250m) equipped with a 2000-element CCD (pixel size of 13.5 µm) and a 1200 g/mm grating blazed at 500 nm. RESULTS AND DISCUSSION Figure 4 shows experimental results from using C2DRR spectroscopy to probe the sooty paraffin diffusion flame. The x-axis (horizontal) corresponds to the detected wavelength, the y-axis (vertical) corresponds to the intensity of the detected light, and the z-axis (into the page) corresponds to the input wavelength of the narrowband OPO, which was scanned using a step size of 0.1 nm. For each step, light from ω4 was collected and spectrally analyzed over a 10-s period (this time corresponded to ∼100 laser pulses/spectrum, which resulted in a satisfactory signal-to-noise ratio), so the plot shown in Figure 4 was generated in ∼0.5 h. The 2D spectrum was then repeated after blocking one of the broadband OPOs, so that the resulting background plot could be subtracted from the unblocked run. The left box in Figure 5 displays the same data as in Figure 4, shown as a contour plot rather than a stacked plot. The x-axis (horizontal) is the detected
wavelength, the y-axis (vertical) is the tunable OPO wavelength, and the z-axis (out of page) is the intensity of the detected light. The right box in Figure 5 is similar to that of Figure 2d, except that the maximum value for the rotational quantum number was increased from Jmax ) 40 to Jmax ) 75. The similarities in overall shape and location between this C2 simulation and the experimental results are striking, and they identify C2 as the molecule responsible for the fingerprint-like pattern. More careful comparison reveals some significant differences. First, some of the features that appear in the experimental plot but not in the simulated plot persisted when the broadband OPOs were blocked and are therefore attributed to stray incoherent light. These include the thick diagonal band on the upper-left-hand corner of the 2D spectrum. Second, several regions of the experimental results clearly show that every other peak is missing or weak. Alternating intensities in the peaks of C2 have been observed previously20-22 and have been attributed to the combined effects of nuclear spin statistics, Hunds spin-orbit coupling case (b), and λ-type doubling. For example, in studies involving high-resolution (1D) absorption spectroscopy, the P and R branches are split into triplets (P1, P2, P3, and R1, R2, R3). These states are further split by λ-type doubling, but the asymmetric states are not populated due to Boson nuclear spin statistics (carbon-12 has a nuclear spin of zero). The resulting peaks are therefore staggered with P1 and P2 nearly identical in wavelength for every other J, resulting in an alternating increase in intensity of the P branch. Resolving the fine details of these effects requires a detector with subwavenumber resolution (such as the detection system used by Prasad and Bernath in ref 20 with a spectral resolution of 0.025 cm-1), which was beyond the capabilities of our detection system. Despite the insufficient spectral resolution of the detector to further explore these finer details, the 2D spectra clearly show the ability to separate and sort groups of peaks according to vibrational sequence and rotational selection rule. Compared to other molecules, C2 is relatively simple and has relatively large rotational constants. For larger and heavier molecules, the smaller rotational constants and higher density of peaks may pose a challenge even for high-resolution spectrom-
Figure 5. Experimental (left box) and simulated (right box, with Jmax ) 75) 2D spectra of C2 in the Swan region shown as contour plots. The 1D spectra shown to the left and the bottom are the emission spectra from a sooty flame detected over the same λ3 and λ4 wavelength ranges. The spectrometer used to obtain the emission spectra had a pixel-to-pixel resolution of 0.009 nm. By comparison, the step size for the 2D experiment was 0.1 nm and the monochromator-ICCD system had a pixel-to-pixel resolution of 0.09 nm. Despite this relatively large step size and poorer resolution, the spectral resolution achieved by the 2D technique is superior to that of the 1D technique.
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Figure 6. Results from preliminary fitting tests. In (a), a preliminary curve-fitting test involving seven curved lines was conducted. The regression lines (shown) were produced using the resulting spectroscopic constants (columns 1 and 2 in Table 2), and the squares represent actual experimental data points. In (b), a preliminary point-fitting test involving selected experimental data points (shown as squares) was conducted. The dots were produced using the resulting spectroscopic constants (columns 3 and 4 in Table 2) and eqs 3-4d in the text. Table 2. Spectroscopic Constants for C2 Obtained by Fitting Curved Lines in the C2DRR Data, by Fitting Selected Points in the C2DRR Data, and Taken from the Literaturea C2DRR line fit
Te ωe ωexe ωeye Be Re De βe a
NIST database23
C2DRR point fit
a3Πu
d3Πg
a3Πu
d3Πg
a3Πu
(716.2) 1641.71 11.51001 -9.5 × 10-5 1.632365 0.0166262 1.2 × 10-8 8 × 10-11
20024.25 1787.23 16.531 -0.5045 1.75912 0.02002 -1.19 × 10-6 3.15 × 10-7
(716.2) 1640.623 11.68883 0.178667 1.634367 0.016943 6.12 × 10-6 -6.3 × 10-8
20020.22 1788.193 16.435 -0.50763 1.752593 0.016048 6.75 × 10-6 8.7 × 10-8
716.2 1641.35 11.67 1.6324 0.01661 6.44 × 10-6
d3Πg 20022.50 1788.22 16.440 -0.5067 1.7527 0.01608 6.7 × 10-6 1.03 × 10-7
Prasad and Bernath20 a3Πu
d3Πg
1641.32959 11.651954 -0.0016947 1.6323654 0.0166250
1788.22201 16.457464 -0.5012829 1.755234 0.01907
The ground-state value for Te ) 716.2 cm-1 was taken from the NIST website and used during fitting. All values are in cm-1.
eters. In such cases, the ability of the 2D technique to separate and sort peaks might provide significant benefits. One could anticipate that the dense bands of peaks (unresolvable using 1D spectroscopy) would appear as curved lines rather than resolved points in C2DRR contour plots. Like the experimental results shown in Figure 5, the peaks that comprise these curved lines might not always be resolvable, but the curved lines themselves could be used extract spectroscopic, structural, and behavioral information. To explore the use of curved lines for extracting spectroscopic information, we conducted a preliminary curve-fitting test. This test neglected fine details (e.g., spin-orbit coupling, λ-type doubling, and nuclear spin statistics) that would be too small to be spectroscopically resolved with the current detection system. The first step involved running a least squares fifth-order polynomial fit of points on the contour plot that formed a curved line. This fitting process was applied to the seven clearest curved lines in the contour plot. The fitting was then repeated using the corresponding curved lines in the simulated plot. The difference between the experimental polynomial points and the simulationbased polynomial points was calculated and minimized by varying the parameters (spectroscopic constants) in the simulation. The (20) Prasad, C. V. V.; Bernath, P. F. Astrophys. J. 1994, 426, 812-821. (21) Kaminski, C. F.; Hughes, I. G.; Ewart, P. J. Chem. Phys. 1997, 106, 53245332. (22) Lloyd, G. M.; Ewart, P. J. Chem. Phys. 1999, 110, 385-392. (23) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules. In NIST Chemistry WebBook; NIST Standard Reference Database 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, March 2003 (http://webbook.nist.gov).
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results are shown in Figure 6a, and the resulting spectroscopic values are given in Table 2. This table also shows results from fitting 31 individual selected points from the experimental and simulated 2D plots (see Figure 6b). For comparison reasons, results from previous studies by other groups that used highresolution 1D spectroscopic techniques are also shown. Despite the relatively poor spectral resolution of the detection system, the spectroscopic constants obtained by fitting the C2DRR data are in good agreement with the literature values. CONCLUSION A new technique, coherent 2D resonance Raman spectroscopy, has been used to separate and sort peaks from C2 in a flame. The technique should serve as a highly accurate method for identification because the detailed arrangement of peaks in the cross-peak region is very sensitive to electronic, vibrational, and rotational constants. As with other 2D techniques, improved resolution results from spreading the peaks across a second dimension. In this technique, peaks are spread across 2D space and sorted by vibrational sequence, rotational selection rule, and rotational quantum numbers. Unlike 1D spectroscopy, the rotational peaks appear ordered by increasing J. These separation and sorting capabilities help facilitate the assignment of peaks. C2DRR spectroscopy is both practical and powerful; since all molecules are Raman-active, the technique could serve as a universal method for fingerprinting molecules. The use of a multichannel detection in this dual broadband multiplex CARS approach permits acquisition with reasonably short acquisition times. The wavelengths for achieving maximum resonance
enhancement (and therefore the best detection limits) are clearly displayed as the largest peaks in the 2D spectra. Future applications in areas such as materials science, air pollution, combustion, and plasma diagnostics may benefit from this technique’s ability to detect, recognize, and determine the structure of both known and previously undiscovered molecules. ACKNOWLEDGMENT This work was supported by the National Science Foundation (Grant CHE-0215878). Additional support was provided by the NIH
(Grants MD-02-005 and 2G11HD037062) and NSF grant EEC0310717. The authors thank Professor Michael Heaven at Emory University for engaging discussions on rotational spectroscopy and Kyndra Cottingham and Kristle McBride for their contributions to related experiments. Received for review March 10, 2005. Accepted June 24, 2005. AC0504215
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